preliminary_04-68393B Manual DCF Chapter S Fast Module
Preliminary version
How the environment determines the efficiency of banks: acomparison between French and Spanish banking industry*Michel DietschUniversité Robert Schuman de Strasbourg, FranceAna Lozano VivasUniversidad de Málaga, SpainPreliminary version(September, 1996)*The research was supported by CNRS and DGICYT into the research program with reference PFECS95-0005.1. IntroductionTo understand the process of financial integration and convergence in Europe, it is necessary to know more about the competitiveness and the efficiency of banks in different European countries. However, cross-countries comparisons have to take into account the potential differences coming from some country-specific aspects of the banking technology, on one hand, and from the environmental and regulatory conditions, on the other hand. In particular, the economic environment are likely to differ significantly across countries and these differences could induce important differences of bank efficiency through different channels. For instance, differences of the income per capita, or differences of the densitydifferences in the nature of the of population across countries could produce significanthousehold’s demand for banking products and services.In this paper, we focus on two countries, France and Spain, and we try to deepen the analysis of the influence of the environment conditions on the cost efficiency of the French and Spanish banking industries. As pointed out by Berger and Humphrey (1996), this issue is not addressed in the international banking efficiency literature. From our point of view, cross-country comparison of efficiency requires to define properly a common frontier which incorporates the country-specific environmental conditions. Moreover, the integration of environmental variables in the analysis would allow to verify the degree of similarity between banking technology.Three categories of environmental variables are taken into account: the main macroeconomic which determine the banking products demand characteristics conditions, the structure and regulation of the banking industry, and the accessibility of banking services.Our results suggest that, before the introduction of environmental variables, the cost efficiency scores of Spanish banks were quite low, compared to those of the French banks. However, when the environmental variables were included in the model, the differences between the two countries banking industries reduced significantly. So, our resultsdemonstrate that the environmental variables appear to play a significant role in the explanation of the different efficiency scores between the two countries. More precisely, our results show that the Spanish banks seem to suffer excess costs, or structural disadvantages, in order to adjust to some environmental compared to French banks, such as the lower density of population, the lower income level of their customers or the lower rate of financial intermediation.A brief survey of the previous literature about cross-country comparisons of efficiency is presented in Section 2. The methodology for evaluating the cross-country efficiency when the particular environmental conditions of each country are taken in account is presented in Section 3. The data and the specification of inputs, outputs and environmental variables are described in Section 4. Section 5 presents the empirical results, and, finally, we provide some concluding remarks in Section 6.2. Previous literature in international comparison of banking efficiencyIn anticipation of the expected lowering of barriers to competition among financial institutions within the European Monetary Union (EMU), many EMU countries have recently experienced consolidation of their domestic banking industry. One reason for this consolidation is the belief that larger banks will be better able to adjust to the needs of the customers when they will be allowed to set up branches in any other country, subject only to the regulations of their home country. As domestic markets become more competitive, current differences in costs and productive efficiency among the banking industries of EMU countries will largely determine each country banking structure and future competitive viability. Thus, it is important to know how different or similar are current banking costsand productive efficiency between countries in order to predict increase in cross-border competition.There appears to be only six studies in the efficiency the effects of the expected literature that attempts todetermine and compare banking performances differences across-countries. Four of them3used nonparametric approaches while two used parametric approaches. In Berg, Forsund, Hjalmarson, and Suominen (1993), DEA analysis were relied upon to capture the differences in efficiency between Norway, Sweden, and Finland, first by defining separate frontiers for each country and comparing the countries pairwise based on each country’s frontier; and then defining a “common” frontier for doing the comparison among countries. Berg, Bukh and Forsund (1995) follow up the study by adding Denmark to the countries sample. The same four countries were investigated in Bergendahl (1995), using mixed optimal strategy for defining the efficient frontier.Fecher and Pestieau (1993) and Pastor, Perez, and Quesada (1995) applied DFA and DEA analysis to 11 OECD countries and 8 developed countries, respectively. The two studies pooled the cross-country data in order to define a common frontier. The former study found reverse results to these obtained by the Berg and al., and Bukh and al. studies taking the same set of countries.1Allen and Rai (1996) by using DFA and SFA carry out a systematic comparison of X-inefficiency measures across 15 developed countries distinguished by different regulatory environments. To do so, the countries were classified, previously, into two groups --universal and separated banking countries, respectively--delineated by their regulatory environment. Universal banking countries permit the functional integration of commercial and investment banking while separated banking countries do not. Once the inefficiency levels of those groups of banks were measured, the regularities in the inefficiency measures were investigated by regressing the firm specific inefficiency measures against various bank and market characteristics.The main caveat of these cross-country studies is that the common frontier is built under the belief that the differences in efficiency across countries only come from1See Berger and Humphrey (1996) for giving the details of the methodologies and results obtained on those studies.bank managerial decisions.2 That is, they are assuming that the mean difference in efficiency is located in differences of technologies. However, it is possible that the underlying technologies of the banking services productions in Europe and other developed countries are quite similar. Thus, the differences in efficiency across countries have to take into account the way in which banking services are produced. This production process is determined by country-specific differences—that are almost always excluded from cost and efficiency analyses—and not only by technology differences. Just as different relative prices of capital and labor inputs will result in different intensity of the use of these inputs in the production process, if the bank minimize costs and if the technology is constant, different national environments will result in different observed inputs, liabilities, and assets mixes and number of branches, again if the technology for producing banking services is constant. If the country-specific variables are an important factor in the explanation of the efficiency differences, then the frontier we obtain if we neglect this factor will generate an overestimation of the inefficiency levels.3If the regulatory and economic environments faced by financial institutions are likely to differ importantly across countries, the cross-country comparisons of the preceding papers are difficult to interpret. It is because in these papers the