QUASI-INVARIANCE OF THE GAMMA PROCESS AND MULTIPLICATIVE PROPERTIES OF THE POISSON--DIRICHL
黑洞四定律
黑洞四定律黑洞四定律是关于黑洞性质及行为的重要定律，对于理解黑洞的基本性质和其与物理学的关系具有重要意义。
黑洞四定律包括黑洞的质量、面积、角动量和电荷四个方面。
下面将逐一介绍这些定律，并提供一些相关参考内容。
1. 黑洞质量定律：黑洞质量定律，也被称为霍金面积定律，它指出黑洞的表面积和质量之间存在着一种关系，即黑洞的表面积正比于其质量的平方。
这个定律是由物理学家斯蒂芬·霍金于1971年提出的。
霍金面积定律是黑洞热力学理论的基础，它将黑洞与热力学的概念进行了联系，使人们能够通过研究黑洞的热力学性质来更好地理解黑洞。
参考内容：- 斯蒂芬·霍金, "Black Hole Explosions?" Nature, vol. 248, pp. 30-31, 1974.- Andrei Barvinsky, George Kunstatter, "Critical Phenomena in Black Hole Physics," Phys. Lett. B, vol. 389, no. 3-4, pp. 231-236, 1996.- 黄绪淇, "黑洞的热力学与量子论," 物理学报, vol. 52, no. 7, pp. 1359-1366, 2003.2. 黑洞面积定律：根据黑洞的面积定律，也称为麦克斯韦-比克尔定律，黑洞的面积与其事件视界的面积成正比。
黑洞的事件视界是黑洞的边界，当物质趋于接近黑洞时，一旦穿过该边界，就无法再逃脱黑洞的引力。
参考内容：- 麦克斯韦, "On the Dynamical Theory of Gases," Proceedings of the Royal Society of Edinburgh, vol. 2, pp. 1-21, 1867.- J. D. Bekenstein, "Black Holes and Entropy," Physical Review D, vol. 7, no. 8, pp. 2333-2346, 1973.- 斯蒂芬·霍金, "Particle Creation by Black Holes," Communications in Mathematical Physics, vol. 43, no. 3, pp. 199-220, 1975.3. 黑洞角动量定律：黑洞角动量定律是根据黑洞旋转的性质推导出来的定律。
Recently
Recently,topological insulator has attracted great interests due to its peculiar band structures and electronic properties.The two-dimensional quantum spin Hall systems and three-dimensional TIs including Bi2Se3,Bi2Te3,and Bi1-xSbx have theoretically proposed and experimentally observed.They have a bulk excitation gap and gapless edge states for 2D TIs and 2D surface at boundaries:1D edge states for 2D TIs and 2D surface states for 3DTIs.The surface states of 3D TIs with an odd number of Dirac cones are robust against(weak and nonmagnetic)disorder scattering and many-body interactions.The Bi2Se3 material has been predicted and verified to have a bulk gap of 0.3 eV and a single Dirac come of surface states.The 3D TIs are expected to show several unique properties when the time reversal symmetry is broken.The latter can be realizes directly by a ferromagnetic insulating(FI) layer attached to the 3D TI surface.The motion of the Dirac electrons is influenced mainly by the magnetization of the FI layer rather than its stray field.This is in contrast to the Schodinger electrons in conventional semiconductor heterostructures modulates by nanomagnets.Some features of Dirac fermions on the surface of a TI have been revealed in the presence of proximate FIfilms,which have no analog in either graphene or 2D Schrodinger electrons.However,the effect of a magnetic superlattice on such kind of 2D carriers has not been examined so far.In this work,we study the band structures and ballistic transport of Dirac electrons on the TI surface under the modulation of a periodic magnetic superiattice.For a finite superlattice,when half of the FI stripes switch their magnetization directions a tunneliing magnetoresistance (MR) witha tunable sign is obtained. The system under consideration is a 2D electron gas on a given surface of a 3D TI like Bi2Sw3,as sketched in Fig.1.The surface is taken to be the(x,y) plane.Two kinds of FI materials with different coercive fields are deposited alternatively on top of the surface to form a magnetic superlattice along the x axis.For simplicity,we assume that all FI stripes have the same width a/2 and magnetization strength mo.The smallest distance between them is a/2.The magnetization of a FI stripe induces an exchange field for the Dirac fermions due to the proximity of TI and ferromagnetism.The easy axis of a FI stripe is usually along its length direction and thus either in parallel(p)or antiparallel (AP) with the +y axis.The initial magnetic superlattice with such a magnetization configuration is shown in Fig.1(a),which has a lattice constant a.For the soft FI material,a small in-plane magnetic field can switch its magnetization orientation.Accordingly,the magnetizations of adjacent FI stripes are changes fron the P to the AP alignment while the lattice constant of the magnetic superlattice turns to be 2a.In the presence of the periodic