WiHArtand ISAComparision_Ver1

合集下载

板式换热器资料

number of transfer units of the heat exchan-
ger
axial dispersive Peclet number, w_ L=AcD capacity rate ratio in the channels, w_ a2=w_ a1 capacity rate ratio of the combined ﬂow,
Keywords: Plate heat exchanger; Maldistribution; Dispersion; Backmixing
1. Introduction
Plate heat exchangers (PHE) have been the most successful type of heat exchangers, which have taken major
w_ g2=w_ g1 characteristic rate ratio of the combined
ﬂow, srg2/srg1 ratio Ua2/Ua1 wall heat capacity rate ratio, Cw/C1 characteristic time ratio in channels, sra2/sra1 transformed time variable in Laplace do-
equations free ﬂow area in a channel [m2]
diagonal matrix, Eq. (41) heat capacity of resident ﬂuid (s) [J KÀ1] speciﬁc heat capacity of ﬂuid (s) [J kgÀ1 KÀ1] axial dispersion coeﬃcient [W mÀ1 KÀ1]

Self-reliance Ralph Waldo Emerson

Self-relianceType Work and Year of Publication......."Self-Reliance" is an essay that urges readers to trust their own intuition and common sense rather than automatically following popular opinion and conforming to the will of the majority. "Self-Reliance" was published in 1841 in a collection entitled Essays. In 1844, Emerson published a second collection, Essays: Second Series. Consequently, in 1847, he changed the title of the first collection to Essays: First Series.ThemesTrust Your Own Inner Voice.......Emerson urges his readers to retain the outspokenness of a small child who freely speaks his mind. A child he has not yet been corrupted by adults who tell him to do otherwise. He also urges readers to avoid envying or imitating others viewed as models of perfection; instead, he says, readersshould take pride in their own individuality and never be afraid to express their own original ideas. In addition, he says, they should refuse to conform to the ways of the popular culture and its shallow ideals; rather they should live up to their own ideals, even if doing so reaps themcriticism and denunciation.Avoid Consistency as an End in ItselfBeing consistent is not always wise. An idea or regimen to which you stubbornly cling can become outmoded tomorrow.Point of ViewEmerson uses first-, second-, and third-person point of view. In the opening paragraph of the essay, he first writes in the first person, telling readers about an experience of his. Then, after only three sentences, he switches to second person, as if he is advising a listener sitting acrossthe table from him. Later, in the paragraph, he switches to third person as he presents an exhortation about humankind in general. Following is the first part of the essay, in which Emerson uses all three points of view–first person in black, second person in red, and third person in blue:I read the other day some verses written by an eminent painter which were original and not conventional. The soul always hears an admonition in such lines, let the subject be what it may. The sentiment they instil[Emerson's spelling of instill] is of more value than any thought they may contain. To believe your own thought, to believe that what is true for you in your private heart is true for all men,—that is genius. Speak your latent conviction, and it shall be the universal sense; for the inmost in due time becomes the outmost,—and our first thought is rendered back to us by the trumpets of the Last Judgment.Familiar as the voice of the mind is to each, the highest merit we ascribe to Moses, Plato, and Milton is, that they set at naught books and traditions, and spoke not what men but what they thought.A man should learn to detect and watch that gleam of light which flashes across his mind from within, more than the lustre of the firmament of bards and sages. Yet he dismisses without notice his thought, because it is his.Style Among the most notable characteristics of Emerson’s writing style are these: (1) thorough development of his thesis through examples, repetition, and reinforcement; (2) coinage of memorable statements of principle, or aphorisms; (3) frequent references (allusions) to historical and literaryfigures, such as Socrates, Galileo, Copernicus, Napoleon, Shakespeare, Franklin, Dante, and Scipio (ancient Roman general who defeated Hannibal), who embody qualities Emerson discusses; (4) frequent use of figurative language to make a point, such as “An institution is the lengthened shadow ofone man” (metaphor) and “They who made England, Italy, or Greece ve nerable in the imagination did so by sticking fast where they were, like an axis of the earth” (simile).Promotion of American CreativityBecause Emerson eschewed imitation (as noted under Theme), he urged Americans to avoid mimicking art and ideas from abroad.He writes: Our houses are built with foreign taste; our shelves are garnished with foreign ornaments; our opinions, our tastes, our faculties, lean, and follow the Past and the Distant....Why need we copy the Doric or the Gothic model? Beauty, convenience, grandeur of thought,and quaint expression are as near to us as to any, and if the American artist will study with hope and love the precise thing to be done by him, considering the climate, the soil, the length of the day, the wants of the people, the habit and form of the government, he will create a house inwhich all these will find themselves fitted, and taste and sentiment will be satisfied also.Emerson and Transcendentalism.......Emerson believed every human being has inborn knowledge that enables him to recognize and understand moral truth without benefit of knowledge obtained through the physical senses. Using this inborn knowledge, a gift of God, an individual can make a moral decision without relying on informationgained through everyday living, education, and experimentation. One may liken this inborn knowledge to conscience or intuition........Emerson and others who believed that this inborn knowledge served as a moral guiding force were known as transcendentalists—that is, they believed that this inner knowledge was a higher, transcendent form of knowledge than that which came through the senses. Because Emerson and his fellow transcendentalists trusted their own inner light as a moral guiding force, they were possessed of a fierce spiritofself-reliance. They were individualists; they liked to make decisions for themselves. If the government adopted a policy or a law that offended their consciences, they generally reacted strongly........Transcendentalism, as Emerson’s moral philosophy was called, did not originate with him or his fellow transcendentalis ts in New England but with the German philosopher Emanuel Kant. He used the German word for transcendental to refer to intuitive or innate knowledge—knowledge that is a priori rather than a posteriori.Epigraph An ancient Latin quotation precedes the essay: Ne te quaesiveris extra(Do not look outside of yourself for the truth.) The Roman satirist and poet Aulus Persius Flaccus (AD 34-63)—usually referred to simply as Persius—wrote those words in Book 1, line 7, of his Satires. The quotation is an apt introductory aphorism for Emerson's essay, for it sums up the central idea of "Self-Reliance" and the transcendental philosophy behind it: that one should rely on his own inner voice—his own intuition and instinct—to make important decisions and put his life on a righteous path. In other words, the quotation says, rely on yourself. Emerson follows the Latin quotation with an English quotation from the epilogue of a verse drama by playwrights Franics Beaumont and John Fletcher, contemporaries of Shakespeare. That quotation, which begins with the words Man is his own star, reinforces the view expressed in the Latin quotation.Summary of the EssayPlease be aware that the following summary condenses the content of “Self-Reliance.” It retains first-person point of view to make the summary more readable and easier to understand. Quotations marks surround the exact wording of Emerson.A man should believe in himself. When he has an original thought, he should embrace it and make it known to others rather than reject it simply because it is his own and therefore unworthy. "Else, to-morrow a stranger will say with masterly good sense precisely what we have thought and felt all the time, and we shall be forced to take with shame our own opinion from another."It is better to exercise the power within yourself than to envy and imitate others. When you are young, you are bold and independent; you assert yourself. You listen to the voice within and express yourself without bias and fear. But as you grow older, yousurrender your liberty to society. You want to be like others, act like others. And so you suppress yourself.However, if you want to be a man, you must be a nonconformist. Unfortunately, though, we let others have too much influence over us. These may be men of vanity and malice who take up philanthropic or noble causes–a bigot, for example, who says he supportsabolition but keeps black people at a distance. He loves from afar.Many men think virtue is the exception rather than the rule. They perform acts of charity as if they were paying a fine or doing a penance."I do not wish to expiate, but to live. My life is for itself and not for a spectacle. I much prefer that it should be ofa lower strain, so it be genuine and equal, than that it should be glittering and unsteady."I do not need or want the approval of other men. What I believe I should do is what concerns me, not what other people think I should do. Of course, it is not easy to follow your own inner voice, for there are always those who will try to make you conform tothe public will. It is easy in the world to live after the world’s opinion; it is easy in solitude to live after our own; but the great "man is he who in the midst of the crowd keeps with perfect sweetness the independence of solitude."Conformity turns your life into a lie because in living according to the will of others you are not being true to yourself. To conform, to please others, you put on a false face, smiling when in the presence of people with whom you feel uncomfortable orpretending to be interested in dull conversation.Consistency can also a problem. If you strive to be consistent in all things, you live according to a pattern—a pattern you are afraid to break out of because you are afraid that people will look down on you. Bosh! "A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may aswell concern himself with his shadow on the wall." What if what you said today is not consistent with what you said yesterday? Why, then, people will misunderstand you. But is that so bad? Socrates and Jesus were misunderstood. So were Galileo and Newton and other wisemen.I wish we could do away with consistency and conformity. Men who listen to themselves rather than to the common herd are true men. Andit is true men who leave their mark on history.If all men became self-reliant, then all of their activities and institutions would be better: religion, education, the way they live, the way they think.Notable Quotations From "Self-Reliance"•Trust thyself: every heart vibrates to that iron string.•Whoso would be a man must be a nonconformist.•What I must do is all that concerns me, not what thepeople think.• A foolish consistency is the hobgoblin of little minds,adored by little statesmen and philosophers and divines. Withconsistency a great soul has simply nothing to do.•Travelling is a fool's paradise.•Insist on yourself; never imitate.•Society never advances. It recedes as fast on one side asit gains on the other.•The civilized man has built a coach, but has lost the useof his feet.•An institution is the lengthened shadow of one man.•Discontent is the want of self-reliance: it is infirmity ofwill.•Nothing can bring you peace but yourself. Nothing canbring you peace but the triumph of principles.。

