Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

基于改进粒子群的薄壁变截面刚架临界载荷优化算法

针对大型变截面薄壁结构的稳定问题，以一类任意约束对称结构受非对称载荷的单跨刚架为研究对象，结构拆分为相关铁木辛柯（Timoshenko）梁，结合差分原理和最优化方法，以每段刚架的每个离散点挠度、临界载荷、轴力、剪力和梁端弯矩为设计变量，建立求解满足边界条件的非线性差分方程模型，提出基于优胜劣汰粒子更新的粒子群（IPSO）临界载荷优化算法。运用JAVA编程语言编制对应优化程序，分析典型算例并核实ABAQUS仿真结果。研究表明，本文提出的优化算法获得了有效的变形位型和高精度的临界载荷计算，能更好地描述刚架受力下位型和载荷的力学关系，进一步为工程设计与分析提供支持。     

面向内容的立体视频帧重要性区分模型研究

异构网络引起的视频传输失真是影响视频终端感知质量的重要因素，通常只能在解码端进行评估和补偿。因此在编码端建立一个面向内容的立体视频传输失真模型，考虑错误隐藏和错误扩散两种失真，通过近似估计视频中各帧对终端质量的贡献度，从而实现每帧重要性的区分。新模型综合考虑了视频帧编码位置以及表征内容的编码模式、运动矢量、视差矢量等关键信息，可以作为视频在异构网络中传输策略的重要依据。     

Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ‐BIBDs are (mod ) and . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ‐RBIBD, namely (mod ) and , are sufficient. A few new pairwise balanced designs are also given.     

Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces

In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ?. Using the set of zero trace operators on ? and two sets of self-adjoint operators on ? denoted by 𝒮^1,0 and 𝒮^1,1, we present some equivalent conditions to the norm retrievable frames in ?. We will also show that the property of norm retrievability for n-dimensional complex Hilbert space ? with n≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames.     

A Complete Solution to the Existence of ‐Cycle Frames of Type

The existence problem of a ‐cycle frame of type is now solved for any quadruple .     

On Some Properties of $c$-Frames

In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.