exchange field generated by N FI stripes,the motion of eletrons on the TI surface can be described by the 2D Dirac Hamiltonianwhere vF is the Fermi velocity,P=(px,py) is the electron momentum,7x and *y are Pauli matrices in spin space,M is the effective exchange field,and my(x) takes a constant value mo in the stripe regions with magnetization aligned to the y axis and zero otherwise.For convenience we express all quantities in dimensionless units by means of the length of the basic unit a and the enegy &*.For a typical value of a=50 nm and the Bi2Se3 material,one has Eoowing to the translational invariance of the system along the y direction,the total wave function of Dirac electrons can be expressed as &&,where ky is the transverse wave vector.At each region with a constant exchange field my,the reduced one-dimensional wave function & for a givenincident energy E can be written aswhere & and & together with the wave amplitudes c(x) and d(x) are piecewise constant.From the requirement of wave function continuity and the scattering boundary conditions,the transmission amplitude t can be calculated by means of the scattering matrix method.Note that t depens strongly not only on the incident energy Eand the transverse wave vector k,but also on the magnetization configuration.The ballistic conductance at zero temperature can be expressed in terms of the transmission amplitudewhere & is the incident angle relative to the x direction.Ef is the Fermi energy ,& is taken as the conductance unit,and & is the length of the device in the y direction.In order to understand the effect of the periodic exchange field on the transport properties of Dirac electrons,it isinstructive to investigate the band structures of a perfect magnetic superiattice on the surface of a 3D TI.For a given Bloch wave vector k ,the band energy E(k) can be derived analytically from the continuity requirement of the wave function and the periodic boundary condition of the superlattice.For the P magnetization configuration shown in Fig.1(a),the transcendental equation is given byNote that the exchange field in this configuration is equivalent to a periodic array of fictitions & magnetic fields with the same height but alternative sign.The result is thus the same as that in Ref.18.It should be emphasized that the physical origin of the magnetic superlattice in Ref.18 is distinct from that considered here.For the AP magnetization configuration shown in Fig.1(b),the analytical expression of the dispersive relation reads Fig.2 (Color online) Dispersion relations of Dirac electrons modulated by the magnetic superlattic witha P and AP configuration.In&and * the band energy Eat two k,values,ky=0(solid line) and ky=-1(dashed line),is plotted as a function of the Bloch wave vector k under the magnetization strenths mo=2 and m0=3.In c and f the variation in E with k,is plotted under two magnetization strengths mo=2 (circle marks) and mo=3（triangular marks）It is clearly seen from Eqs.4and5 that for a given mo and ky the Bloch wave vector k is only relevant to E.Thus the energy spectrum is symmetric with respect to E=0.Hereafter we consider only the nonnegative energy regime.The condition for the analytical expressions.For the Pmagnetization alignment & and the zero-energy solution requires k=0 and & .As for the AP configuration,the system has a symmetry related with the operator T,where T is the time reversal and R is the reflection X (x is a central point of the superlattice).The energy spectrum is thus symmetric about ky =0.The zero-energy solution appears only when k=0 and ky=0.Note that for both cases the zero-energy solution is unique and the transverse velocity & should vanish at &.For a general ky and mo a band gap including the point E=0 will be opened by the periodic magnetic modulation.The size of the band gap depends on the values of ky and mo.The general band features discussed above are reflected in the numerical solutions of Eqs.4and5,which are shown in Fig.2.It canbe observes that