Classification of Cartan Matrices of Hyperbolic Type

In the theory of finite dimensional semisimple Lie algebras,it is known thatthe Cartan matrix A=(a_(ij))_i~n, i=1 has the following properties: (1)a_(ii)=2,i=1,…,n; (2)a_(ij)≤0 for i≠j,a_(ij)∈Z; (3)a_(ij)=0 a_(ji)=0. Now if a matrix A=(a_(ij))_i~n,j\j=1 satisfies (1),(2),(3),then A is called     

On the Problem of Heilbron Type

ＯｎｔｈｅＰｒｏｂｌｅｍｏｆＨｅｉｌｂｒｏｎＴｙｐｅ￥ＴｉａｎＺｈｅｎｇｐｉｎｇ（田正平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＲｏｙａｌＨｏｌｌｏｗａｙａｎｄＢｅｄｆｏｒｄＮｅｗＣｏｌｅｇｅ，ＵｎｉｖｅｒｓｉｔｙｏｆＬｏｎｄｏｎ，Ｅｇｈ...     

Chaos for Subshifts of Finite Type

This paper deals with chaos for subshifts of finite type. We show that for any subshift of finite type determined by an irreducible and aperiodic matrix, there is a finitely chaotic set with full Hausdorff dimension. Moreover, for any subshift of finite type determined by a matrix, we point out that the cases including positive topological entropy, distributional chaos, chaos and Devaney chaos are mutually equivalent.     

Near Difference Sets of Type 2

Since cyclic difference sets have numerous important applications in thetheories as well as in the practice of experiment designs and communication, theyhave been studied in detail, and a certain number of generalizations andvariants have been investigated extensively. In 1973, H.J. Ryser proposed a     

Lie Bialgebras of Generalized Virasoro-like Type

In this paper, Lie bialgebra structures on generalized Virasoro-like algebras are studied. It is proved that all such Lie bialgebras are triangular coboundary.     

Inequalities of Fejér-Jackson Type

 We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of the classical Fejér-Jackson inequality: For all integers n ⩾ 2 and real numbers x ∈ (0,π) we have

On an Inequality of Jenkins Type

ＯｎａｎＩｎｅｑｕａｌｉｔｙｏｆＪｅｎｋｉｎｓＴｙｐｅ￥ＷｅｉＨａｎｂａｉ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２００４３３，Ｐ．Ｒ．Ｃ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐｅｐｅｒ，ｔｈｅａｕ...     

On a Class of Number Fields of Eisenstein Type

In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial xp ?m(m is p-th powerfree and p | m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.     

Lie Bialgebras of a Family of Lie Algebras of Block Type

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.     

On Generic Extensions of Representations of a Dynkin Quiver of Type D

The notion of generic extensions of representations of a Dynkin quiver plays a big role in the study of the structure of the corresponding quantum group. In this paper, we describe the generic extensions of a simple representation by any representation and that of any representation by a simple representation of a Dynkin quiver Q of type D.     

Second Order Complex Equations of Mixed Type

ＳｅｃｏｎｄＯｒｄｅｒＣｏｍｐｌｅｘＥｑｕａｔｉｏｎｓｏｆＭｉｘｅｄＴｙｐｅＳｕｎＨｅｓｈｅｎｇ（孙和生）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ）Ｐ．Ｏ．Ｂｏｘ８００９，Ｂｅｉｊｉｎ...     

Integrals of Cauchy Type in C Space

The earliest paper to study boundary behavior of the integrals of the Cauchy-Martinelli type was[1]. But up to the present, not many boundary behaviors for the integrals of the Cauchy-Fantappi type are discussed. In this paper, we study the boundary behavior for the following form     

Generalization of Weighted Weak Type Hardy Inequalities

;1 .Ifltroduetion and Result In「l」,侧ghted姗k tyPe Hardy 111叫ualities认屺re comide代d,wllel℃the Hal.dy operatorP始de血edbyPf、一户(tM艺以妻0)111 this 11ote,忧co愁ide1’ genel.al Hal-dy operatort恤Haldy oP的tor .The侣ult认as follo桃. Thco泊n Lct声￡beaPositiveBo旧111“Isu犯l0 for all、>0 andand obtain weigllted场咫ak type In叫ualit咄foron R wlixeh认finite onl)ounded se认and ICt、(x)一击工,月,dltthen there 15 a constant A sucll that for allf‘夕(。d一‘)and只>…     

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.     

Characterizations of Bochner–Krall Orthogonal Polynomials of Jacobi Type

Let $\{P_n(x) \}_{n=0}^\infty$ be an orthogonal polynomial system relative to a compactly supported measure. We find characterizations for $\{P_n(x) \}_{n=0}^\infty$ to be a Bochner--Krall orthogonal polynomial system, that is, $\{P_n(x) \}_{n=0}^\infty$ are polynomial eigenfunctions of a linear differential operator of finite order. In particular, we show that $\{P_n(x) \}_{n=0}^\infty$ must be generalized Jacobi polynomials which are orthogonal relative to a Jacobi weight plus two point masses.     

Fixed Points of Sequence of Ćirić Generalized Contractions of Perov Type

Perov used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article, we study fixed point results for the new extensions of sequence of ?iri? generalized contractions on cone metric space, and we give some generalized versions of the fixed point theorem of Perov. The theory is illustrated with some examples. It is worth mentioning that the main result in this paper could not be derived from ?iri?’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.     

The Order of Hypersubstitutions of Type （2, 2）

Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type （2, 2）, i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type （2, 2）. The main result is that the order is 1, 2, 3, 4 or infinite.     

Knuth’s Coherent Presentations of Plactic Monoids of Type A

We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations amongst the relations. Such extended presentations are used for representations of monoids, in particular, it is a way to describe actions of monoids on categories. Moreover, a coherent presentation provides the first step in the computation of a categorical cofibrant replacement of a monoid. Our construction is based on a rewriting method introduced by Squier that computes a coherent presentation from a convergent one. We compute a finite coherent presentation of a plactic monoid from its column presentation and we reduce it to a Tietze equivalent one having Knuth’s generators.     

On Weak Solutions of a Class of Variational Inequalities of Parabolic Type7

§ 1.Ｐｒｅｌｉｍｉｎａｒｙ　ＬｅｔＥｂｅａｒｅｆｌｅｘｉｖｅＢａｎａｃｈｓｐａｃｅｗｉｔｈａｎｏｒｍ‖·‖ ,Ｅ′ｉｔｓｄｕａｌｓｐａｃｅａｎｄ〈· ,·〉ｔｈｅｐａｉｒｂｅｔｗｅｅｎＥ′ａｎｄＥ .ＳｕｐｐｏｓｅｔｈａｔＨｉｓａＨｉｌｂｅｒｔｓｐａｃｅｗｉｔｈｔｈｅｎｏｒｍ |·|ａｎｄｉｎｎｅｒｐｒｏｄｕｃｔ (· ,·)ｓｕｃｈｔｈａｔＥ Ｈ Ｅ′ ,( 1°)ｗｈｅｒｅｔｈｅｆｏｒｍｅｒｓａｒｅｄｅｎｓｅｉｎｔｈｅｌａｔｔｅｒｓａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｉｄｅｎｔｉｃａｌｍａｐｓａｒｅｃｏｎｔ…     

The Limits of a Chebyshev Type Theory of Restricted Range Approximation

Define two extended real-valued functions l(x)and u(x)on X≡[0,1]subjectto the following restrictions: (i)-∞≤l(x)相似文献