体上右线性方程组的反问题

设Ｆ，Ｋ，Ω分别表示一个任意的体、一个具有对合反自同构的体和一个实四元数体，Ｆ^ｎ表示Ｆ上的ｎ维右向量空间．本文推广和改进了实线性方程组的反问题及一系列结果，解决了Ｆ上右线性方程组更具一般性的反问题（简称ＩＰＳ）：给定ｂ∈Ｆ^s和α_ｉ∈Ｆ^ｎ（ｉ＝１，…，ｍ≤ｎ）满足ｒａｎｋ［α₁，…，α_m］＝ｍ，求所有的ｓ×ｎ矩阵Ａ使Ａα_ｉ＝ｂ（ｉ＝１，…，ｍ）．当ｓ＝ｎ时     

最佳有理L∝逼近的存在性

设Ｒ_ｆ（ｐ）∈Ｒ［ａ，ｂ］是函数ｆ的最佳有理Ｌ_p（１≤ｐ＜∞）逼近，Ｅ_ｆ（ｐ）＝‖ｆ－Ｒ_ｆ（ｐ）‖ｐ。本文证明了Ｅ_ｆ（ｐ）／（ｂ－ａ）^1/p是ｐ单调增加且有界的函数。当ｆ∈Ｌ_∞时，ｆ的最佳有理Ｌ_∞逼近必存在。     

Banach空间中强增生算子的非线性方程的解的迭代构造

本文研究ｐ一致光滑Ｂａｎａｃｈ空间Ｘ中Ｉｓｈｉｋａｗａ迭代法．受Ｄｅｎｇ与Ｔａｎ，Ｘｕ的启发，证明了，当Ｔ是从Ｘ到自身的Ｌｉｐｓｃｈｉｔｚ强增生算子时，Ｉｓｈｉｋａｗａ迭代法强收敛到方程Ｔｘ＝ｆ的唯一解；当Ｔ是从Ｘ的有界闭凸子集到自身的Ｌｉｐｓｃｈｉｔｚ严格伪压缩映象时，Ｉｓｈｉｋａｗａ迭代法强收敛到Ｔ的唯一不动点．通过去掉限制ｌｉｍ_ｎ→∞β_ｎ＝０或ｌｉｍ_ｎ→∞α_ｎ＝ｌｉｍ_ｎ→∞β_ｎ＝０，结果改进与推广了Ｔａｎ，Ｘｕ的定理４．１与定理４．２，也把Ｄｅｎｇ的定理１与定理２推广到了ｐ一致光滑Ｂａｎａｃｈ空间的背景．     

一类子空间格

令Ｖ_n（ｑ）是具ｑ个元素的有限域上的ｎ维向量空间．Ｃ［ｎ,ｋ］是Ｖ_n（ｑ）中与某ｋ维子空间相交不为零空间之子空间全体按包含关系所成偏序集,Ｗ_m为其Ｗｈｉｔｎｅｙ数（０≤ｍ≤ｎ）．本文证明了Ｃ［ｎ,ｋ］具Ｓｐｅｒｎｅｒ性质和单峰性质．进一步地,W_m²-qW_m-1W_m+1作为ｑ的多项式具有非负系数,并且W₀≤W_n≤W₁≤W_n-1≤W₂≤…．     

B值L′极值鞅变换的Lp收敛性

本文运用 Ｋｒｏｎｅｃｋｅｒ引理的推广形式对取值于 Ｂａｎａｃｈ空间 Ｂ上的 Ｂ值 Ｌ′极限鞅Ｘ＝（Ｘ_ｎ，Ｆ_ｎ）_ｎ≥0，关于实值可预报序列 Ｖ＝（Ｖ_ｎ，Ｆ_ｎ）_ｎ≥１的鞅变换Ｙ＝((?)V_k(X_k-X_k-1)Ｆ_ｎ）_ｎ≥１的Ｌ^p收敛性进行讨论，获得一     

