窗口Fourier变换反演公式的级数表示——献给陆善镇教授75华诞

本文研究连续窗口Fourier变换的反演公式.与经典的积分重构公式不同,本文证明当窗函数满足合适的条件时,窗口Fourier变换的反演公式可以表示为一个离散级数.此外,本文还研究这一重构级数的逐点收敛及其在Lebesgue空间的收敛性.对于L^2空间,本文给出重构级数收敛的充分必要条件.     

窗口Fourier变换反演公式的级数表示

本文研究连续窗口Fourier变换的反演公式.与经典的积分重构公式不同,本文证明当窗函数满足合适的条件时,窗口Fourier变换的反演公式可以表示为一个离散级数.此外,本文还研究这一重构级数的逐点收敛及其在Lebesgue空间的收敛性.对于L2空间,本文给出重构级数收敛的充分必要条件.     

等周问题求解新探索

将实型Fourier级数延拓成复型Fourier级数,利用复型的Fourier级数和数学分析中的格林公式以及参数方程,借助Parseval等式,对等周问题进行求解.     

关于用几乎 Riesz 平均逼近阶的注记

为,f(x)的 Fourier 级数的几乎 Riesz 平均,并且证明了定理 A ([1]或见[2])以2π为周期的 Lipa 类函数同它的 Fourier 级数的几乎 Riesz平均的逼近阶用下式估计     

无穷级数和的几种求法

从级数和的定义、幂级数和函数的性质、常见函数的幂级数展开,以及Fourier级数理论等多种途径可以来求级数和函数。     

典型群上FOURIER级数的HARDY-LITTLEWOOD型定理

典型群 U_(?),SO(n)及 USP(2n)上 Fourier 级数大于临界指标的 Riesz 球平均,已由龚升等人在中作了研究。本文主要讨论临界阶的 Riesz 球平均以及 Fourier 级数的球部分和,推广了一维 Fourier 级数的 Hardy-Littlewood 混合判别法。本文定理的证明主要就 n 阶酉群 U_n 上进行。由于 SO(n)和 USP(2n)上相应定理的证明本质上是和 U_n 上类似的,因此我们仅在文章最后作一说明。     

奇偶性的推广与傅立叶展开

在傅立叶(Fourier)级数中,偶函数、奇函数的展开式分别为     

牛曼-贝塞尔级数的共轭级数

本文讨论了牛曼-贝塞尔级数的共轭级数，建立了其部分和与相应的共轭Fourier三角级数的部分和之间的关系，同时结出了两个收敛定理。     

k解析函数的Fourier级数

讨论了复平面上k解析函数的性质,并利用k解析函数的泰勒展开定理研究了k解析函数的Fourier级数,推广了经典的解析函数的Fourier级数理论.     

酉辛群上的调和分析Ⅳ-Fourier级数的球求和

本文沿用龚昇[2]中研究酉群上Fourier级数球求和的方法,讨论了酉辛群的同一问题,得到了相应的结果。我们证明了: 酉辛群USp(2n)上任一连续函数的Fourier级数,可以δ次Riesz球求和于它自己,但δ>(n(2n+1)-1)/2; 酉辛群USp(2n)上任一连续函数的Fourier级数,可以按Gauss-Sommerfeld意义的球求和于它自己;     

On the Associated Primes of Matlis Duals of Top Local Cohomology Modules

After motivating the question, we prove various results about the set of associated primes of Matlis duals of top local cohomology modules. In some cases, we can calculate this set. An easy application of this theory is the well-known fact that Krull dimension can be expressed by the vanishing of local cohomology modules.     

COMPARISON OF THE LONG-TIME BEHAVIOR OF LINEAR ITO AND STRATONOVICH PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we point out the different long-time behavior of stochastic partial differential equations when one considers the stochastic term in the Ito or Stratonovich sense. In particular, we prove that the Stratonovich interpretation may not produce modification in the exponential stability of the deterministic model for a wide range of stochastic perturbations, while Ito's one can give different results. In fact, some stabilization or destabilization effect can be obtained.     

On the Image Regularity Condition

In this paper, we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved that IRC implies the existence of generalized Lagrange-John multipliers with first component equal to 1. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can be also nonlinear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that 0 is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives.     