Free subalgebras of Lie algebras close to nilpotent

a r X i v :0805.0723v 2 [m a t h .R A ] 9 M a y 2008FREE SUBALGEBRAS OF LIE ALGEBRAS CLOSE TO NILPOTENTALEXEY BELOV AND ROMAN MIKHAILOVAbstract.We prove that for every automata algebra of exponential growth,the associatedLie algebra contains a free subalgebra.For n ≥1,let L n +2be a Lie algebra with generatorset x 1,...,x n +2and the following relations:for k ≤n ,any commutator of length k whichconsists of fewer than k diﬀerent symbols from {x 1,...,x n +2}is zero.As an application of thisresult about automata algebras,we prove that for every n ≥1,L n +2contains a free subalgebra.We also prove the similar result about groups deﬁned by commutator relations.Let G n +2bea group with n +2generators y 1,...,y n +2and the following relations:for k =3,...,n ,anyleft-normalized commutator of length k which consists of fewer than k diﬀerent symbols from{y 1,...,y n +2}is trivial.Then the group G n +2contains a 2-generated free subgroup.Main technical tool is combinatorics of periodical sequences and period switching.1.Introduction Let A be an associative algebra over a commutative ring with identity,generated by a set S .Denote by A ∼the Lie algebra with the same set of generators S and operation [u,v ]=uv −vu,u,v ∈A.In other words A ∼is the Lie subalgebra of A −generated by the given set S .The algebra A ∼clearly depends on the choice of the set of generators of A .For n ≥1,let L n +2be a Lie algebra with generator set x 1,...,x n +2and following relations:for k ≤n ,any commutator of length k which consists of fewer than k diﬀerent symbols from {x 1,...,x n +2}is zero.For example,the trivial commutators in L n ,which correspond to the case k =3,are:[[x i ,x j ],x i ],i =j.One of the main results of this paper is following:Theorem 1.For every n ≥1,L n +2contains a free Lie subalgebra.The proof of theorem 1is based on the theory of monomial algebras.An algebra with basis X is called monomial if all its deﬁning relations are of the form u =0,where u is a word written in X .Let A be a ﬁnitely generated algebra with generators x 1,...,x s .The Growth function V A (n )equal,the dimension of the space generated by words of length ≤n .If V A (n )grows exponentially,then A has exponential growth ;if polynomially,then A has polynomial growth .Intermediate growth is also possible.The polynomial or exponential growth property does not depend on the choice of the generator set.For n ≥1,let A n +2be the monomial algebra with generators x 1,...,x n +2and the followingrelations:u (x 1,...,x n +2)=0if |u |=k (k ≤n )and u consists of fewer than k symbols from {x 1,...,x n +2}.Clearly,the Lie algebra A ∼n +2is a quotient of L n +2.Hence,Theorem 1willfollow if we will be able to prove that A ∼n +2contains a free subalgebra.The algebra A n +2hasan alternative description,based on the following property:u (x 1,...,x n +2)=0in the algebra A n +2if the distance between two occurrences of the same letter in u (x 1,...,x n +2)is less than n +1.Consider a super-word w =(x 1···x n +1)∞.It is clear that w =0and any series of changes x n +1→x n +2will not yield zero,since the distance between two occurrences of the same letter is still ≤n .With the help of above changes it is possible to get 2M diﬀerent non–zero words.It follows that the number of diﬀerent non–zero words of length k in the monomial algebra A is not less1than2[kb)The positions of the occurrences of a word v of length≥|u|in u∞diﬀers by a period multiple.c)If|v|≥|u|and v2⊂u∞,then v is cyclically conjugate to a power of u.Therefore, nonnilpotent words in A u∞are exactly those words,which are cyclically conjugate to words of the form u k.Proposition3.If uW=W r,then uW is a subword of u∞and W=u n r,where r is an initial segment in u.Remark.The periodicity of an inﬁnite word means its invariance with respect to a shift.In the one-sided inﬁnite case a pre-period appears;in theﬁnite case there appear eﬀects related to the truncation.This,together with superword technique is the essence of a great many combinatorial arguments(see Proposition3)especially Bernside type problems.Proofs of the Shestakov hypothesis(nilpotency of subalgebra of n×n matrix algebra with all words of length ≤n are nilpotent),of the Shirshov height theorem(the normal basis of associative aﬃne P I-algebra A contains only piece-wise periodic words,number of periodic parts is less then h(A), and length of each period is≤n–maximal dimension of matrix algebra satisfying all identities of A)of the coincidence theorem of the nilradical and the Jacobson radical in a monomial algebra, are examples[4],[1],[3].Lemma1(on overlapping).If a subword of length m+n−1occurs simultaneously in two periodic words of periods m and n,then they are the same,up to a shift.Lemma1implies one technical statement,needed in sequelLemma2.Let r=u n v m,n>k,m>l.Then r has not common subwords with u∞of length ≥n|u|+|u|+|v|−1=(n+1)|u|+|v|−1and has not common subwords with v∞of length ≥(m+1)|v|+|u|−1.2.2.Periods switching.Proposition4.Let u,v are not powers of the same word,l|v|>2|u|and s|u|>2|v|.Then v l u s is not a subword of u∞or v∞.This proposition follows from the following assertion which is follows at once from Lemma 1(see[4]):if two periodical superwords of periods m and n have the common part of length >m+n−2,then these words are identical.In this case,u s v l is a subword v∞and u∞. Proposition5.Let u,v are not powers of the same word,l|v|>2|u|and s|u|>2|v|.Then v l u s is not a proper power.Proof.Without loss of generality we may suppose that both u and v are non-cyclic.Suppose that k>1and z k=v l u s for some non-cyclic word z.Without loss of generality we can assume that|v l|≥|u s|.If k≥4,then v l contains z2and from the other hand,v l is subword of z∞.It follows from overlapping lemma1that v is power of z and hence v=z(both z,v are non cyclic).Then u is also power of z and we are done.If k=2then u s is a subword of z and hence of v l.That contradicts overlapping lemma1. If k=3then because|v l|≥|u s|and s|u|>2|v|we have l≥3.In this case|v|<|z|/2and |v l|≥|v|+|z|.By overlapping lemma1we have that v∞=z∞and hence v=z because both are non cyclic.Then z3=v l u s=z l u s and u s=z3−l.Because u is noncyclic u=z.Hence u=v that contradicts conditions of the proposition5. Lemma3.Let r=u n v m,n>k,m>l.Then r is not a subword of W′=v∞/2u∞/2and hence of v p u q for all p,q.Proof.If r is a subword of W′then either u n(i.e.left part of r)is a subword of v∞or v m(i.e. right part of r)is a subword of u∞.Both cases are excluded by proposition4Proposition6.Consider superword W=u∞/2v∞/2,where u=v are diﬀerent noncyclic words. Let S=u k v l and suppose|u k−1|>2|v|,|v k−1|>2|u|,k,l≥2.Then S has just one occurrence in W,which is the obvious one(which we call the“standard occurrence”).Proof.Otherwise the extra occurrence of S is either to the left of the standard occurrence,or to the right.Without loss of generality it is enough to consider the left case.In this case,by Proposition2W is shifted respect to the standard occurrence by a distance divisible by|u|.Hence we have:u s W=W R,i.e.u s W starts with W.We can apply Proposition3and so we get that u∞/2starts with W.Then from combining Lemma1and Proposition2we get that v is cyclically conjugate to u,and|u|=|v|.But in that case W=u k v l is subword of u∞,implying that the relative shifts of u and v are divisible by|u|=|v|,and hence u=v.The proposition is proved. This proposition together with Lemmas2and3impliesCorollary1.Let R=r∞=(u n v m)∞,n>k,m>l.Then all the occurrences of S in R are separated by distances divisible by|r|=n|u|+m|v|.Proof.First of all,as in the proposition6one can deﬁne notion of standard occurrence of S in R.Consider an occurrence of S in R.Then only following cases are logically possible:(1)It naturally corresponds to occurrence of S in W(i.e.power of v in S starts in on thepower of v in W and similarly power of u in S ends in on the power of u in W).(2)It contains completely either u n or v m.(3)It lies on the position of period switching from v m to u m.Second possibility is excluded due to due to Lemma2,third–to due to Lemma3.First possibility due to proposition6corresponds only to standard occurrences and they are separated by distances divisible by|r|=|u n v m|=n|u|+m|v|. Note that r and t are cyclically conjugate,iﬀr∞=t∞.Using this observation and the previous corollary we get a proposition needed in the sequel:Proposition7.Let u,v be diﬀerent non-cyclic words,with|u n|>2|v|and|v n|>2|u|.For all k i,l i≥n,if(k1,l1)=(k2,l2),then u k1v l1and u k2v l2are not cyclically conjugate.Proof.Suppose that r=u k1v l1and t=u k2v l2are cyclically conjugate.Then r∞=t∞and because r,t are not cyclical,|r|=|t|=µ.Let us denote R=(u k2v l2)∞.Let S=u k v l and suppose|u k−1|>2|v|,|v k−1|>2|u|,k,l≥2and also k≤min k1,k2,l≤min(l1,l2).It is clear that such S exist and is a subword of booth r and t.Then due to corollary1all occurrences of S in W are shifted by distance divisible byµ–period of R.It means that any occurrence of S can be extended to occurrence of r as well as to occurrence of t.Hence there exists an occurrences of r=u n1Sv m1and t=u n2Sv m2in W with common part S.If r=t,then n1=n2because|s|=|t|.Without loss of generality we can suppose that n1<n2.In this case m1>m2.Word t is shifted to the left from the word r on the distance d=|u n1|−|u n2|=|v n2|−|v m1|.Consider a unionωof r and t.Thenω=er=ft,|e|=|f|=d.Note that r2is a subword of t∞=W,occurrence of v m1(which is end of r)precedes an occurrence of r.Because|v m2|>d, e=v m2−m1.Similarly f=u n1−n2.From other handωcan be also obtained by extending the subword S of W to the left on the dis-tance|v max(m1,m2)|and to the right on the distance|u max(n1,n2)|andω=u max(n1,n2)v max(m1,m2)= u n1−n2r=tv m2−m1.Hence u n1−n2=v m2−m1;n1=n2;m1=m2.It follows that u,v are powers of the same word s.Because u=v one of this powers is greater than1and booth u and v can not be non cyclic words.But this contradicts to their initial choice.3.Regular Words and Lie bracketsWe shall extend the relation≺by deﬁning the following£-relation(“Ufnarovsky order”): f£g,if,for any two right superwords W1,W2,such that W2(a,b)≻W1(a,b),when ever b≻a, the inequality W2(g,f)≻W1(g,f)holds.This condition is well deﬁned and equivalent to following:f£g iﬀf∞/2≻g∞/2(i.e.,f m≻g n,for some m and n).It is clear that if f≻g, then f£g.The relation£is a linear ordering on the following set of equivalence classes:f∼g,if for some s,f=s l,g=s k.Let us note that eachﬁnite word u uniquely corresponds to the right superword u∞.To equivalent words correspond the same superwords.The relation£corresponds to the relation ≻on the set of superwords.It is known([4],[6])that:A word u is called regular,if one of the following equivalent conditions holds:a)u word is greater all its cyclic conjugates:If u1u2=u,then u≻u2u1.b)If u1u2=u,then u£u2.c)If u1u2=u,then u1£u.A word u is called semi-regular in the following case:If u=u1u2,then,either u≻u2,or u2is a beginning of u.(An equivalent deﬁnition can be obtained if the relation¡is replaced by the relation¢in the deﬁnition of a regular word.)Every semi-regular word is a power of a regular one.It is well-known that every regular word u deﬁnes the unique bracket arrangement[u]such that after opening all Lie brackets u will be a highest term in this expression.Moreover,monomials of such type form a basis in the free Lie algebra(so called Hall–Shirshov basis)(see[2],[6]). We shall need some technical statements:Lemma4([4]).Suppose|u k|£|v2|and u k is a subword of v∞.Then there exists S′cyclically conjugate to S,such that u=(S′)m and v=(S2)n.If,moreover,the initial symbols of u and v are at a distance divisible by|S|in v∞,then S=S′.Corollary2.Let u£v be semi-regular words.Then,for suﬃciently large k and l,the words u k v l are regular andu k1v l1£u k2v l2for k1>k2.Proof.Letδbe a cyclic conjugate of u k v l.It is clear thatδ¤u k v l,we only need to prove inequalityδ=u k v l.In order to do this,we need only to show that u k v l is not cyclic word,but it follows from the proposition5.The next lemma follows from Lemma4and Corollary2.Lemma 5.Let k i>|d|,l i>|u|,for i=1,2.Then u k1d l1and u k2d l2are not cyclically conjugate,provided that u£d and u,d are not conjugate to proper powers of the same word.4.Words in automata algebrasByΦ x1,...,x s will be denoted the free associativeΦ-algebra with generators x1,...,x s.By A a1,...,a s will be denoted an arbitraryΦ-algebra with aﬁxed set of generators a1,...,a s.A word or a monomial from the set of generators M is an arbitrary product of elements in M. The set of all words constitutes a semigroup,which will be denoted by Wd M .The order a1≺···≺a s generates the lexicographic order on the set of words:The grater of two words is the one whoseﬁrst letter is greater;if theﬁrst symbols coincide,then the second letter are compared,then the third letters and so on.Two words are incomparable,only if one of them is initial in the other.By a word in an algebra we understand a nonzero word from its generators{a i}.We can-not speak about the value of a superword in an algebra,but can speak about its equality or nonequality to zero(and,in some cases,about linear dependence).A superword W is called zero superword,if it has aﬁnite zero subword,and it is called a nonzero superword,if it has noﬁnite zero subwords.An algebra A is called monomial,if it has a base of deﬁning relations of the type c=0,where c is a word from a1,...,a s.Obviously,a monomial algebra is a semigroup algebra(it coincides with the semigroup algebra over the semigroup of its words).4.1.Automata algebras.First we recall some well known deﬁnitions from[4].Suppose we are given an alphabet(i.e.,aﬁnite set)X.Byﬁnite automaton(FA)with the alphabet X of input symbols we shall understand an oriented graph G,whose edges are marked with the letters from X.One of the vertices of this graph is marked as initial,and some vertices are marked asﬁnal.A word w in the alphabet X is called accepted by aﬁnite automaton,if there exists a path in the graph,which begins at the initial vertex andﬁnishes in someﬁnal vertex,such that marks on the path edges in the order of passage constitute the word w.By a language in the alphabet X we understand some subset in the set of all words(chains)in X.A language L is called regular or automata,if there exists aﬁnite automaton which accepts all words from L and only them.An automaton is called deterministic,if all edges,which start from one vertex are marked by diﬀerent letters(and there are no edges,marked by the empty chain).If we reject such restriction and also allow edges,marked by the empty chain,then we shall come to the notion of a non-deterministicﬁnite automaton.Also we can allow an automaton to have several initial vertices.The following result from the theory ofﬁnite automata is well known:For each non-deterministic FA there exists a deterministic FA,which accepts the same set of words(i.e.the same language).It will be convenient for us to consider the class of FA,such that all vertices are initial and ﬁnal simultaneously.The reason of this is that the language of nonzero words in a monomial algebra has the following property:each subword of a word belonging to the language,also belongs to it.Suppose throughout that G is the graph of a deterministic FA,v is a vertex of G,and w is a word.If the corresponding path C starting from v exist in G,then one can deﬁne the vertex vw terminal vertex for C.Let A be a monomial algebra(not necessaryﬁnitely deﬁned).A is called an automata algebra, if the set of all of its nonzero words from A generators is a regular language.Obviously,a monomial algebra is an automata algebra,only if the set of its nonzero words is the set of all subwords of words of some regular language.It is known that every automata algebra can be given by a certain deterministic graph,and that everyﬁnitely deﬁned monomial algebra is automata([4],[6]).The Hilbert series for an automata algebra is rational(Proposition5.9[4]).An automata algebra has exponential growth if and only if G has two cycles C1and C2with common vertexv,such that the corresponding words w1,w2(we read them starting from v)are not powers of the same word.In this case the words w1and w2generate a free2-generated associative algebra. If there are no such cycles,A has a polynomial growth.No intermediate growth is possible. The following theorem is the aim of this section:Theorem3.Let A= a1,...,a n be an automata algebra of exponential growth.Then the Lie algebra A∼contains a free2-generator subalgebra.We continue to assume that G is the graph of a deterministic FA.Call a semi-regular word u well–based if it written on a certain cycle C with an initial vertex v;i.e.vu=v.Two semi–regular words u1and u2are pair–wisely well–based if u1and u2are written on cycles C1and C2 with a common initial vertex v and vC1=vC2=v.In this case,for any word W(a,b)the word W(u1,u2)=0in A;in particular u k11u k22=0.Main Lemma.The graph G contains two regular pairwise well–based words u=v. Deduction of Theorem3from the Main Lemma.We may always assume that u£v.Let a≻b and w a regular word.Then(see[4])w(u,v)also is a regular wold.For every regular word u we can choose a unique presentation u=u1u2with regular u1and regular u2of maximal length.In this case[u]=[[u1],[u2]](see[6]).Therefore,w(u,v)can be obtained by setting[u]→a,[v]→b to the word with brackets[w].Since u and v are well-based,for every word R(a,b),one has R(u,v)=0.Let[u],[v]be the results of the regular arrangement of the brackets for u and v respectively.Then[u]=0,[v]=0. Thus we have constructed a one-to-one correspondence between the Hall basis of a Lie algebra, generated by[u],[v]and the Hall basis of a free2-generated Lie algebra with generators a,b. The theorem follows.P4.2.Proof of the Main Lemma.Corollary2implies the following:Proposition8.Suppose the graph G contains two ordered(in the sense of the operation£) pairwise well-based words.Then G contains also two regular pairwise well-based words.It is suﬃcient toﬁnd two ordered semi-regular pairwise well-based words,i.e.with common ﬁnal and initial vertices.For that it is enough to prove the existence of a suﬃciently large number of well-based ordered semi-regular words.In this case,inﬁnitely many of them will have a common initial vertex,hence pairwise well–based,and the main lemma follows.Lemma6.Let u1be a well-based word and u2a cyclically conjugate word.Then u2is also well-based.Proof.Suppose u1=w1w2,u2=w2w1and v is a base vertex of u1.Then v′=vw1is a base vertex of u2.Indeed,v′u2=vw1(w2w1)=v(w1w2)w1=vw1=v′. Corollary3.If u is well-based,then semi-regular word conjugate to u is also well-based.Let u and d be ordered pairwise well-based words(necessarily not semi-regular).Then,for every w(a,b),the word w(u,d)is non-zero.In particular,u k d l are non-zero for all k,l.Now Lemma5,together with the fact that every non–cyclic word uniquely corresponds to a cyclically conjugated regular word,implies that there are inﬁnitely many well–based words. Inﬁnitely many of them will have the same initial vertex and so will be pairwise well based; hence the Main Lemma follows.5.Group theoretical applicationsId(S)denotes the ideal,generated by the set S.Lemma 7.Suppose a and b are homogenous elements of a graded associative algebra A ,such that the subalgebra generated by a,b is free associative algebra with free generators a,b .Let a ′(resp.b ′)be a linear combination of elements in A with degrees strictly greater than the degree of a (resp.b ).Let ˜a =a +a ′,˜b =b +b ′.Then the algebra generated by ˜a ,˜b is a free associative with free generators ˜a ,˜b .This lemma follows from the fact that for every polynomial h (u,v )with non-zero minimal component h ′(u,v ),the minimal component of h (˜a ,˜b )is h ′(a,b )=0.We call an algebra homogenous if all its deﬁning relations are homogenous respect to the set of generators.Let A be a homogenous algebra,and J be an idealof A ,generated by elements of degree ≥1.We call such algebra good .If A/J ≡k and nJ n =0.Every monomial algebra is good.For any x ∈A,the image of x in A/J n is not zero for some n ,so A can be embedded into the projective limit lim ←−A/J n .Lemma 8.Let B be a good homogenous algebra,such that 1+a and 1+b are invertible,a,b ∈J,and the elements a and b are free generators of a free associative subalgebra C of B .Then the group generated by 1+a and 1+b is free.Remark.Note that the pair of two diﬀerent pairwise well–based words in a monomial algebra generates a free associative subalgebra.Proof.Suppose W (1+a,1+b )=1for some non-trivial word W (x,y )=1in the free group.Consider free algebra k x,y and its localization by 1+x,1+y .Then W (1+x,1+y )=1,and,for some n 0=n 0(W ),W (1+¯x ,1+¯y )=1in π(k x,y )=k x,y /Id(x,y )n for all n ≥n 0.In each such image,the elements 1+x and 1+y are invertible,so there is no need for localization.On the other hand,because A is good homogenous,the image of J m ∩C under isomorphism φgenerated by a →x,b →y lies in Id(x,y )n 0,and1=π(φ(W (1+a,1+b )))=W (1+¯x ,1+¯y )=1.Contradiction. Let u and v be two pairwise well based words.They have canonical Lie bracket arrangement;let [u ]and [v ]be corresponding Lie elements (obtained via opening the Lie brackets).Notice that[u ]=u +lexicographically smaller terms ,[v ]=v +lexicographically smaller terms .Hence we have followingLemma 9.Let u and v be two pairwise well based words,and [u ]and [v ]be the corresponding Lie elements (obtained via opening Lie brackets).Then [u ],[v ]generate as a free generators 2-generated free associative algebra (and also free Lie algebra via commutator operation).For n ≥1,consider the monomial algebra A n +2with generators x 1,...,x n +2(see the In-troduction).Adjoint a unit A ′n +2=A n +2∪{1}.The elements ¯xi :=1+x i have inverses ¯x −1i :=1−x i .Consider the group A #n +2generated by the elements 1+x i .Consider the conﬁg-uration of brackets in the generators of the free subalgebra in the Lie algebra A ∼n +2and writethe correspondent Lie elements in the group A #n +2.Lemmas 7and 8,9imply that the subgroupA #n +2generated by these two elements will be free.It is clear from the construction that all left-normalized commutators of length k in A #n +2which consists of fewer that k diﬀerent symbols from {¯x 1,...,¯x n +2},are trivial.Hence,Theorem 2follows.References[1]S.A.Amitsur,L.W.Small:Aﬃne algebras with polynomial identities,Suppl.ai Rendiconti del Circolo Mat.di Palermo,Serie2,31(1992),9-43.[2]Bahturin Yu.,A.:Identities in Lie algebras.M.:Nauka,1985.,pages448(Russian).Engl.transl.(by Bakh-turin):Identical relations in Lie algebras.VNU Science Press,b.v.,Utrecht,1987.x+309pp.[3]Belov A.:About height m.in Algebra,1995,vol.23,N9,p.3551–3553.[4]A.Belov,V.Borisenko and tyshev:Monomial algebras.Algebra4,J,Math.Sci.(New York)87(1997),3463-3575.[5]M.Gromov:Entropy and Isoperimetry for Linear and non-Linear Group Actions,preprint.[6]V.Ufnarovskij:Combinatorial and asymptotic methods in algebra.Algebra,VI,1–196,Encyclopaedia Math.Sci.,57,Springer,Berlin,(1995)。