around the zero-energy solutions the energy spectrum is linear.Thus the Diac point is shifted by the magnetic superlattice with the P configuration but is unchanged in the AP configuration.In both cases,the velocity of the linear spectrum depends on mo.For E>k,the ky-dependent term in Eq.1 can be viewed as a perturbation,resulting in a slow variation in E with ky.For the same ky and mo the band gap of the P configuration overlaps only partly with that of the AP alignment.This may lead to a tunneling MR with a tunable sign.Figure 3 presents the trandmission probability as a function of the Fermi energy and the incident angle & for mo=2.The number of FI stripes is chose to be N=50.The transmission spectrum demonstrate an obvious angular anisotropy for both the P and AP alignment.For the P alignment t is blocked for all incident angles when the incident energy E locates in the full transmission gap.This can be understood from two aspects.One is that in the superlattice region there exists a band gap including E=0 for a large .The transmission is usually rather small as the incident energy falls into a band gap.The other aspect is that for & although the band gap of the incident region requires &.Outside the full transmission gap a large transmission is usually allowable for a negative angle &.The reason is that in the superlattice region the Dirac point is shifted to the k-point.Resonant features under positive incident angles can be seen due to the presence of quasibound states.For the AP alignment the transmission shown in Fig.3b is symmetric with respect to the angle&,as a result of the symmetry mentioned above.The reflection is almost complete in the whole & region for E=&,which is a common part of the band gaps for all available ky.As demonstrated above,the transmission features for the P and AP confifurations are quite distinct.Such a difference is also exhibited in the measurable quantity, the conductance G and G.In Fig.4 the conductance is plotted as a function of the Fermi energy for several values of the exchange field.For a amall mo,there exist several conductance valleys for both the P and AP alignment.With the increasing of mo the valleys move toward the high-energy region and become wider and lower.Finally,the valleys will turn to a conductance-forbidden region.When E lies in the full transmission gap of the P(AP) alianment,the conductance & is rather small while the conductance & can be large.The MR ratio is defined as 7 .The conductance spectrum in Fig.4 indicate a large ME amplitude in the full transmission gaps of both the P and AP alignmeng\t.Since the two kinds of full transmission gaps may have no overlap,the sign of the MR is alternated as the Fermi energy increases.In summary, we have studied the band structures and transport features of Dirac electrons on the surface of a 3D TI subject to a periodic exchange field.The superlattice modulation is provided by a series of equally spaced FI stripes which sre attached to the TI surface.The magnetizations of adjacent FI stripes can be switched between the parallel and antiparallel configurations.The Dirac point is shifted by the magnetic superlattice,we have shown a full transmission gap for both the parallel and antiparallel configurations.For a suitable range of the magnetization strength,the two kinds of trnsmission gaps are nonoverlapped and thus a large MR with a tunable sign can be achieved.。
高中英语世界著名科学家单选题50题
高中英语世界著名科学家单选题50题1. Albert Einstein was born in ____.A. the United StatesB. GermanyC. FranceD. England答案：B。
解析：Albert Einstein（阿尔伯特·爱因斯坦）出生于德国。
本题主要考查对著名科学家爱因斯坦国籍相关的词汇知识。
在这几个选项中，the United States是美国，France是法国，England是英国，而爱因斯坦出生于德国，所以选B。
2. Isaac Newton is famous for his discovery of ____.A. electricityB. gravityC. radioactivityD. relativity答案：B。
解析：Isaac Newton 艾萨克·牛顿）以发现万有引力gravity）而闻名。
electricity是电，radioactivity是放射性，relativity 是相对论，这些都不是牛顿的主要发现，所以根据对牛顿主要成就的了解，选择B。
3. Marie Curie was the first woman to win ____ Nobel Prizes.A. oneB. twoC. threeD. four答案：B。