specification of the common frontier is not correct due to the fact that they do not take into account the influence of the country-specific environmental variables that will justify the use of a common frontier in cross-country comparisons of efficiency.andHere, we propose to compare the cost efficiency of the banking industries in France Spain, introducing in the cost frontier estimations the appropriate environmental2Although Allen and Rai’s paper takes into account the regulatory environments in the distinctionbetween groups of countries in order to compare the inefficiency levels, they specified banks variables and not country variables in order to explain the differences in efficiency.3Pastor et al., 1995, did corrections on efficiency measures by introducing the services provided to customers by the branch network and the degree of solvency determined by the capital ratio. Although it is well known that adding a restriction when it is using DEA increases (or leaves unaltered) the efficiency of all and every bank in the sample, they found that the relative efficiency of the countries banks improved. So, the economic environment of each country is an important explanation of the inefficiencies differences across countries and their integration will permit to avoid that the choice of the technology base influences the results when a common technology base is used for comparisons between countries.variables, so that the cross countries comparisons of efficiency would not be determined by the technology of one of the countries. That is, our goal is to permit the proper comparison of banking efficiency across countries by using a global best-practice econometric frontier, from which the banks in each country would be compared against the same standard.3. MethodologyThe technology of the banks can be defined as the set of the specific methods that the banks use to combine financial and physical inputs in order to produce a certain amount of banking services, such as liquidity and payment services, portfolio services, loans services. Those methods are diversification, pooling of risk, financial information collection and evaluation, risk management, and so on.More or less, the methods used by banks are the same in large industrial countries. So, there is a presumption that the technology should be the same in countries like France and Spain. However, the environmental conditions faced by financial institutions are likely to differ importantly. For instance, the average level of wealth, and the saving behavior of economic agents could be different in countries like France and Spain. The differences in the taxation of saving products could persist across countries in Europe, even if banks could now supply the same products all around Europe. The bankruptcy loan is still different from one country to another, so that the efficiency of the loans contracts differs across countries, and so on.With the aim of addressing the deficiencies found in the methodology applied in the intercountry efficiency comparisons that exist in the literature, we propose here an alternative methodology. In this alternative methodology, the specific environmental conditions of each country play an important role in the definition and specification of the common frontier of different countries.(3)(4)In this model, C represents the total of operating and financial (interests) costs.6 The Yj(j=l,2,3) represent the banking products. The Pm (m=l,2,3) refer to the input prices.7 Smare the share of costs paid to input m.8The term lnx is the systematic error componentThe banking outputs and inputs used in this study are as result of following the value added approach of Berger and Humphrey (1992). In the value added approach, all items on both sides of the balance sheet may be identified as outputs or inputs depending on their contribution to the generation of bank value added. Accordingly, we specified three variable outputs: loans (composed of the value of home loans and other loans), produced deposits (the sum of demand, saving, and time deposits), and other productive assets (the sum of all existing deposits with banks, short-term investments, and other investments). Prices for three variable inputs were also specified: labor, physical capital, and deposits (capturing the interest cost of deposits).The prices of inputs were computed by using the data of the banks themselves. For6That assumes that the banks try to minimize total costs and not only to minimize operating costs.7The definition of the estimated common cost frontier corresponds to the equation system (3)-(4), where the equation (3) contains as additional dependent variables the vector of country-specific variables pointed in the equation (2).8The share equations sum to one, so the physical capital share equation was omitted from the estimation.9Standard symetry and input prices homogeneity constraints are imposed on the total cost function (3).instance, the price of labor was estimated by using the information relative to the wages and taxes associated to the use of labor as they appeared in the banks accounts. Consequently, because we used the prices paid by bank for each factor of production, inefficiencies associated with overpayments to real or financial factors can not be evaluated by our approach. That could be a source of underestimation of the inefficiencies for banks paying factors at higher prices than the market prices.To compute inefficiencies by using DFA the estimate of inefficiency for each firm in a panel data set is determined as the difference between the average residual of each firm and the average residual of the firm on the frontier. That is, the average of the annualfor that bank, residuals for each bank i is computed and it served as an estimate of lnxiaverage residual of each bank i is used in the computation of X-efficiency. The efficiency score is given by the following equation:average cost residual which is assumed to be the completely efficient bank. Therefore, X-EFF is an estimate of the ratio of predicted costs for the most efficient bank to predicted costs for any bank. It is just like measuring X-efficiency by the ratio of predicted costs for the most efficient bank to predicted costs for each bank. Nevertheless, this measure ofother fully during the period. As noted by Berger (1993), this error is likely to be larger for banks near the extremes of the average residual. These banks may have experienced good (bad) luck over the entire period. Consequently, the minimum average residual, which serves here as a benchmark for the calculus of the X-efficiency, could be overestimated. To treat this problem, we have computed truncated measures of X-efficiency, where the value of average residual of the qth ((1-q)th) quantile was given to each observation for which the value of the average residual is below (above) the qth ((1-q)th) quantile value. We have used three values of q: 1%, 5%, and 25%.4. The Data and VariablesData.The data are annual accounting data over the 1988-1992 period for commercial and savings banks10 in France and Spain. It is important to emphasize that, in each country, banks are competing in the same markets and for the same customers. They have in each country quite similar access to the capital markets. In Spain and France, financial innovation and deregulation that generated an increase of competition in the banking industry appeared during the mid-eighties.11Therefore, the period of this study was a period of rapid technological changes in the production of financial and banking services during which the banks had to make strategic decisions to adjust to the new environment and the new competition. In particular, the banks began to reduce the number of employees and tried to adjust to the new environment in substituting capital for labor, specially in France.Only banks that were in existence for all 5 years were kept in the sample. The final sample used in this study contains 223 French banks and 101 Spanish banks12.Variable outputs and inputs.Table 1 presents the average values of bank outputs and inputs prices (converted in U.S.dollars)13 over the period 1988-1992 