Pigeonhole and Choice Principles

We shall investigate certain set‐theoretic pigeonhole principles which arise as generalizations of the usual (finitary) pigeonhole principle; and we shall show that many of them are equivalent to full AC. We discuss also several restricted cases and variations of those principles and relate them to restricted choice principles. In this sense the pigeonhole principle is a rich source of weak choice principles. It is shown that certain sequences of restricted pigeonhole principles form implicational hierarchies with respect to ZF. We state also several open problems in order to indicate the extent to which the whole subject of pigeonhole principles requires further exploration.     

Existence and Relaxation Theorems for Nonlinear Multivalued Boundary Value Problems

In this paper we consider a general nonlinear boundary value problem for second-order differential inclusions. We prove two existence theorems, one for the ``convex' problem and the other for the ``nonconvex' problem. Then we show that the solution set of the latter is dense in the C ¹ (T,R ^N ) -norm to the solution set of the former (relaxation theorem). Subsequently for a Dirichlet boundary value problem we prove the existence of extremal solutions and we show that they are dense in the solutions of the convexified problem for the C ¹ (T,R ^N ) -norm . Our tools come from multivalued analysis and the theory of monotone operators and our proofs are based on the Leray—Schauder principle. Accepted 18 September 1997     

L2 ASYMPTOTIC FOR THE EQUILIBRIUM SOLUTION OF THE F-M EQUATIONS IN THE SPACE-PERIODIC CASE

The L² exponetial asymptotical stability for the equilibrium solution of the F-M equations in the space-periodic case (n = 2) is considered. Under some assumptions on the external force, it can be shown that the weak solution of F-M equations with initial and boundary conditions in space-periodic case approaches the stationary solution of the system exponetially when time t goes to infinite.     

The Weak Compactness of the Sets of L1(

设(     

L1(Ω,F,μ)的子集的弱紧性及其应用

设（Ω,Ｆ,μ）为任一测度空间,μ可以为无限测度,本文给出了Ｌ１（Ω,Ｆ,μ）的任一子集为弱相对紧的充要条件。此外,当μ为　限测度时,我们还讨论了（Ω,Ｆ）上关于μ绝对连续的有限广义测度的集集收敛性,得到了较为满意的结果,它可看作是Ｖｉｔａｌｉ－Ｈａｈｎ－Ｓａｋｓ定理的推广。     

Some remarks on the integration of the Poisson algebra

We prove the integrability of the Poisson algebra of functions with compact supports of a noncompact manifold. We also determine a Lie subalgebra of vector fields which, weakly, integrate the Poisson algebra of a not necessarily compact manifold covered by an exact symplectic manifold.     

Non‐constructive Properties of the Real Numbers

We study the relationship between various properties of the real numbers and weak choice principles.     

Numerical simulation of the Vasilev reflection

We present a high resolution numerical solution of the Vasilev reflection configuration within the framework of depth averaged two-dimensional inviscid shallow water flow. The study provides the details of the steady flow field and shock wave pattern close to the triple point which confirm the four-wave theory. The shape of the reflected shock in the region upstream of the supercritical patch is also investigated.      

铜(Ⅱ)与碘代酪氨酸和相关氨基酸混配配合物的圆二色谱研究--碘对甲状腺激素生物活性的结构作用探索

用圆二色光谱法研究了铜 ( )与 3,5 -二碘基 -L-酪氨酸 (L-I2 tyr) ,L-酪氨酸 (L-Tyr)或 L-高丝氨酸(L-Hser)和 L-/ DL-AA[AA代表精氨酸 (Arg) ,赖氨酸 (L ys) ,天冬酰胺 (Asn) ,谷氨酰胺 (Gln) ,或丙氨酸(Ala) ]三元混配配合物体系在不同离子强度 (I=1 .0或 0 .1 mol/ L KNO3)和溶剂环境 [水 ,5 0 % (体积分数 )乙醇 -水或 5 0 % (体积分数 )二氧六环 -水 ]条件下配合物分子内配体间相互作用 .全部混配配合物的圆二色谱在 5 99～ 6 2 3nm均有负的极大吸收 ,且 Cu(L-I2 tyr) (L-/ DL-Arg)和 Cu(L-I2 tyr) (L-/ DL-L ys)的 Δε异常负(-0 .493～ -1 .0 72 ) ;Cu(L-I2 tyr) (L-/ DL-AA)的 Δε明显比 Cu(L-Tyr) (L-/ DL-AA)负 .讨论了这些混配配合物中配体间相互作用的规律和碘的结构效应 .     

Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over ℝn

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces. The sharpness of some results is also investigated. Received December 1, 1998, Revised May 2, 1999, Accepted May 19, 1999