Assignment Problem is one of the first fundamental problems in the area of combinatorial optimization. Despite its historical roots, the problem has tremendous importance to date, due to its numerous real life applications in like facility location, personnel scheduling, job scheduling, production planning, project assignment, task assignment, time-tabling, vehicle routing, storage space allocation, etc. This book comprises some real life assignment and related problems involving imprecise cost/time parameters. In order to represent those imprecise parameters, interval numbers have been used here as this representation is the best among others. The associated problems have been solved using Genetic Algorithm efficiently. A salient feature of this book is that most of the algorithms have been written in a lucid manner with suitable examples using figures. This book should interest academicians, OR/GA practitioners and executives of different industries and business organizations.
In this thesis we address certain questions arising in the functional analytic study of dynamical systems and differential equations. First, we discuss the operator theoretic counterparts of the central ergodic theoretical notions of strong and weak mixing. These concepts correspond to particular types of asymptotic behaviour of operator semigroups in the weak operator topology. In particular, we carry over classical theorems of Halmos and Rohlin for measure preserving transformations to the Hilbert space operator setting. Further, we illustrate operator semigroup methods and results on a class of telegraph systems with various boundary conditions. We study both linear and nonlinear boundary value problems. The stability of linear telegraph systems is discussed by applying theorems from the previous chapters. For the existence of solutions, we are particularly interested in time-dependent boundary conditions, since this case has little been investigated so far.
The focus area of this paper is on the assignment problem with budget constraints which is one of the application area of combinatorial optimization that operates on the domain of those optimization problems,in which the set of feasible solutions is discrete or can be reduced to discrete,and in which the goal is to find the best solution. It is particularly concerned with solving the unconstrained assignment problems with Hungarian algorithm and the constrained assignment problem by cutting plane or outer linearization algorithm for solving the Lagrangian dual problem in which, at each iteration,the function that approximates the dual function is optimized. The paper is divided in to two chapters. In the first chapter,the classical assignment problem,the problem of finding optimum (minimum or maximum) cost or profit assignment a set of workers or resources to jobs or activities to gather with its mathematical formulation,solution methods and special cases in assignment problems were considered. Under the second chapter, we have considered generalization of the classical assignment problem concerning resource(or budget) constraints, due to the variety of real life problems.
In this work we study the Schrodinger problem using Clifford analysis. We use this approach to present a factorization for time dependent operators in terms of the parabolic-type Dirac operator. In the case of the heat operator we show that it is possible to construct Fischer decomposition. This decomposition can be applied in the characterization of the powers of the associated homogeneous operator. For the case of the Schrodinger operator, we will apply a regularization procedure in order to control the non-removable singularity existing in the hyperplane t=0. We will study the arising operators such as the regularized Teodorescu and Cauchy-Bitsadze operators. The properties of these operators will be used to obtain a Hodge decomposition for the regularized case and general case, in terms of the kernel of the parabolic Dirac operator. In the last chapter we study the cubic non-linear Schrodinger problem using a combination of Witt basis and finite difference approximations. We will show that it is possible to construct a discrete fundamental solution for time dependent discrete Schrodinger operator, via discrete Fourier transform and the arising symbol of the Laplace operator.
Research in probabilistic operator theory generally includes the solutions of random operator equations and random operator inclusion, random extension theorems, limit theorems, measure theoretic problems, spectral theory of random operators and semi groups of random operators and their properties. Various ideas associated with random fixed point theory are used to form a particularly elegant approach for the solution of nonlinear random systems. Now this theory has become full- fledged research area lying at the intersection of nonlinear analysis and probability theory. In this monograpgh those aspects of random solution of random operator equations and random operator inclusion, which fall within the scope of investigation of random fixed point are discussed.
Jensen's inequality for nomalized positive linear maps between the algebras of bounded linear operators on a Hilbert space is one of the most important inequalities in the functional analysis. In this book we establish some operator versions of Bellman's inequality. We also give some Bellman inequalities involving sesquilinear forms and invariant norms. In continuation, we refine the Jensen's operator inequality and use it for a refinement of the Bellman operator inequality. Also, we investigate a notion of relative operator entropy, which develops the theory started by J.I. Fujii and E. Kamei. Afterwards, some inequalities concerning the classical Shannon entropy are drawn from it.