解析：Marie Curie 居里夫人）是第一位获得两项诺贝尔奖的女性。
这题主要考查数字相关的词汇以及对居里夫人成就的了解，她在放射性研究等方面的贡献使她两次获得诺贝尔奖，所以选B。
4. Thomas Edison is well - known for his invention of ____.A. the telephoneB. the light bulbC. the steam engineD. the computer答案：B。
解析：Thomas Edison（ 托马斯·爱迪生）以发明电灯（the light bulb）而闻名。
The decay $rho^{0}to pi^{+}+pi^{-}+gamma$ and the coupling constant g$_{rhosigmagamma}$
a rXiv:n ucl-t h /441v28Ma y2The decay ρ0→π++π−+γand the coupling constant g ρσγA.Gokalp ∗and O.Yilmaz †Physics Department,Middle East Technical University,06531Ankara,Turkey(February 8,2008)Abstract The experimental branching ratio for the radiative decay ρ0→π++π−+γis used to estimate the coupling constant g ρσγfor a set of values of σ-meson parameters M σand Γσ.Our results are quite different than the values of this constant used in the literature.PACS numbers:12.20.Ds,13.40.HqTypeset using REVT E XThe radiative decay processρ0→π++π−+γhas been studied employing different approaches[1,5].There are two mechanisms that can contribute to this radiative decay: thefirst one is the internal bremsstrahlung where one of the charged pions from the decay ρ0→π++π−emits a photon,and the second one is the structural radiation which is caused by the internal transformation of theρ-meson quark structure.Since the bremsstrahlung is well described by quantum electrodynamics,different methods have been used to estimate the contribution of the structural radiation.Singer[1]calculated the amplitude for this decay by considering only the bremsstrahlung mechanism since the decayρ0→π++π−is the main decay mode ofρ0-meson.He also used the universality of the coupling of theρ-meson to pions and nucleons to determine the coupling constant gρππfrom the knowledge of the coupling constant gρter,Renard [3]studied this decay among other vector meson decays into2π+γfinal states in a gauge invariant way with current algebra,hard-pion and Ward-identities techniques.He,moreover, established the correspondence between these current algebra results and the structure of the amplitude calculated in the single particle approximation for the intermediate states.In corresponding Feynman diagrams the structural radiation proceeds through the intermediate states asρ0→S+γwhere the meson S subsequently decays into aπ+π−pair.He concluded that the leading term is the pion bremsstrahlung and that the largest contribution to the structural radiation amplitude results from the scalarσ-meson intermediate state.He used the rough estimate gρσγ≃1for the coupling constant gρσγwhich was obtained with the spin independence assumption in the quark model.The coupling constant gρππwas determined using the then available experimental decay rate ofρ-meson and also current algebra results as3.2≤gρππ≤4.9.On the other hand,the coupling constant gσππwas deduced from the assumed decay rateΓ≃100MeV for theσ-meson as gσππ=3.4with Mσ=400MeV. Furthermore,he observed that theσ-contribution modifies the shape of the photon spectrum for high momenta differently depending on the mass of theσ-meson.We like to note, however,that the nature of theσ-meson as a¯q q state in the naive quark model and therefore the estimation of the coupling constant gρσγin the quark model have been a subject ofcontroversy.Indeed,Jaffe[6,7]lately argued within the framework of lattice QCD calculation of pseudoscalar meson scattering amplitudes that the light scalar mesons are¯q2q2states rather than¯q q states.Recently,on the other hand,the coupling constant gρσγhas become an important input for the studies ofρ0-meson photoproduction on nucleons.The presently available data[8] on the photoproduction ofρ0-meson on proton targets near threshold can be described at low momentum transfers by a simple one-meson exchange model[9].Friman and Soyeur [9]showed that in this picture theρ0-meson photoproduction cross section on protons is given mainly byσ-exchange.They calculated theγσρ-vertex assuming Vector Dominance of the electromagnetic current,and their result when derived using an effective Lagrangian for theγσρ-vertex gives the value gρσγ≃2.71for this coupling ter,Titov et al.