从男性占有欲的角度解读真爱—再读哈代的《苔丝》与小仲马的《茶花女》

《老人与海》中的和谐关系《动物农庄》中的象征意义研究试分析两种婚姻的差异——以薛宝钗和夏洛特为例A Comparative Study of American and Chinese Spatial Language in Business Negotiation 从《人与鼠》看斯坦贝克艺术风格The Use of Symbols in A Farewell to Arms从关联理论看商务信函的礼貌策略《哈利波特》中的励志精神Gender Differences in Language Use从《去吧，摩西》中的“熊”看福克纳对人性的探讨从动态对等角度论英语俚语的翻译文化语境对中西商务谈判的影响美国情景喜剧字幕翻译的归化策略－－以《生活大爆炸》为例合作学习法对英语口语能力的影响——对独立学院非英语专业学生的个案研究女性模糊语在交际中的运用及分析论《了不起的盖茨比》中的象征及其作用英语动画片中的中国元素探究汉语歇后语之英译论托尼•莫里森《宠儿》的哥特式元素汉英禁忌语的对比分析《献给艾米丽的玫瑰》中女主人公的爱情观Resurrection of Self-consciousness in Rebecca分析西方末世论在美国电影中的体现比较研究王维与华兹华斯的自然观中西方节日文化差异研究论商务名片英译——以功能对等为指导《简爱》与《名利场》中家庭女教师形象与命运的对比研究中美企业招聘广告文化对比分析论《金色笔记》中的象征手法从功能对等角度翻译委婉语从美国州名看美国文化多样性A Comparative Study of Refusal in Chinese and American Cultures从许渊冲的“三美论”看唐诗中的典故翻译十九世纪英国女性小说中的两位灰姑娘——伊利莎白•班纳特和简•爱形象比较马尔福的嫉妒论网络自主学习与英语课堂教学的契合从个人英雄主义到爱国主义的升华—《荷马史诗》中阿喀琉斯形象的分析浅析造成盖茨比悲剧的因素矛盾与挣扎的悲剧——浅析《献给艾米丽的玫瑰》中的主人公艾米丽幽默语言的语用分析A Discussion on the Accuracy of Language in Diplomatic Translation中外服装品牌英文标签语言的跨文化研究英语幽默语言的会话含义分析—以《老友记》为例The Environmental Influence on Emily Bront and "Wuthering Heights"《紫色》女主人公性格分析论《荆棘鸟》中的女性意识论中西婚姻观的差异英汉文化中颜色词语象征意义的对比研究新闻报道的倾向性分析——语言学视角从《哈利波特》看儿童的成长命运与性格－－浅论《哈姆雷特》的悲剧因素论原声电影对提高大学生英语听说能力的作用《老人与海》中的象征主义论《推销员之死》中威利的死因论《瓦尔登湖》的生态伦理意蕴从博奕论分析庞培与凯撒内战爆发的原因《德伯家的苔丝》中亚雷形象分析文化语境对中西商务谈判的影响如何设计中学英语课堂中的提问学术论文标题的英译研究《麦田里的守望者》主人公的性格分析从隐私权看中西文化差异从电影《饮食男女》看中西方饮食文化差异(开题报告+论文+文献综述)论《一个温和的建议》中的黑色幽默中美个人理财规划的对比分析从服饰看中西方文化差异与融合从《嘉莉妹妹》看美国梦与道德观《支那崽》的后殖民主义解读从《简•爱》的多译本看中国两性关系的变化《傲慢与偏见》中的婚姻观和中国后婚姻观的比较研究试析索尔•贝娄《只争朝夕》中的犹太寻根主题法律英语中情态动词的语用功能及翻译技巧从符号学理论角度探讨网络命名的文化倾向A Brief Analysis of the Differences and Similarities of Chinese and British Wedding Culture 从爱伦·坡《黑猫》探讨人性的善良与邪恶中西方餐桌礼仪文化对比An Analysis of Sexism in English Advertisements从功能翻译理论看企业简介汉英翻译哥特小说中的反天主教分析：《隐士》个案研究初中英语合作学习商务英语写作中的语用失误研究挣脱枷锁，走向自由——从《人性的枷锁》看毛姆的人生观剖析托尼•莫里森笔下的黑人世界On Emily Bronte's Self-realization Through the Characters in Wuthering Heights论文化对国际市场营销的重要性－－以迪斯尼乐园为例从生态中心主义角度分析康拉德《黑暗的心》试析英语专业学生英语学习焦虑成因论《亚瑟王之死》中的骑士精神中美大学毕业典礼演讲之叙事结构的比较研究The Strategies and Translation of Politeness in English Business Letters《老人与海》中的象征主义论东西方文化中的体态语差异A Contrastive Analysis of Table Manners and Culture between China and Western Countries 从《嘉利妹妹》看德莱塞的女性观论商务谈判口译员的角色英汉拒绝语对比研究海明威短篇小说的叙述艺术－－以《一个明亮干净的地方》为例《麦琪的礼物》的叙事技巧分析中文商标英译研究论《阿甘正传》中的美国梦从生态批评主义角度看《白鲸》的生态观浅析英汉基本颜色词之文化内涵－－以“白”与“黑”为例论英语电影片名的翻译浅谈商务英语于商务信函中的运用从鹿鼎记和唐吉诃德的主要人物的较对比来比中西方侠文化暗夜中的精灵——论《寻欢作乐》中的罗西名词化隐喻在外贸函电中的功能分析论《小镇畸人》中人物的怪诞性《傲慢与偏见》中的三种不同婚姻的分析论托尼莫里森《宠儿》的哥特式元素广告英译汉中的创译原则浅析亨利詹姆斯小说《螺丝在拧紧》中的哥特成分A Survey on Western Culture Learning among Non-English Majors杰克伦敦《野性的呼唤》中人生哲学的主题分析论乔治•艾略特《弗洛斯河上的磨坊》中的环境描写外交辞令中模糊语言的语用分析二元对立模型在伍尔夫《达洛卫夫人》中的应用理想男人随社会变化：从劳里到盖茨比谈中国唐诗中数字的翻译浅析《老人与海》的主人公——圣地亚哥的人物形象分析《女勇士》中美国华裔身份危机的探寻海明威“冰山原理”在《永别了，武器》中的应用及对写作的指导意义浅析英诗翻译的原则和方法——丁尼生《鹰》的不同译文比较英国哥特小说故事情节中的怪诞表现Golding’s Perception of Human Nature Viewed from Lord of the Flies简析比喻在《围城》中的运用微笑着流泪——欧亨利小说赏析从《简爱》两个译本看女性与男性语言使用的差别论汉语政治新词的英译礼貌策略在国际商务谈判中的运用从《雾都孤儿》看查尔斯•狄更斯的善恶观从电影《伴你高飞》看美国文化中人与自然的和谐主题《晚安,妈妈》中公共汽车和洗衣机的象征寓意英汉委婉语及其相关文化心理解读洛克的教育思想研究谈成长中的大卫•科波菲尔的情感波折小学英语学习策略及研究非语言交际在国际商务谈判中的运用中外大学校训对比研究宗教文化与翻译A Comparison of the English Color Terms经贸英语中的缩略语现象及其应用高中英语写作前口语活动设计与实施建议《绝望的主妇》中的中产阶级女性独立意识的研究从中英广告词中分析概念隐喻商务谈判中的模糊语的使用哈克贝利•费恩对“文明世界”的适应Jane Austen’s Opinion towards Marriage in Pride and Prejudice中西文化差异在广告创意中的影射新闻中新兴词语的翻译原则及策略从《丧钟为谁而鸣》看海明威死亡情节成因模糊语在国际商务谈判中的语用功能研究中西方聚会文化差异比较研究从解构主义视角分析迈克尔•翁达杰《英国病人》中小说中心的消失非语言交际中体语的文化分析《好人难寻》的冷漠主题分析从《红楼梦》和《罗密欧与朱丽叶》看中西方爱情悲剧的异同从文学作品中继母形象变迁看社会文化认知的发展传统教法与交际法结合的英语教学探讨《宠儿》中塞斯的性格分析《了不起的盖茨比》中色彩的象征意义（开题报告+论）Mother Tongue Influence on the Learning of a Foreign Language济慈六大颂诗的意象《洛丽塔》—时间的悲剧中美商务接待文化差异重新诠释玛格丽特的人生悲剧根源浅析国际商务谈判文化因素及其对策《心是孤独的猎手》中的主题分析初中英语的传统教学与现代教学的差异关于初中生外语学习焦虑的分析试用标记模式理论分析广告语中的语码混用现象两性英语会话话语分析研究——以小说《简•爱》为例从涉外婚姻分析中西方文化差异《推销员之死》中的家庭问题研究从归化与异化的角度研究《金锁记》的翻译策略汉语习语中文化负载词的英译从酒文化中透析中西文化差异论旅游指南的翻译英语旅游广告的文体分析《喧哗与骚动》中的现代主义从消费文化看《美国悲剧》Stylistic Features of English Financial ReportsComparison and Translation Between Chinese and English Euphemisms A Tentative Analysis of the Reasons for McDonald’s Success《荆棘鸟》女性意识浅析荒岛主义在《蝇王》中的映射从词汇对等角度看《红楼梦》中“笑”一词的英译《永别了，武器》中的自然象征意义黑暗中的光明—《蝇王》的主题探析从春节与圣诞节习俗看中西方文化差异跨文化交际中的移情及其能力的培养广告英语中委婉语的语用研究从目的论角度比较研究《彼得•潘》两个中文译本《那个读伏尔泰的人》英译汉中定语从句的翻译策略论《黑夜中的旅人》中主人公的信仰冲突与融合英语专业学生词汇附带习得The Road to the Outside World：An Analysis of Chinese Martial Arts 跨文化交际中的禁忌习俗《老人与海》中的存在主义分析。