关于常曲率空间中有限点集的几何不等式

本文用代数方法建立了ｎ维球面型空间Ｓ_ｎ（Ｋ）和ｎ维双曲空间Ｈ_ｎ（Ｋ）中有限点集的点与点两两之间之距离的一类几何不等式，本文还建立了ｎ维欧氏空间Ｅ^ｎ中共球有限点集的一类几何不等式．作为本文结果的应用，简洁地得出［３］中的一个重要结果，并得出Ｅ^ｎ中有限点集的两个几何不等式     

一类函数空间的刻画

在Ｏｒｌｉｃｚ空间Ｌ_p（Ｒ^ｎ）中给出一类于空间Ｃ_p^a（Ｒ^ｎ）,利用一标准算子序列的逼近,得到 其等价刻画．     

关于一类S1，13（△（2）mn）插值与逼近

设△^（2）_mn是矩形域Ｄ＝［ａ，ｂ］(?)［ｃ，ｄ］的Ⅱ－型三角剖分．S^1，1₃（△^（2）_mn）是带边界条件的二元三次样条空间：本文我们将讨论一类S^1，1₃（△^（2）_mn）的插值问题，证明了它的存在性，唯一性及逼近阶：如果ｆ∈Ｃ^４（Ｄ），则有｜ｆ－ｓ｜≤ｋ（ｌ）·ｍａ     

半值环的两个交换结果

定理１设Ｒ是半值环，ｎ为固定的正整数，如果Ｒ满足条件：存在依赖于(?)_ｘ，ｙ的两个字ｋ（Ｘ，Ｙ），ｔ（Ｘ，Ｙ），其中｜ｋ｜_X＞１，｜ｔ｜_X＝１，｜ｋ｜_Y≥｜ｔ｜_Y，｜ｔ｜_Y≤ｎ，使ｋ（ｘ，ｙ）－ｔ（ｘ，ｙ）∈Ｉ（Ｒ），则Ｒ是交换环。定理２设Ｒ是半值环，如果Ｒ满足条件：存在正整数ｍ＝ｍ（ｘ，ｙ）＞１，ｎ＝ｎ（ｙ），使得（ｘ^ｎｙ）^m－ｘ     

关于ut= div(|▽u|p-2▽u)方程解的梯度H?lder连续性的一个注记

对文献［１－３］中的结果：u_t= div(|▽u|^p-2▽u)在ΩＴ＝Ω×（０，Ｔ）上弱解的空间梯度是Ｈ?ｌｄｅｒ连续的做一个补充．在这个注记里，讨论了条件ｐ＞ｍａｘ｛１，２Ｎ/Ｎ＋２｝是怎样由ｕ的性质所决定的．属于L^N_loc(Ω_T)空间解的梯度是Ｈ?ｌｄｅｒ连续的条件仅仅是ｐ＞１．     

Extended Local Cohomology and Local Homology

We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion \(\widehat {R}^{\mathcal {a}}\) of a commutative noetherian ring R with respect to a proper ideal \(\mathcal {a}\). In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over \(\widehat {R}^{\mathcal {a}}\), not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors.     

Local Topological Toughness and Local Factors

We localize and strengthen Katona’s idea of an edge-toughness to a local topological toughness. We disprove a conjecture of Katona concerning the conection between edge-toughness and factors. For the topological toughness we prove a theorem similar to Katona’s 2k-factor-conjecture, which turned out to be false for his edge-toughness. We prove, that besides this the topological toughness has nearly all known nice properties of Katona’s edge-toughness and therefore is worth to be considered. Research supported by the “Mathematics in Information Society” project carried out by Alfréd Rényi Institute of Mathematics - Hungarian Academy of Sciences, in the framework of the European Community’s “Confirming the International Role of Community Research” programme. Research supported by the Ministry of Education OTKA grant OTKA T 043520.     

