乘积空间的广义仿紧性

高国士在文[2]中证明了,若X是紧空间,Y是可数仿紧、可数中紧或可数弱仿紧,则X×Y也分別是可数仿紧、可数中紧或可数弱仿紧。本文在X为T_2空间的条件下推广了上述结果,若X为局部紧可数仿紧,Y是可数仿紧、可数中紧或可数弱仿紧,则X×Y也分别是可数仿紧、可数中紧或可数弱仿紧的。     

Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2（R^d）

Let{ψμ} be an orthonormal wavelet of L^2（R^d） and the support of a whole of its Fourier transform be Uμsupp{ψμ}=Пi=1^d[Ai, Di]-Пi=1^d（Bi, Ci）, Ai≤Bi≤Ci≤Di. Under the weakest condition that each │ψμ│, is continuous for ω ∈ δ（Пi=1^d[Ai, Di]）, a characterization of the above support of a whole is given.     

一类带有梯度项的非线性椭圆型方程的解的奇性的讨论

本文主要研究了一类带有梯度项的非线性椭圈型偏微分方程,详细讨论了它的解的奇点可去性的问题。     

Equicompact sets of operators defined on Banach spaces

Let and be Banach spaces. We say that a set denotes the space of all compact operators from into ) is equicompact if there exists a null sequence in such that for all and all . It is easy to show that collectively compactness and equicompactness are dual concepts in the following sense: is equicompact iff is collectively compact. We study some properties of equicompact sets and, among other results, we prove: 1) a set is equicompact iff each bounded sequence in has a subsequence such that is a converging sequence uniformly for ; 2) if does not have finite cotype and is a maximal equicompact set, then, given and a finite set in , there is an operator such that for and all .

     

Construction of an atomic decomposition for functions with compact support

Chang, Krantz and Stein [D.-C. Chang, S.G. Krantz, E.M. Stein, Hp theory on a smooth domain in Rn and elliptic boundary value problems, J. Funct. Anal. 114 (1993) 286-347] proved that if f∈Hp(Rn) and f vanishes outside , then f has an atomic decomposition whose atoms are contained in Ω. The purpose of this paper is to give another proof for the case n/(n+1)<p?1 and Ω a cube. Our argument provides a simple, direct construction of the desired atomic decomposition, and it works in a class of function spaces more general than the usual Hardy spaces.     

Design of a PXR experiment based on the NCEL

Parametric X-ray Radiation （PXR） can be used as a novel, quasi-monochromatic energy-tunable and high-yield X-ray source. It is produced at the Bragg angle by a relativistic electron beam passing through the periodic structure of crystal materials. This article concerns the PXR experiment using low energy electrons （10 MeV） from NCEL （Novel Compact Electron-Linac）. The difficulty of the experiment is to distinguish the PXR photons form the background. The design of the experiment relies mainly on the yield of PXR, the Bremsstrahlung background of the X-rays and the capability of the detector.     

A hybrid numerical simulation of isotropic compressible turbulence

A novel hybrid numerical scheme with built-in hyperviscosity has been developed to address the accuracy and numerical instability in numerical simulation of isotropic compressible turbulence in a periodic domain at high turbulent Mach number. The hybrid scheme utilizes a 7th-order WENO (Weighted Essentially Non-Oscillatory) scheme for highly compressive regions (i.e., shocklet regions) and an 8th-order compact central finite difference scheme for smooth regions outside shocklets. A flux-based conservative and formally consistent formulation is developed to optimize the connection between the two schemes at the interface and to achieve a higher computational efficiency. In addition, a novel numerical hyperviscosity formulation is proposed within the context of compact finite difference scheme for the smooth regions to improve numerical stability of the hybrid method. A thorough and insightful analysis of the hyperviscosity formulation in both Fourier space and physical space is presented to show the effectiveness of the formulation in improving numerical stability, without compromising the accuracy of the hybrid method. A conservative implementation of the hyperviscosity formulation is also developed. Combining the analysis and test simulations, we have also developed a criterion to guide the specification of a numerical hyperviscosity coefficient (the only adjustable coefficient in the formulation). A series of test simulations are used to demonstrate the accuracy and numerical stability of the scheme for both decaying and forced compressible turbulence. Preliminary results for a high-resolution simulation at turbulent Mach number of 1.08 are shown. The sensitivity of the simulated flow to the detail of thermal forcing method is also briefly discussed.     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

Accurate finite difference schemes for solving a 3D micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates

In this study, we propose a 3D generalized micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates, which can be applied to describe the non-equilibrium heating in biological cells. Two improved unconditionally stable Crank-Nicholson schemes are then presented for solving the generalized model. In particular, we delicately adjust the location of the interior grid point that is next to the boundary so that the Neumann boundary condition can be applied directly without discretization. As such, a second-order accurate finite difference scheme without using any fictitious grid points is obtained. The convergence rates of the numerical solution are tested by an example. Results show that the convergence rates of the present schemes are about 2.0 with respect to the spatial variable r, which improves the accuracy of the Crank-Nicholson scheme coupled with the conventional first-order approximation for the Neumann boundary condition.