in each country. We observe that the average10By the First and Second Banking European Directives, these three categories of banks are now submitted to the same regulation.11During these years, new short-term securities were introduced, money market was modernized and it was left open to non-financial firms, new derivatives markets were created, interest rate controls were abolished and, finally, capital controls were suppressed.12Data come from official sources: Anuario de la Confederación de Cajas de Ahorros y del Consejo Superior Bancario, and Commission Bancaire. For the purpose of this study, the three French largest banks were excluded of the French sample, as their size would dominate the scale and distort the estimations. The smallest banks and the foreign banks were also excluded from the French and Spanish samples.13All variables initially measured in domestic currencies -including outputs, inputs prices or environmental variables - were converted into a common currency, following the purchasing power parity hypothesis. Here, we chose the U.S. dollar.size of the total balance sheet and the loans portfolio are very similar. This is due to the fact that our sample contains a lot of regional medium-sized banks. However, the average size of deposits differ across countries. One reason is that in France the time deposits interest rate regulation created an incentive in favor of other liquid investments, such as investments in mutual funds and money market deposits (the so-called OPCVM). So, French banks have to substitute money markets liabilities and bonds to time deposits in order to finance loans.The prices of inputs differ from one country to the other. In particular, we observe that both the labor price and the physical capital price are higher in France. This is mainly the consequence of the differences in the structure and regulation of the labor market and the real estate markets. However, due to the increase of competition in the deposits markets in Spain, the average cost of bank liabilities is higher in this country over the period. That is part of the explanation of the difference in total costs. Indeed, financial costs represent more than two third of total banking costs in Spain.Environmental variables.The environmental variables selected and used in order to identify the common frontier are macroeconomic variables as well as variables which explain the peculiar features of each country banking industry, such as regulatory conditions, banking structure and accessibility of banking services. We categorised those variables in three groups (Table 2). The first group is called “Main conditions”and includes a measure of the density of population, the income per capita, and the density of demand of each country. These indicators describe the main conditions in which banks exert their activities. The density of population is measured by the ratio of inhabitants per square kilometer. We assume that banking services supply in areas of low population density would generate higher banking costs, and at the same time would impede banks to obtain high efficiency levels. On the other hand, the income per capita of a country--measured as the ratio of Gross National Product per number of inhabitants--affects numerous factors related to the demand and supply for deposits and loans. Countries with higher income per capita are expected to have a banking system that operates in a mature environment resulting in more competitive interest rates, profit margins and efficiency levels. Finally, the density of demand, measured by the ratio of deposits by square kilometer,is assumed to be a relevant feature determining efficiency. Banks which operate in markets with a lower density of demand would likely incur higher expenses, ceteris paribus.The second category of environmental variables is called “Bank structure and regulation” and contains variables describing the structure and regulation of the banking industry in each country such as the degree of concentration, the average capital ratio, and the intermediation ratio of the banking industry of each country. The concentration of the banking industry is measured by the Herfindahl index defined as the sum of squared market shares of assets of all banks in each country. In analyzing market structure we consider each country to be a market. Since banks operate exclusively throughout each country and since entry has until recently been restricted by national borders, a national market is appropriate. We expect that higher concentration would be associated with higher costs as well as lower costs. If higher concentration is a result of the market power, concentrationand costs go in the same way. However, it could be possible that higher concentration would be associated with lower costs if the concentration is the result of either superior management or greater efficiency of the production processes. As proxy of regulatory conditions we define the average capital ratio, measured by equity capital as a fraction of total assets. Usually, lower capital ratio imply higher risk taking and greater leverage which could result in increased borrowing costs, leading to lower efficiency levels. The last variable included into the second group of environmental variables is the intermediation ratio, defined as the ratio of total deposits over total loans. By using this variable, it is possible to capture the differences between the two domestic banking industries in terms of their ability to convert deposits into loans. As higher the intermediation ratio is, as higher would be the banking industry costs.Finally, the third category of environmental variables refers to the accessibility of the banking services for customers, measured by the number of branches by square kilometer. This variable is used as a measure of branch density that takes in account the space dimension for each national market. It is also a good indicator of the potential overcapacity of the branch network in each country. This variable could measure the degree of competition in the banking market. Indeed, before the banking deregulation of the mid-eighties, the competition between banks took mainly the form of a non-price competition and during that period the banks compete by increasing their number of branches. This non-price competition strategy appeared in France as well as in Spain.particular, the capital ratio is very different. This difference could be due to the fact that during the period of our study—which precede the effective introduction of the capital ratio international regulation—the solvency constraints imposed by the Spanish banking authorities obliged Spanish banks to maintain a higher level of capital ratio, compared to that of French banks. Another difference between the two domestic banking industries come from the fact that the intermediation ratio is higher in Spain than in France. That means that Spanish banks have to collect a higher level of costly deposits (in terms of operating costs) in order to lend the same amount of loans. In these conditions, it seems more expensive to exert banking activities in Spain than in France, ceteris paribus. However, the degree of concentration of the banking industry is quite the same in the two countries.Finally, the accessibility of banking services is higher in Spain than in France. That is consistent with the previous observation concerning the density of population and the amount of deposits by km2.So, the conditions in which Spanish banks operate seem to produce higher level of operating costs. However, again, we should emphasize the fact that the number of branches could be an indicator of the competition imperfectness in banking markets.5. Empirical ResultsOur empirical exercise starts with the measurement of efficiency scores of each French and Spanish banks from its own national frontier—that is, assuming that the technology used for the banks in each country is different. These results are summarized in Table 3. They show that on average the level of efficiency is the same in France and Spain. This average efficiency level is around 88% over the 1988-1992 period. In other