A CHARACTER OF A CLASS OF FUNCTIONS IN A SEMI-PLANE

Let ψ(r) is a positive function on [0, ∞),ψ(r)∞(r→∞), andLet φ is such function family that if φ(z)∈φ, then φ(z) is analytic in thesemi-plane Rez>0, continuous on Rez≥0, φ(z)≠0, and     

A BRAY-BRENDLE-NEVES TYPE INEQUALITY FOR A RIEMANNIAN MANIFOLD

In this paper,for any local area-minimizing closed hypersurface∑with RcΣ=RΣ/ngΣ,immersed in a(n+1)-dimension Riemannian manifold M which has positive scalar curvature and nonnegative Ricci curvature,we obtain an upper bound for the area of∑.In particular,when∑saturates the corresponding upper bound,∑is isometric to Sⁿand M splits in a neighborhood of∑.At the end of the paper,we also give the global version of this result.     

A Note of log A ≥log B

In this paper,firstty we shall show some equivalent conditions of A＞B＞0;secondly by using the results of ours we shall show some characterizations of the chaotic order(i.e.,log A≥log B)by norm inequalities.     

A CRACK PROBLEM WITH A BROKEN LINE INTERFACE

§０．ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒａｂｌｅｐｌａｎｅｃｒａｃｋｐｒｏｂｌｅｍｓｏｆｃｏｍｐｏｓｉｔｅｍｅｄｉａｆｏｒｔｈｅｃａｓｅｉｎｗｈｉｃｈｔｈｅｉｎｔｅｒｆａｃｅｉｓａｎｉｎｆｉｎｉｔｅｓｔｒａｉｇｈｔｌｉｎｅｗｅｒｅｓｔｕｄｉｅｄ...     

Some remarks concerning matrices of the form A–A′, A−1A′

Matrices and operators of the formA ^–1 A ^* have received a certain amount of attention in recent years. Here some of the literature is surveyed and the caseA ^–1 A is studied for complex matrices withA denoting the transpose ofA. A generalization ofA ^–1 A is introduced.

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Zusammenfassung Matrizen und Operatoren, die in der FormA ^–1 A ^* ausgedrückt werden können, sind in den letzten Jahren häufig studiert worden. Hier wird ein Ueberblick über Teil der relevanten Literatur gegeben und auch der FallA ^–1 A für komplexe Matrizen studiert, wobeiA die Transponierte vonA ist. Es wird auch eine Verallgemeinerung vonA ^–1 A eingeführt.

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Dedicated to Eduard Stiefel by a long time admirer     

A CORRECTION

<正> In my paper entitled'On the Poincaré's groups and the extendeduniversal coverings of closed orientable two-manifolds”,the conversepart of (i) of Number 7 is not valid and should be omitted.The firstplace where this conve(?)se part was used is in the proof of(iii)ofNumber 7.To make the correction,at the end of(i)of Number 5 wereplace“not reduced.”by“not reduced, but (u_(1,1)) (u_(1,2))is reduced”,and to(iii)of Number 5 we add“When u_(1,2) is not the(2p-1)st f.e.     

A NOTE ON A NONLINEAR BOUNDARYVALUE PROBLEM

Asiswellknown,nonlineartwo-pointboundaryvalueproblemisaclassicalbasicproblem.Theresultsofthisproblemareusuallyratherperfect.But,somenewproofsandimprovementsoftheseresultswillbeverymeaningfulandprofittherelatedproblem.Considerthefollowingboundaryvalueproblemwhereh(t,xl,x2)andf(t,xl,x2)arecontinuous,f(t,xl)x2)isboundedfortE[0,r],--co相似文献   

A Degeneracy Criterion for A∞-Structures

In the paper conditions are found under which the A-structure on the homology of a differential algebra degenerates. Examples of such algebras are given. In particular, it is shown that the A-algebra structure on the Milnor coalgebra degenerates, and that if the cohomology of a topological space is a polynomial algebra, then the A-algebra structure on it degenerates.     

A GENERALIZATION OF A RETARDED INEQUALITY AND ITS APPLICATIONS

We prove some new retarded nonlinear integral inequality and present its applications to the global existence of differential equations with delay.     

A HOPF INDEX THEOREM FOR A REAL VECTOR BUNDLE

The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.     