In cellular mobile communication, since there will be conversation in progress in case of handover calls, GOS for them should be less than that for newly originating calls. Basically, there are three channel assignment schemes, fixed, dynamic & hybrid channel assignment schemes for handling newly originating and handover calls. In this study, capacity design for cellular mobile network in area inside ring road in Kathmandu valley has been done according to the findings of data collection and analysis of mobile communication service being provided by Nepal Telecom. Capacity planning has been done with GOS equal to 2% for newly originating calls and 1% for handover calls. In addition to capacity planning, efficient channel assignment scheme in terms of blocking and throughput has been evaluated with optimal utilization of the designed capacity for getting minimum blocking for both types of calls maintaining the blocking for handover calls always less than that for newly originating calls. The simulated values of GOS & throughput for all channel assignment schemes at different penetration have been compared and hybrid channel assignment scheme has been found to be most efficient.
The efficient management of Change Requests (CRs) is fundamental for successful software maintenance; however the assignment of CRs to developers is an expensive aspect in this regard, due to the time and expertise demanded. To overcome this, researchers have proposed automated approaches for CR assignment. Although these proposals present advances to this topic, they do not consider many factors inherent to the assignments, such as: developers’ workload, CRs severity, interpersonal relationships, and developers know-how. Actually, as we demonstrate in this work, CR assignment is a complex activity and automated approaches cannot rely on simplistic solutions. Ideally, it is necessary to consider and reason over contextual information in order to provide an effective automation. Beyond investigating all these aspects through an extensive systematic literature review, this work also proposes a context-aware architecture solution to semi-automated assignment of CRs.
A wireless mesh networks (WMNs) has emerged recently, WMN consist of two types of nodes mesh routers and mesh clients.WMN is dynamically self-organized and self-configured, with the nodes in the network automatically establishing and maintaining mesh connectivity among themselves. Channel assignment is a critical issue in WMN which is the mapping between the available channels and the radios at each node such that the network performance is optimized, and hence the focus of this work along with static channel assignment, multi-radio, multi-channel. Multi-radio MAC can potentially achieve higher network capacity than single-radio MAC. We design and implement a new agent (DSBCA) distributed channel assignment spanner base, the routing protocol Optimize the network performance considering the throughput, end-to-end delay, connectivity and the interference of our channel assignment algorithm. Base on the network simulations NS2.34 on Linux Fedora and our proposed channel assignment algorithm improved the throughput, minimal-connectivity preserving channel assignment algorithm.
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This book is about numerical ranges and spectral properties of Hilbert space operators which have been of great interest to many mathematicians in the past decades. Nice properties with examples are explored. The properties of numerical range, for example, convexity and closedness are well known as proved in the classic Toeplitz - Hausdorff Theorem. In this book, we embark on the relationship between the spectrum and the numerical range of an operator, in particular, when the operator is normal. It is known that for a bounded linear operator on a Hilbert space, the spectrum is contained in the closure of its numerical range. For a normal operator, the numerical radius and the spectral radius coincides with the norm of the operator. These results are actually a contribution to the field of numerical ranges and spectra. For the reader to understand this book, it is paramount that a deep understanding of the theory of operators, especially on Hilbert spaces, General Topology, Functional Analysis and Abstract Algebra be put in place. This book is useful to both undergraduate students and postgraduate students.
This book contains a good literature survey of various mathematical models and routing & wavelengths assignment algorithms in WDM optical networks. Some of the new algorithms for optimization of blocking probability have aslo been covered. This book is good for researchers who are working on optical networks and advancements in fiber optics communication. Mathematical models covered in this book are simple and easy to implement. A good number of routing and wavelength assignment algorithms have also been covered in this book which can be used to reduce blocking probability of the optical network. This book can be very helpful to the research scholars.
This monography presents new results in the theory of differential subordination and superordination, new classes of harmonic univalent and multivalent functions defined by an integral operator, properties of the analytic functions defined by integral Salagean operator, a class of analytic functions defined by Ruscheweyh operator and generalized almost starlike mappings associated with extension of operators for biholomorphic mappings.
