Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Projective geometry and special relativity

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.     

Equilibrium in Queueing Systems with Complementary Products

We study a model of a queueing system with two complementary products/services. In our model, there is one M/M/1 system and another facility that provides instantaneous service. The two services are complementary and the customer has no benefit from obtaining just one of them. We investigate the model under various price structures and ownership assumptions.AMS subject classification: 90B22, 91A10The authors are equal in their contribution to this paper. This paper is submitted by the first author to the Tokyo Institute of Technology as partial fulfillment of the requirements for the Ph.D. program in the Department of Value and Decision Sciences, and the order of names was chosen in compliance with program conditions. This research was supported by the Israel Science Foundation (grant No. 237/02).     

Equilibrium Shapes of Pressure Vessel Domes in Asymmetric Winding

Errors in the programs of winding pressure vessels can lead to an asymmetric reinforcement structure, which affects the equilibrium shape of their domes and the tension in the left and right families of filaments. In this paper, equations determining the equilibrium shape of the domes, the tension in filaments, and the shear stresses between layers are obtained. Examples with winding trajectories in the form of geodesics and constant-deviation lines are considered. It is found that, for pressure vessels, in the absence of external torque, the tension levels in filaments of the left and right families differ considerably. It is also revealed that, for actual friction coefficients in winding, the shear stresses taken up by the binder are insignificant. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 743–752, November–December, 2005.     

管理中的Nash平衡与Braess悖论现象

本给出了交通规划、经济贸易以及其它管理中的一些Nash平衡和Braess悖论实例，分析了Nash平衡和Braess悖论现象及其本质特征，指出它们在管理工作中具有普遗性和潜在应用性。     

MC模式下顾客需求与厂商供应的纳什均衡

在大规模定制(MC，Mass Customization)模式下，基于市场需求的复杂化，厂商对个性化的顾客需求很难做出及时准确的反应，而且由于其自身生产能力的限制，不可能对所有的个性化用户进行一一地满足，只可能对已经存在的个性化需求，根据自身的生产能力和规模，以利润最大化及顾客对产品的满意度为目标，对个性化需求进行较准确地预测，从而正确指导生产。本通过博弈论的方法，提出了一个基于顾客对产品的满意度及企业的利润的一个非合作博弈模型，并给出求解纳什均衡的方法。     

NCD系统的数学理论

无索赔折扣系统(No Claim Discount system,简记为NCD系统)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文尝试建立了NCD系统严谨的数学理论, 重点讨论了NCD系统的数学建模和稳态分析.此外,作为本文必要的数学前提,首先在第2节着重探讨了随机矩阵间的随机优序关系,并将所得结论运用至齐次不可约且遍历的马尔科夫链的研究中,这些内容也有其独立的数学上的兴趣.     

Adsorption Behaviour of 134Cs and 22Na Ions on Tin and Titanium Ferrocyanides

Tin and titanium ferrocyanides were studied as adsorbents for alkali metal ions, viz., ¹³⁴Cs and ²²Na, which represent radioactive wastes. The ferrocyanides were prepared in granular form. The tin version contained 11.2% water, while the titanium version contained 17.7% water. The exchange capacities for Cs⁺ and Na⁺ in the hydrated tin version were about 1.5 and 0.7 meq/g, respectively, while those in the titanium version were 2.2 and 1.2 meq/g, respectively. Drying at 250°C decimated those capacities. The diffusional time constant of Cs⁺ at 25°C, determined via Fick's second law, was of order of magnitude 1 × 10^–3 s^–1, though there were minor differences due to particle size and the form of ferrocyanide. Similarly, the effective diffusivity was of order of magnitude 1 × 10^–8 cm²/s. The titanium version responded slightly faster than the tin version. Likewise, equilibrium measurements in mixtures with sodium nitrate, potassium nitrate, or uranium oxide, showed that the titanium version exhibited significantly greater selectivity for Cs⁺ than did the tin version. Unfortunately, tests of complete elution of the Cs⁺ from the ferrocyanides were mostly disappointing. Work continues on that subject.     

Pseudo-Isotherms Using a Second Order Kinetic Expression Constant

The kinetics of four sorption systems, Cu/tree fern, Pb/tree fern, AB9/activated clay and BR18/activated clay have been studied based on the assumption of a pseudo-second order rate law. Pseudo-isotherms using the pseudo-second order kinetic expression constant have been developed to describe the four liquid-solid sorption systems. The experimental results have been analyzed using a pseudo-Langmuir and a pseudo-Redlich-Peterson isotherm. Both isotherms were found to represent the measured sorption data well. According to the evaluation using the pseudo-Langmuir equation, the monolayer sorption capacities were obtained to be 13.9, 46.6, 124 and 105 mg g^–1 for copper, lead, AB9 and BR18 respectively.     

A Kind of Electrode Enhanced the Electrochemiluminescence

Electrochemiluminescence (ECL), like other chemiluminescence technique, offers high signal-to-noise ratio. Furthermore, it has the advantage over other chemiluminescence techniques of being initiated by a voltage potential. Thus, it provides a better-controlled luminescence. This technique has been used in measuring many kinds of organic and inorganic matters, and analyzing many kinds of antigen, antibody and hapten, such as carcinoembryonic antigen and alpha-fetoprotein, etc1-6. The ele…