布尔矩阵广义逆A－ω，A－d，A－ω

设Ａ是布尔矩阵，而矩阵Ｇ满足ＡＧＡ＝Ａ．（１）如果对所有Ａｘ＝ｙ的向量ｘ，ｙ．有ω（Ｇｙ）≤ω（ｘ）（＊）称Ｇ是Ａ的一个极小权ｇ－逆，表示为Ａ－ω．（２）如果对所有向量ｘ，ｙ，有ｄ（ＡＧｙ，ｙ）≤ｄ（Ａｘ，ｙ）（＊＊）称Ｇ是Ａ的最小距离ｇ－逆，表示为Ａ－ｄ．（３）如果（＊）和（＊＊）都成立，就称Ｇ是极小权最小距离ｇ－逆，表示为Ａ－ωｄ．本文研究这三类广义逆矩阵的最大逆的存在性及表示式．主要结果如下：假定对于矩阵Ａ．Ａ－ω，Ａ－ｄ，Ａ－ωｄ分别存在，那么．（１）存在最大Ａ－ω，当且仅当Ａ中设有两个相同的非零列，且最大Ａ－ω为Ａω＝［ＩＣＡＴ］Ｃ．（２）最大Ａ－ｄ存在，且为Ａｄ＝［ＡＴＡＣＡＴ＋ＡＴ（ＪＡＴ）Ｃ］Ｃ．（３）存在最大Ａ－ωｄ，当且仅当Ａ的所有非零列向量线性独立，且最大Ａ－ωｄ为Ａωｄ＝［ＡＴＡｃＡＴ＋ＡＴ（ＪＡＴ）ｃ＋（ＡＴＪ）ｃＡＴ］Ｃ．其中Ｊ为全１矩阵     

A REMARK ON EXTINCTION OF A CLASS OF SUPERPROCESSES

1.IntroductionSuperprocesses,i.e.,measure-vauedMarkovprocesses,havebeenanattractivetopicintherecenty6ars,whichcanbedefinedasfollows.Let((,Px)..MbeaMarkovprocesswithstrongcontinuousMarkovsemigroupSt(denotebyAitsinfinitesimaloperator,andbyPt(x,y)theassociatedtransitiollfunction).DenotebyMPthesetofallRadonmeasurespsatisfyingandbypC(t)(resp.pCc(t))thesetofpositivelycontinuousfUnctions(resp.withcompactsupport)int-Thesthcalledsuperprocess(X,P#).6MPwithparameters(andopandtakingvalueinMrisdete…     

Nonnegative Rank Factorization of a Nonnegative Matrix A with A A ≥0

In this article we obtain a nonnegative rank factorization of nonnegative matrices A satisfying one or both of the following conditions: (i) AA ? ? 0 (ii) A ? A ? 0, thus providing a new set of conditions that guarantee the existence of a nonnegative least-squares solution of a linear system. Indeed, the characterization of such matrices improves some of the previous known conditions for the existence of a nonnegative least-squares solution of a linear system.     

关于A(A)的若干谱性质

根据共轭相似的定义和性质对A(A-)的性质作进一步的研究,特别是A(A-)的负特征值的分布的结论,将对研究共轭特征值的分布和正规矩阵的特征值分布有重大意义.     

A NOTE ON A COVERING LEMMA OF A CORDOBA AND R FEFFERMAN~(**)

This note simplifies Cordoba-Fefferman's proof on the weak boundedness of strong maximal operator M_8 (with respect to dμ) on L(1+log~(+(n-1))L). Some two-weighted boundedness results on L(1+log~(+α)L) of M_8 are investigated.     

A NOTE ON A CHARACTERIZATION THEOREM OF STRAUSS

Assume that B is a compact subset on the real axis containing at least n+1 points,C(B) the normed linear space of all continuous functions defined on B,with Chebyshevnorm‖·‖,and G=span(g_1,…,g_n) an n-dimensional subspace of C(B).LetG_R={g=sum from j=1 to n a_jg_j:v(x)≤g(x)≤u(x),q_i≤sum from j=1 to n d_(ij)a_j≤p_i for i=1,…,l}where u,v are extended real-valued functions on B subject to -∞≤v(x)相似文献   

A Graceful Numbering of A Class of Graphs

The graphs considered here are finite, undirected and simple. The sets ofvertices and edges of a graph G are denoted by V(G) and E(G), respectively.A graph G is called to be numbered if each vertex υ of G is assigned a nonnegative integer φ(υ), and each edge {u,υ} is assigned the absolute value of thedifference of the numbers at its endpoints, i.e.,|φ(u)-φ(υ)|.     

A SOBOLEV-HARDY INEQUALITY WITH APPLICATION TO A NONLINEAR ELLIPTIC EQUATION

In this paper, when μ< 1/4, and 2 0 and q=2(3-σ),the method is coming from the idea of Pohozaev.     

方阵A、B与AB的关系

利用方阵的Jordan分解与翻转矩阵等技巧,给出方阵A、B及其张量积AB性质间的关系.     

A BIOCHEMICAL OSCILLATION

In this note, we consider a simplest biochemical system that with only two chemical species and two cells. Higgins (1967) suppose that species X and Y react according to the scheme: