R3中一类二次系统的5个极限环

建立了联系R3中一类二次系统与二维流形球面S2的切向量场之间的桥梁,证明了R3中一类二次系统存在5个极限环,而且这5个极限环分别位于该系统的5个不变闭锥上.     

变换乘积与证题(二)

<正>3四次旋转变换的乘积定理4不同中心的四个旋转满足R(A1,90°)R(A2,90°)R(A3,90°)R(A4,90°)=I,则A1A3与A2A4垂直且相等.证明R (A1,90°)R (A2,90°)=R (O,180°).如图14,依定理2,∠A1OA2=90°,∠OA_1A_2=∠OA_2A_1=45°,     

R~3中一类二次齐次向量场的大范围几何性质

本文通过对R3中一类二次齐次向量场的全局分析，得到了正确分析R3中齐次向量场Q（x）（x∈R3）的切量场QT（u）（u∈S2）在球面S2上的拓扑分类的方法，指出了习惯上分析切向量场QT（u）的拓扑分类的一种错误。     

R^3中广义次仿射弹性曲线

本文用Killing场和sl(3,R)的共轭类分类给出了R^3中的广义次仿射弹性曲线，即全多项式次仿射曲率泛函的临界点的完全解。     

R3中一类四次可逆系统的周期轨与极限环问题

本文研究了R3中一类四次可逆系统及其扰动系统的周期轨与极限环问题,利用Poincáre紧化理论讨论了相关平面系统的定性性质,证明了所考虑的系统存在无穷多对称周期轨的结论.然后借助一系列技巧性变换,并利用平均方法证明了R3中这类四次可逆系统的扰动系统在其某周期轨邻域至少存在两个具有不同稳定性的极限环的结论.     

强分次环与非分次模范畴

设R是强群G-分次环,日是G的指数有限的子群.本文讨论强分次环R上一般非分次模的一些性质.首先证明一个与非分次R-模和R(H)-子模有关的Maschke-type定理,然后证明从模范畴R(H)-mod到R-mod的函子HomR(H)(R,-)与R(?)R(H)-是一对自然同构的函子以及等价条件.     

涉及三角形内部一点的几个不等式

在文[1]中,褚小光建立了下述几何不等式:设△ABC内部(包括边界,下同此)任意一点P到顶点A,B,C的距离分别为R1,R2,R3,三边BC,cA,AB的长分别为a,b,c.则 a2R1+b2R2+c2R3≥(R2+R3)(R3+R1)(R1+R2),①等号当且仅当P点位于△ABC的边上时成立.     

一类具临界指数增长的Schrödinger-Poisson系统正解的多重性

本文研究如下非线性Schrdinger-Poisson系统正解的存在性、多重性及集中性,{-ε2△u＋V（x）u＋φu=u2＊-1＋f（u）,x∈R3,-ε2△φ=u2,u（x）〉0,x∈R3,其中ε〉0为参数,V是一个下方有界的正连续位势函数,f是一个次临界的非线性项,2＊=6是R3中的临界指数.利用位势V在全空间的最小值点集的Ljusternik-Schnirelmann畴数性质,结合变分法我们得到了该系统多个正解.     

综合题新编选登

题152 已知a，b，c∈R且三次方程f（x）=x^3-ax^2＋bx-c有三个实根x1，x2，x3。     

一类特殊形状函数的原函数的求法

本文给出函数 P(x)e~(αx)cosβx+Q(x)e~(αx)sinβx的原函数的一种求法,其中P(x)与Q(x)为多项式,α与β为常数,至少有一个不等于零。所给方法计算比较简单,也比较有规律。 1.∫P(x)e~(αx)dx的计算。设P(x)为n次多项式,把P(x)写成:我们研究函数P(x)e~(αx)是否有形如R(x)e~(αx):的函数为原函数。设有 [R(x)e~(αx)]′=P(x)e~(αx),(3)则 [R′(x)+αR(x)]e~(αx)=P(x)e~(αx),即 R′(x)+αR(x)=P(x)。(3′)将R(x)与P(x)的表达式(1)与(2)代入式(3′),得由于式(3″)对x为恒等式,故x的同次冪的系数相等,即由上式中解出α_0与α_k,得由(4)确定的α_k(k=0,1,2,…,n)满足式(3′),因而满足式(3)。所以我们证明了对函数P(x)e~(αx)存在着形如R(x)e~(αx)的函数为其原函数。由于α_0=c_0/α≠0,故R(x)的次数与P(x)的次数相同,而且R(x)的系数     

A new flow on starlike curves in

In this note we find a new evolution equation for starlike curves in . We study the evolution of the subaffine curvature and subaffine torsion under the flow and show that it is completely integrable. The solutions to the evolution which move without changing affine shape are subaffine elastic curves. We integrate the subaffine elastica by quadratures.

