On the Intrinsic Complexity of Elimination Theory

We consider the intrinsic complexity of selected algorithmic problems of classical elimination theory in algebraic geometry. The inputs and outputs of these problems are given by finite sets of polynomials which we represent alternatively in dense form or by straight line programs. We begin with an overview on the known upper bounds for the sequential and parallel time complexity of these problems and show then that in the most important cases these bounds are tight. Our lower bound results include both the relative and the absolute viewpoint of complexity theory. On one side we give reductions of fundamental questions of elimination theory to NP- and P^#-complete problems and on the other side we show that some of these questions may have exponential size outputs. In this way we confirm the intrinsically exponential character of algorithmic problems in elimination theory whatever the type of data structure may be.     

A Generalization of Lazard's Elimination Theorem

Abstract

Using the classical Lazard's elimination theorem, we obtain a decomposition theorem for Lie algebras defined by generators and relations of a certain type.     

On a Theorem of Matiyasevich

Mathematical Notes - Using the restatement of the Riemann hypothesis proposed in a recent paper of Matiyasevich, we explicitly write out the system of Diophantine equations whose unsolvability is...     

On a Theorem of Mislin

An alternative proof is given of a result, originally due toGuido Mislin, giving necessary and sufficient conditions forthe inclusion of a subgroup to induce an isomorphism in modp cohomology.     

On a Theorem of Ossa

If is an elementary abelian -group, Ossa proved that the connective -theory of splits into copies of and of the connective -theory of the infinite real projective space. We give a brief proof of Ossa's theorem.

     

On a Theorem of Strobel

Received April 17, 2000 / Accepted May 9, 2000 / Published online September 14, 2000     

On a Theorem of Grothendieck

A smooth projective morphism p : T S to a smooth variety S is considered. In particular, the following result is proved. The total direct image Rp _*(/n) of the constant étale sheaf /n is locally (in Zariski topology) quasiisomorphic to a bounded complex on S that consists of locally constant, constructible étale sheaves of /n-modules. Bibliography: 2 titles.     

关于一个次可乘定理

本文证明了次可乘定理：设A是一个*代数,A上范数||.||使得（A,||.||）成为完备的赋范线性空间,而且,（I）对于X∈A,||x*x||||x||2;（II）对于正规元x∈A,||x*x||=||x||2,则（A,||.||）是C*-代数．同时,也给出了其对应的C*-等价定理．     

一个线性组合定理的证明

利用初等行变换与初等矩阵的关系,可证明线性组合定理：初等行变换不改变矩阵中列向量的线性关系.     

关于Widder定理的推广

利用解析函数理论及改进了的Holder不等式,并借助于Hardy的技巧建立了广义的Widder不等式,当p=q=2时,得到Widder定理的一个改进.     

On the Modification of Rouche's Theorem for the Queueing Theory Problems

In analytic queueing theory, Rouche's theorem is frequently used to prove the existence of a certain number of zeros in the domain of regularity of a given function. If the theorem can be applied it leads in a simple way to results concerning the ergodicity condition and the construction of the solution of the functional equation for the generating function of the stationary distribution. Unfortunately, the verification of the conditions needed to apply Rouche's theorem is frequently quite difficult. We prove the theorem which allows to avoid some difficulties arising in applying classical Rouche's theorem to an analysis of queueing models.     

On a Generalization of Szemeredi's Theorem

Let N be a natural number and A [1, ..., N]² be a set of cardinalityat least is an absolute constant. We prove that A contains a triple {(k, m), (k+d, m), (k, m+d)},where d > 0. This theorem is a two-dimensional generalizationof Szemerédi's theorem on arithmetic progressions. 2000Mathematics Subject Classification 35J25, 37A15.     

On the Theory of (Dual) Projection for Fuzzy Stochastic Processes

Abstract

In a theory similar to one of real-valued stochastic processes, in this paper, we investigate the projection and dual projection for fuzzy stochastic processes. First, the related concepts of fuzzy stochastic processes are introduced, such as adaption, measurability, optionality, predictability, etc. Subsequently, we study fuzzy stochastic integral and fuzzy measure generated by increasing fuzzy stochastic processes. Moreover, (dual) projection w.r.t. (increasing) fuzzy stochastic processes are discussed. We prove the existence and uniqueness of (dual) optional (predictable) projection for (increasing) fuzzy stochastic processes.