Analogue of Weil representation for abelian schemes

a r X i v :a l g -g e o m /9712021v 1 19 D e c 1997ANALOGUE OF WEIL REPRESENTATION FOR ABELIANSCHEMESA.POLISHCHUK This paper is devoted to the construction of projective actions of certain arithmetic groups on the derived categories of coherent sheaves on abelian schemes over a normal base S .These actions are constructed by mimicking the construction of Weil in [27]of a projective representation of the symplectic group Sp(V ∗⊕V )on the space of smooth functions on the lagrangian subspace V .Namely,we replace the vector space V by an abelian scheme A/S ,the dual vector space V ∗by the dual abelian scheme ˆA ,and the space of functions on V by the (bounded)derived category of coherent sheaves on A which we denote by D b (A ).The role of the standard symplectic form on V ⊕V ∗is played by the line bundle B =p ∗14P ⊗p ∗23P −1on (ˆA ×S A )2where P is the normalized Poincar´e bundle on ˆA ×A .Thus,the symplectic group Sp(V ∗⊕V )is replaced by the group of automorphisms of ˆA ×S A preserving B .We denote the latter group by SL 2(A )(in [20]the same group is denoted by Sp(ˆA ×S A )).We construct an action of a central extension of certain ”congruenz-subgroup”Γ(A,2)⊂SL 2(A )on D b (A ).More precisely,if we write an element of SL 2(A )in the block form a 11a 12a 21a 22 then the subgroup Γ(A,2)is distinguished by the condition that elements a 12∈Hom(A,ˆA )and a 21∈Hom(ˆA,A )are divisible by 2.We construct autoequivalences F g of D b (A )corresponding to elements g ∈Γ(A,2),such the composition F g ◦F g ′diﬀers from F gg ′by tensoring with a line bundle on S and a shift in the derived category.Thus,we get an embedding of the central extension of Γ(A,2)by Z ×Pic(S )into the group of autoequivalences of D b (A ).The 2-cocycle of this central extension is described by structures similar to the Maslov index of a triple of lagrangian subspaces in a symplectic vector space.However,the situation here is more complicated since the construction of the functor F g requires a choice of a Schr¨o dinger representation of certain Heisenberg group G g associated with g .The latter is a central extension of a ﬁnite group scheme K g over S by G m such that the commutation pairing K g ×K g →G m is non-degenerate.If the order of K g is d 2then a Schr¨o dinger representation of G g is a representation of G g in a vector bundle of rank d over S such that G m ⊂G g acts naturally.Any two such representations diﬀer by tensoring with a line bundle on S .The classical example due to D.Mumford arises in the situation when there is1a relatively ample line bundle L on an abelian schemeπ:A→S.Then the vector bundleπ∗L on S is a Schr¨o dinger representation of the Mumford group G(L)attached to L,this group is a central extension of theﬁnite group scheme K(L)by G m where K(L)is the kernel of the symmetric homomorphismφL:A→ˆA associated with L. Our Heisenberg groups G g are subgroups in some Mumford groups and there is no canonical choice of a Schr¨o dinger representation for them in general(this ambiguity is responsible for the Pic(S)-part of our central extension ofΓ(A,2)).Moreover, unless S is a spectrum of an algebraically closedﬁeld,it is not even obvious that a Schr¨o dinger representation for G g exists.Our main technical result that deals with this problem is the existence of a”Schr¨o dinger representation”forﬁnite symmetric Heisenberg group schemes of odd order established in section2.Further we observe that the obstacle to existence of such a representation is an elementδ(G g)in the Brauer group of S,and that the map g→δ(G g)is a homomorphism.This allows us to use the theory of arithmetic groups to prove the vanishing ofδ(G g).When an abelian scheme A is equipped with some additional structure(such as a symmetric line bundle)one can sometimes extend the above action of a central exten-sion ofΓ(A,2)on D b(A)to an action of a bigger group.The following two cases seem to be particularly interesting.Firstly,assume that a pair of line bundles on A andˆA is given such that the composition of the corresponding isogenies between A andˆA is the morphism of multiplication by some integer N>0.Then we can construct an action of a central extension of the principal congruenz-subgroupΓ0(N)⊂SL2(Z) on D b(A)(note that in this situation there is a natural embedding ofΓ0(N)into SL2(A)but the image is not necessarily contained inΓ(A,2)).Secondly,assume that we have a symmetric line bundle L on A giving rise to a principal polarization.Then there is a natural embedding of Sp2n(Z)into SL2(A n),where A n denotes the n-fold ﬁbered product over S,which is an isomorphism when End(A)=Z.In this case we construct an action of a central extension of Sp2n(Z)on D b(A n).The main point in both cases is to show the existence of relevant Schr¨o dinger representations.Both these situations admit natural generalizations to abelian schemes with real multipli-cation treated in the same way.For example,we consider the case of an abelian scheme A with real multiplication by a ring of integers R in a totally real number ﬁeld,equipped with a symmetric line bundle L such thatφL:A →ˆA is an R-linear principal polarization.Then there is an action of a central extension of Sp2n(R)by Z×Pic(S)on D b(A n).When R=Z we determine this central extension explicitly using a presentation of Sp2n(Z)by generators and relations.It turns out that the Pic(S)-part of this extension is induced by a non-trivial central extension of Sp2n(Z) by Z/2Z via the embedding Z/2Z֒→Pic(S)given by an element(π∗L)⊗4⊗ωA is the restriction of the relative canonical bundle of A/S to the zero section.Also we show that the restriction of this central extension to certain congruenz-subgroup Γ1,2⊂Sp2n(Z)splits.In the case when S is the spectrum of the algebraically closedﬁeld the constructions2of this paper were developed in[22]and[20].In the latter paper the Z-part of the above central extension is described in the analytic situation.Also in[22]we have shown that the above action of an arithmetic group on D b(A)can be used to construct an action of the corresponding algebraic group over Q on the(ungraded)Chow motive of A.In the present paper we extend this to the case of abelian schemes and their relative Chow motives.Under the conjectural equivalence of D b(A n)with the Fukaya category of the mir-ror dual symplectic torus(see[12])the above projective action of Sp2n(Z)should correspond to a natural geometric action on the Fukaya category.The central exten-sion by Z appears in the latter situation due to the fact that objects are lagrangian subvarieties together with some additional data which form a Z-torsor(see[12]). The paper is organized as follows.In theﬁrst two sections we studyﬁnite Heisen-berg group schemes(non-degenerate theta groups in the terminology of[14])and their representations.In particular,we establish a key result(Theorem2.3)on the existence of a Schr¨o dinger representation for a symmetric Heisenberg group scheme of odd order.In section3we consider another analogue of Heisenberg group:the central extension H(ˆA×A)ofˆA×S A by the Picard groupoid of line bundles on S.We develop an analogue of the classical representation theory of real Heisenberg groups for H(ˆA×A).Schr¨o dinger representations forﬁnite Heisenberg groups enter into this theory as a key ingredient for the construction of intertwining operators.In section4we construct a projective action ofΓ(A,2)on D b(A),in section5—the corresponding action of an algebraic group over Q on the relative Chow motive of A. In section6we study the group SL2(A),the extension of SL2(A)which acts on the Heisenberg groupoid.In section7we extend the action ofΓ(A,2)to that of a bigger group in the situation of abelian schemes with real multiplication.In section8we study the corresponding central extension of Sp2n(Z).All the schemes in this paper are assumed to be noetherian.The base scheme S is always assumed to be connected.We denote by D b(X)the bounded derived category of coherent sheaves on a scheme X.For a morphism of schemes f:X→Y ofﬁnite cohomological dimension we denote by f∗:D b(X)→D b(Y)(resp.f∗:D b(Y)→D b(X))the derived functor of direct(resp.inverse)image.For any abelian scheme A over S we denote by e:S→A the zero section.For an abelian scheme A(resp. morphism of abelian schemes f)we denote byˆA(resp.ˆf)the dual abelian scheme (resp.dual morphism).For every line bundle L on A we denote byφL:A→ˆA the corresponding morphism of abelian schemes(see[17]).When this is reasonable a line bundle on an abelian scheme is tacitly assumed to be rigidiﬁed along the zero section(one exception is provided by line bundles pulled back from the base).For every integer n and a commutative group scheme G we denote by[n]=[n]G:G→G the multiplication by n on G,and by G n⊂G its kernel.We use freely the notational analogy between sheaves and functions writing in particular F x= Y G y,x dy,where x∈X,y∈Y,F∈D b(X),G∈D b(Y×X),instead of F=p2∗(G).31.Heisenberg group schemesLet K be aﬁniteﬂat group scheme over a base scheme S.Aﬁnite Heisenberg group scheme is a central extension of group schemes(1.1)0→G m→G p→K→0such that the corresponding commutator form e:K×K→G m is a perfect pairing. Let A be an abelian scheme over S,L be a line bundle on A trivialized along the zero section.Then the group scheme K(L)={x∈A|t∗x L≃L}has a canonical central extension G(L)by G m(see[17]).When K(L)isﬁnite,G(L)is aﬁnite Heisenberg group scheme.A symmetric Heisenberg group scheme is an extension0→G m→G→K→0 as above together with an isomorphism of central extensions G →[−1]∗G(identical on G m),where[−1]∗G is the pull-back of G with respect to the inversion morphism [−1]:K→K.For example,if L is a symmetric line bundle on an abelian scheme A (i.e.[−1]∗L≃L)with a symmetric trivialization along the zero section then G(L)is a symmetric Heisenberg group scheme.For any integer n we denote by G n the push-forward of G with respect to the morphism[n]:G m→G m.For any pair of central extensions(G1,G2)of the same group K we denote by G1⊗G2their sum(given by the sum of the corresponding G m-torsors).Thus,G n≃G⊗n.Note that we have a canonical isomorphism of central extensions(1.2)G−1≃[−1]∗G opwhere[−1]∗G op is the pull-back of the opposite group to G by the inversion morphism [−1]:K→K.In particular,a symmetric extension G is commutative if and only if G2is trivial.Lemma1.1.For any integer n there is a canonical isomorphism of central exten-sions[n]∗G≃G n(n+1)2where[n]∗G is the pull-back of G with respect to the multiplication by n morphism [n]:K→K.In particular,if G is symmetric then[n]∗G≃G n2.Proof.The structure of the central extension G of K by G m is equivalent to the following data(see e.g.[3]):a cube structure on G m-torsor G over K and a trivial-ization of the corresponding biextensionΛ(G)=(p1+p2)∗G⊗p∗1G−1⊗p∗2G−1of K2. Now for any cube structure there is a canonical isomorphism(see[3])[n]∗G≃G n(n+1)2which is compatible with the natural isomorphism of biextensions([n]×[n])∗Λ(G)≃Λ(G)n2≃Λ(G)n(n+1)2.4The latter isomorphism is compatible with the trivializations of both sides when G arises from a central extension.Remark.Locally one can choose a splitting K→G so that the central extension is given by a2-cocycle f:K×K→G m.The previous lemma says that for any 2-cocycle f the functions f(nk,nk′)and f(k,k′)n(n+1)2diﬀer by a canonical coboundary.In fact this coboundary can be written explicitly in terms of the functions f(mk,k)for various m∈Z.Proposition1.2.Assume that K is annihilated by an integer N.If N is odd then for any Heisenberg group G→K the central extension G N is canonically trivial, otherwise G2N is trivial.If G is symmetric and N is odd then G N(resp.G2N if N is even)is trivial as a symmetric extension.bining the previous lemma with(1.2)we get the following isomorphism: [n]∗G≃G n(n+1)2≃G n⊗(G⊗G op−1)n(n−1)2=1for n=2N(resp.for n=N if N is odd).Hence, the triviality of G n in these cases.Corollary1.3.Let G→K be a symmetric Heisenberg group such that the order of K over S is odd.Then the G m-torsor over K underlying G is trivial.Proof.The isomorphism(1.2)implies that the G m-torsor over K underlying G2is trivial.Together with the previous proposition this gives the result.If G→K is a(symmetric)Heisenberg group scheme,such that K is annihilated by an integer N,n is an integer prime to N then G n is also a(symmetric)Heisenberg group.When N is odd this group depends only on the residue of n modulo N(due to the triviality of G N).We call aﬂat subgroup scheme I⊂K G-isotropic if the central extension(1.1) splits over I(in particular,e|I×I=1).Ifσ:I→G is the corresponding lifting,then we have the reduced Heisenberg group scheme0→G m→p−1(I⊥)/σ(I)→I⊥/I→0where I⊥⊂K is the orthogonal complement to I with respect to e.If G is a symmetric Heisneberg group,then I⊂K is called symmetrically G-isotropic if the restriction of the central extension(1.1)to I can be trivialized as a symmetric ex-tension.Ifσ:I→G is the corresponding symmetric lifting them the reduced Heisenberg group p−1(I⊥)/σ(I)is also symmetric.5Let us deﬁne the Witt group WH sym (S )as the group of isomorphism classes of ﬁnite symmetric Heisenberg groups over S modulo the equivalence relation generated by[G ]∼[p −1(I ⊥)/σ(I )]for a symmetrically G -isotropic subgroup scheme I ⊂K .The (commutative)addition in WH sym (S )is deﬁned as follows:if G i →K i (i =1,2)are Heisenberg groups with commutator forms e i then their sum is the central extension0→G m →G 1×G m G 2→K 1×K 2→0so that the corresponding commutator form on K 1×K 2is e 1⊕e 2.The neutral element is the class of G m considered as an extension of the trivial group.The inverse element to [G ]is [G −1].Indeed,there is a canonical splitting of G ×G m G −1→K ×K over the diagonal K ⊂K ×K ,hence the triviality of [G ]+[G −1].We deﬁne the order of a ﬁnite Heisenberg group scheme G →K over S to be the order of K over S (specializing to a geometric point of S one can see easily that this number has form d 2).Let us denote by WH ′sym (S )the analogous Witt group of ﬁnite Heisenberg group schemes Gover S of odd order.Let also WH(S )and WH ′(S )be the analogous groups deﬁned for all (not necessarily symmetric)ﬁnite Heisenberg groups over S (with equivalence relation given by G -isotropic subgroups).Remark.Let us denote by W(S )the Witt group of ﬁnite ﬂat group schemes over S with non-degenerate symplectic G m -valued forms (modulo the equivalence relation given by global isotropic ﬂat subgroup schemes).Let also W ′(S )be the analogous group for group schemes of odd order.Then we have a natural homomorphism WH(S )→W(S )and one can show that the induced map WH ′sym →W ′(S )is anisomorphism.This follows essentially from the fact that a ﬁnite symmetric Heisen-berg group of odd order is determined up to an isomorphism by the corresponding commutator form,also if G →K is a symmetric ﬁnite Heisenberg group with the commutator form e ,I ⊂K is an isotropic ﬂat subgroup scheme of odd order,then there is a unique symmetric lifting I →G .Theorem 1.4.The group WH sym (S )(resp.WH ′sym (S ))is annihilated by 8(resp.4).Proof .Let G →K be a symmetric ﬁnite Heisenberg group.Assume ﬁrst that the order N of G is odd.Then we can ﬁnd integers m and n such that m 2+n 2≡−1mod(N ).Let αbe an automorphism of K ×K given by a matrix m −n n m .Let G 1=G ×G m G be a Heisenberg extension of K ×K representing the class 2[G ]∈WH ′sym (S ).Then from Lemma 1.1and Proposition 1.2we get α∗G 1≃G −11,hence 2[G ]=−2[G ],i.e.4[G ]=0in WH ′(S ).If N is even we can apply the similar argument to the 4-th cartesian power of G and the automorphism of K 4given by an integer 4×4-matrix Z such that Z t Z =6(2N−1)id.Such a matrix can be found by considering the left multiplication by a quaternion a+bi+cj+dk where a2+b2+c2+d2=2N−1.2.Schr¨o dinger representationsLet G be aﬁnite Heisenberg group scheme of order d2over S.A representation of G of weight1is a locally free O S-module together with the action of G such that G m⊂G acts by the identity character.We refer to chapter V of[14]for basic facts about such representations.In this section we study the problem of existence of a Schr¨o dinger representation for G,i.e.a weight-1representation of G of rank d(the minimal possible rank).It is well known that such a representation exists if S is the spectrum of an algebraically closedﬁeld(see e.g.