Structural stability and robustness to bounded rationality for non-compact cases

We study the model M consisting of “general games” with noncompact action space, together with an associated abstract rationality function. We prove that M is structurally stable and robust to ϵ-equilibria for “almost all” parameters. As applications, we investigate structural stability and robustness to bounded rationality for noncooperative games, multiobjective optimizations and fixed point problems satisfying existence and some continuity conditions. Specifically, we introduce concrete rationality functions for such three kinds of problems with both payoffs and strategy sets, objective functions and domain spaces, and correspondence and domain spaces as parameters, respectively, and show the generic structural stability and robustness to bounded rationality for the corresponding model Ms.     

Uncomputability and undecidability in economic theory

Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory[Noam Nisan, Tim Roiughgarden, Éva Tardos, Vijay V. Vazirani (Eds.), Algorithmic Game Theory, Cambridge University Press, Cambridge, 2007] and Algorithmic Statistics[Péter Gács, John T. Tromp, Paul M.B. Vitányi, Algorithmic statistics, IEEE Transactions on Information Theory 47 (6) (2001) 2443-2463] are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory - and its applied branches, say computational complexity theory or algorithmic information theory - and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general - but concise - analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory (The qualification ‘recursive’ here has nothing to do with ‘recursion theory’. Instead, this is a reference to the mathematical formalizations of the rational economic agent’s intertemporal optimization problems, in terms of Markov Decision Processes, (Kalman) Filtering and Dynamic Programming, where a kind of ‘recursion’ is invoked in the solution methods. The metaphor of the rational economic agent as a ‘signal processor’ underpins the recursive macroeconomic paradigm.), are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics.     

Quantum chemical study of the structure of tricyclic saturated hexafluoro-1,3-butadiene dimers

Results of a quantum-chemical study of the molecular structure of dimerization products of saturated 1,3-butadiene and hexafluoro-1,3-butadiene (tricyclo[3.3.0.0^2.6]octane, dodecafluorotricyclo[4.2.0.0^2.5]octane (I), and dodecafluorotricyclo[3.3.0.0^2.6]octane (II)) are presented. The calculated symmetry of the molecule of I in vacuum (C ₂) differs from its symmetry in the single crystal (C _b , XRD). The most stable of dimers (II) contains C-C bonds with a length of up to 1.573 Å and a four-atom cycle with angles of 82.3°.     

Formation of negative oxidation states of platinum and gold in redox ionic liquid: Electrochemical evidence

The electrochemical reduction of noble metal electrodes in the presence of redox ionic liquid, 1-ferrocenylethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [FcEMIM][TFSI], was investigated by cyclic voltammetry. Our experiments suggest the formation of metal with negative oxidation states, in the cases of platinum and gold electrodes [M_n⁻, FcEMIM⁺]. By analogy with the previous work, the formation of these phases is concomitant with the insertion of the supporting electrolyte; which correspond in our experimental condition to the redox cation of the ionic liquid. As an exciting result, the electrochemical investigations of the reduced electrode in electrolytic solution, containing solvent and supporting electrolyte, evidence the presence of the ferrocene groups at the electrode surface. Moreover, the reduced electrode exhibits the presence of the ferrocene even after, contact with air, after ultrasound, and after physical polishing, highlighting the large stability of this organo-metallic phases formed in this media. The AFM investigations demonstrate the morphological change of the platinum surface after the reduction process. Finally, our works bring a formal electrochemical proof of the presence of the ionic liquid cation inside the electrode material after the cathodic treatment in this media.     

Equilibrium adsorption of a cyclopentane—benzene vapor mixture on active carbon

The data on adsorption of cyclopentane, benzene, and their mixture on active carbon were analyzed by the statistical thermodynamic model. A method to describe the state of a binary mixture in single micropores was offered. A substantial negative deviation from Raoult's law predicted by the concept of an ideal adsorption solution is a consequence of a decrease in the excessive Helmholtz energy brought about by progressive filling when values of the excessive energy are positive over a wide range of adsorption. The excessive values found for the entropy and internal energy of a mixture of molecules in a single micropore are negative due to the heterogeneity of the adsorption field. The approach suggested adequately describes the experimental data and can be used for the determination of differential heats of adsorption. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1070–1076, June, 1999.     

Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k₁₂ of the second virial coefficient and non-random two liquid model parameters τ₁₂ and τ₂₁ were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO₂ + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.     

开挖过程中边坡稳定性研究及两种安全系数之间的转化

为了研究边坡在开挖过程中的安全状况,以及有限元强度折减法和极限平衡法所求得的安全系数之间的关系,分别采用有限元软件ANSYS和极限平衡软件Slope／W对开挖过程各个阶段边坡的稳定性进行了计算分析．通过研究两种方法所采用的屈服准则的内在联系,找到了这两种方法所求得安全系数的转化方法,并对利用两种方法求出的边坡安全系数进行了对比分析．研究结果表明,在开挖过程中,边坡的安全系数会出现先增大后减小的现象;在平面应变条件下,采用平面应变莫尔一库仑匹配DP5准则求出的边坡安全系数,与传统极限平衡法求出的边坡安全系数最接近,误差小于8％．     

水飞蓟素在水中溶解度的测定及关联

通过自制的固-液平衡装置测定了从293.15K到313.15K温度下水飞蓟素在水中的溶解度.实验数据用理想溶液模型及经验方程进行了关联.其中经验方程1误差最小,经验方程2和理想溶液模型关联也得到了较满意的结果.     

对山西省保险业发展影响因素的实证分析

利用山西1996年到2010年间的保费收入、国内生产总值、固定资产投资、城乡居民储蓄存款余额、人口数和人均可支配收入这六个变量,对影响山西保险业发展的各因素间的长期均衡关系进行了实证分析.结果表明:国内生产总值、城乡居民储蓄存款余额对山西省保险业的发展有显著的正向影响,并结合山西保险业现阶段情况,对山西保险的发展和规范提出了相关建议.     

一类具有阶段结构的捕食系统解的渐近性

目的讨论一类具有阶段结构的捕食-被捕食模型解的渐近性。方法利用代数方程讨论该模型平衡点的存在性,应用Hurwitz判别法则及特征方程对模型平衡点的稳定性进行分析。结果给出了该模型的平衡点局部渐近稳定的充分条件,并且利用计算机进行模拟仿真,得到了直观可视化结果。结论模型的各个平衡点在一定条件下可以是局部渐近稳定的。