words, French and Spanish banks are on average equally efficient in their respective countries. However, given these results, it is not possible to predict what will happen if the banks would decide to operate in the other country. That is, it is not possible to conclude whether the French or Spanish banks will reach the same efficiency level in the othercountry than they get in their own country. To answer this question, we have to measure efficiency scores from a common frontier, and for that purpose we defined the common frontier by following the traditional approach. We measured the efficiency levels of each country banks from a common frontier by pooling the data set of the banks of the two countries, Table 4. The results show that while the average efficiency level of the French banks appear to be 58%, the Spanish banks are operating with an average efficiency level of only 9%. This surprising result is in accordance with our assumption that if the country-specific variables are an important factor in the then the frontier we build while neglecting this the inefficiency levels.explanation of the efficiency differences,factor will generate an overestimation ofintroduce those variables in the common frontier, the efficiency levels improve significantly in both countries.The influence of the environmental variables seems in general to conform to the expectations (Table 6). All the coefficients on the environmental variables in the estimation of the cost function are significant at the 1% level of confidence. That proves the effectiveness of the role of such variables. First, we consider the role of the “main conditions” or macroeconomic conditions. Contrary to the expectations, the sign of the coefficient of the density of population variable is positive. That shows that a higher density contributes to increase banking costs, instead of to decrease them, as expected. The reason could come in part from the characteristics of the banking competition. In particular, if banks compete by opening more branches, for strategic reasons, that could create an inflation of the bank operating costs. Moreover, in this form of non price competition, banks should have to open branches in large cities where the real estate is most costly and the salaries higher. The sign of the income per capita is also positive, which shows that the higher is the development level of the economy, the higher are the operating and financial costs that the banks suffer when supplying a given level of services. The sign of the density of the demand is negative. The explanation could be that it is likely more costly to give satisfaction to a less important demand of banking services, because that demand is less informed and less concentrated. Another argument is that a more important demand permits banks to extract higher scale and scope economies.Second, we consider the variables describing the structure and competition of the domestic banking industry. We observe that the banking costs are increasing with the degree of imperfection of the banking competition. In particular, the sign of the Herfindhal index variable is positive. If we take that index as a measure of the market power of banks, the positive sign tends to demonstrate that higher market power induces banks to spend more in staff or personal expenses. On the other hand, the sign of the intermediation rate variable is positive, showing that a greater amount of deposits by unit of loans induce logically an increase of banking costs. And finally, the sign of the capital ratio is negative showing that it is less costly to produce banking services if the banks are better capitalized. As mentioned before, one explanation could come from the existence of a negative relationship between bank risk and bank borrowing costs.Third, we consider the accessibility of the banking products for the customers. The observation shows that the sign of this variable is positive. The lower the density of bank。
PRELIMINARY FORMING APPARATUS, PRELIMINARY FORMIN
专利名称：PRELIMINARY FORMING APPARATUS,PRELIMINARY FORMING METHOD ANDMAIN FORMING METHOD THAT USE THEAPPARATUS, AND FILM WITH PICTURE 发明人：IMAI, Kunio申请号：JP2003009853申请日：20030804公开号：WO04/056552P1公开日：20040708专利内容由知识产权出版社提供摘要：A preliminary forming apparatus and preliminary forming method capable of performing preliminary forming with high dimensional accuracy between a picture on a film and a three-dimensional shape of the formed film, and a film with picture used in the apparatus and method are provided. A preliminary forming apparatus has a vertical clamp member (68j) for sandwiching and holding a film with picture supplied by a film-supplying device and having a through hole (68a), and has a heating device (70) for heating the film with picture, being approachable to and departable from a preliminary form portion (F). A preliminary forming die (80) for preliminary forming that is performed through the through hole (68a) and a film die-cutting device for die-cutting that is performed after the preliminary forming are approachable to and departable from the preliminary form portion (F). The preliminary forming die (80) is provided with a convex die that is brought in contact with a plasticized film with picture and a concave die for receiving the convex die to perform vacuum forming. A pitch detection portion (68n’) for detecting a film mark (M1) is provided within one pitch width with respect to a film flowdirection (X) of a film (4) with picture which film is opposed to the preliminary form portion (F).申请人：IMAI, Kunio地址：JP国籍：JP代理机构：KITAMURA, Koji更多信息请下载全文后查看。
6药质量控制研究和质量标准制订之漫谈
（三）药理毒理研究资料
16、药理毒理研究资料综述。 17、主要药效学试验资料及文献资料。 18、一般药理研究的试验资料及文献资料。 19、急性毒性试验资料及文献资料。 20、长期毒性试验资料及文献资料。 21、过敏性（局部、全身和光敏毒性）、溶血性和局部（血管、 皮肤、粘膜、肌肉等）刺激性等主要与局部、全身给药相关的特 殊安全性试验研究和文献资料。 22、复方制剂中多种成份药效、毒性、药代动力学相互影响的 试验资料及文献资料。 23、致突变试验资料及文献资料。 24、生殖毒性试验资料及文献资料。 25、致癌试验资料及文献资料。 26、依赖性试验资料及文献资料。 27、动物药代动力学试验资料及文献资料。
这是由于胍丁胺以硫酸盐的形式存在，且分子含有 易于质子化的氨基和胍基，具有极强的亲水性，这一性 质与硫酸胍丁胺油水分配系数的研究结论是一致的。
熔点
➢ 毛细管法
按照中国药典(2000年版二部) 的方法测量其熔点。 实验中随温度升高，硫酸胍丁胺的颜色开始呈棕黄， 然后逐渐变棕褐色，固相消失不明显，无法获得本品 的准确熔点。
2、改变给药途径且尚未在国内外上市销售的制剂。 3、已在国外上市销售但尚未在国内上市销售的药品：
（1）已在国外上市销售的原料药及其制剂； （2）已在国外上市销售的复方制剂； （3）改变给药途径并已在国外上市销售的制剂。 4、改变已上市销售盐类药物的酸根、碱基（或者金属元素），但不改变其 药理作用的原料药及其制剂 。
Impurities in Drug Substance (ICH) Q3A (R)
Classification of impurities
Organic Impurities (Process and drug related)
预样件(Pre-Prototype和样件(Prototype材料供应商程序
欢迎共阅通用汽车公司预样件(Pre-Prototype)和样件(Prototype)材料供应商程序文件GP11本程序适用于所有提供新预样件和样件材料的供应商，(无论是内部的，合作的或外部的)。
所有材料都应满足本程序中提出的要求。
“供应商”一词用来指通用汽车采购部门的主要承包商。
预样件(Pre-Prototype)和样件(Prototype)工作的目的是为了组装和测试生产用的零部件，总成系统和汽车，以便确认设计和组装过程。
预样件和样件阶段的零件认可确保对零件的问题的确定和修正，减少零件偏差对设计评估、制造和组装的影响准备的供采购部门评估的零件和文件。
本程序含如下内容：1－02－0提交要求3－0运输方式预样件和样件要求GP111－0预样件和样件零件和文档的要求：零件将按照GM授权的图纸，模板，模具和/或其它工程设计记录，指定材料制作。
如果与工程要求相偏离，请与你的采购部门来联系取得正式授权许可。
所有提供预样件和样件材料的供应商，都应该有完整的、文档化的和可供检查的如下所列的项目。
对具体年型的样件零件，其记录应保存至该年型正常生产后2个月。
（年型指整车车型）1.通用汽车供应商对预样件和样件材料的保证书(例子A)2.设计记录3.检验结果和检验与/或测试设备4.材料合格证5.零件重量(质量)6.系列化信息7.生产材料和工艺1－1个保证书。
1-2和公差).,更1-3/或测参考。
按2进行文档记录。
(的零件)进行全部检验。
其它颜色的相同零1-3B1-3C1-3D1-3E检验和/或测试设备(当要求时)1-3A完整的特性检验－－除非采购部门规定，否则应对三个(3)零件做完整的特性检验。
1-3B主要产品特性检验－－对所有超过1-3B中指定数量生产的零件，如设计记录上有规定，应检查关键产品检验点的检验结果是否与要求一致。
1-3C工艺更改检验－－因为工艺更改或对原始零件的修正而提交的要求，只需要检验改变的部分和其它任何受改变影响的区域。
Preliminary Studies
Other Research Plan Sections….
animals, select agents, MPI, consortium, support, resource sharing
Appendix
New Research Strategy Section
Current Application Background and Significance
Preliminary Studies Supporting Feasibility
Rat Model to Study Methotrexate-Induced CNS Injury. Purpose was to a) develop a rat model that employed intraventricular administration of methotrexate, and b) assess effects of methotrexate on cells in the CNS. Summary of Methods: Fisher 344 male rats were anesthetized and methotrexate (4 mg/kg) was administered through the left lateral ventricle with an Alzet osmotic pump and brain infusion cannula. After rats regain consciousness, they were returned to their cages, and examined daily for signs of CNS toxicity, infection, neurological damage, and/or failure to thrive. Animals received either methotrexate (n = 4) or artificial CSF (n = 3), and were euthanized 2 days later. Histological studies of sections from brain cortex were assessed for astrocyte reactivity using glial fibrillary acidic protein (GFAP), a commonly used marker to identify astrocytosis in a wide range of neurological injury studies. Figure 1 shows GFAP positive cells in brain cortex taken after 2 days of treatment with methotrexate or artificial CSF.
