带有免疫反应的病毒动力学模型的全局稳定性

利用Lyapunov函数研究了带有免疫反应的病毒动力学模型的全局稳定性.当基本再生数R0≤1时.病毒在体内清除;当R0>1时,病毒在体内持续生存.并且模型的正解当免疫再生数R1≤1时,趋于无免疫平衡点,当R1>1.趋于地方病平衡点.     

等比数列的一个性质

文 [1 ]给出了等差数列的一个性质 :设 {an}是以 d为公差的等差数列 ,则有a1+ a2 +… + ann =am+ 1+ am+ 2 +… + an-mn - 2 m .本文运用类比的方法 ,得到等比数列的一个类似的性质 .性质　设 {an}是公比为 q( q>0 )的等比数列 ,则有( a1a2 … an) 1n =( am+ 1am+ 2 … an-m) 1n-2 m,其中 n >2 m.证明　当 n为奇数时 ,n- 2 m也为奇数 .( a1. a2 .… . an) 1n　 =( a1. a1q . a1q2 .… . a1qn-1) 1n　 =( an1. q1+ 2 + 3 +… + n-1) 1n,　 =( an1. qn( n-1)2 ) 1n =a1. qn-12 .( am+ 1. am+ 2 .… . an-m) 1n-2 m　 =( a1qm . a1qm+ 1.… . a…     

与Seyfert星系NGC3516成协的X射线源的光学光谱证认*——非宇宙学红移的可能证据

为了检验有关类星体红移本质的争论 ,研究了Seyfert星系NGC35 1 6周围的6个X射线源 ,对其中的 5个源进行了光谱观测 .观测结果和已知结果表明S1 1 0 2 +72 46 ,S1 1 0 8+ 72 2 6 ,Q1 1 0 6 + 72 44,Q1 1 0 5 + 72 42 ,Q1 1 0 5 + 72 38和Q1 1 0 7+ 72 32是红移分别为 0 .0 89,0 .32 8,0 .6 90 ,0 .92 9,1 .399和 2 .1 0的活动星系核 .这些活动星系核的一些特殊性质倾向于支持类星体有非宇宙学红移的理论 .     

四边形的内接三角形的一个性质

图1我们先了解关于圆内接三角形的一个性质.如图1,△x1y1z1为⊙O的内接三角形,P为圆内一点,x1P、y1P、z1P与圆分别交于x2、y2、z2.则△x1y1z1△x2y2z2=Px1·Py1·Pz1Px2·Py2·Pz2.注本文等式中的“△xyz”均表示△xyz的面积.简证设⊙O的半径为R,连z1O并延长交圆于y1′,连x1y1′,则∠x1y1z1=∠x1y1′z1.于是△x1y1z1=12x1y1·y1z1·sin∠x1y1z1=12x1y1·y1z1·sin∠x1y1′z1=12x1y1·y1z1·x1z12R=14Rx1y1·y1z1·x1z1.同理△x2y2z2=14Rx2y2·y2z2·x2z2.故△x1y1z1△x2y2z2=x1y1·y1z1·x1z1x2y2·y2z2·x2z2=     

一类全纯映射的增长性

§ 1.　NotationsandFormulas　　Let(N ,dS2 N)beaHermitianmanifoldofdimensionn ,anddS2 NitsHermitianmertric.Let{e1～ ,Λen～}oftype (1 ,0 )tangentvectorsconstitutealocalunitaryframefieldinanopensetofM .Let{ω1 ,Λωn}betheunitarycoframewhichconsistsofncomplex valuedlineardifferen tialformsoftype (1 ,0 )suchthatdS2 N =ωαω-α. (1 )Hereandbelowthesummationconventionisused ,i.e .,therepeatedindexmeanssummation .LetBbethebundleofallunitaryframesofN .Thentheforms{ωα}areformsinB .Itiswellkn…     

Sn+1(1)内凸超曲面为边界的区域的第一特征值估计

M是Sn+1(1)内紧致嵌入凸超曲面.M分Sn+1(1)为两个连通区域Ω1和Ω2. Ω1=M和Ω1是凸的.本文估计了Ω1的Laplace算子的第一特征值的下界.     

关于局部双全纯映射的推广的Roper-Suffridge算子

§ 1.　Introduction　　LetUbetheunitdiskinCandBnbetheunitballinCn.In 1 995 ,RoperandSuffridgeintroducedanextensionoperator.ThisoperatorisdefinedforanormalizedlocallybiholomorphicfunctionfonUbyΦn(f) (z) =F(z) =(f(z1 ) ,f′(z1 )z′) ,z =(z1 ,z′)∈Bn,(1 .1 )wherez1 ∈U ,z′=(z2 ,… ,zn)∈Cn- 1 ,andthebranchofthesquarerootischosensuchthatf′(0 ) =1 .TheRoper Suffridgeextensionoperatorhasthefollowingimportantproperties:(a)IffisanormalizedconvexfunctiononU ,thenFisanormalizedconvexmappingon…     