[10]in their study of the structure of theφ-meson photoproduction amplitude based on one-meson exchange and Pomeron-exchange mechanisms used the coupling constant gφσγwhich they calculated from the above value of gρσγinvoking unitary symmetry arguments as gφσγ≃0.047.They concluded that the data at low energies near threshold can accommodate either the second Pomeron or the scalar mesons exchange,and the differences between these competing mechanisms have profound effects on the cross sections and the polarization observables.It,therefore,appears of much interest to study the coupling constant gρσγthat plays an important role in scalar meson exchange mechanism from a different perspective other than Vector Meson Dominance as well.For this purpose we calculate the branching ratio for the radiative decayρ0→π++π−+γ,and using the experimental value0.0099±0.0016for this branching ratio[11],we estimate the coupling constant gρσγ.Our calculation is based on the Feynman diagrams shown in Fig.1.Thefirst two terms in thisfigure are not gauge invariant and they are supplemented by the direct term shown in Fig.1(c)to establish gauge invariance.Guided by Renard’s[3]current algebra results,we assume that the structural radiation amplitude is dominated byσ-meson intermediate state which is depicted in Fig. 1(d).We describe theρσγ-vertex by the effective LagrangianL int.ρσγ=e4πMρMρ)2 3/2.(3)The experimental value of the widthΓ=151MeV[11]then yields the value g2ρππ2gσππMσ π· πσ.(4) The decay width of theσ-meson that follows from this effective Lagrangian is given asΓσ≡Γ(σ→ππ)=g2σππ8 1−(2Mπ2iΓσ,whereΓσisgiven by Eq.(5).Since the experimental candidate forσ-meson f0(400-1200)has a width (600-1000)MeV[11],we obtain a set of values for the coupling constant gρσγby considering the ranges Mσ=400-1200MeV,Γσ=600-1000MeV for the parameters of theσ-meson.In terms of the invariant amplitude M(Eγ,E1),the differential decay probability for an unpolarizedρ0-meson at rest is given bydΓ(2π)31Γ= Eγ,max.Eγ,min.dEγ E1,max.E1,min.dE1dΓ[−2E2γMρ+3EγM2ρ−M3ρ2(2EγMρ−M2ρ)±Eγfunction ofβin Fig.5.This ratio is defined byΓβRβ=,Γtot.= Eγ,max.50dEγdΓdEγ≃constant.(10)ΓσM3σFurthermore,the values of the coupling constant gρσγresulting from our estimation are in general quite different than the values of this constant usually adopted for the one-meson exchange mechanism calculations existing in the literature.For example,Titov et al.[10] uses the value gρσγ=2.71which they obtain from Friman and Soyeur’s[9]analysis ofρ-meson photoproduction using Vector Meson Dominance.It is interesting to note that in their study of pion dynamics in Quantum Hadrodynamics II,which is a renormalizable model constructed using local gauge invariance based on SU(2)group,that has the sameLagrangian densities for the vertices we use,Serot and Walecka[14]come to the conclusion that in order to be consistent with the experimental result that s-waveπN-scattering length is anomalously small,in their tree-level calculation they have to choose gσππ=12.Since they use Mσ=520MeV this impliesΓσ≃1700MeV.If we use these values in our analysis,we then obtain gρσγ=11.91.Soyeur[12],on the other hand,uses quite arbitrarly the values Mσ=500 MeV,Γσ=250MeV,which in our calculation results in the coupling constant gρσγ=6.08.We like to note,however,that these values forσ-meson parameters are not consistent with the experimental data onσ-meson[11].Our analysis and estimation of the coupling constant gρσγusing the experimental value of the branching ratio of the radiative decayρ0→π++π−+γgive quite different values for this coupling constant than used in the literature.Furthermore,since we obtain this coupling constant as a function ofσ-meson parameters,it will be of interest to study the dependence of the observables of the reactions,such as for example the photoproduction of vector mesons on nucleonsγ+N→N+V where V is the neutral vector meson, analyzed using one-meson exchange mechanism on these parameters.AcknowledgmentsWe thank Prof.Dr.M.P.Rekalo for suggesting this problem to us and for his guidance during the course of our work.We also wish to thank Prof.Dr.T.M.Aliev for helpful discussions.REFERENCES[1]P.Singer,Phys.Rev.130(1963)2441;161(1967)1694.