list of FEM books and articles
Books∙Finite Element Procedures, K. J. Bathe, Prentice Hall, Englewood Cliffs, NJ, 1996.∙The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, T. J.R. Hughes, Prentice Hall, Englewood Cliffs, NJ, 1987.∙The Finite Element Method, 4th ed., Vol. 1, O. C. Zienkiewicz and R. L. Taylor, McGraw-Hill, London, 1989.∙The Finite Element Method, 4th ed., Vol. 2, O. C. Zienkiewicz and R. L. Taylor, McGraw-Hill, London, 1991.∙Finite Elements of Nonlinear Continua, J. T. Oden, McGraw-Hill, New York, 1972.∙Nonlinear Finite Elements for Continua and Structures, 3rd ed., T. Belytschko, W. K.Liu and B. Moran, John Wiley & Sons, Chichester, UK, 2000.∙Finite Elements: their design and performance, R. H. MacNeal, Marcel Dekker, New York, New York, 1994.∙The Finite Element Analysis of Shells - Fundamentals, D. Chapelle and K. J. Bathe, Springer-Verlag, Berlin Heidelberg, 2003.∙Inelastic Analysis of Solids and Structures, M. Kojic and K. J. Bathe, Springer-Verlag, Berlin Heidelberg, 2005.∙Concepts and Applications of Finite Element Analysis, 4th ed., R. D. Cook, D. S.Malkus, M. E. Plesha and R. J. Witt, John Wiley & Sons, NJ, 2002.∙Finite Element Programming, 4th ed., E. Hinton and D. R. J. Owen, Academic Press, London, 1977.∙The Finite Element Method Displayed, G. Dhatt and G. Touzot, John Wiley & Sons, Norwich, 1984.∙Techniques of Finite Elements, B. Irons and S. Ahmad, John Wiley & Sons, New York, 1981.∙An Introduction to the Finite Element Method, 3rd ed., J. N. Reddy, McGraw-Hill, New York, 2006.∙Numerical methods for non-linear problems, Volume 2: Proceedings of the Second International Conference, Universidad Politecnica de Barcelona, Spain, April 9-13, 1984, C.Taylor, E. Hinton and D. R. J. Owen, Pineridge Press, Swansea, UK, 1984.∙An Introduction to Nonlinear Finite Element Analysis, J. N. Reddy, Oxford University Press, New York, 2004.∙Computer Methods in Structural Analysis, J. L. Meek, Chapman & Hall, London, 1991. ∙Finite Element Method: Basic Technique and Implementation, P. Tong and J. N.Rossettos, MIT Press, Cambridge, Mass., 1977.∙Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd ed., J. Bonet and R.D. Wood, Cambridge University Press, UK, 2008.∙Dynamics of Structures, 2nd ed., R. W. Clough and J. Penzien, McGraw-Hill, New York, 1993.∙Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd ed.,A. K. Chopra, Prentice Hall, Upper Saddle River, NJ, 2001.∙Introduction to Finite Element Vibration Analysis, M. Petyt, Cambridge University Press, UK, 1990.∙Fundamentals of Structural Dynamics, 2nd ed., R. R. Craig Jr. and A. J. Kurdila, John Wiley & Sons, New Jersey, 2006.∙Matrix Analysis of Structural Dynamics: Applications and Earthquake Engineering, F.Y. Cheng, Marcel Dekker, New York, 2001.∙Structural Dynamics: Theory and Applications, J. W. Tedesco, W. G. McDougal and C.A. Ross, Addison Wesley Longman, California, 1999.∙Structural Dynamics: Theory and Computation, 5th ed., M. Paz and W. Leigh, Springer Science, New York, 2004.∙Fundamentals of Finite Element Analysis, D. V. Hutton, McGraw-Hill, New York, 2004. ∙Analysis and Design of Elastic Beams - Computational Methods, W. D. Pilkey, John Wiley & Sons, NJ, 2002.∙Matrix Analysis of Framed Structures, 3rd ed., W. Weaver Jr. and J. R. Gere, Kluwer Academic Publishers, Massachusetts, 2001.∙Theory of Matrix Structural Analysis, J. S. Przemieniecki, McGraw-Hill, New York, 1968.∙Structural Analysis and Behavior, F. Arbabi, McGraw-Hill, New York, 1991.∙Matrix Structural Analysis, 2nd ed., W. McGuire, R. H. Gallagher and R. D. Ziemian, John Wiley & Sons, MA, 2000.∙Mechanics of Composite Materials, 2nd ed., R. M. Jones, Taylor & Francis, New York, 1999.∙Theory of Plates and Shells, 2nd ed., S. P. Timoshenko and S. Woinowsky-Krieger, McGraw-Hill, New York, 1959.∙Theory of Elasticity, 3rd ed., S. P. Timoshenko and J. N. Goodier, McGraw-Hill, New York, 1970.∙Strength of Materials, J. P. Den Hartog, Dover Publications, New York, 1977.∙Advanced Strength of Materials, J. P. Den Hartog, Dover Publications, New York, 1987.∙Formulas for Stress, Strain and Structural Matrices, 2nd ed., W. D. Pilkey, John Wiley & Sons, NJ, 2005.∙Roark's Formulas for Stress and Strain, 6th ed., W. C. Young, McGraw-Hill, New York, 1989.∙Matrix Computations, 3rd ed., G. H. Golub and C. F. Van Loan, John Hopkins University Press, Baltimore, 1996.∙Programming the Finite Element Method, 3rd ed., I. M. Smith and D. V. Griffiths, John Wiley & Sons, Chichester, UK, 1998.∙An Introduction to the Finite Element Method: Theory, Programming and Applications,E. G. Thompson, John Wiley & Sons, NJ, 2004.∙Applied Finite Element Analysis, L. J. Segerlind, John Wiley & Sons, New York, 1984. ∙Finite Element Analysis with Error Estimators: An Introduction to the FEM and Adaptive Error Analysis for Engineering Students, J. E. Akin, Elsevier Butterworth-Heinemann, MA, 2005.∙Non-linear Finite Element Analysis of Solids and Structures - Volume 1: Essentials, M.A. Crisfield, John Wiley & Sons, Chichester, UK, 1991.∙Non-linear Finite Element Analysis of Solids and Structures - Volume 1: Advanced Topics, M. A. Crisfield, John Wiley & Sons, Chichester, UK, 1997.∙Theory and Problems of Finite Element Analysis, G. R. Buchanan, Schaum's Outline Series, McGraw-Hill, New York, 1995.∙Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods, R. Szilard, John Wiley & Sons, NJ, 2004.∙Fundamental Finite Element Analysis and Applications, M. A. Bhatti, John Wiley & Sons, NJ, 2005.∙Advanced Topics in Finite Element Analysis of Structures, M. A. Bhatti, John Wiley & Sons, NJ, 2006.∙Introduction to Finite Elements in Engineering, 3rd ed., T. R. Chandrupatla and A. D.Belegundu, Prentice Hall, 2002.∙The Finite Element Method for Three-dimensional Thermomechanical Applications, G.Dhondt, John Wiley & Sons, Chichester, UK, 2004.∙Classical and Computational Solid Mechanics, Y. C. Fung, P. Tong, World Scientific Co. Pte. Ltd, UK, 2001.Articles∙R. H. MacNeal and R. L. Harder, A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Element in Analysis and Design, North Holland, Vol. 1, pp 3-20, 1985.∙K. J. Bathe, Solution Methods of Large Generalized Problems in Structural Engineering, Report UC SESM 71-20, Civil Engineering Department, University of California, Berkeley, 1971.∙K. J. Bathe, H. Ozdemir and E. L. Wilson, Static and Dynamic Geometric and Material Nonlinear Analysis, Report UC SESM 74-4, Civil Engineering Department, University ofCalifornia, Berkeley, 1974.∙K. J. Bathe, Solution Methods for Large Eigenvalue Problems in Structural Engineering, Report UC SESM 71-20, Civil Engineering Department, University of California, Berkeley, 1971.∙ E. N. Dvorkin and K. J. Bathe, A Continuum Mechanics Based Four-Node Shell Element for General Nonlinear Analysis, Engineering Computations, Vol. 1, pp 77-88, 1984.∙ E. L. Wilson, Structural Analysis of Axisymmetric Solids, AIAA Journal, Vol. 3, No. 12, 1965, pp 2269-2274.∙ E. L. Wilson, Elastic Dynamic Response of Axisymmetric Structures, Report UC SEMM 69-02, Civil Engineering Department, University of California, Berkeley, 1969.∙ D. Chapelle and K. J. Bathe, Fundamental Considerations for the Finite Element Analysis of Shell Structures, Computers & Structures, Vol 66, No. 1, 1998, pp 19-36∙ D. Chapelle and K. J. Bathe, The mathematical shell model underlying general shell elements, Int. J. Numer. Meth. Engng., Vol 48, 2000, pp 289-313∙T. J. R. Hughes, R. L. Taylor and W. Kanoknukulchai, A Simple and Efficient Finite Element for Plate Bending, International Journal for Numerical Methods in Engineering, Vol.11, 1977, pp 1529-1543.∙T. J. R. Hughes and M. Cohen, The 'Heterosis' Finite Element for Plate Bending, Computers & Structures, Vol. 9, 1978, pp 445-450.∙T. J. R. Hughes and T. E. Tezduyar, Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element, Journal of Applied Mechanics, Vol. 48, 1981, pp 587-596.