Solution of a problem of Z. Daróczy,J. Jarczyk and W. Jarczyk and generalization of a theorem of R. Ger and T. Kochane

We generalize a theorem proved by R. Ger and T. Kochanek [4]. Hence we obtain the solution of a problem posed by Z. Daróczy, J. Jarczyk and W. Jarczyk [2].     

Contents of Vol.23 Ser.A

No.1入Iareh 2008 Applieation of a neural network optimization eombinatorial predietion model to 011一gas yield forecasting···················，··，··············‘········……DENG Ybng DU Zhi一min LUY‘n一ni(l) 5     

Contents of Vol.17 Ser.A

No.1　 March 2 0 0 2The Weak Exponential Asym ptotic Stability of Impulsive Differential SystemFeng Weizhen　 Chen Yongshao ( 1 )……………………………………………………………………………………Existence of a Single Rub- Impact Period- n Motion for the Rotor Systems with Rigid ConstraintsLi Qunhong　 L u Qishao ( 7)……………………………………………………………………………………………Positive Periodic Solution of Single Species Model with Feedback Regulation and Infinite DelayLi X…     

On the Distribution of the Limit of Products of I.I.D. 2×2 Random Stochastic Matrices

This article gives sufficient conditions for the limit distribution of products of i.i.d. 2×2 random stochastic matrices to be continuous singular, when the support of the distribution of the individual random matrices is finite.     

Contents of Vol.17

ArticlesThe Existence of Order-Preserving Coupling for Two-DimentionalDiffusion Processes...................... Wu Xianyuan (1)A Method to Determine the Ridge Parameter in Ridge Regression............................................................. Wang Mingjin and Wang Jinlong (7)Two New Relative Efficiency of the Parameter Estimatein the Growth Curve Model............................... Duan Qingtang and Gui Qingming (14)Another Approach to Stochastic Thiele's Differential Eq…     

On a Problem of A.C. Woods

ＯｎａＰｒｏｂｌｅｍｏｆＡ．Ｃ．ＷｏｏｄｓＺｈａｎｇＷｅｎｐｅｎｇ（张文鹏）（ＮｏｒｔｈｗｅｓｔＵｎｉυｅｒｓｉｔｙ，Ｘｉ＇ａｎ，Ｓｈａａｎｘｉ，７１００６９）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＰａｎＣｈｅｎｇｂｉａｏＲｅｃｅｉｖｅｄＪａｎ．１１，１９９４...     

On a Problem of D. H. Lehmer

The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the difference between a D. H. Lehmer number and its inverse modulo p （an odd prime）, A interesting mean square value formula is also given.     

On the Continuous Singularity of the Limit Distribution of Products of I.I.D. d×d Stochastic Matrices

This article gives sufficient conditions for the limit distribution of products of i.i.d. d×d random stochastic matrices, d finite and 2, to be continuous singular, when the support of the distribution of the individual random matrices is finite or countably infinite. Proofs are based on applications of the multivariate Central Limit Theorem.     

Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H ¨older estimates of harmonic functions on a class of connected post critically finite(p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket,the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.     

H ¨older Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H ¨older estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian ...     

Solution to a Problem of J.P.Hutchinson and P.B.Trow

Use of the Pigeonhole Principle to solve the following problem was discussed in several books, for example [1,2]. Suppose a player (e. g., tennis or chess) practices on d consecutive days, playing at least one game a day and a total of no more than b games where d相似文献   

Analytic solutions of P.D.E’s

The purpose of this paper is to explain the celebrated results by Cattabriga-De Giorgi [5], [6] on partial differential equations with constant coefficients in the space of real analytic functions. These results caught the mathematical world by surprise in the early 70’s, when solvability on convex domains was supposed to be very likely due to the enormous development of Functional Analysis. Now, 30 years later, we have a much easier understanding of them. In particular non-existence of solutions for inR _x1,y1,x2 ³ is explained in terms of complex analysis, by the absence of a fundamental system of neighborhoods ofR _x1,y1,x2 ³ in C _z1,z2 ² . On the other hand, existence of solutions inR ², the other main result of [6], also became elementary. It is a case of analytic solvability for all operators whose principal part is a product of a hyperbolic and an elliptic term. I dedicate this paper to the memory of Lamberto Cattabriga for his masterful example in Mathematics and life. To the memory of Lamberto Cattabriga     

A sharp inequality for the tail probabilities of sums of i.i.d. r.v.’s with dominatedly varying tails

Let F be a distribution function supported on (-∞, ∞) with a finite mean μ. In this note weshow that if its tail F = 1 - F is dominatedly varying, then for any γ＞ max{μ, 0}, there exist C(γ) ＞ 0 and D(γ) ＞ 0 such thatC(γ)nF(x) ≤ Fn*(x) ≤ D(γ)nF(x),for all n ≥ 1 and all x ≥γn. This inequality sharpens a classical inequality for the subexponential distributioncase.