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     

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 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 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.     

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.     

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 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...     

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 UNIFIED APPROACH TO A CLASS OF STIRLING-TYPE PAIRS

ＡＵＮＩＦＩＥＤＡＰＰＲＯＡＣＨＴＯＡＣＬＡＳＳＯＦＳＴＩＲＬＩＮＧ┐ＴＹＰＥＰＡＩＲＳＸＵＬＩＺＨＩ（Ｌ．Ｃ．ＨＳＵ）ＡＮＤＹＵＨＯＮＧＱＵＡＮＡｂｓｔｒａｃｔ．Ｈｅｒｅｐｒｅｓｅｎｔｅｄｉｓａｕｎｉｆｉｅｄａｐｐｒｏａｃｈｔｏａｗｉｄｅｃｌａｓ...     

A NOTE ON A STRONG UNIQUENESS THEOREM OF SITRAUSS

In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient constraints.     

A Hamiltonian Game

1. Introduction F.Harary(1)introduced achievement games and avoidance games on graphs. A. Papaioannou (2) studied the achievement games for Hamilton-path(H-path,for short) and Hamilton-cycle (H-cycle, for short). In this paper, we will study the avoidance game for H-path and get the following result: Ifp≥5, B can win in the game.     

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:     

A Probability Anecdote

The use of probability ideas to solve apparently unrelated problems is a fascinating subject. Paul Erd(?)s is a noted exponent of such uses and has proved many results in analysis, number theory and combinatorics in this way. A famous example is Serge Bernstein's brilliant proof of Weierstrass's theorem on approximation of continuous functions by polynomials. Another example is the nondifferentiability of Brownian sample functions (of which a quick proof is due to     

A Combinatorial Problem

This formula is actually impractical for large n. However it seems not easy to sera closed form except for the particular case α=1. We hope the interested reader would like to try his hand at the evaluation or simplification of the summation mentioned above.     

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 NOTE ON A STRONG UNIQUENESS THEOREM OF STRAUSS

In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfyingcoefficient constraints.