Hamilton－Cayley定理的另一种证法

本文提出了线性代数中重要的Ｈａｍｉｌｔｏｎ－Ｃａｙｌｅｙ定理的另一种证明．     

Cauchy-Binet定理与Laplace定理的等价证明

本文运用分块矩阵及多元多项式的性质对行列式求值中的Cauchy-Binet 定理与Laplace 定理给出了等价证明.     

A Generalization of Niho’s Theorem

In this note, we generalize Niho’s theorem on cross-correlation functions of binary m-sequences. Our theorem applies both to binary and non-binary sequences. AMS Classification: 11T24, 94A55 Research supported by the Academy of Finland, grant 200213.     

A Proof of Sharkovsky's Theorem

This paper presents a variation on the standard directed graph proof. This variation makes use of the natural representation of the symmetric group given by one-dimensional maps.     

A New Proof of the Mullineux Conjecture

Let S _d denote the symmetric group on d letters. In 1979 Mullineux conjectured a combinatorial algorithm for calculating the effect of tensoring with an irreducible S _d-module with the one dimensional sign module when the ground field has positive characteristic. Kleshchev proved the Mullineux conjecture in 1996. In the present article we provide a new proof of the Mullineux conjecture which is entirely independent of Kleshchev's approach. Applying the representation theory of the supergroup GL(m | n) and the supergroup analogue of Schur-Weyl Duality it becomes straightforward to calculate the combinatorial effect of tensoring with the sign representation and, hence, to verify Mullineux's conjecture. Similar techniques also allow us to classify the irreducible polynomial representations of GL(m | n) of degree d for arbitrary m, n, and d.     

f-Rings and the Stone-Weierstrass Theorem

Using an appropriate notion of separating subring, it is shown that the classical Stone-Weierstrass Theorem for compact Hausdorff spaces is ultimately a result about f-rings. As an application the constructively valid Stone-Weierstrass Theorem for compact completely regular frames is obtained.     

Weierstrass逼近定理的应用

讨论 Weierstrass逼近定理的应用 .运用 Weierstrass逼近定理 ,我们对于连续偶函数和连续奇函数的性质进行了进一步的刻划 .     

A Topological Intersection Theorem with Applications in H-Spaces

In this paper, a topological intersection theorem of a family of sets with H-convex sections is established. As an application to this theorem, the Nash equilibrium of abstract economy, the Ky-Fan minimax theorem, and an existence problem of solution for quasi-variational inequality are studied. The results presented in this paper modify and extend the corresponding results given in the literature.AMS Subject Classification (2000) 47H10This work is supported by the Foundation of Yunnan Science Technology Commission, China.     

Real C*-Algebras, United KK-Theory, and the Universal Coefficient Theorem

We define united KK-theory for real C*-algebras A and B such that A is separable and B is -unital, extending united K-theory in the sense that KK^CRT( , B) = K^CRT(B). United KK-theory combines real, complex, and self-conjugate KK-theory; but unlike unaugmented KK-theory for real C*-algebras, it admits a Universal Coefficient Theorem. For all separable A and B in which the complexification of A is in the bootstrap category, KK^CRT(A,B) appears as the middle term of a short exact sequence whose outer terms involve the united K-theory of A and B. As a corollary, we prove that united K-theory classifies KK-equivalence for real C*-algebras whose complexification is in the bootstrap category.Mathematics Subject Classification (2000): 19K35, 46L80.     

Bernoulli序列的无规则性定理的一种分析证法

本文的目的是要利用纯分析的方法，证明Ｂｅｒｎｏｕｌｉ序列的无规则性定理．     

A Simple Proof of the Borel Extension Theorem and Weak Compactness of Operators

Let T be a locally compact Hausdorff space and let C ₀(T) be the Banach space of all complex valued continuous functions vanishing at infinity in T, provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X-valued -additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map u: C ₀(T) X when c ₀ X are obtained. The proof of the latter result is independent of the use of powerful results such as Theorem 6 of [6] or Theorem 3 (vii) of [13].     

On a Theorem of T. Gneiting on α-Symmetric Multivariate Characteristic Functions

T. Gneiting (1998, J. Multivariate Analysis64, 131–147) proved a relation between the primitives of the classes Φ_d(2) and Φ_d(1) of 2- and 1-symmetric characteristic functions on ^d, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the calculus of generalized hypergeometric functions.     

On The Correlation Of Binary M-sequences

We obtain the upper bound O(2^14n/15 n^−1/5) on the number of distinct values of all possible correlation functions between M-sequences of order n .     

sl(2,F)PBW定理的另一种证明

设F是任意域,L是F上任意一个李代数,文献[1]给出了关于L的PBW定理及证明.本文对L=sl(2,F)我们给出了PBW定理的另一种证明方法.     

A Theorem of Liouville Type for p-Harmonic Morphisms

In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if : MNis a p-harmonic morphism (p2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E _p (), or (2p–2)-energy E _2p–2() is finite, then is constant.     

Ramanujan's Master Theorem for Hermitian Symmetric Spaces

In this paper we generalize Ramanujan's Master Theorem to the context of a Siegel domain of Type II, which is the Hermitian symmetric space of a real non-compact semisimple Lie group of finite center. That is, the spherical transform of a spherical series can be expressed in terms of the coefficients of this series.     

A Variation of an Extremal Theorem Due to Woodall

We consider a variation of an extremal theorem due to Woodall [12, or 1, Chapter 3] as follows: Determine the smallest even integer (₃C₁,n), such that every n-term graphic sequence = (d₁, d₂,..., d_n) with term sum () = d₁ + d₂ + ... + d_n (₃C₁,n) has a realization G containing a cycle of length r for each r = 3,4,...,l. In this paper, the values of (₃C_l,n) are determined for l = 2m – 1,n 3m – 4 and for l = 2m,n 5m – 7, where m 4.AMS Mathematics subject classification (1991) 05C35Project supported by the National Natural Science Foundation of China (Grant No. 19971086) and the Doctoral Program Foundation of National Education Department of China     

pm-Rings and the Prime Ideal Theorem

A commutative ring A with unit is called a pm-ring if every prime ideal of A is contained in a unique maximal ideal, and a Gelfand ring if a+b=1 in A implies that (1+ar)(1+bs)=0 for some r,s∈A. It was shown earlier, in a somewhat circuitous way involving pointfree topology, that “pm implies Gelfand” iff the Prime Ideal Theorem holds. The present note provides an alternative, more direct and entirely ring theoretical proof of a somewhat augmented version of this result.     

Higher-Order Optimality Conditions for Set-Valued Optimization

This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhäuser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map.     

The quartile operator and pointwise convergence of Walsh series

The bilinear Hilbert transform is given by

It satisfies estimates of the type

In this paper we prove such estimates for a discrete model of the bilinear Hilbert transform involving the Walsh Fourier transform. We also reprove the well-known fact that the Walsh Fourier series of a function in , with converges pointwise almost everywhere. The purpose of this exposition is to clarify the connection between these two results and to present an easy approach to recent methods of time-frequency analysis.