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).     

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 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.     

ON THE ORDER OF APPROXIMATION FOR THE RATIONAL INTERPOLATION TO |x|

The order of approximation for Newman-type rational interpolation to |x| is studied in this paper. For general set of nodes, the extremum of approximation error and the order of the best uniform approximation are estimated. The result illustrates the general quality of approximation in a different way. For thespecial case where the interpolation nodes are xi= (i/n)(i= 1,2,…,n;r>0) , it is proved that the exact order of approximation is O(1/n),O(1/nlogn) and O(1/n), respectively, corresponding to O1.     

ON THE ORDER OF APPROXIMATION FOR THE RATIONAL INTERPOLATION TO ｜x｜

The order of approximation for Newman-type rational interpolation to |x| is studied in this paper. For general set of nodes, the extremum of approximation error and the order of the best uniform approximation are estimated. The result illustrates the general quality of approximation in a different way. For the special case where the interpolation nodes are $x_i = \left( {\frac{i}{n}} \right)^r (i = 1,2, \cdots ,n;r > 0)$x_i = \left( {\frac{i}{n}} \right)^r (i = 1,2, \cdots ,n;r > 0) , it is proved that the exact order of approximation is O( \frac1n ),O( \frac1nlogn ) and O( \frac1n^r )O\left( {\frac{1}{n}} \right),O\left( {\frac{1}{{n\log n}}} \right) and O\left( {\frac{1}{{n^r }}} \right) , respectively, corresponding to 01.     

PROOF OF A CONJECTURE RELATED TO THE PARABOLIC CLASS NUMBERS OF SOME FUCHSIAN GROUPS

This paper proves a conjecture given in [6], which is concerning with the parabolic class numbers of some Fuchsian groups.     

HOMOGENEOUS HYPERCOMPLEX STRUCTURES I–THE COMPACT LIE GROUPS

We obtain a complete list of homogeneous hypercomplex structures on the compact Lie groups. The substantial results are formulated and proved entirely in terms of the structure theory of Lie groups and algebras.     

ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.     

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.     

THE AUTOMORPHISMS OF NON-DEFECTIVE ORTHOGONAL GROUPS IN CHARACTERISTIC 2

Let V be a non-defective n-dimensional quadratic space over a field F of characteristic2.In this paper we prove that,when n≥6 with n≠8 and F≠F_2,any automorphism ofΩ(V)orO'(V)has the standard type Φ_g,sending σ to gσg~(-1),where g is a semilinearautomorphism of V which preserves the quadratic structure.Therefore the automorphismgroups Aut Ω(V) and Aut O'(V)are isomorphic to PΓO(V).As a corollary,Aut O(V)and Aut O~+(V) are isomorphic to PΓO(V)as well.     

THE EQUITYPE AND QUASI-EQUITYPE DECOMPOSITIONS OF PERMUTATIONS BY PERMUTATIONS OF ORDER 2 OR 3

In this papar,we give some conditions and methods about expressing an evenpermutation as a product of two equitype permutations of order 2 or 2; and expres-sing an odd permutation as a product of two quasi-equitype involutions.We provethat any even permutation can be expressed as a product of two equitypeinvolutions. And except one special case,any even permutation Can be expressedas a product of two equitype permutations of order 3.     

THE COMPLETE LANGLANDS PARAMETERS CORRESPONDING TO THE REPRESENTATIONS OF THE CLASSICAL GROUPS WITH INTEGRAL REGULAR INFINITESIMAL CHARACTERS

1.CompleteLanglandsParametersandL-PacketsInthissectionwereviewsomebasicfactsfrom[1].Wedenotethesetsofrealnumbers,complexnumbersandintegersbyR,CandZ,respectively.SupposethatGisaconnectedcomplexreductivealgebraicgroup.WehaveanextendedgrouPGrforG,andvGrisanE-groupforGr.WedenotethesetofLanglandsparametersandthesetofgeometricparametersforvGrbYp(vG')andX(VG'),respectively.ThereisanaturalmapfromP(VG')toX(vG').ItinducesabijectionfromequivalenceclassesofLanglandsparameterstogeometricparamet…     

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 EXISTENCE OF PERIODIC SOLUTIONS TO CERTAIN FOURTH ORDER DIFFERENTIAL EQUATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＴＯＣＥＲＴＡＩＮＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＦｅｎｇＣｈｕｎｈｕａ（冯春华）（ＧｕａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，广西师范大学，邮编：５...     

ON THE DISTRIBUTION OF THE VALUES OF MEROMOPHIC FUNCTIONS OF INFINITE ORDER

<正> ⅠNTRODUCTIONIn 1896,Borel established the well known theorem relative tothe distribution of moduli of values for an integral function f(z) offinlite positive order O“The exponent of convergence of the moduliof the zeros of f(z)-α is equal to Q for every constant α exceptpossiibly one value of α at most.”Afterwards he proved a moregeneral theorem in replacing a by an integral function π(z) of orderless than o. Concerning the distribution of argulnents o[" values fora meromorphic fumctionf(z) of finite positive order, Viliron discoveredin 1929 the existence of what he called “direction of Borel” and     

COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE ORTHOGONAL GROUPS

All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.     

2~2p~3阶群的构造

设G是2~2p~3阶群,S_2,S_p分别为G之sylow 2-群与sylow p-群,由于p≠3,S_pΔG,且S_p∩S_2=1,G=S_2S_p由ο(S_2)=4,知S_2或为循环群或为初等交换群,由ο(S_p)=p~3(p≠2),推出共有五种类型的群。 1.S_p=(?)Z_p, 由群之扩展理论,容易得到如下5个群:     

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS＊＊

The author investigates the hyper order of Solutions of the higher order linear equation, and improves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].     

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.