Q-正则Loewner空间中的拟对称映射

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.     

The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.     

A problem in extremal quasiconformal extensions

A constantK ₀ ^(m) (h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK ₀(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and sufficient condition is established forK ₀ ^(m) (h) =K ₁(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK ₀ ^(m) (h)<K ₁(h), wherek ₁(h) is the maximal dilatation ofh.     

Generalized Equilibrium Problems and Generalized Complementarity Problems

From a general minimax inequality or an abstract lopsided saddle-point theorem, we deduce general Karamardian-type equilibrium theorems and generalized complementarity theorems. Our new results extend a number of well-known earlier works of many authors.     

THE GLOBAL THEOREM OF A.N.BERLINSKII

ＳｏｃａｌｔｈｅＢｅｒｌｉｎｓｋｉｔｈｅｏｒｅｍｆｏｒｐｌａｎａｒｑｕａｄｒａｔｉｃＳｙｓｔｅｍ（ＱＳ）ｉｓ：ＴｈｅｏｒｅｍＡ［１］ＳｕｐｐｏｓｅｔｈａｔａＱＳｈａｓ４ｆｉｎｉｔｅｃｒｉｔｉｃａｌｐｏｉｎｔｓ（ＣＰｓ），Ｉｆｔｈｅｑｕａｄｒｉｌａ...     

一类非线性积分,微分方程的逼近解

在不主紧型条件和耗散型条件的情形下，得到了Ｂａｎａｃｈ空间中一类非线性积分，微分方程的逼近解。     

The Equivalence of Several Basic Theorems for Subdifferentials

Several different basic tools are used for studying subdifferentials. They are a nonlocal fuzzy sum rule in (Borwein et al., 1996; Zhu, 1996), a multidirectional mean value theorem in (Clarke and Ledyaev, 1994; Clarke et al., 1998), local fuzzy sum rules in (Ioffe, 1984, 1990) and an extremal principle in (Kruger and Mordukhovich, 1980; Mordukhovich, 1976, 1980, 1994). We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

关于多项式系数微分方程复振荡理论的两个结果

本文证明了：如果ａ_ｋ－ｊ（ｊ＝１，…，ｋ）为多项式，ｄｅｇａ_ｋ－ｊ＝ｎ_ｋ－ｊ，存在某个ａ_ｋ－s（１≤ｓ≤ｋ）满足：当１≤ｊ＜ｓ时，ｎ_ｋ－ｊ／ｊ≤ｎ_ｋ－s／ｓ；当ｓ＜ｊ≤ｋ时，ｎ_ｋ－ｊ＜ｎ_ｋ－s－（ｊ－ｓ）．如果Ｆ≠０是整函数且满足σ（Ｆ）＝β＜（ｎ_ｋ－s＋ｓ）／ｓ，那么微分方程ｆ^（ｋ）＋ａ     

Simple Constructions of Almost k-wise Independent Random Variables

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity.