Some Penrose transforms in complex differential geometry Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The other concerns obstructions to the embedding of CR structures on the three-sphere.     

Formation and construction of shock for p -system

The paper concerns the formation and construction of shocks. The process of transform from a smooth solution to a shock is precisely described. Meanwhile, the singularity structure and estimates of solutions near the starting point of the shock are also obtained     

Formation and construction of shock forp-system

The paper concerns the formation and construction of shocks. The process of transform from a smooth solution to a shock is precisely described. Meanwhile, the singularity structure and estimates of solutions near the starting point of the shock are also obtained     

Separation of Variables and the Computation of Fourier Transforms on Finite Groups,II

We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast Fourier Transform algorithms we make explicit use of the path algebra connection to the construction of Gel’fand–Tsetlin bases and work in the setting of quivers. We relate this framework to the construction of a configuration space derived from a Bratteli diagram. In this setting the complexity of an algorithm for computing a Fourier transform reduces to the calculation of the dimension of the associated configuration space. Our methods give improved upper bounds for computing the Fourier transform for the general linear groups over finite fields, the classical Weyl groups, and homogeneous spaces of finite groups, while also recovering the best known algorithms for the symmetric group.     

On the Floer homology of cotangent bundles

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T* M of a compact orientable manifold M. The first result is a new L^∞ estimate for the solutions of the Floer equation, which allows us to deal with a larger—and more natural—class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Floer homology and the singular homology of the free loop space of M in the periodic case, or of the based loop space of M in the Lagrangian intersection problem. The idea for the construction of such an isomorphism is to consider a Hamiltonian that is the Legendre transform of a Lagrangian on T M and to construct an isomorphism between the Floer complex and the Morse complex of the classical Lagrangian action functional on the space of W^1,2 free or based loops on M. © 2005 Wiley Periodicals, Inc.     

Cascades aléatoires et équations de Navier-Stokes

This work concerns the incompressible Navier-Stokes equation in. The non linear integral equation satisfied bx the Fourier transform of the Laplacian of the velocity field can be interpreted in terms of a branching Markov process and of a composition rule defined along the associated tree. We derive from this representation new classes where global existence and uniqueness can be proven.     

Generalized Watson transforms I: General theory

This paper introduces two main concepts, called a generalized Watson transform and a generalized skew-Watson transform, which extend the notion of a Watson transform from its classical setting in one variable to higher dimensional and noncommutative situations. Several construction theorems are proved which provide necessary and sufficient conditions for an operator on a Hilbert space to be a generalized Watson transform or a generalized skew-Watson transform. Later papers in this series will treat applications of the theory to infinite-dimensional representation theory and integral operators on higher dimensional spaces.

     

Bergman空间上拟齐次Toeplitz算子的乘积

使用Mellin变换作为工具,讨论了Bergman空间上以拟齐次函数为符号的Toeplitz算子的乘积问题,得出了当拟齐次函数的度处于三种不同情况时两个Toeplitz算子乘积仍是Toeplitz算子的充分必要条件.     

具有主动约束层阻尼板的振动杂交控制*

本文研究了局部附加主动约束阻尼层(LACL)板的主、被动杂交控制问题.基于弹性、粘弹性、压电材料的本构关系,建立了系统的控制方程.利用Galerkin方法和GHM方法将偏微分方程转换为维数不高的常微分方程组,应用LQR方法进行了数值模拟.计算结果表明,这种主动和被动结合的杂交控制方式具有良好的控制效果.     

关于一类具阻尼项的非线性波方程的Cauchy问题

The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.     

DOG小波变换像空间的描述

本文给出了DOG小波变换像空间的再生核函数的具体表达式及等距恒等式,并利用再生核函数的结构对DOG小波变换的像空间作出了具体的描述,使得对其像空间的形成有了更直观和更深刻的认识.这既为一般小波变换像空间的描述奠定了基础,又为该小波变换的实际运用提供理论依据.     