∙K. J. Bathe and Lee-Wing Ho, A Simple and Effective Element for Analysis of General Shell Structures, Computers & Structures, Vol 13, 1981, pp 673-681∙K. J. Bathe, A. Iosilevich and D. Chapelle, An evaluation of the MITC shell elements, Computers & Structures, Vol 75, 2000, pp 1-30∙S. F. Pawsey, The Analysis of Moderately Thick to Thin Shells by the Finite Element Method, Report UC SESM 70-12, Civil Engineering Department, University of California,Berkeley, 1977.∙J. P. Hollings and E. L. Wilson, 3-9 Node Isoparametric Planar or Axisymmetric Finite Element, Report UC SEMM 78-03, Civil Engineering Department, University of California, Berkeley, 1969.∙R. J. Melosh, Basis for Derivation of Matrices for the Direct Stiffness Method, AIAA Journal, Vol. 1, No. 7, 1963, pp 1631-1637.∙ B. M. Irons, Engineering Applications of Numerical Integration in Stiffness Methods, AIAA Journal, Vol. 4, No. 11, 1966, pp 2035-2037.∙ E.L. Wilson, A. Der Kiureghian, E.P. Bayo, Short Communications A Replacement for the SRSS Method in Seismic Analysis, Earthquake Engineering and Structural Dynamics, Vol.9, 1981, pp 187–194.∙J. S. Archer, Consistent Matrix Formulations for Structural Analysis Using Finite-Element Techniques, AIAA Journal, Vol. 3, No. 10, 1965, pp 1910-1918.。
Preliminary Draft
New topographic functionals:RORS and DRSEdward Earl and David MetzlerPreliminary DraftThis(draft)paper is a continuation of"A new topographic functional"[2], which de…nes omnidirectional relief and steepness(ORS).Refer to that paper for background concepts and notation.1Reduced ORS(RORS)It is common to see a list of the highest N peaks in a region,for example,the top 531peaks in Colorado,known as the"fourteeners"—the peaks exceeding14,000 feet.However,such height-based lists must include some sort of cuto¤criterion, to avoid listing trivial subpeaks(or,in the logical extreme,an in…nity of points surrounding the summit of the highest peak on the list).Some measures,notably topographic prominence[1],need no such cuto¤;such a measure automatically factors in the independence of a summit,meaning that no trivial subpeak will get a high value.We created RORS to have this feature:it is a measure of a summit’s2independent impressiveness.In particular,we will see that its most important property is that it is automatically discrete:for any">0,the set of points p with RORS(p)>"is discrete(and hence…nite,in a bounded domain).However,our particular de…nition of RORS involves more choices than we made for ORS,some of which are justi…ed more on aesthetic than mathematical grounds.To…x ideas,consider the example of the Teton Range in Wyoming.The highest point,and the point with the highest ORS value(ORS=683m),is the summit of the Grand Teton.See the topographic map or better,view the range in Google Earth(go to N43.74W110.8).If we were to make a list of the"best"points,as judged by ORS,in the range,the summit of the Grand Teton would clearly top the list.But what should be number two?Certainly not the second-highest boulder on the same summit,and perhaps not even nearby peaks such as Mount Owen(just north of the Grand Teton),which is overshadowed signi…cantly by its neighbor,and which could reasonably be considered a subsidiary point on the same massif. The RORS value of Mount Owen will be substantially reduced,compared to its ORS value,by the presence of the Grand Teton nearby.One way to say this is that,given that the Grand Teton has a high ORS value,the fact that Mount Owen has a high ORS value does not convey that much new information,since Mount Owen is part of the same massif.The RORS value of Mount Owen is supposed to re‡ect,roughly,the relief and steepness that it has apart from its being a part of the Grand Teton massif.1The exact number depends on exactly what list is used.2Actually,RORS,like ORS,can be applied to any point on a landscape.However the points with large RORS values tend to be(but are not always)summits.1The number two on the RORS-ranked list for the Teton Range is in fact Mount Moran,which is signi…cantly more independent that Mount Owen.We present ORS and RORS numbers for selected points in the Teton Range in Section2.We…rst de…ne the RORS of a reference point p0relative to a speci…c set of points p1;:::;p n,and a landscape function h.3One should think of p0as a summit to be evaluated,and p1;:::;p n as nearby,more impressive summits.To obtain RORS,we modify the integrand in the de…nition of ORS so that each sample point contributes only to the extent that"viewing"p0from x is"more impressive"than viewing p1;:::;p n.Precisely,we setu i(x)=h(p i) h(x)k p i x k(i=0;:::;n)andv i(x)=f(u i(x))wheref(u)= 4 3 2u arctan u ln u2+1 arctan2u 1=2is the modi…ed slope function used in ORS.Then for each i=1;:::;n,v0(x) v i(x)is a measure of the"impressiveness"of the reference point p0as seen from sample point x,masked,or reduced,by the impressiveness of the point p i. Hence a simple candidate for the new integrand ismin f max(v0(x) v i(x);0)g:i=1;:::;nNote that taking the max with zero prevents negative contributions;once a nearby peak has stolen all of a certain sample point’s contribution to RORS(p0), it can’t do any more damage.Similarly,using min(instead of,for example, subtracting the sum of the v i)lets only the most signi…cant detractor act at each sample point.These are choices we make on empirical and practical grounds; one could use other conventions.We actually perform one more modi…cation on the functions v i before collect-ing them to build the RORS integrand.To explain this,consider two scenarios. In the…rst,p0lies directly between the sample point x and a better peak p1; one can think,for example,of p0as a subpeak on a ridge of p1,with the sample point at the base of the ridge.In the second scenario,p0and p1are diamet-rically opposed as viewed from x;for example,they could be on opposite sides of a valley,with the sample point on the valley‡oor.In the latter scenario,it is plausible to consider p0as more independent of p1than it is in the former, due to the relative position of the two peaks as viewed from the sample point. You can see these two scenarios in the Swiss Alps in Google Earth:Scenario1, Scenario2.To distinguish these situations,we introduce an angle weighting,as 3In the remainder of the paper we will always use h(p)as the reference height for a reference point p.2follows.For i =1;:::;n ,we let i (x )be the angle between the rays !xp 0and !xp i,and we let w i (x )=12(1+cos i (x ))=cos 2i (x )2Note that w i varies from 1,in the ridge scenario,down to 0,in the valley scenario.We then de…ne the RORS integrand g to beg (x )=min f max(v 0(x ) w i (x )v i (x );0):i =1;:::;n gand we de…ne 4RORS(p 0;p 1;:::;p n ;h )=k g k 2=24Z R 2g (x )dA (x )351=2This gives a notion of the "impressiveness"of a point as reduced by a speci…c list of other points.To make a "best"list for a region,one then follows the following procedure to obtain an absolute (not relative)version of RORS.The …rst point on the list,say p 1is the maximum of ORS for the region.The second point is the point whose RORS,relative to p 1,is maximum.The third is the4Weuse single integral signs throughout this paper,in contrast to our use of double integralsfor subsets of R 2in the previous paper.This is to avoid cumbersome quadruple integral notation for DRS.3point whose RORS,relative to p0;p1,is maximum,and so on.This yields a list with the property that the n th entry is the best among all points considered relative to the points above it on the list.However,if done by the letter,this procedure is obviously cumbersome, especially if we want a long list of best peaks.However,it is easy to make approximations and simpli…cations that reduce the time required to compute RORS signi…cantly.First,since RORS ORS,one need not consider points that do not have a relatively high ORS value.Second,since the e¤ect of re-duction falls o¤relatively quickly with distance,one need not include far-away peaks as potential reducers.Third,reducing by many points almost never pro-duces much more reduction than reducing by the most"powerful"(usually the closest)two or three reducing points.Nonetheless,calculating the top50points by RORS in a U.S.state,for example,is a compute-intensive process.It is also somewhat sensitive to small errors in the data,but that is unavoidable for a measure of this type—RORS is a"winner-take-all"measure,where two peaks that are close to being tied (and close physically to each other)can get forcibly separated on the list,with one being declared the winner,and the other getting drastically reduced by the winner.It is easy to show that any measure that is automatically discrete will have this property,so this type of sensitivity is unavoidable.