Some Q-Q Probability Plots to Test Spherical and Elliptical Symmetry

Abstract

This article proposes some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations. Some correlation coefficients as numerical measures of detecting deviation from spherical or elliptical symmetry are recommended, and the empirical percentiles of these correlation coefficients are calculated by simulation. The simulation results for data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also.     

Multipliers and Herz type spaces

Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced.     

On the behavior of the oscillatory solutions of first or second order delay differential equations

Some new results are given concerning the behavior of the oscillatory solutions of first or second order delay differential equations. These results establish that all oscillatory solutions x of a first or second order delay differential equation satisfy x(t)=O(v(t)) as t→∞, where v is a nonoscillatory solution of a corresponding first or second order linear delay differential equation. Some applications of the results obtained are also presented.     

On some multi-dimensional quadrature formulas with number-theoretic nets

In the present paper some multi-dimensional quadrature formulas of periodic functions are established by means of the number-theoretic method. Some results of Hua and Wang^[2] are generalized or improved.This project is supported by the National Natural Science Foundation of China.     

一些结构线性系统的SBE与P-SBE的比较

很多重要的结构矩阵都属于Rn或Cn上纯量积定义的Jordan代数J或者是Lie代数L.本文比较线性系统AX=B关于近似解的范数型结构向后误差(SBE)与偏结构向后误差(P-SBE).这里系数矩阵A∈J或A∈L.在给出若干预备性结果后,先对单右端项情形比较SBE与P-SBE,然后对多右端项情形比较.部分结果是Sun近期的一些结果的推广.     

Some applications of Briot—Bouquet differential subordination

Some applications of Briot—Bouquet differential subordination are obtained which improve or extend a number of classical results in the univalent function theory.     

Wick calculus for nonlinear Gaussian functionals

This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the S-transform which is also described without the introduction of generalized random variables.     

On the approximation of the continuous functions by some Hermite-Fejer interpolation polynomials

The object of this note is to improve Some wellknown results, which are related with the approximation problems of the continuous functions by Hermite-Fejér interpolation which based on the zeros of Chebyshev polynomials of the first or second kind.     

Scattering of Plane Harmonic Waves in an Infinite Elastic Solid by an Arbitrary Configuration of Two-dimensional Obstacles

The problem of the multiple scattering of plane harmonic wavesin an infinite elastic solid by arbitrary configurations oftwo-dimensional obstacles is considered. Sets of integral equationsrelating the multiple scattering functions to the single scatteringfunctions are derived. The integral equations are replaced bya set of algebraic equations which are then solved by an iterativeprocedure. Some results are given for the scattering of a planeharmonic P or SV wave by an identical pair of parallel circularcylindrical cavities.     

Comments on abstract convexity structures on topological spaces

All results in “Some properties of abstract convexity structures on topological spaces” by S.-w. Xiang and H. Yang [S.-w. Xiang, H. Yang, Some properties of abstract convexity structures on topological spaces, Nonlinear Analysis 67 (2007) 803-808] and “A further characteristic of abstract convexity structures on topological spaces” by S.-w. Xiang and S. Xia [S.-w. Xiang, S. Xia, A further characteristic of abstract convexity structures on topological spaces, J. Math. Anal. Appl. 335 (2007) 716-723] are shown to be consequences of known ones or can be stated in more general forms.     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional differential equations of order q (1 < q ≤ 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.     

弱SS-半置换性极小子群对有限群超可解性的影响

引入弱SS-半置换子群的概念,介绍了弱SS-半置换子群的性质,结合有限群G的极小于群的弱SS-半置换性,并结合C-正规性来讨论有限群的超可解性及幂零性,得到了有限群超可解及幂零的若干充分或充要条件,同时推广了某些著名结果.     

Some higher-order modifications of Newton’s method for solving nonlinear equations

In this paper we consider constructing some higher-order modifications of Newton’s method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units. This construction can be applied to any iteration formula, and per iteration the resulting methods add only one additional function evaluation to increase the order. Some illustrative examples are provided and several numerical results are given to show the performance of the presented methods.     

Limit Theorems for Stopped Functionals of Markov Renewal Processes

Some results for stopped random walks are extended to the Markov renewal setup where the random walk is driven by a Harris recurrent Markov chain. Some interesting applications are given; for example, a generalization of the alternating renewal process.     

交连续dcpo的遗传性和不变性

讨论了交连续dcpo的遗传性和不变性,证明了如下结论:(1)交连续dcpo对于开子空间和闭子空间都是可遗传的;(2)交连续dcpo在加最大元和去最小元运算下保持交连续性;(3)交连续dcpo的收缩核为交连续dcpo.另外,给出了交连续的主理想刻画的一个直接证明;构造了反例说明交连续dcpo对于主滤子是不可遗传的;也构造了反例说明所有主滤子都交连续的一个dcpo,自身不必是交连续的.     

Graphs having circuits with at least two chords

All 2-connected non-bipartite graphs are characterized which have a minimal valency ≥3 and which have no odd circuit with two or more chords. From this it is derived that in each graph with chromatic number ≥4 containing no complete 4-graph there is an odd circuit with two or more chords. This result was conjectured by P. Erdös. Corresponding results for even circuits and for circuits with a fixed edge are obtained. Some related problems of the Turán type are solved.     

A generalized BPX multigrid framework covering nonnested V-cycle methods

More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and it produces a variable V-cycle, or nonuniform convergence rate V-cycle methods, or other nonoptimal results in analysis thus far.

This paper completes a long-time effort in extending the BPX multigrid framework so that it truly covers the nonnested V-cycle. We will apply the extended BPX framework to the analysis of many V-cycle nonnested multigrid methods. Some of them were proven previously only for two-level and W-cycle iterations. Some numerical results are presented to support the theoretical analysis of this paper.

     

Some remarks on holomorphic functions and taylor series in C

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.     

Existence of solutions of games with some non-convexity

Some inf-sup and saddle point theorems are proved for functionsf: X×Y → IR (=reals). The general theorems weaken some of the convexity conditions that are usually imposed onX, Y, andf. Some special cases are considered — these results impose some convexity in the hypotheses but still treat situations not covered by classical theorems.     

OSCILLATION FOR NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＦＯＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（申建华）（王志成）湖南大学，邮编：４１００８２ＳｈｅｎＪｉａｎｈｕａ；ＷａｎｇＺｈｉｃｈｅｎｇ（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，）Ａｂｓｔｒａｃｔ...