[14],V,2.5.5). Another example is the following.As we already mentioned one can associate a ﬁnite Heisenberg group scheme G(L)(called the Mumford group)to a line bundle L on an abelian schemeπ:A→S such that K(L)isﬁnite.Assume that the base scheme S is connected.Then R iπ∗(L)=0for i=i(L)for some integer i(L) (called the index of L)and R i(L)π∗(L)is a Schr¨o dinger representation for G(L)(this follows from[17]III,16and[16],prop.1.7).In general,L.Moret-Bailly showed in [14]that a Schr¨o dinger representation exists after some smooth base change.The main result of this section is that for symmetric Heisenberg group schemes of odd order a Schr¨o dinger representation always exists.Let G be a symmetricﬁnite Heisenberg group scheme of order d2over S.Then lo-cally(in fppf topology)we can choose a Schr¨o dinger representation V of G.According to Theorem V,2.4.2of[14]for any weight-1representation W of G there is a canon-ical isomorphism V⊗HomG (V,V)≃O.Choose an open covering U i such that there existSchr¨o dinger representations V i for G over U i.For a suﬃcentlyﬁne covering we have G-isomorphismsφij:V i→V j on the intersections U i∩U j,andφjkφij=αijkφik on the triple intersections U i∩U j∩U k for some functionsαijk∈O∗(U i∩U j∩U k).Then(αijk) is a Cech2-cocycle with values in G m whose cohomology class e(G)∈H2(S,G m) doesn’t depend on the choices made.Furthermore,by deﬁnition e(G)is trivial if and only if there exists a global weight-1representation we are looking for.Using the language of gerbs(see e.g.[8])we can rephrase the construction above withoutﬁxing an open ly,to eachﬁnite Heisenberg group G we can associate the G m-gerb Schr G on S such that Schr G(U)for an open set U⊂S is the category of Schr¨o dinger representations for G over U.Then Schr G represents the cohomology class e(G)∈H2(S,G m).Notice that the class e(G)is actually represented by an Azumaya algebra A(G) which is deﬁned as follows.Locally,we can choose a Schr´o dinger representation V for G and put A(G)=End(V)≃Endisomorphism f:V→V′(since any other G-isomorphism diﬀers from f by a scalar), hence these local algebras glue together into a global Azumaya algebra A(G)of rank d2.In particular,d·e(G)=0(see e.g.[9],prop.1.4).Now let W be a global weight-1representation of G which is locally free of rank l·d over S.Then we claim that EndG (W)≃Mat l(O).Now we claim that there is a global algebra isomorphismA(G)⊗End(W).Indeed,we have canonical isomorphism of G-modules of weight1(resp.−1)V⊗Hom G(V∗,W∗) →W∗).Hence,we have a sequence of natural morphismsEnd G(V∗,W∗)⊗Hom(V)⊗Hom G×G(V∗⊗V,W∗⊗W)→End G(W)—the latter map is obtained by taking the image of the identity section id∈V∗⊗V under a G×G-morphism V∗⊗V→W∗⊗W.It is easy to see that the composition morphism gives the required isomorphism.This leads to the following statement. Proposition2.1.For anyﬁnite Heisenberg group scheme G over S a canonical element e(G)∈Br(S)is deﬁned such that e(G)is trivial if and only if a Schr¨o dinger representation for G exists.Furthermore,d·e(G)=0where the order of G is d2, and if there exists a weight-1G representation which is locally free of rank l·d over S then l·e(G)=0.Proposition2.2.The map[G]→e(G)deﬁnes a homomorphism WH(S)→Br(S). Proof.First we have to check that if I⊂K is a G-isotropic subgroup, I⊂G its lifting, and G)=e(G).Indeed,there is a canonical equivalence of G m-gerbs Schr G→SchrProof.Let[G]∈WH′sym(S)be a class of G in the Witt group.Then4[G]=0by Theorem1.4,hence4e(G)=0by Proposition2.2.On the other hand,d·e(G)=0 by Proposition2.1where d is odd,therefore,e(G)=0.Let us give an example of a symmetricﬁnite Heisenberg group scheme of even order without a Schr¨o dinger representation.First let us recall the construction from [23]which associates to a group scheme G over S which is a central extension of aﬁnite commutative group scheme K by G m,and a K-torsor E over S a class e(G,E)∈H2(S,G m).Morally,the mapH1(S,K)→H2(E,G m):E→e(G,E)is the boundary homomorphism corresponding to the exact sequence0→G m→G→K→0.To deﬁne it consider the category C of liftings of E to to a G-torsor.Locally such a lifting always exists and any two such liftings diﬀer by a G m-torsor.Thus,C is a G2-gerb over S,and by deﬁnition e(G,E)is the class of C in H2(S,G m)Note that e(G,E)=0if and only if there exists a G-equivariant line bundle L over E,such that G m⊂G acts on L via the identity character.A K-torsor E deﬁnes a commutative group extension G E of K by G m as follows. Choose local trivializations of E over some covering(U i)and letαij∈K(U i∩U j) be the corresponding1-cocycle with values in K.Now we glue G E from the trivial extensions G m×K over U i by the following transition isomorphisms over U i∩U j:f ij:G m×K→G m×K:(λ,x)→(λe(x,αij),x)where e:K×K→G m is the commutator form corresponding to G.It is easy to see that G E doesn’t depend on a choice of trivializations.Now we claim that if G isa Heisenberg group then(2.1)e(G,E)=e(G⊗G E)−e(G).This is checked by a direct computation with Cech cocycles.Notice that if E2is a trivial K-torsor then G2E is a trivial central extension of K,hence G E is a symmetric extension.Thus,if G is a symmetric Heisenberg group,then G⊗G E is also symmetric. As was shown in[23]the left hand side of(2.1)can be ly,consider the case when S=A is a principally polarized abelian variety over an algebraically closedﬁeld k of characteristic=2.Let K=A2×A considered as a(constant)ﬁnite group scheme over A.Then we can consider E=A as a K-torsor over A via the morphism[2]:A→A.Now if G→A2is a Heisenberg extension of A2(deﬁned over k)then we can consider G as a constant group scheme over A and the class e(G,E) is trivial if and only if G embeds into the Mumford group G(L)of some line bundle L over A(this embedding should be the identity on G m).When NS(A)=Z this means, in particular,that the commutator form A2×A2→G m induced by G is proportional9to the symplectic form given by the principal polarization.When dim A≥2there is a plenty of other symplectic forms on A2,hence,e(G,E)can be non-trivial.Now we are going to show that one can replace A by its general point in this example.In other words,we consider the base S=Spec(k(A))where k(A)is the ﬁeld of rational functions on A.Then E gets replaced by Spec(k(A))considered asa A2-torsor over itself corresponding to the Galois extension[2]∗:k(A)→k(A):f→f(2·)with the Galois group A2.Note that the class e(G,E)for any Heisenberg extension G of A2by k∗is annihilated by the pull-back to E,hence,it is represented by the class of Galois cohomology H2(A2,k(A)∗)⊂Br(k(A))where A2acts on k(A) by translation of argument.It is easy to see that this class is the image of the class e G∈H2(A2,k∗)of the central extension G under the natural homomorphism H2(A2,k∗)→H2(A2,k(A)∗).From the exact sequence of groups0→k∗→k(A)∗→k(A)∗/k∗→0we get the exact sequence of cohomologies0→H1(A2,k(A)∗/k∗)→H2(A2,k∗)→H2(A2,k(A)∗)(note that H1(A2,k(A)∗)=0by Hilbert theorem90).It follows that central exten-sions G of A2by k∗with trivial e(G,E)are classiﬁed by elements of H1(A2,k(A)∗/k∗).Lemma2.4.Let A be a principally polarized abelian variety over an algebraically closedﬁeld k of characteristic=2.Assume that NS(A)=Z.Then H1(A2,k(A)∗/k∗)= Z/2Z.Proof.Interpreting k(A)∗/k∗as the group of divisors linearly equivalent to zero we obtain the exact sequence0→k(A)∗/k∗→Div(A)→Pic(A)→0,where Div(A)is the group of all divisors on A.Note that as A2-module Div(A) is decomposed into a direct sum of modules of the form Z A2/H where H⊂A2is a subgroup.Now by Shapiro lemma we have H1(A2,Z A2/H)≃H1(H,Z),and the latter group is zero since H is a torsion group.Hence,H1(A2,Div(A))=0.Thus, from the above exact sequence we get the identiﬁcationH1(A2,k(A)∗/k∗)≃coker(Div(A)A2→Pic(A)A2).Now we use the exact sequence0→Pic0(A)→Pic(A)→NS(A)→0,10where Pic0(A)=ˆA(k).Since the actions of A2on Pic0(A)and NS(A)are trivial we have the induced exact sequence0→Pic0(A)→Pic(A)A2→NS(A).The image of the right arrow is the subgroup2NS(A)⊂NS(A).Note that Pic0(A)= [2]∗Pic0(A),hence this subgroup belongs to the image of[2]∗Div(A)⊂Div(A)A2. Thus,we deduce thatH1(A2,k(A)∗/k∗)≃coker(Div(A)A2→2NS(A)).Let[L]⊂NS(A)be the generator corresponding to a line bundle L of degree1on A. Then L4=[2]∗L,hence4·[L]=[L4]belongs to the image of Div(A)A2.On the other hand,it is easy to see that there is no A2-invariant divisor representing[L2],henceH1(A2,k(A)∗/k∗)≃Z/2Z.It follows that under the assumptions of this lemma there is a unique Heisenberg extensions G of A2by k∗with the trivial class e(G,E)(the Mumford extension corresponding to L2,where L is a line bundle of degree1on A).Hence,for g≥2 there exists a Heisenberg extension with a non-trivial class e(G,E)∈Br(k(A)).3.Representations of the Heisenberg groupoidRecall that the Heisenberg group H(W)associated with a symplectic vector space W is a central extension0→T→H(W)→W→0of W by the1-dimensional torus T with the commutator form exp(B(·,·))where B is the symplectic form.In this section we consider an analogue of this extension in the context of abelian schemes(see[22],sect.7,[23]).Namely,we replace a vector space W by an abelian scheme X/S.Bilinear forms on W get replaced by biextensions of X2.Recall that a biextension of X2is a line bundle L on X2together with isomorphismsL x+x′,y≃L x,y⊗L x′,y,L x,y+y′≃L x,y⊗L x,y′—this is a symbolic notation for isomorphisms(p1+p2,p3)∗L≃p∗13L⊗p∗23L and (p1,p2+p3)∗L≃p∗12L⊗p∗13L on X3,satisfying some natural cocycle conditions (see e.g.[3]).The parallel notion to the skew-symmetric form on W is that of a skew-symmetric biextension of X2which is a biextension L of X2together with an isomorphism of biextensionsφ:σ∗L →L−1,whereσ:X2→X2is the permutation of11factors,and a trivialization∆∗L≃O X of L over the diagonal∆:X→X2compati-ble withφ.A skew-symmetric biextension L is called symplectic if the corresponding homomorphismψL:X→ˆX(whereˆX is the dual abelian scheme)is an isomor-phism.An isotropic subscheme(with respect to L)is an abelian subscheme Y⊂X such that there is an isomorphism of skew-symmetric biextensions L|Y×Y≃O Y×Y. This is equivalent to the condition that the composition Y i→XψL→ˆXˆi→ˆY is zero. An isotropic subscheme Y⊂X is called lagrangian if the morphism Y→ker(ˆi) induced byψL is an isomorphism.In particular,for such a subscheme the quotient X/Y exists and is isomorphic toˆY.Note that to deﬁne the Heisenberg group extension it is not suﬃcient to have a symplectic form B on W:one needs a bilinear form B1such that B(x,y)=B1(x,y)−B1(y,x).In the case of the real symplectic space one can just take B1=B/2,however in our situation we have to simply add necessary data.An enhanced symplectic biextension(X,B)is a biextension B of X2such that L:=B⊗σ∗B−1is a symplectic biextension.The standard enhanced symplectic biextension for X=ˆA×A,where A is any abelian scheme,is obtained by settingB=p∗14P∈Pic(ˆA×A×ˆA×A),where P is the normalized Poincar´e line bundle on A×ˆA.Given an enhanced symplectic biextension(X,B)one deﬁnes the Heisenberg groupoid H(X)=H(X,B)as the stack of monoidal groupoids such that H(X)(S′)for an S-scheme S′is the monoidal groupoid generated by the central subgroupoid P ic(S′)of G m-torsors on S′and the symbols T x,x∈X(S′)with the composition lawT x◦T x′=B x,x′T x+x′.The Heisenberg groupoid is a central extension of X by the stack of line bundles on S in the sense of Deligne[4].In[22]we considered the action of H(ˆA×A)on D b(A)which is similar to the stan-dard representation of the Heisenberg group H(W)on functions on a lagrangian sub-space of W.Below we construct similar representations of the Heisenberg groupoid H(X)associated with lagrangian subschemes in X.Further,we construct inter-twining functors for two such representations corresponding to a pair of lagrangian subschemes,and consider the analogue of Maslov index for a triple of lagrangian subschemes that arises when composing these intertwining functors.To deﬁne an action of H(X)associated with a lagrangian subscheme one needs some auxilary data described as follows.An enhanced lagrangian subscheme(with respect to B)is a pair(Y,α)where Y⊂X is a lagrangian subscheme with respect to X,αis a line bundle on Y with a rigidiﬁcation along the zero section such that an isomorphism of symmetric biextensionsΛ(α)≃B|Y×Y is given,whereΛ(α)=12。