(Recall that ORS, on the other hand,is continuous in the input data,and in the cases of interest to us,even Lipschitz.But it is certainly not automatically discrete—it serves a di¤erent purpose from RORS.)2Examples of RORS calculationsWe will present a number of examples of RORS calculations in a later draft of this paper.At this point we refer the reader to our lists on the Peaklist website. 3Domain Relief and Steepness(DRS)First we recall from[2]the de…nition of DRS of a region.Roughly,it is the RMS average of the ORS value for every point in the domain.But note two modi…cations:…rst,given a bounded domain K R2,and a landscape function h,we rede…ne ORS to use sample points only within the given domain.Second, instead of declaring our modi…ed slope integrand f to have f(u)=0for u<0, we extend it as an even function.55This change is not essential,but it does make the resulting formula more symmetric.It is easy to verify that using the original convention for f instead results in a de…nition of DRS p2times that given here.that is1=4Hence,with notation as in Section ??of [2],we de…ne the new version of ORS,appropriate to this setting,asORS(p ;h 0;h;K )=k f u k 2;K =24Z Kf 2h 0 h (x )k p x k dA (x )351=2and we de…neDRS(h;K )=241A (K )ZK ORS 2(p ;h (p );h;K )dA (p )351=2where A (K )is the area of K .(If A (K )=0we de…ne DRS(h;K )=0;we will justify this below.)This can be expressed directly in terms of the (new)modi…ed slope integrand f as follows.Abusing notation slightly,let u (p ;x )=(h (p ) h (x ))=k p x k .ThenDRS(h;K )=1p k f u k 2;K=241A (K )Z K Kf 2 h (p ) h (x )k p x k dA (p )dA (x )351=2Note that this (quadruple)integral is symmetric in the variables p and x ,and that it has units of length,just as ORS does (recall that f is dimensionless).Now we turn to results that go further than what we had in [2],but are not yet optimal.First,we note that DRS satis…es obvious scaling and invariance properties akin to those satis…ed by ORS .We won’t write them down explicitly.Next,we want to give a simple property of DRS which clari…es exactly how much it is like,and how much it is unlike,and ordinary RMS average.The di¤erence comes from taking sample points only from the region K .For an ordinary average,the following inequality would be an equality.Lemma 1Let the landscape function h be …xed and suppose K =K 1[K 2with K 1;K 2disjoint.ThenDRS 2(h;K ) A (K 1)DRS 2(h;K 1)+A (K 2)DRS 2(h;K 2)A (K )5Proof.Let g(K)=A(K)DRS2(h;K).Theng(K)=Z K K f2(u(p;x))dA(p)dA(x)=Z K1 K1f2(u(p;x))dA(p)dA(x)+Z K2 K2f2(u(p;x))dA(p)dA(x)+2Z K1 K2f2(u(p;x))dA(p)dA(x)g(K1)+g(K2)which is what we wanted to show.We refer to this property as the"superadditivity"of DRS(although more properly it is g which is superadditive).Proposition2DRS is continuous as a function of h in the L1norm. Proof.This is clear since DRS is(the square root of)an integral of ORS2, which is continuous in L1.In fact,DRS is substantially better than this simple proposition indicates, since it averages out the variation in ORS.With mild hypotheses,it is probably Lipschitz in h with respect to the L1norm.In other words,a tall but skinny feature will contribute only a small amount to DRS:We have not yet worked out the details,however.But even L1continuity is signi…cant,since DRS is a measure of ruggedness,which would ordinarily be calculated with derivatives.We can also look at continuity in the region K.We de…ne a metric on the set of bounded measurable regions K by taking the area(Lebesgue measure)of the symmetric di¤erence:d(K;K0)=m(K K0)There is another way to write this metric.Let K be the characteristic function of K.This is in L1exactly when K has…nite area.Then it is easy to see thatd(K;K0)=k K K0k1In other words,taking the characteristic function embeds the set of bounded measurable regions isometrically into L1.Proposition3Fix a landscape h.Then DRS(h;K)is continuous as a function of K with respect to the metric d.6Proof.On the set of regions K with positive area,it is enough to show thatthe function g(K)=A(K)DRS2(h;K)is continuous.Note that in general, d(K;K[K0) d(K;K0) d(K;K[K0)+d(K0;K[K0)Hence we can assume without loss of generality that K K0,and we let L=K0 K.We haveg(K)=Z K K f2(u(p;x))dA(p)dA(x)sog(K0) g(K)=Z K0 K0f2(u(p;x))dA(p)dA(x) Z K K f2(u(p;x))dA(p)dA(x) =Z L K f2(u(p;x))dA(p)dA(x)+Z K L f2(u(p;x))dA(p)dA(x)+Z L L f2(u(p;x))dA(p)dA(x)2Z L ORS2(p;h(p);h;K)dA(p)+Z L ORS2(p;h(p);h;L)dA(p)2Z L ORS2(p;h(p);h)dA(p)+Z L ORS2(p;h(p);h)dA(p)3A(L)k h k21=3d(K;K0)k h k21using the‡agpole bound on ORS.Hence g is actually Lipschitz,and DRS is continuous.Now we just need to show that as K shrinks to zero area,its DRS value(notjust g(K))goes to zero.We haveDRS2(h;K)=1A(K)Z K K f2(u(p;x))dA(p)dA(x)42A(K)Z K K j u(p;x)j dA(p)dA(x)4 2supx2K Z K j u(p;x)j dA(p)7Now,in polar coordinates centered at x ,j u (p ;x )j =j h (p ) h (x )j k p x k =j h (p ) h (x )j r2k h k 1r(a.e.)Hence we need to boundZ K 1rdA (p )which,for a …xed area A (K )=k ,is clearly maximized in the case where K is a disc of radius a =p k= centered at x ,in which caseZ K 1r dA (p )=Z 2 0Z p k= 0dr d =2p kand this is independent of x ,soDRS 2(h;K ) 16 2k h k 1p A (K )which clearly shows continuity as A (K )!0.We now look at some optimization problems for DRS :Problem 1:Given a …xed landscape h and a set K 0,…nd a subset K K 0which maximizes DRS (h;K ).Problem 2:Given a …xed landscape h ,a set K 0,and k >0,…nd a subset K K 0which maximizes DRS (h;K )subject to the constraint A (K )=k .Problem 1is a little more natural than Problem 2,since it lacks the area parameter.Note that the fact that DRS (h;K )!0as A (K )!0means that this problem will avoid a simple pathology that found be found in most problems of the form "…nd the region with the greatest average X "—usually,a search for such a region will simply converge on the maximum of X on the region.The superadditivity of DRS avoids such a pathology—a small region will always have a small DRS simply because it includes very few sample points.However in our numerical calculations for real-world landscapes,the optimal region does tend to be fairly small—not surprisingly,the horizontal scale of the optimal region approaches (in order of magnitude,at least)the vertical scale.So it can be a single massif or a small,particularly rugged subrange of a larger range.We will discuss particular examples below.However,beyond this simple,avoided pathology,there is a much larger prob-lem of whether a minimizing region exists at all,even in Problem 2,with a …xed8area.It is unclear whether,without further assumptions on K or h ,we will get a sequence of progressively better regions which has no limit (in an appropriate topology).This is of course a classic situation in the calculus of variations,and we have not yet investigated this problem thoroughly.We can lay out a modi…ed problem:Problem 3:Given a …xed landcape h ,in some class C L 1,a class K of allowed regions,and a set K 02K ,…nd a subset K K 0,with K 2K ,which maximizes DRS (h;K ).We hope that the classes C and K need not be too restrictive to guarantee a solution.Two examples of our vague thinking along these lines:Questions:(1)If h is smooth (say C 1)then can we guarantee a solution to Problem 3,with no a priori restriction on K ?Will the optimal K have a relatively nice boundary?Must we make explicit assumptions about the niceness of the set of critical points of h ?