连续切波变换的高维奇异性分析

在高维数据处理过程中,确定高维平方可积函数的奇异性有着重要的意义,它可作为模式识别、数据挖掘、频谱分析、大型机械故障诊断、航空航天、遥感与控制以及三维图像处理的基础.本文首先给出高维平方可积函数的连续切波变换重构公式;其次研究几种特殊函数的切波系数的衰减性质;最后运用重构公式中的切波系数刻画平方可积函数的奇异支撑集.本文的结果推广了Kutyniok和Dahlke等人给出的一些已知结果.     

Improved convergence towards generalized Euler-Mascheroni constant

We propose new simple sequences approximating the Euler-Mascheroni constant and its generalization, which converge faster towards their limits than those considered by DeTemple [D.W. DeTemple, A quicker convergence to Euler’s constant, Am. Math. Monthly 100 (5) (1998) 468-470], Sînt?m?rian [A. Sînt?m?rian, A generalization of Euler’s constant, Numer. Algorithms 46 (2) (2007) 141-151] and Vernescu [A. Vernescu, A new accelerate convergence to the constant of Euler, Gazeta Matem., Ser. A, Bucharest XVII(XCVI) (4) (1999) 273-278].     

Analytic proof of dual variational formula for the first eigenvalue in dimension one

The first non-zero eigenvalue is the leading term in the spectrum of a self-adjoint operator. It plays a critical role in various applications and is treated in a large number of textbooks. There is a well-known variational formula for it (called the Min-Max Principle) which is especially effective for an upper bound of the eigenvalue. However, for the lower bound of the spectral gap, some dual variational formulas have been obtained only very recently. The original proofs are probabilistic. Some analytic proofs in one-dimensional case are proposed and certain extension is made. Project supported in part by the National Natural Science Foundation of China (Grant No. 19631060), Qiu Shi Science & Technology Foundation, DPFIHE, MCSEC and MCMCAS.     

Symmetries of the Partial Order of Traces

This paper deals with the automorphism group of the partial order of finite traces. We show that any group can arise as such an automorphism group if we allow arbitrary large dependence alphabets. Restricting to finite dependence alphabets, the automorphism groups are profinite and possess only finitely many simple decomposition factors. Finally, we show that the partial order associated with the Rado graph as dependence alphabet does not give rise to a homogeneous domain thereby answering an open question from Boldi, P., Cardone, F. and Sabadini, N. (1993).     

Carleman不等式的一种推广

本文对 Ｃａｒｌｅｍ ａｎ 不等式作出一种推广．     

Some relationships for the double modified generalized analytic function space Fourier–Feynman transform and its applications

In this paper we first introduce the concept of a double modified analytic function space Fourier–Feynman transform using the double modified analytic function space integral. We then proceed to establish the existence of the modified analytic function space Fourier–Feynman transform for all functionals in the Banach algebra. Finally we use this double modified analytic function space transform to explain various physical phenomenon.     

Continuity of the Filter with Unbounded Observation Coefficients

In this article, we study the continuity with respect to the trajectories of the observation process for the filter associated with nonlinear filtering problems when the coefficients depend on both the signal and the observation and the observation coefficient is unbounded.

To achieve this task we define a formal unnormalized filter and prove by limiting arguments that it is related to the original filter through a generalized Bayes formula, and is locally Lipschitz continuous with respect to the uniform norm.     

期权定价理论中的物理学

布朗运动理论是布莱克－舒尔斯期权定价理论的基础，这意味着现代金融工程需要物理学。现代金融学向定量科学发展是历史的必然，物理学进入金融业也是势在必行，但是，金融工程是一项大的综合性工程，物理模型只是它的一，且要走的路还很长，还有许多工作需要物理学家去做，特别是要用新的物理思想，构造出新的、实用的模型。     

An extension of clark' formula

The representation formula of Clark (1970) and Haussmann (1979) is established for Brownian functional in the space D^1.1     

Transformation formulae for continuous semimartingales and certain non-regular real functions on the sequence space i p

Transformation formulae for continuous semimartingales and twice continuously partially differentiable real functions on the sequence spaces l^p, 1<p<oo, are proved. Also mappings f are treated for which the derivatives do not exist at the zeroes of f, but which fulfil some boundedness conditions. Furthermore, an approximative formula for the function x^x, x>1/2, is obtained. As an application a representation for the p-norm of a semimartingale is given.