A Chaotic System May be Simple

ＡＣｈａｏｔｉｃＳｙｓｔｅｍＭａｙｂｅＳｉｍｐｌｅＬｉａｏＧｏｎｇｆｕ（廖公夫）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）ＦａｎＱｉｎｊｉｅ（范钦杰）（Ｄｅｐａｒｔｍｅｎｔｏｆ...     

Equicentralizer Subgroups of Sporadic Simple Groups

A subgroup H of a group C is called an equicentralizer subgroup of G if thecentralizers of its nonidentity elements are all equal. We discuss the equicentrali-zer subgroups of sporadic simple groups. Using the orders of centralizers of theelements and the structure of the maximal subgroups, we prove that the equicent-     

Simple Lie Algebras and Complete Lie Algebras

ＳｉｍｐｌｅＬｉｅＡｌｇｅｂｒａｓａｎｄＣｏｍｐｌｅｔｅＬｉｅＡｌｇｅｂｒａｓ＊）ＹａｎｇＱｉ（杨奇）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ，３０００７２）ＭｅｎｇＤａｏｊｉ（孟道骥）（Ｄ...     

Covering Numbers of the Sporadic Simple Groups

Let G be a finite nonabelian simple group. The covering number of G is the sm-allest integer n such that C~n=G for every nontrivial conjugacy class C of G andis denoted by cn(G). The extended covering number of G, denoted by ecn(G), is     

A Simple System with Topological Entropy Infinit

Ｌｅｔ（Ｘ，ｄ）ｂｅａｍｅｔｒｉｃｓｐａｃｅ，ａｎｄｆ：Ｘ→Ｘｂｅａｕｎｉｆｏｒｍｌｙｃｏｎｔｉｎｕｏｕｓｍａｐ．Ｗｈｅｎ（Ｘ，ｄ）ｉｓａｃｏｍｐａｃｔｍｅｔｒｉｃｓｐａｃｅ，ｐｅｏｐｌｅｂｅｌｉｅｖｅｔｈａｔｆｈａｓｐｏｓｉｔｉｖｅｔｏｐｏｌｏｇｉ...     

Simple Cohen–Macaulay Codimension 2 Singularities

In this article, we provide a complete list of simple isolated Cohen–Macaulay codimension 2 singularities together with a list of adjacencies which is complete in the case of fat point and space curve singularities.     

A Simple Multistart Algorithm for Global Optimization

1.IntroductionConsidertheunconstrainedoptimizationproblem:findx*suchthatf(x*)~caf(x),(1)wheref(x)isanonlinearfllnctiondefinedonW"andXCR".Ourobjectiveistofindtheglobalminimizeroff(x)inthefeasibleset.Withoutassuminganyconditionsonf(x)globaloptimizationproblemsareunsolvableinthefollowingsensefnoalgorithmcanbeguaranteedtofindaglobalminimizerofageneralnonlinearfunctionwithinfinitelymanyiterations.Supposethatanalgorithmappliedtoanonlinearfunctionf(x)producesiteratesxlandterminatesafterKiterations.…     

Simple nonstandard proofs of Daniell–Kolmogorov-type theorems

This brief note employs a proof technique essentially due to Lindstr?m, based on the Loeb measure construction, to obtain short and simple proofs of theorems of the Daniell?CKolmogorov type.     

Some Simple Estimates for the Singular Values of Matrices

Abstract We first provide a simple estimate for ||A~(-1)||_∞ and ||A~(-1)||_1 of a strictly diagonally dominant matrixA. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scalingwith a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness ofthe new bounds.     

On Injective Simple Modules Over a Noetherian Commutative Ring

It is proved in[1]that an injective simple module over a noetherian commu-tative ring must be projective.Because every noetherian ring R is a finite directsum of indecomposable rings,say R=R_1(?)…(?)R_n,every simple R-module Smustbe a simple R_i-module for some i and every R-homomorphismσ:M→S must sa-tisfyσ(R_jM)=0(j≠i).Thus it is easy to know theorem2 in[1]is equivalentto the following statement which can be proved much easier.     

Simple Poisson–Farkas Algebras and Ternary Filippov Algebras

We establish connection between the differentiably simple associative commutative algebras with unity and the simple Filippov algebras.     

Simple algorithms for decoding systematic Reed–Solomon codes

A simple algorithm for decoding nonsystematic Reed–Solomon codewords was proposed by A. Shiozaki and independently by S. Gao. We first exhibit the companion algorithm for decoding systematic Reed–Solomon codes. Next, we improve this algorithm into one that is identical to traditional Reed–Solomon decoding. The algorithm will then be adjusted to work with nonstandard Reed–Solomon codes. Finally, we modify the algorithm into one that decodes Reed–Solomon codes with erasures that is slightly more efficient than existing techniques.     

A Simple Stochastic Model of Air–Naval Combat

Consideration is given to a scenario where a fleet of ships, each armed with the same anti-aircraft weapon, is attacked by identical aircraft in line-ahead formation. It is assumed that each aircraft uses its weapon against one ship, but all ships use their weapons against each aircraft as it attacks in turn. A difference equation for the bivariate probability distribution of ship and aircraft casualties is obtained, and some analytic results are derived by decomposition of the problem. Using data from the sinking of the HMS Prince of Wales and HMS Repulse in World War II to estimate parameter values, a numerical solution of the difference equation is provided. A separate method for computing the ultimate or terminal form of the distribution is given.     

A Simple Proof of Dieudonn-Manin Classification Theorem

The Dieudonn-Manin classification theorem on φ-modules (φ-isocrystals) over a perfect field plays a very important role in p-adic Hodge theory. In this note, in a more general setting we give a new proof of this result, and in the course of the proof, we also give an explicit construction of the Harder-Narasimhan filtration of a φ-module.     

A Class of Regular Simple ω2-semigroups-Ⅱ

In this paper, we study regular simple ω2-semigroups in which D｜Es = Wd by the generalized Bruck-Reilly extension and obtain its structure theorem.     

On Simple ℤ2-Invariant and Corner Function Germs

Mathematical Notes - V. I. Arnold has classified simple (i.e., having no moduli for the classification) singularities (function germs), and also simple boundary singularities: function germs...     

Simple Harish-Chandra supermodules over the super Schrdinger algebra

We study the N=1 super Schrdinger algebra S in(1+1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper also describes the structure of all Verma supermodules and determines all simple Harish-Chandra supermodules over S.     

A Simple Analytical and Numerical Approach for Pricing Compound Options

A compound option is simply an option on an option. In this short paper, by using a martingale technique, we obtain an analytical formula for pricing compound European call options. Numerical results are given to explain some economic phenomenon.     

On Generators and Relations of Simple Groups of Lie Type

1. Introduction Let L be a simple Lie algebra over C, rank L>1, K a field, R.Steinberg proved a theorem (Cf.〔1〕 and 〔2〕 12.1) which leads to the definition ofUniversal Chevalley groups through generators and relations such that a simple Chevalley group is isomrphic to the quotient group of the corresponding Universal Chevalley group modulo its centre. Steiberg′s theorem playsan importent role in dealing with Chevalley groups.