(2)For an arbitrary h 2L 1,if we require K to be convex,can we guarantee a solution to Problem 3?Note that even if one or both of these questions has a positive answer,nei-ther is particularly satisfactory,since both restrictions are rather severe for our setting.Mountain ranges have vertical cli¤s,so h is typically not even continu-ous (although it usually isn’t a horribly discontinuous function,so perhaps some sort of piecewise smoothness is an appropriate assumption).And the shape one would expect to get "naturally"(without a priori restriction on K )for a maxi-mizer would not usually be convex (picture the contours of a mountain range).But both questions are reasonable starting points,about which we have though a bit—but we’re not yet willing to write anything down.However,turning from the pure approach to a more applied,numerical ap-proach,we see no signs of any major practical obstacle to solving (approxi-mately)Problems 1and 2.Coarse-gridded numerical approximations to this problem yield stable results.For example,our calculations indicate that the most rugged region in the contiguous 48states is the Picket Range of the North Cascades,in Washington State.[3](And no,the optimal regions don’t tend to be convex,or even always connected.)We won’t go into the details of the calculations here (at least for this draft)but we will mention one practical note about how we actually proceed with Problem 2.We actually consider a slightly more general form of DRS ,namelyDRS q (h;K )=241A (K )q Z KORS 2(p ;h (p );h;K )dA (p )351=2Note that the ordinary case is when q =1,and if q =0then we get the "total"L 2norm,instead of the "average".So clearly the analog of Problem 1is silly for the case q =0,as the optimal region will always be all of K 0.But for 0<q <1,the analog of Problem 1is just as well-de…ned as it is for q =1,and it will tend to give larger and larger optimal regions as q decreases.It is not much harder to see that adjusting q gives an alternate parametrization to using A (K )for problem 2.This has proved convenient,as it avoids having to deal9with the…xed-area constraint in that problem.So in our calculations presentedon the website,we have actually looked for overall maximizers of DRS q for various q,to indirectly solve Problem2.It may also very well be the case that some DRS q with q=1is of as muchor more interest in its own right than DRS=DRS1.It has an extra arbitrary parameter,and we see no clear reason to pick some paricular q=1,which iswhy we prefer DRS1.But further investigation may make us prefer some other choice of q.References[1]"Topographic prominence",http:/wiki/Topographic_prominence[2]Edward Earl and David Metzler,"A new topographic functional",submitted to the American Mathematical Monthly.Available at/spire/theory/paper.pdf[3]/spire/10。
菲利斯·C·亨特选书库指南说明书
Title
ABOVE LEVEL Bones Harry Potter and the Sorcerer’s Stone If That Breathes Fire, We’re Toast! Monster Hunt Seymour Simon’s Top 50 Questions Readers: Poisonous Animals Seymour Simon’s Top 50 Questions Readers: Wild Earth Testing the Ice
Ape Escapes! And More True Stories of Animals Behaving Badly
Alexander Newman
NF
640L
Hands Around the Library
Susan L. Roth & Karen Leggett Abouraya
NF
760L
Chews Your Destiny
Rhode Montijo
F
580L
Hi, Koo!
Jon J. Muth
F
My Freedom Trip: A Child’s Escape from North Korea
Frances Park
NF
510L
Ruth and the Green Book
Grade 3 Title List
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S
Fast Module CPU-F .................................................................................................................S-3 S.1 Introduction .......................................................................................................................S-3 S.2 Differences between digsycompact CPU-F and CPU-E........................................................S-3 S.2.1 Hardware ...................................................................................................................S-3 S.2.2 Software.....................................................................................................................S-3 ® S.3 Pin Assignment digsy compact Subunit CPU-F ....................................................................S-4 S.4 Technical Data ..................................................................................................................S-6 S.4.1 Absolute maximum ratings ........................................................................................S-6 S.4.2 Dynamic properties....................................................................................................S-7 S.4.2.1 Voltage supply ....................................................................................................S-7 S.4.2.2 Digital inputs digsy®compact Subunit CPU-F .........................................................S-7 S.4.2.3 Digital and counting inputs digsy®compact Subunit CPU-F ....................................S-8 ® S.4.2.4 Analog inputs digsy compact Subunits CPU-F .......................................................S-8 ® S.4.2.5 Special analog inputs digsy compact Subunit CPU-F ............................................S-8 ® S.4.2.6 Digital outputs digsy compact Subunit CPU-F........................................................S-9 S.4.2.7 Analog outputs digsy®compact Subunit CPU-F.......................................................S-9 S.4.2.8 RS232.................................................................................................................S-9 ® S.4.2.9 CAN digsy compact Subunit CPU...........................................................................S-9 ® S.5 Description of the digsy compact Subunit CPU-F ...............................................................S-10 S.5.1 Analog inputs ...........................................................................................................S-10 S.5.2 Analog outputs.........................................................................................................S-13 S.5.3 Asynchronous interfaces .........................................................................................S-15 S.5.4 CAN-Interface ..........................................................................................................S-16 S.5.5 Application Memory .................................................................................................S-17 S.5.5.1 DCF-Configuration (and memory model) : .......................................................S-17 S.5.5.2 DCF-FLASH-Configuration (and memory model) : ..........................................S-18 S.5.6 serial access : SEA_10x.LIB ...................................................................................S-19 S.5.6.1 User Memory : serial EEPROM........................................................................S-19 S.5.6.2 User Memory :serial nonvolatile RAM ..............................................................S-20 S.5.6.2.1 Access during the process ...........................................................................S-21 S.5.6.2.2 Autosave on power down and startup..........................................................S-21 S.5.6.3 ASC1: user programmable serial Interface ......................................................S-22 S.5.7 New Library DCx_V64x.LIB for all DCx up from V6.4.x ..........................................S-23 S.5.7.1 New Trigonometric Functions by Tables ..........................................................S-24 S.5.7.2 CRC-Build- Function ........................................................................................S-25 S.5.8 New SysIn-Variables for all DCx up from V6.4.x .....................................................S-25 S.5.8.1 Retain data block variables ..............................................................................S-25 S.5.8.2 manufacturing variables ...................................................................................S-26 S.5.8.3 Serial EEPROM variables ................................................................................S-26 S.5.8.4 EEPROM CAN-configuration variables ............................................................S-27 S.5.8.5 EEPROM RS232-configuration variables ........................................................S-28 S.5.8.6 other EEPROM configuration variables ...........................................................S-28