修正的CES模型与印度经济增长分析

通过对CES模型的修正，反映技术水平对一国经济增长的影响，并将修正后的模型用于对印度过去近30年经济增长的实际分析，得出结论：20世纪90年代以来，印度经济增长过程中在劳动技术水平有所提高的同时，资本技术水平却较为显著地下降，因此印度政府应深化经济体制改革，提高资本的使用效率。     

随机Solow经济增长模型及其解的性质

１９８７年诺贝尔（Ｎｏｂｅｌ）经济学奖获得者Ｓｏｌｏｗ教授，建立了确定性的经济增长模型（１９５６年）．它比较真实地描述了现实世界申的确定性的经济增长状况，然而对不确定性的现象，往往误差较大，甚至失效．本文把Ｓｏｌｏｗ模型扩展到随机情形，扩展了Ｂａｎａｃｈ压缩映像原理和不动点定理，获得了随机Ｓｏｌｏｗ模型主要方程和随机解的一些性质．     

社会主义市场经济的数学问题初探——兼论市场经济宏观调控的手段

本文首先给出计划经济和市场经济相结合的数学模型;然后用线性规划的对偶理论证明其解的存在性和解的可操作性,从而证明了计划经济和市场经济是能够结合的,且给出具体结合的方法;最后还给出模型中若干数量的经济解释。     

Formulating an objective for an economy

This paper is dedicated to the memory of E.M.L. Beale. Not a small part of Martin Beale's success in developing and solving large-scale mathematical programs is attributed to the care he took in properly formulating his models.Our presentation concerns our efforts to also properly formulate a model. Our model is an economic model used for technology assessment. In order for it to be useful, it is important that the dual variables represent as realistically as possible real world prices. This required us to formulate the model as a time-staged economic equilibrium model. Our main result is a proof that an equilibrium formulation using expected aggregate demand can under certain conditions be replaced by one in which the economy is driven by an aggregate utility or objective function, one that promotes economic growth subject to physical flow constraints. We show that such an objective function always exists except for populations consisting of significantly large classes of people whose consumption patterns differ radically one from another. Assuming that the latter is not the case, this equivalent formulation means that mathematical programming software can be applied to efficiently solve the model. This paper summarizes an extensive paper entitled Deriving a Utilty Function for the U.S. Economy [3]. The main theorems are stated without proof.The authors wish to thank Kenneth Arrow, Gerard Debreu, Robert Dorfman, Dale Jorgenson and Lawrence J. Lau for their helpful comments.Research of this report was partially supported by the National Science Foundation Grants DMS-8420623, SES-8518662 and ECS-8617905; U.S. Department of Energy Grant DE-FG03-87ER25028; Office of Naval Research Contract N0004-85-K-0343, Electric Power Research Institute Contract RP 5006-01, and the Center for Economic Policy Research at Stanford University.     

Finite population corrections for ranked set sampling

Ranked set sampling (RSS) for estimating a population mean is studied when sampling is without replacement from a completely general finite populationx=(x ₁,x ₂,...,x _N ). Explicit expressions are obtained for the variance of the RSS estimator and for its precision relative to that of simple random sampling without replacement. The critical term in these expressions involves a quantity =(x–)(x–) where is anN × N matrix whose entries are functions of the population sizeN and the set-sizem, but where does not depend on the population valuesx. A computer program is given to calculate for arbitraryN andm. When the population follows a linear (resp., quadratic) trend, then is a polynomial inN of degree 2m+2 (resp., 2m+4). The coefficients of these polynomials are evaluated to yield explicit expressions for the variance and the relative precision of for these populations. Unlike the case of sampling from an infinite population, here the relative precision depends upon the number of replications of the set sizem.Prepared with partial support from the Statistical Analysis and Computing Branch. Environmental Statistics and Information Division, Office of Policy, Planning, and Evaluation, United States Environmental Protection Agency, Washington, DC under a Cooperative Agreement Number CR-821531. The contents have not been subjected to Agency review and therefore do not necessarily reflect the views of the Agency and no official endorsement should be inferred.     

Efficient condensation of carboxylic acids with alcohols catalyzed by fluorous ammonium triflates

The use of fluorous ammonium salts as metal-free catalysts for the direct condensation of equimolar amounts of carboxylic acids and aliphatic alcohols has been investigated. Esterification reactions were thus conveniently carried out under mild fluorous biphasic conditions, in the presence of 1 mol % of fluorous ammonium triflate and without recourse to any additional water removal technique. Good to excellent ester yields were obtained in the case of primary and secondary aliphatic alcohols. The fluorous salt was easily recovered by simple phase separation and reused at least three times without considerable loss of activity.     

高校实验教学中心贵重仪器的数据经济

The paper discusses how to reduce the cost of scientific research and the operation cost of valuable instruments in the laboratory teaching center of universities, while assuring accurate data acquisition during teaching. The paper expounds the relationship and importance of main factors in the data economy, such as Instrument manager, student, valuable instruments, and rules and regulations. Furthermore, some improvement suggestions are proposed.     

Organo‐ and Organometallic‐Catalytic Intramolecular [1,5]‐Hydride Transfer/Cyclization Process through C(sp3)–H Bond Activation

The direct functionalization of C(sp³)–H bonds is one of the most synthetically powerful research areas in current organic synthesis. Organocatalytic C(sp³)–H bond activation reactions have recently been developed in addition to the traditional metal‐catalyzed C(sp³)–H activation reactions. In this review, we aim to give a brief overview of organo‐ and organometallic internal redox cascade reactions with respect to the mechanism, the reactivity of hydrogen donors and acceptors, and the migration modes of hydrogen.

     

Acid Catalyzed Multicomponent Reaction to Access Functionalized N-Benzhydryl Amides: A Tandem Ritter Reaction

Acid catalyzed multicomponent reaction (MCR) for the synthesis of N-benzhydryl amide derivatives from aldehydes, N,N-disubstituted arylamines and nitriles is reported. The reaction is compatible with electronically differentiating aryl/heteroaryl aldehydes/acetals, different nucleophiles (cyclic and acyclic N,N-disubstituted arylamines,β-naphthols, 1,3 dicarbonyl, 1,3,5-trimethoxy benzene), alkyl nitriles, aryl/heteroaryl nitriles in catalytic TFA/TfOH through tandem Ritter reaction. The one-pot MCR with broad substrate scope generated a wide variety of sterically hindered N-substituted amides and is successfully applied for the synthesis of isoindolinone.     

Recent Progress of Single-Atom Alloys in Heterogeneous Catalytic Reactions

In decades, heterogeneous catalysis has played a more significant role in social progress. However, the exorbitant price and low reserves vastly limit the application of noble metal catalysts, which are extensively used in heterogeneous catalysis. The single-atom-alloy catalysts (SAAs) have been regarded as a crucial way to improve the dispersion ratio of noble metal while maintaining great heterogeneous catalytic performance by dispersing noble metal single atoms on the surface of another metal. Besides the benefit from the metal bonds between noble metals and support metals, SAAs is also a unique method to construct metallic metal single atoms and obtain its characteristic catalytic performance, which is not possessed by other single atoms catalysts with positive electricity metal atoms. Most recently, SAAs have been demonstrated to catalyze a lot of significant heterogeneous reactions. This review will introduce the synthesis methods of SAAs and then summarize their applications in heterogeneous catalysis.