Local Units Versus Local Projectivity Dualisations: Corings with Local Structure Maps

We unify and generalize different notions of local units and local projectivity. We investigate the connection between these properties by constructing elementary algebras from locally projective modules. Dual versions of these constructions are discussed, leading to corings with local comultiplications, corings with local counits, and rings with local multiplications.     

Local hyperbolicity

The paper defines and studies a property of functions of several complex variables analytic at the origin which is called local hyperbolicity with respect to a given real direction. For homogeneous polynomials it reduces to ordinary hyperbolicity. Local hyperbolicity is also extended so as to correspond to the hyperbolicity of nonhomogeneous polynomials.     

Local bootstrap

The local bootstrap method draws bootstrap samples from a neighborhood of each data point. Unlike the common bootstrap, it is especially useful for heteroscedastic data. This paper considers local bootstrap of y for a data set {(x _i , y _i )} with the neighborhood defined by the window in a kernel regression model. It shows that for each x, the bootstrap distribution and moments converge almost surely to the true distribution and moments of y respectively, and this convergence is also uniform in x within the data set.     

Local branching

The availability of effective exact or heuristic solution methods for general Mixed-Integer Programs (MIPs) is of paramount importance for practical applications. In the present paper we investigate the use of a generic MIP solver as a black-box ``tactical' tool to explore effectively suitable solution subspaces defined and controlled at a ``strategic' level by a simple external branching framework. The procedure is in the spirit of well-known local search metaheuristics, but the neighborhoods are obtained through the introduction in the MIP model of completely general linear inequalities called local branching cuts. The new solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the MIP solver at hand. It alternates high-level strategic branchings to define the solution neighborhoods, and low-level tactical branchings to explore them. The result is a completely general scheme aimed at favoring early updatings of the incumbent solution, hence producing high-quality solutions at early stages of the computation. The method is analyzed computationally on a large class of very difficult MIP problems by using the state-of-the-art commercial software ILOG-Cplex 7.0 as the black-box tactical MIP solver. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the new method exhibits consistently an improved heuristic performance: in 23 out of 29 cases, the MIP solver produced significantly better incumbent solutions when driven by the local branching paradigm. Mathematics Subject Classification (2000):90C06, 90C10, 90C11, 90C27, 90C59     

Local automorphisms

We show that any linear map on a finite dimensional CSL algebra which at each point is equal to the value of some automorphism of is either an automorphism or can be factored as an automorphism and the transpose of a self-adjoint summand of . New examples of local mappings are constructed.

     

Cofiniteness of Local Cohomology Modules Over Regular Local Rings

It is well known that for a Noetherian ring R, an ideal I ofR, and M a finitely generated R-module, the local cohomologymodules are not always finitely generated. On the other hand, if R is local and m is its maximalideal, then are Artinian modules, which is equivalent to the following two properties: (i) (ii) the vector space has finite dimension over k, where k = R/m. Taking these facts into account, Grothendieck [9] made the followingconjecture. 1991 Mathematics Subject Classification 13H05, 13H10,13D45.     

Local Stability and Local Convergence of the Basic Trust-Region Method

It is proved that the iterative sequence constructed by the Basic Trust-Region Algorithm (see Conn et al. in Trust-region methods, MPS-SIAM series on optimization, Philadelphia, 2000), which uses the Cauchy point method, is locally stable and linearly convergent in a neighborhood of a nonsingular local minimizer.     

On Local Descent to Metaplectic Groups and Local Theta Correspondence

Let F be a p-adic field of characteristic 0.We study a twisted local descent construction for the metaplectic groups Sp_(2 n)(F),and also its relation to the corresponding local descent construction for odd special orthogonal groups via local theta correspondence.In consequence,we show that this descent construction gives irreducible supercuspidal genuine representations of Sp_(2n)(-F) parametrized by a simple local L-parameter φ_τ corresponding to an irreducible supercuspidal representation τ of GL_(2n)(F) of symplectic type,and the genericity of the representations constructed can be indicated by a local epsilon factor condition.In particular,this local descent construction recovers the local Shimura correspondence for supercuspidal representations.