On the associativity of the product of measure spaces

If we arbitrarily choose finitely many measure spaces, then the existence of a product of these measure spaces can be proved. It is well known that this operation is not associative which is a substantial difficulty. In this paper we show that the associative law remains true between the σ-algebras of the product spaces, and we give an extension of the Fubini's theorem. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Asymptotic Expansion of Hadamard Products

We consider functions f and g which are holomoxphic on closed sectors in C where they admit an asymptotic representation at ∞ in the form of power series in z^-1. We give a simple geometrical condition under which the Hadamard product f*g of f and g porsesses again an asymp totic expansion at ∞. It turns out that the asymptotic expansion of f*g is essentially the formal Hsdamd product of the asymptotic expansions of f and g. Our result yields a slight generaliestion of a well known theorem of W. B. Ford.     

Multipermutation-Based Intersection Theorem and Its Applications

In this paper, we introduce a multipermutation-based intersection theorem on the product space of several unit simplices, called the simplotope. This theorem gives a substantial generalization of an intersection result of Scarf on the unit simplex (Ref. 1). By using this new result, we also obtain a multipermutation-based generalization of the Brouwer fixed-point theorem on the simplotope. Furthermore, we apply this new result to an economic equilibrium model with indivisibilities and obtain an equilibrium existence theorem.     

Duality for Semiantichains and Unichain Coverings in Products of Special Posets

Saks and West conjectured that for every product of partial orders, the maximum size of a semiantichain equals the minimum number of unichains needed to cover the product. We prove the case where both factors have width 2. We also use the characterization of product graphs that are perfect to prove other special cases, including the case where both factors have height 2. Finally, we make some observations about the case where both factors have dimension 2. Work supported in part by NSA Award No. H98230-06-1-0065.     

A -sampling theorem and product formula for continuous -Jacobi functions

In this paper we derive a q-analogue of the sampling theorem for Jacobi functions. We also establish a product formula for the nonterminating version of the q-Jacobi polynomials. The proof uses recent results in the theory of q-orthogonal polynomials and basic hypergeometric functions.

     

某些乘积图上接触过程的完全收敛定理的证明

该文证明了当传染参数充分大时,乘积图G_1×G_2×Z上的接触过程满足完全收敛定理,其中G_1和G_2是任意无穷、局部有限的可迁图(从而度有界).该结果在一定程度上推广了文献[1]的结果.     

A direct product decomposition of QMV algebras

We study the direct product decomposition of quantum many-valued algebras (QMV algebras) which generalizes the decomposition theorem of ortholattices (orthomodular lattices).In detail,for an idempo- tent element of a given QMV algebra,if it commutes with every element of the QMV algebra,it can induce a direct product decomposition of the QMV algebra.At the same time,we introduce the commutant C(S) of a set S in a QMV algebra,and prove that when S consists of idempotent elements,C(S) is a subalgebra of the QMV algebra.This also generalizes the cases of orthomodular lattices.     

A mod 2 index theorem for the twisted Signature operator

A mod 2 index theorem for the twisted Signature operator on 4 _q + 1 dimensional manifolds is established. This result generalizes a result of Farber and Turaev, which was proved for the case of orthogonal flat bundles, to arbitrary real vector bundles. It also provides an analytic interpretation of the sign of the Poincare-Reidemeister scalar product defined by Farber and Turaev. Project partially supported by the National Natural Science Foundation of China (Grant No. 19525102), the Fok Ying-Tung Foundation and the Qiu Shi Foundation.     

Translated Brownian Motions and Associated Wick Products

Abstract

The concept of Wick product is strongly related to the underlying Brownian motion we have fixed on the probability space. Via the Girsanov's theorem we construct a family of new Brownian motions, obtained as translations of the original one, and to each of them we associate a Wick product. This produces a family of Wick products, named γ-Wick products, parameterized by the performed translations. We aim to describe this family of products. We also define a new family of stochastic integrals, which are related in a natural way to the γ-Wick products.     

Nonlinear functional boundary value problems involving the product of two nonlinearities

In this work, an existence theorem for the nonlinear quadratic two-point boundary value problems of functional differential equations is proved using a nonlinear alternative of Leray–Schauder type involving the product of two operators in Banach algebras. An example is also given to illustrate the abstract results presented here.     

Existence of solutions to the Riemann problem for 2 × 2 conservation laws

We consider the Riemann problem for a class of 2?×?2 systems of conservation laws which do not satisfy the strictly hyperbolicity condition. Our main assumption is that the product of non-diagonal elements within the F?echet derivative (Jacobian) of the flux is nonnegative. By improving a vanishing viscosity approach, we establish the existence of solutions to the Riemann problem for those systems.     

Orthogonal rational functions with complex poles: The Favard theorem

Let {φn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions, the rational functions φn form an orthonormal system with respect to a Hermitian positive-definite inner product.     

内积函数的表示

本文首先定义了内积函数,这个概念推广了内积的定义.然后定义了Hilbert空间（H,〈·,·〉）上由严格正算子A诱导的范数,这个范数与由〈·,·〉诱导的范数是等价的.进一步,证明了所有的内积函数与线性有界的严格正算子全体之间存在一一对应关系.     

Four counterexamples to the Fubini theorem

In this paper we study signed measures. Our main results are as follows: the Fubini theorem is not true in the general case; the Jordan parts of a transition measure are not necessarily transition measures; the operation of taking the Jordan parts does not necessarily commute with multiplying by the initial measure; the product of σ-bounded measures need not be a σ-bounded measure. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 124–127, July, 1997. Translated by S. S. Anisov     

直观Menger内积空间及其在积分方程中的应用

首先引出和定义了直观的Menger内积空间的概念,然后在完备的直观的Menger内积空间中得出了一个新的不动点定理.作为应用,利用文中所得的结果,研究了线性Volterra积分方程解的存在性和唯一性.     

Quantitative estimates for bivariate Stancu operators

In this paper, we introduce Voronovskaja‐type and Grüss–Voronovskaja‐ type theorems in quantitative mean with the help of the usual modulus of continuity for bivariate Stancu operators, which are different from a tensor product setting.     

Limit theorems for random permanents with exchangeable structure

Permanents of random matrices extend the concept of U-statistics with product kernels. In this paper, we study limiting behavior of permanents of random matrices with independent columns of exchangeable components. Our main results provide a general framework which unifies already existing asymptotic theory for projection matrices as well as matrices of all-iid entries. The method of the proofs is based on a Hoeffding-type orthogonal decomposition of a random permanent function. The decomposition allows us to relate asymptotic behavior of permanents to that of elementary symmetric polynomials based on triangular arrays of rowwise independent rv's.