Beurling Dimension of Gabor Pseudoframes for Affine Subspaces

Pseudoframes for subspaces have been recently introduced by Li and Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for discrete subsets of ℝ ^d by employing a certain generalized Beurling density. We present several properties of Beurling dimension including a comparison with other notions of dimension showing, for instance, that our notion includes the mass dimension as a special case. Then we prove that Gabor pseudoframes for affine subspaces satisfy a certain Homogeneous Approximation Property, which implies invariance under time–frequency shifts of an approximation by elements from the pseudoframe. The main result of this paper is a classification of Gabor pseudoframes for affine subspaces by means of the Beurling dimension of their sets of parameters. This provides us, in particular, with a Nyquist dimension which separates sets of parameters of pseudoframes from those of non-pseudoframes and which links a fixed value to sets of parameters of pseudo-Riesz sequences. These results are even new for the special case of Gabor frames for an affine subspace.      

L2(Rd)的Gabor框架的扰动

本文研究了L2(Rd)上以矩阵平移和调制的Gabor框架的扰动,得到了若干有意义的结果.     

Modified zeta functions as kernels of integral operators

The modified zeta functions _∑n∈Kn−s, where K⊂N, converge absolutely for . These generalise the Riemann zeta function which is known to have a meromorphic continuation to all of C with a single pole at s=1. Our main result is a characterisation of the modified zeta functions that have pole-like behaviour at this point. This behaviour is defined by considering the modified zeta functions as kernels of certain integral operators on the spaces L²(I) for symmetric and bounded intervals I⊂R. We also consider the special case when the set K⊂N is assumed to have arithmetic structure. In particular, we look at local Lp integrability properties of the modified zeta functions on the abscissa for p∈[1,∞].     

The road to equal-norm Parseval frames

The construction of equal-norm Parseval frames is fundamental for many applications of frame theory. We present a construction method based on a system of ordinary differential equations, which generates a flow on the set of Parseval frames that converges to equal-norm Parseval frames. We developed this method to address a question posed by Vern Paulsen: How close is a nearly equal-norm, nearly Parseval frame to an equal-norm Parseval frame? The distance estimate derived here can be used to substantiate numerically found, approximate constructions of equal-norm Parseval frames. The estimate is valid for a fairly general class of frames — requiring that the dimension of the Hilbert space and the number of frame vectors is relatively prime. In addition, we re-phrase our distance estimate to show that certain projection matrices which are nearly constant on the diagonal are close in Hilbert-Schmidt norm to ones which have a constant diagonal.     

A simple mathematical model for approximate analysis of tall buildings

The focus of this article is to present a new and simple mathematical model that may be used to determine the optimum location of a belt truss reinforcing system on tall buildings such that the displacements due to lateral loadings would generate the least amounts of stress and strain in building’s structural members. The effect of belt truss and shear core on framed tube is modeled as a concentrated moment applied at belt truss location, this moment acts in a direction opposite to rotation created by lateral loads. The axial deformation functions for flange and web of the frames are considered to be cubic and quadratic functions respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection, rotation of the plane section, and unknown coefficients of shear lag, the mathematical model is developed. The proposed model shows a good understanding of structural behavior; easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stage which requires less time. Numerical examples are given to demonstrate the ease of application and accuracy of the proposed modeled.     

A representing system generated by the Szegö kernel for the Hardy space

In this paper we give an explicit construction of a representing system generated by the Szegö kernel for the Hardy space. Thus we answer an open question posed by Fricain, Khoi and Lefèvre. We use frame theory to prove the main result.     

Return map structure and entrainment in a time-state-scale re-entrant system

From the perspective of a heterarchy, endo-physics, or internal measurement, a time-state-scale re-entrant system has been proposed [Y.-P. Gunji, K. Sasai, S. Wakisaka, BioSystems (submitted for publication)]. However, the dynamical structure of this system has yet to be estimated. Because the return map of the time-space re-entrant system results from the twisted coupling between the temporal and state-scale states, it is analytically determined. The attractors of entrainment in the interactive re-entrant system are also determined by a particular recursive rule, and it is also shown that a resulting return map can control the attractors of the interactive systems.     

A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials

Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh poly-nomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11(6) (2013), 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.     

Quaternary selenostannates Na2−xGa2−xSn1+xSe6 and AGaSnSe4 (A=K, Rb, and Cs) through rapid cooling of melts. Kinetics versus thermodynamics in the polymorphism of AGaSnSe4

The quaternary alkali-metal gallium selenostannates, Na_2−xGa_2−xSn_1+xSe₆ and AGaSnSe₄ (A=K, Rb, and Cs), were synthesized by reacting alkali-metal selenide, Ga, Sn, and Se with a flame melting-rapid cooling method. Na_2−xGa_2−xSn_1+xSe₆ crystallizes in the non-centrosymmetric space group C2 with cell constants a=13.308(3) Å, b=7.594(2) Å, c=13.842(3) Å, β=118.730(4)°, V=1226.7(5) Å³. α-KGaSnSe₄ crystallizes in the tetragonal space group I4/mcm with a=8.186(5) Å and c=6.403(5) Å, V=429.1(5) Å³. β-KGaSnSe₄ crystallizes in the space group P2₁/c with cell constants a=7.490(2) Å, b=12.578(3) Å, c=18.306(5) Å, β=98.653(5)°, V=1705.0(8) Å³. The unit cell of isostructural RbGaSnSe₄ is a=7.567(2) Å, b=12.656(3) Å, c=18.277(4) Å, β=95.924(4)°, V=1741.1(7) Å³. CsGaSnSe₄ crystallizes in the orthorhombic space group Pmcn with a=7.679(2) Å, b=12.655(3) Å, c=18.278(5) Å, V=1776.1(8) Å³. The structure of Na_2−xGa_2−xSn_1+xSe₆ consists of a polar three-dimensional network of trimeric (Sn,Ga)₃Se₉ units with Na atoms located in tunnels. The AGaSnSe₄ possess layered structures. The compounds show nearly the same Raman spectral features, except for Na_2−xGa_2−xSn_1+xSe₆. Optical band gaps, determined from UV-Vis spectroscopy, range from 1.50 eV in Na_2−xGa_2−xSn_1+xSe₆ to 1.97 eV in CsGaSnSe₄. Cooling of the melts of KGaSnSe₄ and RbGaSnSe₄ produces only kinetically stable products. The thermodynamically stable product is accessible under extended annealing, which leads to the so-called γ-form (BaGa₂S₄-type) of these compounds.     

地球同步轨道碎片观测图像分级检测方法

为了快速检测出地球同步轨道带光学观测图像中的空间碎片,提出了一种基于信噪比的分级检测方法.首先分析实测数据,得出观测图像中不同信噪比碎片运动相似的特性.对于高信噪比碎片,采取帧差法快速检测,并利用多帧图像计算速度信息;对于低信噪比碎片,根据高信噪比碎片检测结果得到的速度信息,采用改进的动态规划检测方法.实际图像检测结果表明:当递归方程的搜索窗口为5pixel×5pixel时,分级检测方法检测性能最好;当累积帧数大于5帧时,检测时间比传统动态规划方法减少了87%以上.分级检测方法具有检测率高、虚警率低、计算量小的优势,适合地球同步轨道带光学观测图像中空间碎片的检测.