Delay-constrained anycast routing problem in WDM networks with wavelength conversions

Anycast routing and wavelength assignment problem has been intensively studied in wavelength-division multiplexing (WDM) networks, however, real-time application where packets have explicit expiration deadlines is not taken into consideration. In a WDM network, each link is associated with limited wavelengths available for channel connections. Data transmission over one wavelength to another requires wavelength conversion, which causes a long delay of message transmission. When the network and the set of anycast routing requests are given, the delay-constrained wavelength conversions anycast routing (DWCAR) problem is to find a set of light-paths, one for each source, for anycasting message to one member of the anycast destination group. The objective is to find a minimum number of wavelength conversions with the constraint that the sum of delays along every path must not exceed a given delay-bound. In this paper, we present a Tabu-search based delay-constrained anycast routing algorithm (TSDA) to solve this NP-complete problem, and compare it to a simple K shortest path based anycast algorithm (KSPA). Simulation results show TSDA achieves an average 40–50% improvement in required wavelength conversions.     

Implementing duplex crossed cube communication patterns on optical linear arrays

Crossed cubes are a class of promising parallel communication patterns. This paper addresses the issue of how to implement a half-duplex or full-duplex crossed cube on a WDM optical network with linear array topology. For either of these two communication patterns, a routing scheme, that is an embedding scheme, is proposed, and a wavelength assignment scheme under the embedding scheme is designed. The number of required wavelengths under the embedding scheme is shown to attain the minimum.     

Fixed Point Theorem of Cone Expansion and Compression of Functional Type

The fixed point theorem of cone expansion and compression of norm type is generalized by replacing the norms with two functionals satisfying certain conditions to produce a fixed point theorem of cone expansion and compression of functional type. We conclude with an application verifying the existence of a positive solution to a discrete second-order conjugate boundary value problem.     

Formulating and Solving the Minimum Dominating Cycle Problem

This paper introduces a formulation for the Minimum Dominating Cycle Problem. Additionally, a Branch and Cut algorithm, based on that formulation, is also investigated. So far, the algorithm contains no primal heuristics. However, it managed to solve to proven optimality, in acceptable CPU times, all test instances with up to 120 vertices.     

Static and dynamic routing and wavelength assignment algorithms for future transport networks

In this paper, two static and three dynamic routing algorithms have been proposed and compared to some of the existing algorithms on the basis of blocking probability. The two proposed static routing and wavelength assignment (RWA) algorithms reduce the blocking probability to maximize the utilization of network. For dynamic algorithms, first a model with no weights assignments is presented and then three algorithms are proposed and analysed with weight assignment resulting in reduction of blocking probability. All these algorithms are analysed and compared with four wavelength assignment schemes which are first-fit, random, most used and least used. It is shown that our proposed static algorithms give the best performance for first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate routing algorithm gives the lowest blocking probability. For dynamic routing, it has been shown that our proposed algorithm “less weight to maximum empty and nearest” gives the least blocking probability as compared to the other dynamic routing algorithms for random, most used and least used wavelength assignment strategies.     

基于经验模态分解和支持向量机的车型声频识别

车型自动识别是智能交通系统的重要组成部分。针对现有车型识别存在的问题,提出利用经验模态分解和支持向量机的车型声频识别方法。将车辆行驶的声音信号进行分解,以分解不同模态的能量作为特征向量,并以此作为训练样本对支持向量机构成的车型识别器进行训练,通过对小汽车和卡车的声音信号处理结果表明:利用车辆声音信号能够正确识别不同的车型,识别准确率达95%,是车型识别的有效方法。     

模糊均衡问题的求解及应用

根据实际均衡问题研究的需要,给出了模糊向量、模糊值函数、模糊矩阵等新概念,建立了模糊均衡问题的数学模型,即模糊线性互补问题。在引入新的模糊期望的基础上,研究了其性质,并据此给出了模糊线性互补问题的一种确定型等价式及此类问题的均衡解的概念。用实例说明了所提模型和方法的合理性及应用前景。     

求解一般约束优化问题的修正BFGS信赖域算法

借鉴无约束优化问题的BFGS信赖域算法,建立了非线性一般约束优化问题的BFGS信赖域算法,并证明了算法的全局收敛性．数值实验表明,算法是有效的．     

Uniqueness of Quasi-Regular Solutions for a Bi-Parabolic Elliptic Bi-Hyperbolic Tricomi Problem

The Tricomi equation $ yu_{xx} + u_{yy} = 0 $ was established in 1923 by Tricomi who is the pioneer of parabolic elliptic and hyperbolic boundary value problems and related problems of variable type. In 1945 Frankl established a generalization of these problems for the well-known Chaplygin equation $ K(\,y)u_{xx} + u_{yy} = 0 $ subject to the Frankl condition 1 + 2( K / K ')' > 0, y <0. In 1953 and 1955 Protter generalized these problems even further by improving the above Frankl condition. In 1977 we generalized these results in R n ( n > 2). In 1986 Kracht and Kreyszig discussed the Tricomi equation and transition problems. In 1993 Semerdjieva considered the hyperbolic equation $ K_1 (\,y)u_{xx} + (K_2 {\rm (\,}y{\rm )}u_y )_y + ru = f $ for y<0. In this paper we establish uniqueness of quasi-regular solutions for the Tricomi problem concerning the more general mixed type partial differential equation $ K_1 (\,y)(M_2 {\rm (}x{\rm )}u_x )_x + M_1 (x)(K_2 {\rm (\,}y{\rm )}u_y )_y + ru = f $ which is parabolic on both lines x = 0; y = 0, elliptic in the first quadrant x > 0, y > 0 and hyperbolic in both quadrants x< 0, y > 0; x > 0, y< 0. In 1999 we proved existence of weak solutions for a particular Tricomi problem. These results are interesting in fluid mechanics.     

Discontinuous Oblique Derivative Problem for Second Order Equations of Mixed Type in General Domains

In [L. Bers (1958). Mathematical Aspects of Subsonic and Transonic Gas Dynamics . Wiley, New York; A.V. Bitsadze (1988). Some Classes of Partial Differential Equations . Gordon and Breach, New York; J.M. Rassias (1990). Lecture Notes on Mixed Type Partial Differential Equations. World Scientific, Singapore; H.S. Sun (1992). Tricomi problem for nonlinear equation of mixed type. Sci. in China ( Series A ), 35 , 14-20], the authors proposed and discussed the Tricomi problem of second order equations of mixed type in a special domain, and in [G.C. Wen (1998). Oblique derivative problems for linear mixed equations of second order. Sci. in China ( Series A ), 41 , 346-356], the author discussed the oblique derivative problem of second order equations of mixed type in a special domain. The present article deals with the discontinuous oblique derivative problem for quasilinear second order equations of mixed (elliptic-hyperbolic) type in general domains. Firstly, we give the formulation of the above boundary value problem, and then prove the existence of solutions for the above problem in general domains, in which the complex analytic method is used.