[2]V.N.Baier and V.A.Khoze,Sov.Phys.JETP21(1965)1145.[3]S.M.Renard,Nuovo Cim.62A(1969)475.[4]K.Huber and H.Neufeld,Phys.Lett.B357(1995)221.[5]E.Marko,S.Hirenzaki,E.Oset and H.Toki,Phys.Lett.B470(1999)20.[6]R.L.Jaffe,hep-ph/0001123.[7]M.Alford and R.L.Jaffe,hep-lat/0001023.[8]Aachen-Berlin-Bonn-Hamburg-Heidelberg-Munchen Collaboration,Phys.Rev.175(1968)1669.[9]B.Friman and M.Soyeur,Nucl.Phys.A600(1996)477.[10]A.I.Titov,T.-S.H.Lee,H.Toki and O.Streltrova,Phys.Rev.C60(1999)035205.[11]Review of Particle Physics,Eur.Phys.J.C3(1998)1.[12]M.Soyeur,nucl-th/0003047.[13]S.I.Dolinsky,et al,Phys.Rep.202(1991)99.[14]B.D.Serot and J.D.Walecka,in Advances in Nuclear Physics,edited by J.W.Negeleand E.Vogt,Vol.16(1986).TABLESTABLE I.The calculated coupling constant gρσγfor differentσ-meson parametersΓσ(MeV)gρσγ500 6.97-6.00±1.58 8008.45±1.77600 6.16-6.68±1.85 80010.49±2.07800 5.18-9.11±2.64 90015.29±2.84900 4.85-10.65±3.14 90017.78±3.23Figure Captions:Figure1:Diagrams for the decayρ0→π++π−+γFigure2:The photon spectra for the decay width ofρ0→π++π−+γ.The contributions of different terms are indicated.Figure3:The pion energy spectra for the decay width ofρ0→π++π−+γ.The contri-butions of different terms are indicated.Figure4:The decay width ofρ0→π++π−+γas a function of minimum detected photon energy.Figure5:The ratio Rβ=Γβ。
固体物理专业术语
费密能级 Fermi level 费密球 Fermi sphere 费密面 Fermi surface 费密温度 Fermi temperature 费密速度 Fermi velocity 费密半径 Fermi radius 恢复力常数 Constant of restorable force 绝热近似 Adiabatic approximation
反演 Inversion 分子晶体 Molecular Crystal 切变模量 Shear module 双原子链 Diatomic linear chain 介电常数 Dielectric constant 化学势 Chemical potential 内能 Internal energy
分布函数 Distribution function 夫伦克耳缺陷 Frenkel defect 比热 Specific heat 中子散射 Neutron scattering
纯金属 Ideal metal 体心立方 Body-centered cubic 体心四方布喇菲格子 Body-centered tetragonal Bravais lattices 卤化碱晶体 Alkali-halide crystal 劳厄衍射 Laue diffraction 间隙原子 Interstitial atom 间隙式扩散 Interstitial diffusion 肖特基缺陷 Schottky defect
有效电荷 Effective chaБайду номын сангаасges 弛豫时间 Relaxation time 弛豫时间近似 Relaxation-time approximation 扩展能区图式 Extended zone scheme 自由电子模型 Free electron model 自由能 Free energy 杂化轨道 Hybrid orbit
飞行器制导与控制系统优化设计及弹道仿真
分类号：密级：ＵＤＣ：编号：工学硕士学位论文飞行器制导与控制系统优化设计及弹道仿真硕士研究生：马娜娜指导教师：于秀萍教授学位级别：工学硕士学科、专业：控制理论与控制工程所在单位：自动化学院论文提交日期：2014年12月26日论文答辩日期：2015年03月10日学位授予单位：哈尔滨工程大学Classified Index:U.D.C:A Dissertation for the Degree of M. EngAircraft Guidance and Control System Optimization Designand Trajectory SimulationCandidate: Ma NanaSupervisor: Prof. Yu XiupingAcademic Degree Applied for: Master of EngineeringSpeciality: Control Theory and Control Engineering Date of Submission: December，2014Date of Oral Examination: March，2015University: Harbin Engineering University哈尔滨工程大学学位论文原创性声明本人郑重声明：本论文的所有工作，是在导师的指导下，由作者本人独立完成的。
有关观点、方法、数据和文献的引用已在文中指出，并与参考文献相对应。
除文中已注明引用的内容外，本论文不包含任何其他个人或集体已经公开发表的作品成果。
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正态-逆Gamma先验下线性模型中回归系数和误差方差Bayes估计的改进
正态-逆Gamma先验下线性模型中回归系数和误差方差Bayes估计的改进许凯;何道江【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2014(000)002【摘要】在正态-逆Gamma先验下，研究线性模型中回归系数和误差方差 Bayes 估计的优良性，改进了已有的结果，去掉了附加条件。
在Pitman准则下，证明回归系数的Bayes 估计优于最小二乘估计(LSE)，并讨论误差方差的Bayes估计在均方误差准则下相对于LSE的优良性。
最后进行Monte Carlo模拟研究，进一步验证了理论结果。
%The superiority of Bayes estimation of regression coeffcients and error variance in linear model was studied based on normal-inverse Gamma priors.The existed results were complemented without the additive conditions.It was shown that the Bayes estimation of regression coefficients is superior to the least squares estimator (LSE ) under the Pitman closeness criterion. And the superiority of the Bayes estimation of error variance over LSE was also investigated in terms of the mean square error criterion. Finally, a Monte Carlo simulation was carried out to verify the theoretical results.【总页数】5页(P251-255)【作者】许凯;何道江【作者单位】安徽师范大学数学计算机科学学院，安徽芜湖 241003;安徽师范大学数学计算机科学学院，安徽芜湖 241003【正文语种】中文【中图分类】O212.2【相关文献】1.在受约束线性模型中误差方差及回归系数和误差方差同时估计的可容... [J], 张双林2.线性模型中回归系数和误差方差同时的经验Bayes估计及其优良性? [J], 陈玲;韦来生3.具有正态逆伽玛先验的正态分布中的方差参数在Stein损失下的贝叶斯后验估计量 [J], 解宇涵;宋文和;周明琴;张应应4.正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性 [J], 许凯; 何道江; 徐兴忠5.线性模型中回归系数和误差方差的同时Bayes估计的优良性 [J], 陈玲; 韦来生因版权原因，仅展示原文概要，查看原文内容请购买。
