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.     

亚纯函数及其微分多项式的唯一性

设f是非常数亚纯函数,g是f的线性微分多项式．a和b是f的两个不同的小函数．本文证明如果f和g几乎CM分担a和b,则f≡g;此外,若f是非常数整函数,且f和f^(k)(k≥1)IM分担a和b,b-a≠Pe^λz,测f≡g．     

N指标d维广义Wiener过程象集的m项代数和的几个性质

设珮犠（狋）：犚犖＋ →犚犱是犖指标犱维广义Ｗｉｅｎｅｒ过程，对任意紧集犈１，…，犈犿犚犖＞ ，该文研究了犿项代数和珮犠（犈１）…珮犠（犈犿）的Ｈａｕｓｄｏｒｆｆ维数，Ｐａｃｋｉｎｇ维数和正的Ｌｅｂｅｓｇｕｅ测度及内点的存在性． 其结果包含并推广了布朗单的结果．     

On a bifurcation governed by hysteresis nonlinearity

We consider autonomous systems with a nonlinear part depending on a parameter and study Hopf bifurcations at infinity. The nonlinear part consists of the nonlinear functional term and the Prandtl--Ishlinskii hysteresis term. The linear part of the system has a special form such that the close-loop system can be considered as a hysteresis perturbation of a quasilinear Hamiltonian system. The Hamiltonian system has a continuum of arbitrarily large cycles for each value of the parameter. We present sufficient conditions for the existence of bifurcation points for the non-Hamiltonian system with hysteresis. These bifurcation points are determined by simple characteristics of the hysteresis nonlinearity.     

Electrical conduction and dielectric properties of vanadium phosphate glasses doped with lithium

AC conductivity and dielectric studies on vanadium phosphate glasses doped with lithium have been carried out in the frequency range 0.2-100 kHz and temperature range 290-493 K. The frequency dependence of the conductivity at higher frequencies in glasses obeys a power relationship, σ_ac=Aω^s. The obtained values of the power s lie in the range 0.5≤s≤1 for both undoped and doped with low lithium content which confirms the electron hopping between V⁴⁺ and V⁵⁺ ions. For doped glasses with high lithium content, the values of s≤0.5 which confirm the domination of ionic conductivity. The study of frequency dependence of both dielectric constant and dielectric loss showed a decrease with increasing frequency while they increase with increasing temperature. The results have been explained on the basis of frequency assistance of electron hopping besides the ionic polarization of the glasses. The bulk conductivity increases with increasing temperature whereas decreases with increasing lithium content which means a reduction of the V⁵⁺.     

Potential formation and high density plasma production on the tandem mirror GAMMA 10

GAMMA 10 experiments have advanced in high density experiments after the last EPS Workshop where we reported high density plasma production by using an ion cyclotron range of frequency heating at a high harmonic frequency and neutral beam injection in the central cell. Recently a high density plasma was obtained with much improved reproducibility than before and without degradation of diamagnetic signal. The high density plasma was attained by adjusting the spacing of the conducting plates installed in the anchor transition regions. Dependencies of particle confinement time, ion energy confinement time and plasma confining potential on plasma density were obtained for the first time in the high density region. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreus, Switzerland, June 23–24, 2002.     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

Cn中不同域的复合算子

令Ω1与Ω2与C^n中的两个有界齐性域，假设φ：1Ω→Ω2是一个全纯映射。在本中，我们研究相应的复合算子Cφ：β（Ω2）→β（Ω1）的有界性和紧性，特别地，我们讨论取B^n和U^n的情形。     

关于AOR迭代法的研究

本文论证了严格对角占优矩阵之AOR法的误差估计式中的误差估计常数hγ,ω（0≤γ≤ω0）的最小值是h1,1.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.