A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz distributions

We reformulate and prove the Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz tempered distributions and Fourier hyperfunctions.     

氟化类金刚石薄膜的拉曼和红外光谱结构研究

关键词：     

Self-commutator inequalities in higher dimension

Three natural multi-dimensional substitutes for the self-commutator of a Hilbert space operator are introduced and generalizations of Putnam's inequality to tuples of operators with semidefinite self-commutators are indicated. In addition, a Riesz transform model is developed and investigated.

     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

一种新型电流互感器校验仪

电子式电流互感器的出现对互感器的校验提出了新的要求,必须对互感器的数字量输出进行校验。以LabVIEW作为开发工具研制出一种新型电流互感器校验仪,它发挥虚拟仪器灵活、可自定义、具有强大数据处理和分析功能、易于嵌入数字补偿以及开发周期短等特点。该校验仪利用离散Fourier变换(DFT)方法和数字补偿技术,能准确地测定出电子式电流互感器及传统电流互感器的比差、角差、频率、谐波等多个技术性能指标,且具有便于携带、易于拓展功能、开发周期短、检定工作效率高等优点。经对比校验,该校验仪比差为0.05%,角差在2′以内。     

KL-变换/JPEG和JPEG/KL-变换压缩性能分析

对ＫＬ－变换（ＫＬＴ）／ＪＰＥＧ和ＪＰＥＧ／ＫＬＴ构成的多光谱图象数据压缩系统的性能及优缺点进行了分析比较。在充分利用多光谱图象数据统计特征的基础上，将ＫＬＴ应用于多光谱数据压缩系统来消除谱相关性。仿真实验结果表明，ＫＬＴ／ＪＰＥＧ压缩系统的综合性能优于ＪＰＥＧ／ＫＬＴ压缩系统     

基于小波变换的人脸特征定位

文章在小波分析的基础上,提出了一种在图像的小波分解数据域中实现对称变换的方法,并把这种方法运用于人脸特征的定位,这种方法可以提高人脸特征定位的效率。     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.