Efficiency and risk in Japanese banking

E ciency and risk in Japanese bankingYener Altunbas a ,Ming-Hau Liu b ,Philip Molyneuxc,*,Rama Seth d,1aThe Business School,South Bank University,Southwark Campus,103Borough Road,London,SE10AA,UKbNanyang Business School,NTU,Singapore 639798,SingaporecSchool of Accounting,Banking and Economics,University of Wales Bangor,Gwynedd,Bangor,LL572DG,UKdFederal Reserve Bank of New York,New York,NY 10045,USAReceived 18April 1997;accepted 27July 1999AbstractThis paper investigates the impact of risk and quality factors on banks Õcost by using the stochastic cost frontier methodology to evaluate scale and X -ine ciencies,as well as technical change for a sample of Japanese commercial banks between 1993and 1996.Loan-loss provisions are included in the cost frontier model to control for output quality,with a ®nancial capital and a liquidity ratio included to control risk.Following the ap-proach suggested in Mester (1996)we show that if risk and quality factors are not taken into account optimal bank size tends to be overstated.That is,optimal bank size is considerably smaller when risk and quality factors are taken into account when mod-elling the cost characteristics of Japanese banks.We also ®nd that the level of ®nancial capital has the biggest in¯uence on the scale e ciency estimates.X -ine ciency estimates,in contrast,appear less sensitive to risk and quality factors.Our results also suggest that scale ine ciencies dominate X -ine ciencies.These are important ®ndings because they contrast with the results of previous studies on Japanese banking.In particular,the results indicate an alternative policy prescription,namely,that the largest banks shouldJournal of Banking &Finance 24(2000)1605±1628/locate/econbase*Corresponding author.Tel.:+44-1248-382170;fax:+44-1248-364760.E-mail address:p.molyneux@ (P.Molyneux).1The views expressed are those of the author and do not necessarily re¯ect those of the Federal Reserve Bank of New York or the Federal Reserve System.0378-4266/00/$-see front matter Ó2000Elsevier Science B.V.All rights reserved.PII:S 0378-4266(99)00095-31606Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628shrink to bene®t from scale advantages.It also seems that®nancial capital has the largest in¯uence on optimal bank size.Ó2000Elsevier Science B.V.All rights reserved.JEL classi®cation:G21;D21;G23Keywords:Japanese banks;Cost functions;Economies of scale;Ine ciencies;Technical change1.IntroductionStudies of the Japanese banking industry have typically found strong evi-dence of scale economies across a broad range of bank sizes(see for example, Kasuya,1986;Yoshioka and Nakajima,1987;Tachibanaki et al.,1991; Fukuyama,1993;McKillop et al.,1996).The aforementioned studies provide an indication of the cost characteristics of the Japanese banking industry, however,they may be limited because they do not take into account the risks associated with banks'operations.This is a particularly relevant issue in Japanese banking given that the system has experienced substantial asset quality problems and low levels of capitalisation since the early1990s(see Bank of Japan,1995,1996).Recent studies such as those Hughes and Mester (1993),Hughes et al.(1995),McAllister and McManus(1993),Mester(1996) and Clark(1996)have drawn attention to the fact that bank e ciency studies typically ignore the impact of risk on banks'costs or pro®ts and they suggest that risk characteristics need to be incorporated in the underlying industry cost or pro®t functions because,`unless quality and risk are controlled for,one might easily miscalculate a bank's level of ine ciency'(Mester,1996,p.1026). For instance,Hughes et al.(1995)in their study on1989±90US banks which exceed$1billion in asset size,®nd that when they control for risk,inexhaustible economies of scale that increase with size are prevalent.When risk neutrality is imposed on the estimation,the large scale economies disappear and constant returns to scale are obtained.McAllister and McManus(1993)also show that for larger US banks estimates of scale economies are increased when they control for risk.(This tends to be more prevalent for banks up to$1billion in asset size.)In contrast,Hughes and Mester(1993)®nd that estimates of in-creasing returns to scale for a wide range of bank sizes become constant returns when asset quality,®nancial capital and risk are taken into account.Clark (1996)also re-emphasises the in¯uence of risk factors in the cost characteristics of US banks and shows how risk can statistically in¯uence e ciency levels±in particular,he shows how X-ine ciency estimates tend to become smaller (about3%from9%)when risk factors are incorporated in frontier estimations. In order to advance the aforementioned literature,this paper evaluates cost e ciency and technical change for Japanese commercial banks by comparingY.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281607 results obtained from two cost functions speci®cations.First we use the sto-chastic cost frontier methodology to estimate scale economies,scale e ciencies and X-ine ciency,as well as technical change,for a sample of Japanese commercial banks between1993and1996using a three input±three output Fourier-¯exible cost function speci®cation.The three outputs include total loans,total securities and total o -balance sheet items(nominal value).We then compare these results with those generated by a similar cost function which also includes variables controlling for risk and quality factors.In ad-dition,we also evaluate the sensitivity of scale economy and X-ine ciency estimates to various risk and quality variables.Our results show that when the underlying cost function speci®cation does not control for risk and quality factors,scale economies are prevalent for all but the largest Japanese banks.Those larger than Yen10,000billion exhibit signi®cant diseconomies.Overall,Japanese banks appear to be relatively scale e cient.When risk and quality factors are taken into account,however,only the very smallest banks exhibit signi®cant economies with the majority of banks experiencing signi®cant diseconomies of scale which appear to get larger with asset size.Estimates derived from the model including risk and quality variables suggested that there are widespread scale ine ciencies in the Japanese banking market.These results suggest that bank minimum e cient scale be-comes smaller after controlling for risk,a®nding similar to that of Hughes and Mester(1993).This contrasts with the results of Hughes et al.(1995)and McAllister and McManus(1993)who®nd either minimum e cient scale is increased or scale economies are never exhausted after controlling for risk.Our results also point to the limitations of previous studies on the cost character-istics of Japanese banking and also suggest di erent policy conclusions, namely,that the largest banks should reduce their size if they wish to bene®t from scale economies.In contrast to the scale estimates and ClarkÕs(1996)®ndings on US banking,X-ine ciency scores appear to be less sensitive to the inclusion of risk and quality variables.The mean level of X-ine ciency for the largest banks range between5%and7%.This also indicates that the largest Japanese banks should focus on reducing managerial and other ine ciencies, as well as reducing their size if they are to generate cost savings.Finally,this study also®nds that technical change has reduced bank cost,but at a declining rate,between1993and1996.2.MethodologyFollowing Mester(1996),Cebenoyan et al.(1993)and Allen and Rai(1996) we use the stochastic cost frontier methodology.This approach labels a bank as ine cient if its costs are higher than those predicted for an e cient bank producing the same input/output con®guration and the di erence cannot beexplained by statistical noise.The cost frontier is obtained by estimating a Fourier Flexible cost function with a composite error term,the sum of a two-sided error representing random¯uctuations in cost and a one-sided positive error term representing ine ciency.The single-equation stochastic cost function model can be given asTC TC Q i Y P i e i Y 1 where TC is observed total cost,Q i is a vector of outputs,and P i is an input price vector.Following Aigner et al.(1977),we assume that the error term of the cost function ise u v Y 2 where u and v are independently distributed.u is usually assumed to be dis-tributed as half-normal,that is,a one-sided positive disturbance capturing the e ects of ine ciency,and v is assumed to be distributed as two-sided normal with zero mean and variance r2,capturing the e ects of the statistical noise. Observation-speci®c estimates of technical ine ciency,u,can be calculated by using the distribution of the ine ciency term conditional on the estimate of the composed error term,as proposed by Jondrow et al.(1982).The mean of this conditional distribution for the half-normal model is shown asE u i j e irk1 k2f e i k a r1ÀF e i k a re i kr!Y 3where F(á)and f(á)are the standard normal distribution and the standard normal density function,respectively.E(u j e)is an unbiased but inconsistent estimator of u i,since regardless of N,the variance of the estimator remains non-zero(see Greene,1993a,pp.80±82).Jondrow et al.(1982)have shown that the ratio of the variability(standard deviation,r)for u and v can be used to measure a bankÕs relative ine ciency,where k r u a r v,is a measure of the amount of variation stemming from ine ciency relative to noise for the sam-ple.Estimates of this model can be computed by maximising the likelihood function directly(see Olson et al.,1980).Kaparakis et al.(1994),Allen and Rai (1996)and Mester(1996)all use the half-normal speci®cation to test for in-e ciency di erences between®nancial institutions mainly in the US market.22See Bauer(1990)for an excellent review of the frontier literature and how di erent stochastic assumptions can be made.Cebenoyan et al.(1993)and Berger and DeYoung(1997),for example, use the truncated normal model.Mester(1993)in common with many(non-banking)studies uses the half-normal distribution.Stevenson(1980)and Greene(1990)have used normal-gamma model. Altunbas and Molyneux(1994)®nd that e ciency estimates are relatively insensitive to di erent distributional assumptions when testing the half normal,truncated normal,normal-exponential and gamma e ciency distributions,as all distributions yield similar ine ciency levels for the German banking markets.1608Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628The Fourier-¯exible cost function used to calculate X-ine ciencies(as well as scale economies and technical change)incorporates a two-component error structure and is estimated using the maximum likelihood procedure.3First we estimate a cost function that controls for risk and quality factors and then we compare the results with those derived from the same cost function excluding all and then individual risk and quality variables(because we use three risk and quality variables there are®ve cost functions estimates in total).The cost function is given aslnTC a03i 1a i ln Q i3i 1b i ln P i s1ln E k1lnNPL a Lk2lnL a TA t1T 123i 13j 1d ij ln Q i ln Q j 43i 1 3j 1c ij ln P i ln P j /1ln E ln E t11T253i 1 3i 1q ij ln P i ln Q j3i 1w i s ln P i ln E3i 1h i s ln Q j ln E3i 1 a i cos z i b i sin z i3i 13j 1a ij cos z i z jb ij sin z i z j e Y 4 where ln TC the natural logarithm of total costs(operating and®nancial cost); ln Q i the natural logarithm of i th bank outputs;ln P i the natural logarithm of i th input prices;ln E the natural logarithm of®nancial capital;4ln NPL/L the3Spong et al.(1995),Berger et al.(1997)and Mitchell and Onvural(1996)have suggested that the Fourier-¯exible functional form should be preferred over the translog because the former better approximates the underlying cost function across a broad range of outputs.The semi-non-parametric Fourier functional form has desirable mathematical and statistical properties because an(in®nite)Fourier series is capable of representing any function exactly and even truncated Fourier series can approximate a function reasonably well throughout its entire range.In contrast, when using parametric methods like the translog,one holds the maintained hypothesis that the bank industryÕs true cost function has the translog form.If this maintained hypothesis is false misspeci®cation error occurs.When using the Fourier functional form,one avoids holding any maintained hypothesis by allowing the data to reveal the true cost function through a large value of ®tted parameters.For ease of exposition,however,we choose to use the translog functional form to illustrate the impact risk and quality factors have on Japanese commercial banksÕcost e ciencies. 4Note that the®nancial capital variable(E)is fully interactive with the output(Q)and input price(P)variables but NPL/L and L/TA are not.This is because the inclusion of more than one of the risk/quality variables would signi®cantly reduce the degrees of freedom,due to the expansion of Fourier terms and the limited number of observations.Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281609natural logarithm of the ratio of non-performing loans to total loans;ln L/TA the natural logarithm of the ratio liquid assets to total assets;T time trend; Z i the adjusted values of the log output ln Q i such that they span the interval [0,2p];a,b,d,c,k,/,h,w,q,k,a,b and t are coe cients to be estimated. Since the duality theorem requires that the cost function must be linearly homogeneous in input prices,the following restrictions have to be imposed on the parameters in Eq.(4):3 i 1b i 1Y3i 1c ij 0for all j Y3 i 1q ij 0Y3i 1W ij 0for all j X5Furthermore,the second order parameters of the cost function in Eq.(4)must be symmetric,that is,d ij d ji for all i Y j Yc ij c ji for all i Y j X6For the de®nition of inputs and outputs we use a variation of the intermedi-ation approach proposed by Sealey and Lindley(1977)where the inputs,la-bour,physical capital and deposits are used to produce earning assets.Two of our outputs,total loans and total securities are earning assets and we also include total o -balance sheet items(measured in nominal terms)as a third output.Although the latter are technically not earning assets,this type of business constitutes an increasing source of income for banks and therefore should be included when modelling banks'cost characteristics,otherwise,total output would tend to be understated(Jagtiani and Khanthavit,1996). Following Mester(1996)we use loan-loss provisions as a proportion of total loans as the output quality proxy.5We also use a variable to account for li-quidity risks because liquidity holdings(particularly those imposed by the authorities)represent a cost to bank that hold a higher proportion of cash and liquid assets have higher costs.As suggested in Hughes and Mester(1993)and Mester(1996)the level of equity capital,rather than the equity-to-assets ratio is included to control for di erences in risk preferences.6We also include a time5Berger and DeYoung(1997)argue that this variable may be a function of management e ciency,e cient banks will be better underwriters and monitors and hence will have lower losses, and hence it is endogenous,not exogenous.One referee also pointed out that a similar argument could be made for the liquidity risk variable,e cient mangers will hold only low levels of liquid assets,while ine cient mangers will hold excess amount of these low-yield assets.6As Mester(1996,p.1026)states,``Financial capital should be accounted for in the cost function and the level rather than the price of®nancial capital should be included since there is good reason to believe that cost-minimisation does not fully explain a bankÕs capital level±e.g.,regulations set minimum capital-to-assets ratios,and bank managers may be risk averse''.1610Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628trend in our cost frontier to capture the missing time dimension of inputs or other dynamics that are not modelled explicitly.7The cost frontiers are estimated using the random e ects panel data ap-proach(as in Lang and Welzel,1996).We use the panel data approach because technical e ciency is better studied and modelled with panels(See Baltagi and Gri n,1988;Cornwell et al.,1990;Kumbhakar,1993).The random e ects model is preferred over the®xed e ects model because the latter is considered to be the more appropriate speci®cation if we are focusing on a speci®c set of N ®rms.Moreover,and if N is large,a®xed e ects model would also lead to a substantial loss of degrees of freedom(See Baltagi,1995).Within sample scale economies are calculated as in Mester(1996)and are evaluated at the mean output,input price,quality and®nancial capital levels for the respective size quartiles.A measure of overall economies of scale(SE)is given by the following cost elasticity by di erentiating the cost function in Eq.(4)with respect to output.8This gives us:SE3i 1o ln TC o ln Q i3i 1a i123i 13j 1d ij ln Q j3i 13j 1q ij ln P i3i 1h i s ln El i3i 1 Àa i sin Z i b i cos Z i 2l i3i 13j 1Àa ij sin Z i Z jb i cos Z i Z j X 7 If SE`1then increasing returns to scale,implying economies of scale.If SE 1then constant returns to scale.If SE b1then decreasing returns to scale,implying diseconomies of scale. Following McKillop et al.(1996)and Lang and Welzel(1996)the rate of technical progress may be inferred from changes in a®rmÕs cost function over time.A time trend variable,T,serves as a proxy for disembodied technical change.The time-trend is aÔcatch-allÕvariable that captures the e ects of7One referee suggested that because annual economic conditions are not controlled for in the cost function speci®cations the time trend will capture more than just technological factors.Ideally one should control for exogenous conditions that change over time(e.g.economic indicators, competition,®nancial regulations).To this end a method suggested by DeYoung and Hasan(1998) was recommended where non-performing loans were decomposed into two components,exogenous and internal.Unfortunately data limitations did not allow us to undertake such a breakdown. 8Evano and Israilevich(1995)make the distinction between scale elasticity and scale e ciency where the former is measured as in Eq.(7),and the latter measures the change in output required to produce at minimum e cient scale.Throughout this paper references to economies and diseconomies of scale relate to scale elasticities.Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281611technological factors:i.e.learning by doing and organisational changes al-lowing for the more e cient use of existing inputs,together with the e ects of other factors,such as changing environmental regulations(see Baltagi and Gri n,1988;Nelson,1984).Technical progress allows the®rm to produce a given output,Q,at lower levels of total cost over time,holding input prices and regulatory e ects constant.In order to estimate the impact of technical change we calculate the variation in the total cost due to a given change in technology. This can be measured by the partial derivative of the estimated cost function with respect to the time trend(T)and can be shown as follows:T C o ln TCo Tt1 t11T X 8The parameters on Eq.(8)capture the pure e ect of technical change,that is the decline in costs,keeping constant input proportions.93.Data and resultsOur data comprise the population of Japanese commercial banks listed in the London based IBCA bank credit rating agencies Bankscope(1997)dat-abase for the years1993±1996,and consists of139banks for each year from 1993to1995and136in1996.10The median asset size of banks included was Yen1.6trillion and the average asset size was Yen5trillion(see Appendix A for more details).Table1provides the descriptive statistics for the input, output and control variables for1996.This shows that for1996the median bank had Yen1.19trillion in loans,Yen334billion in securities and Yen41 billion of o -balance sheet items.Non-performing loans as a proportion of gross loans ranged between0.29%and9.5%,the latter®gure perhaps sug-gesting that some banks faced substantial credit quality problems. Various structural tests were undertaken to test for data poolability and heteroscedasticity and the results of these are shown in Table2.Homosce-dasticity,which implies the disturbance variance is constant across observa-tions,is not rejected at the one percent level for the whole sample applying the Goldfeld and Quandt,(1965)test.11The question of whether to pool the data9As in Lang and Welzel(1996),we do not include the interactive terms of outputs and input prices.Hence we are not able to measure the technical change associated with changes in output (scale augmenting in our estimates of technical change)and the technical change with the use of inputs due to changes in input prices.10The data set includes commercial bank only and excludes long-term credit banks and trust bank.11WhiteÕs(1980)test was also undertaken to investigate cross-sectional heteroscedasticity and we could not reject the hypothesis of homoscedasticity at the1%level of signi®cance.1612Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628or not naturally appears with panel data.In the econometric model,we assume that estimated parameters are the same over time.However,this assumption can be tested using Chow Õs (1960)test.Table 2shows that Chow Õs test forTable 1Descriptive statistics of the outputs,inputs and control variables used in the model,1996a Variable DescriptionMean Median St.Dev.Min MaxTC Total cost (YEN bil)165.740.8506.9 4.14291.5P 1Price of labour (YEN bil)(total personnel expenses/total asset)0.00890.00910.00230.00010.0142P 2Price of funds (%)(total interest expenses/total funds)0.01180.01010.00670.00510.0579P 3price of physical capital (%)(total depreciation and othercapital expenses/total ®xed assets)0.32470.27200.20140.18420.9419Q 1Total loans (domestic loans,foreign loans and trust a/c loans)(YEN bil)3373.01186.07903.098.046,887.0Q 2total securities (trading securities,Japanese public bonds,other investments and equity investments)(YEN bil)1189.0334.03005.032.023,098.0Q 3O balance sheet Items (contin-gent liabilities,acceptances,guarantees and L/Cs)(YEN bil)297.941.11029.9 1.55820.4Etotal equity (YEN bil)179.158.7417.3 4.62855.0NPL/L Non-performing loans/total loans (%)2.40 1.89 1.780.299.54L/TA Cash and due from banks/total assets (%) 4.293.62 2.630.8315.22TTime trend±±±19931996aNumber of observed banks:136.Table 2Structural test results Test performed Test statistics Degrees of freedom Critical value Decision Goldfeld±Quandt Test Hetroscedasticity 1.110n 1 382,n 2 170F 0X 01 n 1Àk Y n 2Àk 1X 250Rejected Poolability1.0023k 150Y N À4k 353F 0X 01 150Y 353 1X 00Not-rejected Translog form55.689k 18v 20X 05 28X 869Rejected No risk and quality variables91.144k 9v 20X 05 16X 916Rejected No equity variables 87.288k 7v 20X 05 14X 067Rejected No NPL/L variables 15.510k 1v 20X 05 3X 842Rejected No L/TA variables 3.333k 1v 20X 05 3X 842Not-rejected No technical progress41.022k 2v 20X 055X 991RejectedY.Altunbas et al./Journal of Banking &Finance 24(2000)1605±162816131614Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±1628 poolability over time yields an F-value of1.002which is distributed as F(150, 353)under the null hypothesis:H0X b t b for t 1Y F F F Y T,and this test does not reject poolability across time periods.We also undertake likelihood ratio tests,as an alternative to the F-statistic for testing hypotheses about s,k1and k2(see Greene,1993b),to see if the cost function that included the risk and quality variables(RQCF)di ered signi®-cantly from the standard model(CF).The likelihood ratio test rejects the hypothesis that the two models CF and RQCF are not signi®cantly di erent. Similar tests were also undertaken to see whether the inclusion of individual risk and quality variables as well as the time trend signi®cantly altered the model.Table2shows the likelihood ratio statistics indicating that all but the L/TA variables have a signi®cant in¯uence on model speci®cation.This sug-gests that the equity and non-performing loans variables provide the bulk of information relating to quality and risk factors.Table3shows the estimated scale,X-ine ciencies and technical change results(parameter estimates are given in Appendix A).The®ndings from the RQCF model which controls for risk and quality factors con¯ict with the re-sults from previous studies on Japanese banking in that we®nd scale econo-mies to be much smaller.For instance,McKillop et al.(1996)®nd evidence of ÔappreciableÕscale economies in their study using data from the®ve largest Japanese banks,and their results support the earlier®ndings of Kasuya(1986), Tachibanaki et al.(1991)and Fukuyama(1993).Our results show that dis-economies of scale become much more widespread and optimal bank size falls from around Yen5±10trillion to Yen1±2trillion when risk and quality factors are taken into account.Estimates of scale economies for the largest Japanese commercial banks tend to be overstated when the underlying cost function speci®cation does not control for these factors.This®nding also contrasts with the studies by Hughes et al.(1995)and McAllister and McManus(1993)on US banks which®nd that either optimal bank size increases or scale economies are never exhausted when risk and quality variable included.The con¯icting results could be related to a variety of factors including:di erent institutional struc-tures,the decline in capital strength of Japanese banks during the1990s;the di erent time frame covered and growth variation in the output/input mix of Japanese compared with US banks.Unlike Clark(1996)who®nds that risk variables signi®cantly alter X-inef-®ciency estimates for US banks,we®nd that in the case of Japanese banks the ine ciency results from both models are similar.Mean levels of ine ciency range between5%and7%,with no discernible trend across size classes.This suggests that if the average bank in each size class used its inputs as e ciently as possible it could decrease its costs somewhere in the region of5±7%.These X-ine ciency scores are similar to the results found in recent US studies(see Berger and DeYoung(1997)and Berger and Humphrey(1997)).Overall the results from the model which controls for risk and quality factors(RQCF)Table3Scale economies,ine ciencies and technical change for Japanese commercial banks1993±1996aTotal assets sizes(Yen bil)1993199419951996 RQCF CF RQCF CF RQCF CF RQCF CFScale economies b1±5000.773Ã0.9810.774Ã0.9830.769Ã0.9900.774Ã0.991 500±10000.889Ã0.949Ã0.885Ã0.944Ã0.879Ã0.945Ã0.875Ã0.947Ã1000±20000.9810.946Ã0.9780.946Ã0.9780.949Ã0.9770.948Ã2000±3000 1.050ÃÃ0.965ÃÃ 1.050ÃÃ0.967ÃÃ 1.0440.961ÃÃ1.0440.964Ã3000±5000 1.091Ã0.934Ã 1.093Ã0.938Ã 1.090Ã0.936Ã 1.086Ã0.932Ã5000±10,000 1.212Ã 1.008 1.210Ã 1.000 1.204Ã0.995 1.196Ã0.999 >10,000 1.457Ã 1.063ÃÃ 1.455Ã 1.063ÃÃ 1.455Ã 1.072Ã 1.456Ã 1.081ÃScale ine ciency c1±5000.2230.0780.2630.0970.2330.0830.1940.029 500±10000.1660.1710.1500.1930.1500.2020.1510.166 1000±20000.0000.1530.0000.1720.0000.1340.0000.125 2000±30000.0450.1680.0670.1450.0650.0830.0780.081 3000±50000.0690.2040.0800.1640.0720.1690.0720.102 5000±10,0000.2340.0000.2150.0000.1750.0000.1340.000 >10,0000.2970.2290.2540.2250.2490.2400.2590.251 Ine ciency scores1±5000.0730.0650.0720.0650.0690.0630.0740.070 500±10000.0550.0460.0560.0470.0530.0410.0710.053 1000±20000.0470.0430.0500.0500.0530.0470.0600.055 2000±30000.0490.0450.0600.0580.0640.0550.0680.064 3000±50000.0510.0460.0640.0580.0610.0510.0760.059 5000±10,0000.0560.0670.0700.0810.0530.0530.0370.045 >10,0000.0760.0600.0850.0690.0610.0490.0930.086 All0.0560.0500.0610.0570.0580.0500.0680.060Overalltechnicalprogress d)0.040Ã)0.046Ã)0.026Ã)0.031Ã)0.012Ã)0.016Ã0.002)0.001ÃFor the scale economy estimates,statistically di erent from one at the one percent level for two-tailed test for the scale results,for the technical progress estimates statistically di erent from zero at the one percent level.ÃÃFor values signi®cantly di erent from one at the10%level.a Results reported in the table are derived from estimated coe cients for a single equation panel data model1993±1996.Estimates calculated for the mean values within each size category.b The scale economies measure is SE o ln TC a o ln Q1 o ln TC a o ln Q2 o ln TC a o ln Q3 where TC is the actual cost of producing the average output bundle at the average input prices,®nancial capital and quality factors;Q i is the volume of output i.SE`1indicates increasing re-turns to scale;SE b1indicates decreasing returns to scale;SE 1indicates constant returns to scale.c The scale ine ciency measure is derived from the methodology suggested by Evano and Israi-levich(1995).d Overall technical progress can be measured as the elasticity of total cost TC with respect to time t, i.e.,T C o lnTC a o T.Y.Altunbas et al./Journal of Banking&Finance24(2000)1605±16281615。