q-对称熵损失函数下Gamma分布的尺度参数的估计
分类号： ＡＭ Ｓ２０ １ ２ １ （００ ６Ｆ ０
中图分类号： ２２ Ｏ １． ５
文献标识码： Ａ
１ 引言
在参数估计 问题上 ，我们 常见的损 失函数有平方损 失，绝对值 损失 ，近年来 ，熵 损失 函数 也引起 人们的注意，对称熵 损失函数（是在熵 损失函数的基础上提 出来的 ，不难推 出，在指数 】
［ Ａ－ＡＴ］ ＋ｑ ＋ ｏ ｑ－ｑｑ＝ｒ ＇ ￣ ｑ （ ） ３ ／
（
嵩 ｔｌｔＡ ｎｅｄ － ａ－ｔ －＇ｄ Ｘ
＜慨
＜， 。 。
３ 估计量［ ｃ ｒ＋翻 的容许性
在 ｒ 一 先验 分布 下 ，Ｂ ｙｓ ａｅ估计 都有形式 ［ ｃ Ｔ＋ｄ＿ 。下面对ｃＷ的不 同取值情 况分别讨 １。 Ｓｄ 论［ ｃ ＋ｄ 的可容许性和不可容许性 。以下令 ｃ ｌ ＝ ＝ （ａ ｑ，同时设ｎ 、 Ｐｎ－） ｑ ／ ＞ ｑ 。 定理３１ Ｊ 当 ０ ｃ ｃ， ．【 ＜ ｄ＞０时，估计量 ｌ ｅ Ｔ＋ｄ一是可容许 的。 １ 引理３１ 】 在（对称熵损失函数下，假 定Ｅｌｑ ．［ １ － ａ ＜＋。 ， ｌ 。 ＜＋ 。 。 ，则风 险函数Ｒ（， 关 ａ ）
熵 损失 函数 下Ｇ ｍｍ 分布 的尺度 参数的最 小风险 同变 估计（ Ｅ 、贝叶斯（ ａｅ） 、最小 ａ ａ ＭＲ ） Ｂ ｙｓ估计 最大（ ｎ ａ） Ｍｉｉ ｘ估计等 。我们还对这 些估计量 的可容许性和不可 容许性进 行 了讨论，最后分别对 ｎ
指 数 分布 和 Ｇａ ｍｍａ 布 在 两种 损 失 函数 下 的估 计 结 果 进 行 了数 值 比较 。 分 关 键 词 ：贝 叶斯 估 计 ； 同 变估 计 ；最 小 最 大 估 计 ；尺 度 参 数 ；可 容 许 性 ；ｑ对 称 熵 损 失 函数 －
固体物理词汇汉英对照
元素的电负性 Electronegativities of elements
元素的电离能 Ionization energies of the elements
元素的结合能 Cohesive energies of the elements
六方密堆积 Hexagonal close-packed
费密-狄喇克分布函数 Fermi-Dirac distribution function
费密电子气的简并性 Degeneracy of free electron Fermi gas
费密 Fermi
费密能 Fermi energy
费密能级 Fermi level
费密球 Fermi sphere
正交晶系 Orthorhombic crystal system
正则振动 Normal vibration
正则坐标 Normal coordinates
立方晶系 Cubic crystal system
立方密堆积 Cubic close-packed
四方晶系 Tetragonal crystal system
金刚石结构 Diamond structure
金属的结合能 Cohesive energy of metals
金属晶体 Metallic Crystal
转动轴 Rotation axes
转动-反演轴 Rotation-inversion axes
转动晶体法 Rotating crystal method
切应变 Shear strain
八画
周期性重复单元 Periodic repeated unit
底心正交格子 Base-centered orthorhombic lattice
2022考研英语阅读捕获希格斯粒子
2022考研英语阅读捕获希格斯粒子Looking for the Higgs捕获希格斯粒子Enemy in sight?敌军现身?The search for the Higgs boson is closing in on its quarry希格斯玻色子的讨论接近其目标ON JULY 22nd two teams of researchers based at CERN, Europe s main particle-physicslaboratory, near Geneva, told a meeting of the European Physical Society in Grenoble thatthey had found the strongest hints yet that the Higgs boson does, in fact, exist.7月22日，驻欧洲粒子物理讨论所的两组讨论人员在格勒诺布尔欧洲物理协会的一次会议上声称，他们已经得到迄今为止最有力的线索，将力证希格斯玻色子的确真实存在。
The Higgs is thelast unobserved part of the Standard Model, a 40-year-old theory which successfullydescribes the behaviour of all the fundamental particles and forces of nature bar gravity.希格斯粒子是基础模型中最终一个尚未观测到的组件，基础模型已有40年的历史，它胜利地描述了全部基础粒子的行为及除重力以外的全部自然力。
Mathematically, the Higgs is needed to complete the modelbecause, otherwise, none of theother particles would have any mass.在数学层面上，希格斯粒子对于完成模型是必不行少的，这是由于，一旦缺少它，全部的其它粒子都将会失去质量。
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De nition. The gamma process on the space X with parameter measure is
Z Z
a generalized process on the space D with the law P? = P? ( ) (called the gamma measure on the space (X; )) given by the characteristic functional (Laplace transform) (1.1)
loi P? du processus gamma classique et des proprietes correspondantes des mesures de Poisson{Dirichlet PD( ). Nous deduisons la propriete de quasi-invariance de la loi P? par rapport a un \gros" groupe multiplicatif et l'identite de Markov{Krein directement de la transformation de Laplace de P?. La quasi-invariance de la loi P? permet d'obtenir des proprietes de quasi-invariance des lois de Poisson{Dirichlet PD( ). On obtient les proprietes correspondantes d'invariance pour des analogues - nis de P? et PD( ). Nous montrons en n que la loi P? peut ^tre consideree comme une limite de lois de processus stables dont le e parametre tend vers 0. Notre approche se fonde sur la consideration simultanee du processus gamma (surtout sa transformation de Laplace) et sa partie simpliciale { des mesures de Poisson{Dirichlet.
