System bandwidth and the existence of generalized shift-invariant frames

We consider the question whether, given a countable family of lattices ${({\mathrm{\Gamma }}_j)}_{j\in J}$ in a locally compact abelian group G, there exist functions ${(g_j)}_{j\in J}$ such that the resulting generalized shift-invariant system ${(g_j(??\gamma ))}_{j\in J,\gamma \in {\mathrm{\Gamma }}_j}$ is a tight frame of $L^2(G)$. This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system.     

Bandwidth of the strong product of two connected graphs

The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x)-f(y)|:xy∈E(G)} taken over all proper numberings f of G. The strong product of two graphs G and H, written as G(S_P)H, is the graph with vertex set V(G)×V(H) and with (u₁,v₁) adjacent to (u₂,v₂) if one of the following holds: (a) u₁ and v₁ are adjacent to u₂ and v₂ in G and H, respectively, (b) u₁ is adjacent to u₂ in G and v₁=v₂, or (c) u₁=u₂ and v₁ is adjacent to v₂ in H. In this paper, we investigate the bandwidth of the strong product of two connected graphs. Let G be a connected graph. We denote the diameter of G by D(G). Let d be a positive integer and let x,y be two vertices of G. Let denote the set of vertices v so that the distance between x and v in G is at most d. We define δ_d(G) as the minimum value of over all vertices x of G. Let denote the set of vertices z such that the distance between x and z in G is at most d-1 and z is adjacent to y. We denote the larger of and by . We define η(G)=1 if G is complete and η(G) as the minimum of over all pair of vertices x,y of G otherwise. Let G and H be two connected graphs. Among other results, we prove that if δ_D(H)(G)?B(G)D(H)+1 and B(H)=⌈(|V(H)|+η(H)-2)/D(H)⌉, then B(G(S_P)H)=B(G)|V(H)|+B(H). Moreover, we show that this result determines the bandwidth of the strong product of some classes of graphs. Furthermore, we study the bandwidth of the strong product of power of paths with complete bipartite graphs.     

Spanning 3-colourable subgraphs of small bandwidth in dense graphs

A conjecture by Bollobás and Komlós states the following: For every γ>0 and integers r2 and Δ, there exists β>0 with the following property. If G is a sufficiently large graph with n vertices and minimum degree at least and H is an r-chromatic graph with n vertices, bandwidth at most βn and maximum degree at most Δ, then G contains a copy of H.This conjecture generalises several results concerning sufficient degree conditions for the containment of spanning subgraphs. We prove the conjecture for the case r=3.     

矩形孔光子晶体波导慢光特性

在线缺陷光子晶体波导中,利用矩形孔和椭圆孔分别替代临近线缺陷的第二行和第一、三行圆形孔,构成矩形孔光子晶体波导结构.利用平面波展开法对波导的慢光特性进行仿真分析,研究矩形孔的非对称性对慢光带宽和色散特性的影响.研究表明,在慢光区域平均群折射率变化为±10%的情况下,与圆形孔线缺陷波导相比,得到的导模能更好地限制在禁带中,而且当矩形孔宽度参量小于高度参量时,导模可以得到归一化延迟带宽积更大、带宽更宽、色散更小的慢光.通过对波导中矩形孔参量的优化,得到的慢光归一化延迟带宽积最大为0.402,此时带宽为44.4nm,群速度色散为8.0ps2/mm.     

红外探测器光电性能测量系统方案研究

本文提出了一种新型的由微机控制的全自动红外探测器件光电性能测量系统,针对系统的硬件组成部分及其设计思想做了详细的讨论.     

Inhomogeneous spin state in the organic conductor κ-(BEDT-TTF)4Hg2.78Cl8

The static and dynamical local spin susceptibility of the nonstoichiometric organic conductor, κ-(BEDT-TTF)₄Hg_2.78Cl₈, is studied by ¹³C NMR spectroscopy from room temperature down to 1.7 K. We observe a gradual growth of inhomogeneity in the spin state as a spectral broadening down to the lowest temperature, which is sustained even under 0.4 GPa but suppressed under 0.8 GPa. The emergence of the inhomogeneity is discussed in the light of the doped triangular-lattice Mott insulator.     

Analysis of cyclic queueing networks with parallelism and vacation

The aim of this paper is to improve the machine interference model with vacation to deal with more recent problems of the communication area. To this scope the model is extended to include parallelism in the vacation station. The underlying Markov process is analyzed and a state arrangement is found that yields an efficient matrix-analytic technique that substantially lowers down the time- and space-complexity of standard methods. A numerical example of the method effectiveness is presented, and an example of resource allocation is introduced that finds applications in the QoS management of wireless networks. The author is thankful to the anonymous referees for the improvements their comments have earned to the quality of the presentation and to the completeness of the paper. The author is thankful to Giuseppe Iazeolla, whose careful reading of the original draft of this paper led to significant improvements in its overall quality. This work was partially supported by funds from the FIRB project “Performance Evaluation of Complex Systems: Techniques Methodologies and Tools” and by the University of Roma TorVergata project on High Performance ICT Platforms.     

Bandwidth packing with priority classes

The bandwidth packing problem is defined as the selection and routing of messages from a given list of messages with prespecified requirements on demand for bandwidth. The messages have to be routed over a network with given topology so that the generated revenue is maximized. Messages to be routed are classified into two priority classes. An integer programming based formulation of this problem is proposed and a Lagrangean relaxation based methodology is described for solving this problem. A general purpose heuristic is then developed for generating feasible solutions of good quality. Several numerical experiments are conducted using a number of problem parameters such as number of messages, ratio of messages for lower and higher priority classes, capacity of links, and demand distribution of messages belonging to different classes and high quality solutions to the priority bandwidth packing problem are generated under the different situations.     

Generating asymptotically optimal broadcasting schedules to minimize average waiting time

The performance of a Video-on-Demand broadcasting scheme is commonly evaluated by the maximum waiting time encountered by the customer before viewing can start. This paper addresses the issue of minimizing the average waiting time. Recently, we proposed Harmonic Block Windows scheduling to specifically minimize the average waiting time for given bandwidth. Here, we present an efficient heuristic algorithm that generates asymptotically optimal Harmonic Block Windows schedules. Using simulation, we demonstrate that, as we increase the “block size”, the normalized average waiting time of these schedules approaches the theoretical minimum achievable by any “fixed start points” schedule.     

全光纤模式转换器的设计及优化

提出了一种新型全光纤LP02模宽带模式转换器.基于模式匹配原理采用双芯光纤设计,利用LP11模作为中间过渡模式,实现了宽带模式转换.运用光束传播法和模式耦合理论分析了光纤参量对有效折射率的影响,选择合适的光纤参量实现了模式匹配,分析了纤芯距离等参量对模式转换效率和带宽的影响,对比相同光纤参量下,直接和间接模式转换方法,数值模拟表明,采用间接法能够有效提高模式转换带宽,当要求转换效率大于80%时,这种模式转换器带宽能够达到121nm.