     

平面上的星形仿射弹性曲线

次仿射弹性曲线是全平方次仿射曲率泛函的临界点.该文对平面上的星形仿射曲线进行了研究，用椭圆函数的方法解出了次仿射弹性曲线的次仿射曲率，并运用Killing 场和sl(2, R)的共轭类分类用积分给出了次仿射弹性曲线的完全解.     

R2中广义次仿射弹性曲线的一个注记

§1 .　IntroductionTheclassicalelastictheorydealswithacurveinR2 orR3 whichisacriticalpointforthetotalsquaredcurvaturefunctionalonregularcurveswithfixedlengthsatisfyinggivenboundaryconditions.ThiscouldtracebacktoDanielBernoulli( [1]) .Duringrecenttwodecades,severalauthors( [2 ],[3],[4 ])consideredthegeneralizationsoftheelasticatothespaceforms.ThispaperdealswiththeaffinestarlikecurvesinR2 .Westudythecriticalpointforthetotalpolynomialsubaffinecurvaturefunctionalonthosestarlikecurvessatisfyingg…     

Zur Theorie Subaffiner Inzidenzgruppen

Starting with an axiomatic characterisation of subaffine incidence spaces, some basic theorems on subaffine incidence groups are proved. Desarguesian subaffine incidence groups are characterized by NB-nearmodules, and local algebras are characterized by special subaffine incidence groups. It is proved that desarguesian twosided strict subaffine incidence groups are represented by bilocal algebras.     

Ideal-Based k-Zero-Divisor Hypergraph of Commutative Rings

Let R be a commutative ring,I an ideal of R and k ≥ 2 a fixed integer.The ideal-based k-zero-divisor hypergraph HkI(R) of R has vertex set ZI(R,k),the set of all ideal-based k-zero-divisors of R,and for distinct elements x1,x2,…,xk in ZI(R,k),the set {x1,x2,…,xk} is an edge in HkI(R) if and only if x1x2…xk ∈ I and the product of the elements of any (k-1)-subset of {x1,x2,…,xk} is not in I.In this paper,we show that H3I(R) is connected with diameter at most 4 provided that x2 (∈) I for all ideal-based 3-zero-divisor hypergraphs.Moreover,we find the chromatic number of H3 (R) when R is a product of finite fields.Finally,we find some necessary conditions for a finite ring R and a nonzero ideal I of R to have H3I (R) planar.     

交换主理想整环上立方幂等矩阵的线性保持

设Ｒ（≠Ｆ_３）是特征不为２的交换主理想整环,Ｍ_ｎ（Ｒ）定义Ｒ上的ｎ×ｎ矩阵模,本文刻划当ｎ≥ｍ时从Ｍ_ｎ（Ｒ）到Ｍ_ｎ（Ｒ）的保持立方幂等矩阵的线性映射的形式,由此推广了Ｃｈａｎ和Ｌｉｍ的一个结果（［１,定理３］）．     

GL_2 OVER FULL RINGS

In this paper the authors generalize the result of B.R.McDonald.The following resultis obtained.Let R be a(1,6)-full ring,or(3,3)-full ring,or(2,4)-full ring,and R has theproperty T.G is an SL_2(R)-normal subgroup of GL_2(R).Then there is an ideal A in Rsuch thatSC(R,A)(?)G(?)GC(R,A).     

关于拟平坦模的几个注记

本文所有的环均指有单位元的环,模均指酉模。左R-模M称为拟内射的,如果对任意N相似文献   

Appell Bases for Monogenic Functions of Three Variables

Monogenic (or hyperholomorphic) functions are well known in general Clifford algebras but have been little studied in the particular case ${\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}}$ R 3 → R 3 . We describe for this case the collection of all Appell systems: bases for the finite-dimensional spaces of monogenic homogeneous polynomials which respect the operator ${D = \partial_{0} - \vec{\partial}}$ D = ? 0 ? ? → . We prove that no purely algebraic recursive formula (in a specific sense) exists for these Appell systems, in contrast to the existence of known constructions for ${\mathbb{R}^{3} \rightarrow \mathbb{R}^{4}}$ R 3 → R 4 and ${\mathbb{R}^{4} \rightarrow \mathbb{R}^{4}}$ R 4 → R 4 . However, we give a simple recursive procedure for constructing Appell bases for ${\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}}$ R 3 → R 3 which uses the operation of integration of polynomials.     

9个经典Ramsey数R(3,t)的新下界

本文研究了经典Ramsey数R(3,t)的下界问题.利用素数阶循环图的性质改进一般阶循环图团数的计算方法,获得了9个经典Ramsey数R(3,t)的新下界:R(3,29)≥183,R(3,30)≥189,R(3,32)≥213,R(3,33)≥218,R(3,34)≥226,R(3,35)≥231,R(3,36)≥239,R(3,37)≥244,R(3,38)≥256,其中前三个结果分别改进了迄今已知的最好的下界,后6个结果是本文首次报道的.