The Efficient Computation of Fourier Transforms on Semisimple Algebras

We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier transform for a large class of finite groups. We continue to find efficiencies by exploiting a connection between Bratteli diagrams and the derived path algebra and construction of Gel’fand–Tsetlin bases. Particular results include highly efficient algorithms for the Brauer, Temperley–Lieb, and Birman–Murakami–Wenzl algebras.     

Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions

The aim of this paper is to investigate rational approximations to solutions of some linear Fuchsian differential equations from the perspective of moduli of linear differential equations with fixed monodromy group. One of the main arithmetic applications concerns the study of linear forms involving polylogarithmic functions. In particular, we give an explanation of the well-poised hypergeometric origin of Rivoal’s construction on linear forms involving odd zeta values.     

交叉对角化TOeplitz预条件子的构造空间

1 问题的提出一个n阶方阵Tn被称为Toeplitz矩阵,如果它满足     

On Fourier Orthogonal Projections in the Rotation Algebra

Projections are constructed in the rotation algebra that areorthogonal to their Fourier transform and which are fixed underthe flip automorphism. Such projections are expected in a constructionof an inductive limit structure for the irrational rotationalgebra that is invariant under the Fourier transform (namely,as two circle algebras of the same dimension, which are swappedby the Fourier transform, plus a few points). The calculationis based on Rieffel's construction of the Schwartz space asan equivalence bimodule of rotation algebras as well as on thetheory of theta functions.     

Numerical evaluation of new quadrature rules using refinable operators

This paper concerns the construction of quadrature rules based on the use of suitable refinable quasi-interpolatory operators introduced here. Convergence analysis of the obtained quadrature rules is developed and numerical examples are included.     

Assessing Similarity of Random sets via Skeletons

Methodology and Computing in Applied Probability - The paper concerns a method for assessing similarity of realisations of random sets based on a construction of their morphological skeletons and a...     

Solving the random diffusion model in an infinite medium: A mean square approach

This paper deals with the construction of an analytic-numerical mean square solution of the random diffusion model in an infinite medium. The well-known Fourier transform method, which is used to solve this problem in the deterministic case, is extended to the random framework. Mean square operational rules to the Fourier transform of a stochastic process are developed and stated. The main statistical moments of the stochastic process solution are also computed. Finally, some illustrative numerical examples are included.     

Wavelets on the Two-Sphere and Other Conic Sections

We survey the construction of the continuous wavelet transform (CWT) on the twosphere. Then we discuss the discretization of the spherical CWT, obtaining various types of discrete frames. Finally, we give some indications on the construction of a CWT on other conic sections.     

Phaseless inverse discrete Hilbert transform and determination of signals in shift‐invariant space

In this paper, we first address the uniqueness of phaseless inverse discrete Hilbert transform (phaseless IDHT for short) from the magnitude of discrete Hilbert transform (DHT for short). The measurement vectors of phaseless IDHT do not satisfy the complement property, a traditional requirement for ensuring the uniqueness of phase retrieval. Consequently, the uniqueness problem of phaseless IDHT is essentially different from that of the traditional phase retrieval. For the phaseless IDHT related to compactly supported functions, conditions are given in our first main theorem to ensure the uniqueness. A condition on the step size of DHT is crucial for the insurance. The second main theorem concerns the uniqueness related to noncompactly supported functions. It is not the trivial generalization of the first main theorem. Our third main result is on the determination of signals in shift‐invariant spaces by phaseless IDHT. Note that the measurements used for the determination are the DHT magnitudes. They are the approximations to the Hilbert transform magnitudes. Recall that for the existing methods of phaseless sampling (a special phase‐retrieval problem), to determine a signal depends on the exact measurements but not the approximative ones. Therefore, our determination method is essentially different from the traditional phaseless sampling. Numerical simulations are conducted to examine the efficiency of phaseless IDHT and its application in determining signals in spline Hilbert shift‐invariant space.