Abstract. In this paper we describe new fundamental properties du processus gamma et proprietes multiplicatives des distributions de Poisson{Dirichlet
Resume. Dans cette Note, nous decrivons certaines proprietes fondamentales de la
1. Introduction: de nition of the gamma process.
In this section we present a de nition of the gamma process on an arbitrary space. This general de nition turns out to be more convenient for our purposes than the process on the interval. Let (X; ) be a standard Borel space with a non-atomic nite non-negative meaP sure , andP (X ) = be the total charge of . We denote by D = f zi xi ; xi 2 let X; zi 2 R; jzij < 1g a real linear space of all nite real atomic measures on X .
X
a(x)d (x)
= exp ?
X
log(1 + a(x))d (x) ;
M = a : X ! R+ :
Z
X
j log a(x)jd (x) < 1 :
It follows from the above Poisson construction and formula (1.1) that each function R a 2 M correctly de nes a measurable linear functional 7! fa ( ) = X a(x)d (x) on D, and formula (1.1) holds for all a 2 M. + Denote by D1 D+ the simplex of all normalized atomic measures. Then + = D+ 0; 1), that is each 2 D+ can be represented as D 1 (1.2) = ( = (X ); (X )): The second coordinate in this decomposition is the total charge of the measure , and the rst one is called the normalization of the measure . The following lemma presents a well-known independence property of the gamma process. Lemma 1. In representation (1.2) the gamma measure is a product measure P? = G P? , that is the total charge (X ) of the gamma process and the normalized gamma process = = (X ) are independent. The distribution G of the total charge is the gamma distribution on R+ with shape parameter and scale parameter 1, i.e. dG = ?(1 ) t ?1 e?t dt, t > 0.
Remarks. 1. This independence property characterizes the gamma process in the
class of Levy processes (see Lu??]). 2. The random probability measure = = (X ) is known in the literature as the Dirichlet process on the space X with parameter measure (see Fe73]). 3. Our de nition of the gamma process on an arbitrary space is closely related to a particular case of the completely random measure considered in Ki93], chapter 8. 4. It is clear that the ordinary de nition of the gamma subordinator on R+ is obtained for X = R+ and equal to the Lebesgue measure.
SPb. Math. Society Preprint 1999-12 14 Apr 1999
QUASI-INVARIANCE OF THE GAMMA PROCESS AND MULTIPLICATIVE PROPERTIES OF THE POISSON{DIRICHLET MEASURES
N. Tsilevich, A. Vershik, M. Yor
E P?
exp ?
where a is an arbitrary non-negative bounded Borel function on the space X . The correctness of this de nition is guaranteed by the following explicit construction (see Ki93], chapter 8). Consider a Poisson point process on the space X R+ with mean measure , where is the Levy measure of the gamma process, ?1 e?z dz , z 2 R+. We associate with a realization = f(xi ; zi)g that is d (z ) = z P of this process an element = zi xi 2 D. Then is a random atomic measure obeying the law P? . So the gamma measure is concentrated on the cone D+ D consisting of all nite positive atomic measures on X. Let M = M(X; ) be the set of (classes mod 0 of) non-negative measurable functions on the space X with -summable logarithm,