基于逻辑斯缔映射的三参数混沌动力学系统的行为研究

基于逻辑斯缔映射的三参数混沌动力学系统为 xn+1=μxn(1 -xλn+c) .本文讨论了参数λ∈ (0 ,5 .2 ) ,μ∈ (0 ,1 2 .8) ,0 <|c| 1 .1 5 条件下该系统的行为特性 .在用计算机模拟 0 >c -1 .1 5 条件下该系统的行为时 ,发现了嵌入周期 1 轨道中的混沌动力学过程 .该过程显现出一种通向混沌的新途径 ,混沌区内部具有特殊的秩序结构     

两总体的逐步统计分辨数学模型及其应用

本文介绍了基于马氏准则下逐步统计分辨数学模型的基本原理 .对山东省胶南市 1 985～ 1 994年共 1 0年的第二代玉米螟百株累计卵量及其影响因素的历史观测数据资料进行了数量分析 ,建立了 4个逐步统计分辨数学模型 :Y1( X) =-4 2 .7655X1+0 .0 357X2 -2 .731 5X3Y2 ( X) =-2 7.74 58X1-0 .0 50 6X2 -2 .1 548X3Y3( X) =-62 .0 1 1 0 X1-0 .1 668X2 -2 .4 681 X3Y4 ( X) =-1 9.550 7X1-0 .0 94 0 X2 -1 .3831 X3运用这些模型 ,对历史资料进行回报验证 ,其历史符号率分别为 90 %、1 0 0 %、1 0 0 %、90 % .将 1 995、1 996两年观测数据作为独立样本进行试报 ,其预报结果与实际一致 .     

矩阵的特征向量的摄动

<正> 考虑下述问题R_1=AQ_1-Q_1T_1,其中,A 为 n 阶方阵,T_1为 m 阶方阵 (m相似文献   

A Note on c-Supplemented Subgroups of Finite Groups

A subgroup H of a finite group G is said to be c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is contained in H _G , where H _G is the largest normal subgroup of G contained in H. In this article, we prove that G is solvable if every subgroup of prime odd order of G is c-supplemented in G. Moreover, we prove that G is solvable if and only if every Sylow subgroup of odd order of G is c-supplemented in G. These results improve and extend the classical results of Hall's articles of (1937) and the recent results of Ballester-Bolinches and Guo's article of (1999), Ballester-Bolinches et al.'s article of (2000), and Asaad and Ramadan's article of (2008).     

A Note on Large Characteristic Subgroups

It is known that if a group G has an abelian subgroup of finite index n, then it contains an abelian characteristic subgroup A of index at most nⁿ. The aim of this paper is to improve this bound by showing that the characteristic subgroup A can be chosen of index at most n². Examples prove that this bound is the best possible. Our main result is obtained as an application of a general method for the construction of large characteristic subgroups.     

Cuccia定理的一个推广

For a finite group G,let S(G)be the set of minimal subgroups of odd order of G which are complemented in G.It is proved that if every minimal subgroup X of odd order of G which does not belong to S(G),C_G(X)is either subnormal or abnormal in G.Then G solvable.     

A Note on Solitary Subgroups of Finite Groups

We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups.     

一类可解的（q）－群

有限群Ｇ叫（ｑ）－群，如果Ｇ中每个次正规子群均为拟正规子群，群Ｇ叫Ｅｑ－群，若Ｇ中每个子群在Ｇ中拟正规或自正规，有限群Ｇ叫内Ｅｑ－群，如果Ｇ本身不是Ｅｑ－群，但Ｇ的每个真子群是Ｅｑ－群，本文确定了Ｅｑ－群的结构与内Ｅｑ－群的分类．     

有限群的Fuzzy次正规子群与Fuzzy极大子群

本文研究了有限群的Ｆ次正规子群，得出了一个Ｆ子群是Ｆ次正规子群的充要条件，讨论了Ｆ次正规子群的一些重要性质。另外，本文还引入了有限群的Ｆ极大子群的概念，给出了Ｆ子群是Ｆ极大群的充要条件。最后，给出了三个定理，讨论了有限群Ｇ可解、超可解、幂零与Ｇ的Ｆ次正规子群、Ｆ极大子群之间的联系。     

A Generalized Hughes Property of Finite Groups

Abstract

A Hughes cover for exponent p(pa prime number) of a finite group is a union of subgroups whose (non-empty) complement consists of elements of order p. A proper Hughes subgroup is an instance of a Hughes cover; and its parent group is soluble by a well-known result of Hughes and Thompson. More generally an earlier result of the authors shows that a group with a Hughes cover of fewer than psubgroups is soluble. This article treats the insoluble groups having a Hughes cover for exponent pwith exactly psubgroups: the almost simple groups with this property form a restricted class of projective special linear groups.     

Parabolic subgroups of Vershik-Kerov's group

In this note we show that all parabolic subgroups of Vershik-Kerov's group (i.e. subgroups containing --the group of infinite dimensional upper triangular matrices) are net subgroups for a wide class of semilocal rings .

     

Frattini子群的推广

本文研究了任意群G的Fratini子群Frat(G)的两种推广形式fnFrat(G)和fcFrat(G),得到了这两类子群与Frat(G)类似的相关性质.     

关于“L—Fuzzy群同态与同构及其性质”一文的注记

文（１）给出了Ｌ－Ｆｕｚｚｙ群间的同态映射，满同态映射以及Ｌ－Ｆｕｚｚｙ群的Ｌ－正规子群等概念。本文指出以上三种定义的不合理性，并给出它们的合理性定义。