invariants and K-spectrums of local theta lifts

arXiv:1302.1031v2 [math.n 1.1. Let WR be a ﬁnite dimensional symplectic real vector space. Throughout this paper (G, G′) will denote a type I irreducible reductive dual pair in Sp(WR ). Such dual pairs are listed in Table 1 in Section 2.1. We follow the notation in [15] closely. Let Sp(WR ) be the metaplectic double cover of Sp(WR ). For any subgroup E of Sp(WR ), let E denote its inverse image in Sp(WR ). We choose a maximal compact subgroup U of Sp(WR ) such that K := G ∩ U and K ′ := G′ ∩ U are maximal compact subgroups of G and G′ respectively. Hence K and K ′ are maximal compact subgroups of G and G′ respectively. The choice of U determines a unique complex structure on WR with the following property: there is a positive deﬁnite Hermitian form , on the resulting complex vector space W so that the imaginary part of , coincides with the symplectic form on WR , and U coincides with the unitary group attached to (W, , ). We choose the oscillator representation of Sp(WR ) whose Fock model Y is realized as the space C [W ] of complex polynomials on W with the U action as described in Appendix A.1. Let ς denote the minimal U-type of Y . It is a one dimensional representation of U acting on the space of constant functions in C [W ]. Let ς |E denote the restriction of ς to E for any subgroup E of U. Let g = k ⊕ p denote the complexiﬁed Cartan decomposition of the Lie algebra of G corresponding to the maximal compact subgroup K . Likewise we deﬁne g′ = k′ ⊕ p′ for G′ . Let ρ be an irreducible admissible genuine (g, K )-module. By (2.5) in [15], Y /(∩ψ∈Homg,K (Y ,ρ) ker ψ ) ≃ ρ ⊗ Θ(ρ) where Θ(ρ) is a (g′ , K ′ )-module called the full (local) theta lift of ρ. Theorem 2.1 in [15] states that if Θ(ρ) = 0, then Θ(ρ) is a (g′ , K ′ )-module of ﬁnite length with an inﬁnitesimal character and it has a unique irreducible quotient θ(ρ) called the (local) theta lift of ρ.