On a Toeplitz Representation of the H1/2 Norm

Some representations of the H1/2 norm are used as Schur complement preconditioner in PCG based domain decomposition algorithms for elliptic problems. These norm representations are efficient preconditioners but the corresponding matrices are dense, so they need FFT algorithm for matrix-vector multiplications. Here we give a new matrix representation of this norm by a special Toeplitz matrix. It contains only O(log(n)) different entries at each row, where n is the number of rows and so a matrix-vector computation can be done by O(nlog(n)) arithmetic operation without using FFT algorithm. The special properties of this matrix assure that it can be used as preconditioner. This is proved by estimating spectral equivalence constants and this fact has also been verified by numerical tests.     

A funny property of sphere and equations over groups

In this paper we present and prove a simple but non-obvious topological fact. This fact is so simple and funny that can be included in a collection of puzzles or suffested as a problem for a school mathematical tournament. The aim of this article is to present a method by which this fact, in spite of its unserious character. can be applied to produce new non-trivial group-theoretic results.     

On the Multilevel Structure of Global Optimization Problems

In this paper we will discuss the multilevel structure of global optimization problems. Such problems can often be seen at different levels, the number of which varies from problem to problem. At each level different objects are observed, but all levels display a similar structure. The number of levels which can be recognized for a given optimization problem represents a more complete measure of the difficulty of the problem with respect to the standard measure given by the total number of local minima. Moreover, the subdivision in levels will also suggest the introduction of appropriate tools, which will be different for each level but, in accordance with the fact that all levels display a similar structure, will all be based on a common concept namely that of local move. Some computational experiments will reveal the effectiveness of such tools.     

Incoherence correction strategies in statistical matching

Several economic applications require to consider different data sources and to integrate the information coming from them. This paper focuses on statistical matching, in particular we deal with incoherences. In fact, when logical constraints among the variables are present incoherencies on the probability evaluations can arise. The aim of this paper is to remove such incoherences by using different methods based on distances minimization or least commitment imprecise probabilities extensions. An illustrative example shows peculiarities of the different correction methods. Finally, limited to pseudo distance minimization, we performed a systematic comparison through a simulation study.     

Possibilistic Linear Programming with Fuzzy If-Then Rule Coefficients

In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzzy numbers. Scenario decomposed fuzzy numbers (SDFNs) reflect a fact that we may have different estimations of possible ranges of uncertain variables depending on scenarios, which are expressed by fuzzy if-then rules. The properties of SDFNs are investigated. Possibilistic linear programming problems with SDFNs are formulated by two different approaches, fractile and modality optimization approaches. It is shown that the problems are reduced to linear programming problems in fractile optimization models with the necessity measures and that the problems can be solved by a linear programming technique and a bisection method in modality optimization models with necessity measures. A simple numerical example is given.     

Logic and probabilistic systems

Following some ideas of Roberto Magari, we propose trial and error probabilistic functions, i.e. probability measures on the sentences of arithmetic that evolve in time by trial and error. The set of the sentences that get limit probability 1 is a theory, in fact can be a complete set. We prove incompleteness results for this setting, by showing for instance that for every there are true sentences that get limit probability less than . No set as above can contain the set of all true sentences, although we exhibit some containing all the true sentences. We also consider an approach based on the notions of inner probability and outer probability, and we compare this approach with the one based on trial and error probabilistic functions. Although the two approaches are shown to be different, we single out an important case in which they are equivalent. Received March 20, 1995     

On the linearization of the equations of motion of a rotating disk

In this paper, we present a consistent approach to reduce the fully nonlinear equations of a rotating disk to the classical linear equation derived by Lamb and Southwell and the nonlinear equations derived by Nowinski. The approach recognizes the fact that the out-of-plane deflection and the in-plane deflections are of different orders of magnitude. By using the ratio between the plate thickness and the outer radius as a measurement and carefully examining the reasonable magnitudes of all the variables involved, the fully nonlinear equations can be non-dimensionalized with all the terms being sorted according to their orders of magnitude. It is found that the classical linear equation derived by Lamb and Southwell can be recovered if all the terms of the lowest order of magnitude in the fully nonlinear equations are retained. If all the terms of the lowest two orders of magnitude are retained, Nowinski’s equations can then be recovered. Furthermore, the terms arising from in-plane deformation and rotary inertia are of the highest order and can be ignored in most of the applications.