The highly competitive environment in today's wireless and cellular network industries is making the management of systems seek for better and more advance techniques to keep masses of data, complexity of systems and deadline constrains under control with a lower cost and higher efficiency. Therefore, the management is getting significant attentions by researchers in order to increase the efficiency of the resource usage to provide high quality services. Two of the cornerstones of the management system in wireless and cellular network are carrier assignment and packet scheduling. Therefore, this work focuses on analysis and development of carrier assignment and packet scheduling methods in multi-band Wi-Fi and LTE-A networks.
The problem of distributing goods from depots to consumers plays an important role in the management of many distribution systems, and therefore when it is programmed efficiently it may yield significant savings. In a typical distribution system, trucks provide pick-up and delivery services to customers that are geographically dispersed in a given area. In many of its applications, the main objective of distribution is to find a set of routes for such trucks, satisfying a variety of constraints, so as to minimize the total distribution cost. This work focuses on a decision model for a real world problem. The problem reveals itself as assignment of trucks to routes by Latex Foam Rubber Products Limited-Kumasi, Ghana. This study addresses the problem of finding an efficient assignment of the limited number of trucks at the company’s disposal to the routes they ply while serving its customers outside the metropolis. In this work we use a solution procedure based on Munkres Assignment Algorithm for optimal assignment of non-homogenous fleet of trucks to a given set of routes, where Latex Foam Rubber Products Limited-Kumasi, distributes its products to its customers.
Calculus on time scales was established in 1988 by Stefan Hilger. It includes both the classical derivative and the forward difference operator as special cases. It also includes Riemann integrals and finite sums as inverse operations. However, it does not include the Jackson q-difference operator on the real numbers and the Jackson q-integral on R. Also, it does not include neither the difference operator on R and associated Norlund sums nor the Hahn difference operator. This book extends the definition of time scales in a way such that the previous difference operators and their associated sums are included. In addition, new illustrative examples will be given.
This book explains the port operations and proposes approaches that aim to improve the most important successive steps in container terminal management activities. A multi-period assignment problem that seeks to allocate vessels to berthing spaces and quay cranes is proposed to handle the quayside operations. Subsequently, on the yard side, a discrete-event simulation model for the real life detailed processes performed during the handling of import containers is developed. In particular, the model focuses on the storage assignment problem at the operational level in a container terminal with a multiple-berth structure. An approach by means of a hierarchical structure is adapted to partition the assignment problem into two sub-problems and solve each of them using separate decision rules. Suggested storage policies are evaluated in view of the overall performance of the container terminal.
When dealing with stress assignment on the word level, many exceptions to hitherto defined principles can be found in the English language. While some exceptions can be explained by word or morpheme boundaries, others do not fit so easliy into the underlying systematicity of English stress behaviour. Some are often described as simply being idiosyncratic. A new statistical analysis reveals that many of these exceptions do share some common features to a certain extent, in particular in their orthography. Can this kind of features be used to establish additional rules in order to account for exceptional cases of English stress assignment? Or is there no other means but to consider these cases as lexcially exceptional?
In the book the author investigates spaces of sequences with components belonging to an vector space.These spaces represent a generalization of the known Musielak-Orlicz sequence spaces and are generated by so-called pregenfunctions and genfunctions M.A part of the book is devoted to a superposition operator in considered spaces.The author considers in the spaces in question two equivalent semimetrics (which under some conditions are metrics)and F-norms (if M is a genfunction).Some properties of the considered spaces and their subsets are established.Criteria of the action,boundedness and continuity of the superposition operator are found.The book represents an interest for specialists in functional analysis and is comprehensible to the students-mathematicians of older years.Besides,it is possible to find here themes for diploma theses.
Modern day public transport assignment faces lots of problems. Solutions may exist but needs some form of backings. A sensitivity analysis in most cases could just be sufficient to provide this backing. The developments in this book are very important for students, academic researchers and policy makers. The book provides an extensive review on transit assignment, sensitivity analysis and OmniTRANS. It highlights important conclusions such as:- - Passenger access-egress distances significantly affects their access stop choices. - The travel distance parameter of the generalized cost function has the highest influence on transit assignment - The number of transfers to be made by passengers significantly determines their generalized cost of travel - A carefully conducted partial sensitivity analysis can provide better predictions than a Monte-Carlo sensitivity analysis. As a policy advice to public transport operators in Flanders-Belgium, the developments in this book suggest that; to improve transit assignment, it is sufficient to reduce passengers access-egress distances & the number of transfers either through the institution of more direct transit lines or missing links.