OSHA现场作业手册说明书

DIRECTIVE NUMBER: CPL 02-00-150 EFFECTIVE DATE: April 22, 2011 SUBJECT: Field Operations Manual (FOM)ABSTRACTPurpose: This instruction cancels and replaces OSHA Instruction CPL 02-00-148,Field Operations Manual (FOM), issued November 9, 2009, whichreplaced the September 26, 1994 Instruction that implemented the FieldInspection Reference Manual (FIRM). The FOM is a revision of OSHA’senforcement policies and procedures manual that provides the field officesa reference document for identifying the responsibilities associated withthe majority of their inspection duties. This Instruction also cancels OSHAInstruction FAP 01-00-003 Federal Agency Safety and Health Programs,May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045,Revised Field Operations Manual, June 15, 1989.Scope: OSHA-wide.References: Title 29 Code of Federal Regulations §1903.6, Advance Notice ofInspections; 29 Code of Federal Regulations §1903.14, Policy RegardingEmployee Rescue Activities; 29 Code of Federal Regulations §1903.19,Abatement Verification; 29 Code of Federal Regulations §1904.39,Reporting Fatalities and Multiple Hospitalizations to OSHA; and Housingfor Agricultural Workers: Final Rule, Federal Register, March 4, 1980 (45FR 14180).Cancellations: OSHA Instruction CPL 02-00-148, Field Operations Manual, November9, 2009.OSHA Instruction FAP 01-00-003, Federal Agency Safety and HealthPrograms, May 17, 1996.Chapter 13 of OSHA Instruction CPL 02-00-045, Revised FieldOperations Manual, June 15, 1989.State Impact: Notice of Intent and Adoption required. See paragraph VI.Action Offices: National, Regional, and Area OfficesOriginating Office: Directorate of Enforcement Programs Contact: Directorate of Enforcement ProgramsOffice of General Industry Enforcement200 Constitution Avenue, NW, N3 119Washington, DC 20210202-693-1850By and Under the Authority ofDavid Michaels, PhD, MPHAssistant SecretaryExecutive SummaryThis instruction cancels and replaces OSHA Instruction CPL 02-00-148, Field Operations Manual (FOM), issued November 9, 2009. The one remaining part of the prior Field Operations Manual, the chapter on Disclosure, will be added at a later date. This Instruction also cancels OSHA Instruction FAP 01-00-003 Federal Agency Safety and Health Programs, May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045, Revised Field Operations Manual, June 15, 1989. This Instruction constitutes OSHA’s general enforcement policies and procedures manual for use by the field offices in conducting inspections, issuing citations and proposing penalties.Significant Changes∙A new Table of Contents for the entire FOM is added.∙ A new References section for the entire FOM is added∙ A new Cancellations section for the entire FOM is added.∙Adds a Maritime Industry Sector to Section III of Chapter 10, Industry Sectors.∙Revises sections referring to the Enhanced Enforcement Program (EEP) replacing the information with the Severe Violator Enforcement Program (SVEP).∙Adds Chapter 13, Federal Agency Field Activities.∙Cancels OSHA Instruction FAP 01-00-003, Federal Agency Safety and Health Programs, May 17, 1996.DisclaimerThis manual is intended to provide instruction regarding some of the internal operations of the Occupational Safety and Health Administration (OSHA), and is solely for the benefit of the Government. No duties, rights, or benefits, substantive or procedural, are created or implied by this manual. The contents of this manual are not enforceable by any person or entity against the Department of Labor or the United States. Statements which reflect current Occupational Safety and Health Review Commission or court precedents do not necessarily indicate acquiescence with those precedents.Table of ContentsCHAPTER 1INTRODUCTIONI.PURPOSE. ........................................................................................................... 1-1 II.SCOPE. ................................................................................................................ 1-1 III.REFERENCES .................................................................................................... 1-1 IV.CANCELLATIONS............................................................................................. 1-8 V. ACTION INFORMATION ................................................................................. 1-8A.R ESPONSIBLE O FFICE.......................................................................................................................................... 1-8B.A CTION O FFICES. .................................................................................................................... 1-8C. I NFORMATION O FFICES............................................................................................................ 1-8 VI. STATE IMPACT. ................................................................................................ 1-8 VII.SIGNIFICANT CHANGES. ............................................................................... 1-9 VIII.BACKGROUND. ................................................................................................. 1-9 IX. DEFINITIONS AND TERMINOLOGY. ........................................................ 1-10A.T HE A CT................................................................................................................................................................. 1-10B. C OMPLIANCE S AFETY AND H EALTH O FFICER (CSHO). ...........................................................1-10B.H E/S HE AND H IS/H ERS ..................................................................................................................................... 1-10C.P ROFESSIONAL J UDGMENT............................................................................................................................... 1-10E. W ORKPLACE AND W ORKSITE ......................................................................................................................... 1-10CHAPTER 2PROGRAM PLANNINGI.INTRODUCTION ............................................................................................... 2-1 II.AREA OFFICE RESPONSIBILITIES. .............................................................. 2-1A.P ROVIDING A SSISTANCE TO S MALL E MPLOYERS. ...................................................................................... 2-1B.A REA O FFICE O UTREACH P ROGRAM. ............................................................................................................. 2-1C. R ESPONDING TO R EQUESTS FOR A SSISTANCE. ............................................................................................ 2-2 III. OSHA COOPERATIVE PROGRAMS OVERVIEW. ...................................... 2-2A.V OLUNTARY P ROTECTION P ROGRAM (VPP). ........................................................................... 2-2B.O NSITE C ONSULTATION P ROGRAM. ................................................................................................................ 2-2C.S TRATEGIC P ARTNERSHIPS................................................................................................................................. 2-3D.A LLIANCE P ROGRAM ........................................................................................................................................... 2-3 IV. ENFORCEMENT PROGRAM SCHEDULING. ................................................ 2-4A.G ENERAL ................................................................................................................................................................. 2-4B.I NSPECTION P RIORITY C RITERIA. ..................................................................................................................... 2-4C.E FFECT OF C ONTEST ............................................................................................................................................ 2-5D.E NFORCEMENT E XEMPTIONS AND L IMITATIONS. ....................................................................................... 2-6E.P REEMPTION BY A NOTHER F EDERAL A GENCY ........................................................................................... 2-6F.U NITED S TATES P OSTAL S ERVICE. .................................................................................................................. 2-7G.H OME-B ASED W ORKSITES. ................................................................................................................................ 2-8H.I NSPECTION/I NVESTIGATION T YPES. ............................................................................................................... 2-8 V.UNPROGRAMMED ACTIVITY – HAZARD EVALUATION AND INSPECTION SCHEDULING ............................................................................ 2-9 VI.PROGRAMMED INSPECTIONS. ................................................................... 2-10A.S ITE-S PECIFIC T ARGETING (SST) P ROGRAM. ............................................................................................. 2-10B.S CHEDULING FOR C ONSTRUCTION I NSPECTIONS. ..................................................................................... 2-10C.S CHEDULING FOR M ARITIME I NSPECTIONS. ............................................................................. 2-11D.S PECIAL E MPHASIS P ROGRAMS (SEP S). ................................................................................... 2-12E.N ATIONAL E MPHASIS P ROGRAMS (NEP S) ............................................................................... 2-13F.L OCAL E MPHASIS P ROGRAMS (LEP S) AND R EGIONAL E MPHASIS P ROGRAMS (REP S) ............ 2-13G.O THER S PECIAL P ROGRAMS. ............................................................................................................................ 2-13H.I NSPECTION S CHEDULING AND I NTERFACE WITH C OOPERATIVE P ROGRAM P ARTICIPANTS ....... 2-13CHAPTER 3INSPECTION PROCEDURESI.INSPECTION PREPARATION. .......................................................................... 3-1 II.INSPECTION PLANNING. .................................................................................. 3-1A.R EVIEW OF I NSPECTION H ISTORY .................................................................................................................... 3-1B.R EVIEW OF C OOPERATIVE P ROGRAM P ARTICIPATION .............................................................................. 3-1C.OSHA D ATA I NITIATIVE (ODI) D ATA R EVIEW .......................................................................................... 3-2D.S AFETY AND H EALTH I SSUES R ELATING TO CSHO S.................................................................. 3-2E.A DVANCE N OTICE. ................................................................................................................................................ 3-3F.P RE-I NSPECTION C OMPULSORY P ROCESS ...................................................................................................... 3-5G.P ERSONAL S ECURITY C LEARANCE. ................................................................................................................. 3-5H.E XPERT A SSISTANCE. ........................................................................................................................................... 3-5 III. INSPECTION SCOPE. ......................................................................................... 3-6A.C OMPREHENSIVE ................................................................................................................................................... 3-6B.P ARTIAL. ................................................................................................................................................................... 3-6 IV. CONDUCT OF INSPECTION .............................................................................. 3-6A.T IME OF I NSPECTION............................................................................................................................................. 3-6B.P RESENTING C REDENTIALS. ............................................................................................................................... 3-6C.R EFUSAL TO P ERMIT I NSPECTION AND I NTERFERENCE ............................................................................. 3-7D.E MPLOYEE P ARTICIPATION. ............................................................................................................................... 3-9E.R ELEASE FOR E NTRY ............................................................................................................................................ 3-9F.B ANKRUPT OR O UT OF B USINESS. .................................................................................................................... 3-9G.E MPLOYEE R ESPONSIBILITIES. ................................................................................................. 3-10H.S TRIKE OR L ABOR D ISPUTE ............................................................................................................................. 3-10I. V ARIANCES. .......................................................................................................................................................... 3-11 V. OPENING CONFERENCE. ................................................................................ 3-11A.G ENERAL ................................................................................................................................................................ 3-11B.R EVIEW OF A PPROPRIATION A CT E XEMPTIONS AND L IMITATION. ..................................................... 3-13C.R EVIEW S CREENING FOR P ROCESS S AFETY M ANAGEMENT (PSM) C OVERAGE............................. 3-13D.R EVIEW OF V OLUNTARY C OMPLIANCE P ROGRAMS. ................................................................................ 3-14E.D ISRUPTIVE C ONDUCT. ...................................................................................................................................... 3-15F.C LASSIFIED A REAS ............................................................................................................................................. 3-16VI. REVIEW OF RECORDS. ................................................................................... 3-16A.I NJURY AND I LLNESS R ECORDS...................................................................................................................... 3-16B.R ECORDING C RITERIA. ...................................................................................................................................... 3-18C. R ECORDKEEPING D EFICIENCIES. .................................................................................................................. 3-18 VII. WALKAROUND INSPECTION. ....................................................................... 3-19A.W ALKAROUND R EPRESENTATIVES ............................................................................................................... 3-19B.E VALUATION OF S AFETY AND H EALTH M ANAGEMENT S YSTEM. ....................................................... 3-20C.R ECORD A LL F ACTS P ERTINENT TO A V IOLATION. ................................................................................. 3-20D.T ESTIFYING IN H EARINGS ................................................................................................................................ 3-21E.T RADE S ECRETS. ................................................................................................................................................. 3-21F.C OLLECTING S AMPLES. ..................................................................................................................................... 3-22G.P HOTOGRAPHS AND V IDEOTAPES.................................................................................................................. 3-22H.V IOLATIONS OF O THER L AWS. ....................................................................................................................... 3-23I.I NTERVIEWS OF N ON-M ANAGERIAL E MPLOYEES .................................................................................... 3-23J.M ULTI-E MPLOYER W ORKSITES ..................................................................................................................... 3-27 K.A DMINISTRATIVE S UBPOENA.......................................................................................................................... 3-27 L.E MPLOYER A BATEMENT A SSISTANCE. ........................................................................................................ 3-27 VIII. CLOSING CONFERENCE. .............................................................................. 3-28A.P ARTICIPANTS. ..................................................................................................................................................... 3-28B.D ISCUSSION I TEMS. ............................................................................................................................................ 3-28C.A DVICE TO A TTENDEES .................................................................................................................................... 3-29D.P ENALTIES............................................................................................................................................................. 3-30E.F EASIBLE A DMINISTRATIVE, W ORK P RACTICE AND E NGINEERING C ONTROLS. ............................ 3-30F.R EDUCING E MPLOYEE E XPOSURE. ................................................................................................................ 3-32G.A BATEMENT V ERIFICATION. ........................................................................................................................... 3-32H.E MPLOYEE D ISCRIMINATION .......................................................................................................................... 3-33 IX. SPECIAL INSPECTION PROCEDURES. ...................................................... 3-33A.F OLLOW-UP AND M ONITORING I NSPECTIONS............................................................................................ 3-33B.C ONSTRUCTION I NSPECTIONS ......................................................................................................................... 3-34C. F EDERAL A GENCY I NSPECTIONS. ................................................................................................................. 3-35CHAPTER 4VIOLATIONSI. BASIS OF VIOLATIONS ..................................................................................... 4-1A.S TANDARDS AND R EGULATIONS. .................................................................................................................... 4-1B.E MPLOYEE E XPOSURE. ........................................................................................................................................ 4-3C.R EGULATORY R EQUIREMENTS. ........................................................................................................................ 4-6D.H AZARD C OMMUNICATION. .............................................................................................................................. 4-6E. E MPLOYER/E MPLOYEE R ESPONSIBILITIES ................................................................................................... 4-6 II. SERIOUS VIOLATIONS. .................................................................................... 4-8A.S ECTION 17(K). ......................................................................................................................... 4-8B.E STABLISHING S ERIOUS V IOLATIONS ............................................................................................................ 4-8C. F OUR S TEPS TO BE D OCUMENTED. ................................................................................................................... 4-8 III. GENERAL DUTY REQUIREMENTS ............................................................. 4-14A.E VALUATION OF G ENERAL D UTY R EQUIREMENTS ................................................................................. 4-14B.E LEMENTS OF A G ENERAL D UTY R EQUIREMENT V IOLATION.............................................................. 4-14C. U SE OF THE G ENERAL D UTY C LAUSE ........................................................................................................ 4-23D.L IMITATIONS OF U SE OF THE G ENERAL D UTY C LAUSE. ..............................................................E.C LASSIFICATION OF V IOLATIONS C ITED U NDER THE G ENERAL D UTY C LAUSE. ..................F. P ROCEDURES FOR I MPLEMENTATION OF S ECTION 5(A)(1) E NFORCEMENT ............................ 4-25 4-27 4-27IV.OTHER-THAN-SERIOUS VIOLATIONS ............................................... 4-28 V.WILLFUL VIOLATIONS. ......................................................................... 4-28A.I NTENTIONAL D ISREGARD V IOLATIONS. ..........................................................................................4-28B.P LAIN I NDIFFERENCE V IOLATIONS. ...................................................................................................4-29 VI. CRIMINAL/WILLFUL VIOLATIONS. ................................................... 4-30A.A REA D IRECTOR C OORDINATION ....................................................................................................... 4-31B.C RITERIA FOR I NVESTIGATING P OSSIBLE C RIMINAL/W ILLFUL V IOLATIONS ........................ 4-31C. W ILLFUL V IOLATIONS R ELATED TO A F ATALITY .......................................................................... 4-32 VII. REPEATED VIOLATIONS. ...................................................................... 4-32A.F EDERAL AND S TATE P LAN V IOLATIONS. ........................................................................................4-32B.I DENTICAL S TANDARDS. .......................................................................................................................4-32C.D IFFERENT S TANDARDS. .......................................................................................................................4-33D.O BTAINING I NSPECTION H ISTORY. .....................................................................................................4-33E.T IME L IMITATIONS..................................................................................................................................4-34F.R EPEATED V. F AILURE TO A BATE....................................................................................................... 4-34G. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-35 VIII. DE MINIMIS CONDITIONS. ................................................................... 4-36A.C RITERIA ................................................................................................................................................... 4-36B.P ROFESSIONAL J UDGMENT. ..................................................................................................................4-37C. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-37 IX. CITING IN THE ALTERNATIVE ............................................................ 4-37 X. COMBINING AND GROUPING VIOLATIONS. ................................... 4-37A.C OMBINING. ..............................................................................................................................................4-37B.G ROUPING. ................................................................................................................................................4-38C. W HEN N OT TO G ROUP OR C OMBINE. ................................................................................................4-38 XI. HEALTH STANDARD VIOLATIONS ....................................................... 4-39A.C ITATION OF V ENTILATION S TANDARDS ......................................................................................... 4-39B.V IOLATIONS OF THE N OISE S TANDARD. ...........................................................................................4-40 XII. VIOLATIONS OF THE RESPIRATORY PROTECTION STANDARD(§1910.134). ....................................................................................................... XIII. VIOLATIONS OF AIR CONTAMINANT STANDARDS (§1910.1000) ... 4-43 4-43A.R EQUIREMENTS UNDER THE STANDARD: .................................................................................................. 4-43B.C LASSIFICATION OF V IOLATIONS OF A IR C ONTAMINANT S TANDARDS. ......................................... 4-43 XIV. CITING IMPROPER PERSONAL HYGIENE PRACTICES. ................... 4-45A.I NGESTION H AZARDS. .................................................................................................................................... 4-45B.A BSORPTION H AZARDS. ................................................................................................................................ 4-46C.W IPE S AMPLING. ............................................................................................................................................. 4-46D.C ITATION P OLICY ............................................................................................................................................ 4-46 XV. BIOLOGICAL MONITORING. ...................................................................... 4-47CHAPTER 5CASE FILE PREPARATION AND DOCUMENTATIONI.INTRODUCTION ............................................................................................... 5-1 II.INSPECTION CONDUCTED, CITATIONS BEING ISSUED. .................... 5-1A.OSHA-1 ................................................................................................................................... 5-1B.OSHA-1A. ............................................................................................................................... 5-1C. OSHA-1B. ................................................................................................................................ 5-2 III.INSPECTION CONDUCTED BUT NO CITATIONS ISSUED .................... 5-5 IV.NO INSPECTION ............................................................................................... 5-5 V. HEALTH INSPECTIONS. ................................................................................. 5-6A.D OCUMENT P OTENTIAL E XPOSURE. ............................................................................................................... 5-6B.E MPLOYER’S O CCUPATIONAL S AFETY AND H EALTH S YSTEM. ............................................................. 5-6 VI. AFFIRMATIVE DEFENSES............................................................................. 5-8A.B URDEN OF P ROOF. .............................................................................................................................................. 5-8B.E XPLANATIONS. ..................................................................................................................................................... 5-8 VII. INTERVIEW STATEMENTS. ........................................................................ 5-10A.G ENERALLY. ......................................................................................................................................................... 5-10B.CSHO S SHALL OBTAIN WRITTEN STATEMENTS WHEN: .......................................................................... 5-10C.L ANGUAGE AND W ORDING OF S TATEMENT. ............................................................................................. 5-11D.R EFUSAL TO S IGN S TATEMENT ...................................................................................................................... 5-11E.V IDEO AND A UDIOTAPED S TATEMENTS. ..................................................................................................... 5-11F.A DMINISTRATIVE D EPOSITIONS. .............................................................................................5-11 VIII. PAPERWORK AND WRITTEN PROGRAM REQUIREMENTS. .......... 5-12 IX.GUIDELINES FOR CASE FILE DOCUMENTATION FOR USE WITH VIDEOTAPES AND AUDIOTAPES .............................................................. 5-12 X.CASE FILE ACTIVITY DIARY SHEET. ..................................................... 5-12 XI. CITATIONS. ..................................................................................................... 5-12A.S TATUTE OF L IMITATIONS. .............................................................................................................................. 5-13B.I SSUING C ITATIONS. ........................................................................................................................................... 5-13C.A MENDING/W ITHDRAWING C ITATIONS AND N OTIFICATION OF P ENALTIES. .................................. 5-13D.P ROCEDURES FOR A MENDING OR W ITHDRAWING C ITATIONS ............................................................ 5-14 XII. INSPECTION RECORDS. ............................................................................... 5-15A.G ENERALLY. ......................................................................................................................................................... 5-15B.R ELEASE OF I NSPECTION I NFORMATION ..................................................................................................... 5-15C. C LASSIFIED AND T RADE S ECRET I NFORMATION ...................................................................................... 5-16。

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Wi-HART 7.1 Approach
Improvement from 7.0 to 7.1
Remaining Gap
Difference Assessment
Distributed Vs. Centralized
Distributed system management (versus Centralized) to balance load and support scalability
Yes. Optional
No
No System Command Management Accesibility of as a certain distributable management role without commands fixed addresses.
Major
Command Accessability (control plane) to Security/System Manager
Tied to HART
Universal device addressing/ tunnelling
Intermediate
Intermediate
Yes
No
No
Major
Field Routers and Field Devices
Technology
ISA100.11a Approach
Wi-HART 7.0 Approach
Not necessary. Battery powered non-routing field devices are allowed
All devices are required to posses capability to route. Network manager decides to use routing or not
Most network configuration Can be restricted commands are restricted to network manager
Most network configuration commands are restricted to network manager
MAJOR
Tied to HART
Technology
ISA100.11a Approach
Wi-HART 7.0 Approach
Wi-HART 7.1 Approach
Improvement from 7.0 to 7.1
Remaining Gap
Difference Assessment
All devices need HART Unique Address Join Key, Network Nickname and Network ID must be written using standard wired HART All adapters must translate between Wireless and legacy protocols Universal Application Layer - Multi-protocol
Alignment to TAI (International Atomic Time)
All nodes align to ASN to UTC International No such stipulations conversion Atomic Time (TAI) and every Future versions of ISA are Time slots of differing and All slots need to be of All slots need to be of expected to unequal duration equal duration equal duration Flexible and can support slots of
Time Slot Duration and ASN related
Time measured in time slots
Time is Time measured in Time measured in measured in slots (not suitable for slots (not suitable for International flexible time slots). flexible time slots). Atomic Time (TAI Time measured in Time measured in - French slots (not suitable for slots (not suitable for derivative) not flexible time slots); flexible time slots); time slots - not TTL is a misnomer - it TTL is a misnomer - it tied to time slot is just a hop count is just a hop count duration Flexible to be defined to any duration
Yes
No
No
Major Sepcificaiton of NWK Intermediate layers for backbone communicait ons Major
CSMA/TDMA
Technology ISA100.11a Approach Wi-HART 7.0 Approach Wi-HART 7.1 Approach Improvement Remaining from 7.0 to 7.1 Gap Difference Assessment
Intermediate
Field device advertisement.
All devices advertise
Minor
Distributed Vs Centralized Management
Technology
ISA100.11a Approach
Wi-HART 7.0 Approach
Wi-HART 7.1 Approach
Improvement from 7.0 to 7.1
Remaining Gap
Difference Assessment
Field Routers and Devices
All devices must possess the capability to route
Major areas of difference
• • • • • • • • • • Backbone Routing CSMA/TDMA Time Measurement and Time Slot duration Tied to HART Field Routers and Field Devices Distributed Vs Centralized Management Peer to Peer Routing Dual Cast Fragmentation and Reassembly Security
ISA 100 Topology
ISA Peer to Peer Routing
WirelessHART Topology
Backbone Routing
Technology ISApproach Wi-HART 7.1 Approach Improvement from 7.0 to 7.1 Remaining Gap Difference Assessment
MINOR
Single Point Failure of Network Manager
No
Yes
Yes
Minor
Peer to Peer Routing & Gateway Capacity
Technology
ISA100.11a Approach
Wi-HART 7.0 Approach
Wi-HART 7.1 Approach
All devices are required to posses capability to route. Network manager decides to use routing or not All devices need this functionality None non-routing field devices
Improvement from 7.0 to 7.1
Remaining Gap
Difference Assessment
Peer to Peer Communications
Gateway/Backbone Router can use the No direct peer to peer No direct peer to peer backbone for peer to allowed for security allowed for security peer reasons reasons communications
Not tied to HART
Tied to HART
Tied to HART
Major
No
Yes
YES
Adapters can tunnel multiple protocols
Adapters need translation to HART
translation
Wireless Handhelds as Maintenance devices and provisioning devices
CSMA Related
CSMA / TDMA (Carrier Sense Multiple Access/Time Division Multiple Access)