A NOTE OF THE SPECTRUM OF HOMOGENEOUS COMPACT OPERATORS

In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.     

THE APPLICATION OF STABLE GROUPS TO BIOLOGICAL STRUCTURES

The properties of the stable group theory are discussed. The mathematical models of the insect legs, a pair of hands, and human chromosomes are established using stable group theory. The two postulates: the prime-number principle and the symmetric principle, and a new evolution theory in the biology are suggested. The brain structures and the structures of the nervous system can be studied using above two principles.     

THE INVARIANT CONTINUOUS-TRACE C^＊-ALGEBRAS BY THE ACTIONS OF COMPACT ABELIAN GROUPS

1.IntroductionLet(A,G,a)beaC*-dynamicsystem.TherelationbetweenAxosGandAhasbeenstudiedforalongtime,andconsiderableprogresshasbeenmade.SpeciallyifAisacontinuous-traceC*-algebra,I.Raeburnandhiscollaboratorsgotrichresultsseveralyearsago.Forexample,[17]and119]saythatifAisparacompact,Gisabelianandaislocallyunitary,thenAiscontinuous-traceiffAxosGiscontinuous-trace.Inotherdirection,therelationbetweenAxosGandA"withGcompacthasalsobeenstudiedformanyyears.Themovementofthispaperistoinvestigatethec…     

THE STRUCTURES OF GROUPS OF ORDER 2~3P~2

In this paper,the following theorem is proved:Let p be a prime distinet from 3 and 7,then the groups of order 2~3 p~2 have1)60 types when p=1(mod 8),2)52 types when p=5(mod 8),3)42 types when p=3,7(mod 8).     

ON THE SUBGROUP LATTICE CHARACTERIZATION OF FINITE SIMPLE GROUPS OF LIE TYPE

Any finite simple group of Lie type is proved to be determined by its subgroup lattice up to isomorphism.     

JACKSON‘S THEOREM FOR COMPACT GROUPS

In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut^-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.     

CONVERGENCE OF A CLASS OF MEANS OF H~p FUNCTIONS(0

《分析论及其应用》1993,(4)

MINIMAL SURFACES IN 3—DIMENSIONAL SOLVABLE LIE GROUPS

The author studies minimal surfaces in 3-dimensional solvable Lie groups with left invariant Riemannian metrics. A Weierstraβ type integral representation formula for minimal surfaces is obtained.     

ADDENDUM TO“THE STRUCTURES OF GROUPS OF ORDER 2~3p~2n

The present paper is a complement to the paper[1].It is proved that groups oforder 2~37~2 have 44 types.     

ALGEBRAIC GROUPS ASSOCIATED WITH GRADED LIE ALGEBRAS OF CARTAN TYPE

§０．ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｋｎｏｗｎｔｈａｔｏｖｅｒａｌｇｅｂｒａｉｃａｌｙｃｌｏｓｅｄｆｉｅｌｄｓｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃ０，ｔｈｅｒｅｅｘｉｓｔｓａｇｏｏｄｃｏｒｅｓｐｏｎｄｅｎｃｅｂｅｔｗｅｅｎｔｈｅｃｏｎｎｅｃｔｅｄ...     

MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

In this note,we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups).Firstly we show an (H^1,L^q)multiplier result.We also give an (Ha^p,Ha^p)multiplier results under a similiar condition of Lu Yang type ,In section 2,we obtain a result about the boundedness of multipliers on weighted Besov spaces.     

THE MORSE CRITICAL GROUPS OF THE MINMAX THEOREM

The author gives a new min-max theorem and studies the local homology propertiesof critical points that is got by min-max theorem.In particular,this result includes manymin-max theorem of link type,which can be applicable to nonlinear analysis.     

TWO-DIMENSIONAL SINGULAR INTEGRAL EQUATIONS OF THE HYPERCOMPLEX FUNCTIONS

ＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＥＱＵＡＴＩＯＮＳＯＦＴＨＥＨＹＰＥＲＣＯＭＰＬＥＸＦＵＮＣＴＩＯＮＳ（刘春根）￥ＬｉｕＣｈａｎｇｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈＮａｎｋａｉＵｎｉｖ．，Ｔｉａｎｊｉｎ５００７１，Ｃｈｉｎａ．...     

MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

In this nate we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L2) multiplier result. We also give an (H(?),H(?)) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.     

THE SPECTRUM OF THE LAPLACE OPERATION ON COMPACT SUBMANIFOLDS

1IntroductionLetiM.g)beac0mpactn-dimensi0nd1Riemannianmanffold.ByAwedenotetheLaplacianartingonpf0rnaonM.Thenwehavethespectrumforeachp:Oneoftlieprob1emonspectraisasf0110ws:Let(M,g)and(M,g)becompactoritabieRicmannianmanif01dswithSpecp(M.g)=Specp{M-g),thenis(M,g)isometricto(M-j)?Thisprob1emisprovedtobewrongbyJ.Milnorin1964.Butwhen(M,g)and(M.g)aresonlespecialffiemannianmanifolds.undercertainconditi0ns.wecanprovethat(M.g)'sisometricto{M.j).Foran-din1ensi0nsubmanitbldMinSN,wedenotetheleng…     

THE CHARACTER TABLE OF SYMMETRIC GROUPS

This paper gives two methods to construct simultaneously the character tables of thesymmetric groups■_(n-1),■_n,and ■_(n+1)with the aid of the character table of ■_(n-2)as well asthe author's formulae cited in[9].These methods require merely the rational operation ofintegers.     

ON THE DEFORMATION OF SOME LIE ALGEBRAS

Suppose (L[]) be a real or complex Lie algebra. We prove in this paper the following results, 1. Lie algebra L is semisimple, if and only if every deformation of L is semisimple; 2. when dim L=3, the nontrivial deformation of L exists if and only if dim [LL]≠3.     

SPECTRUM OF THE LAPLACIAN OF COMPACT MANIFOLDS

ＳＰＥＣＴＲＵＭＯＦＴＨＥＬＡＰＬＡＣＩＡＮＯＦＣＯＭＰＡＣＴ　ＭＡＮＩＦＯＬＤＳ￥ＸｕＳｅｎｌｉｎ（徐森林）ＣｈｅｎＣｈｕｎｓｈｅｎｇ（陈春生）ＺｈａｎｇＨｅａｄｉｎｇ（张华明）ＣｈｅｎＧｕａｎｇｈｕａ（陈广华）（Ｄｅｐｔ．ｏｆＸａｔｈ．，Ｕｎｉｖ...     

THE GROUPS OF ORDER qn · p

We describe a method to determine up to isomorphism the groups of order q ⁿ · p for a fixed prime-power q ⁿ and indeterminate prime p ≠ q. We report on the explicit construction of all groups of order 2 ⁿ · p for n ≤ 8 and 3 ⁿ · p for n ≤ 6. In particular, we show that there are 1 090 235 groups of order 768.