a semidefinite optimization based approach for global optimization of multi row facility layout abstract this paper is concerned with the multi row facility layout problem given a set of rectangular departments a fixed number of rows and weights for each pair of departments the problem consists of finding an assignment of departments to rows and the positions of the departments in each row so that the total weighted sum of the center to center distances between all pairs of departments is minimized we show how to extend our recent approach for the space free multi row facility layout problem to general multi row facility layout as well as some special cases thereof to the best of our knowledge this is the first global optimization approach for multi row layout that is applicable beyond the double row case a key aspect of our proposed approach is a model for multi row layout that expresses the problem as a discrete optimization problem and thus makes it possible to exploit the underlying combinatorial structure in particular we can explicitly control the number and size of the spaces between departments we construct a semidefinite relaxation of the discrete optimization formulation and present computational results showing that the proposed approach gives promising results for several variants of multi row layout problems on a variety of benchmark instances

derivation of the time dependent propagator for the three dimensional schrodinger equation with one point interaction an explicit formula for the time dependent propagator of the schrodinger equation with one point interaction in three dimensions is given the derivation is based on the inverse laplace transformation applied to the corresponding resolvent

spectral analysis of a flat plasma sheet model the spectral analysis of the electromagnetic field on the background of an infinitely thin flat plasma layer is carried out this model loosely imitates a single base plane from graphite and it is of interest for theoretical studies of fullerenes by making use of the hertz potentials the solutions to maxwell equations with the appropriate matching conditions at the plasma layer are derived and on this basis the spectrum of electromagnetic oscillations is determined the model is naturally split into the te sector and tm sector both the sectors have positive continuous spectra but the tm modes have in addition a bound state namely the surface plasmon this analysis relies on the consideration of the scattering problem in the te and tm sectors the spectral zeta function and integrated heat kernel are constructed for different branches of the spectrum in an explicit form as a preliminary the rigorous procedure of integration over the continuous spectra is formulated by introducing the spectral density in terms of the scattering phase shifts the asymptotic expansion of the integrated heat kernel at small values of the evolution parameter is derived by making use of the technique of integral equations developed earlier by the same authors the local heat kernel green s function or fundamental solution is also constructed as a by product a new method is demonstrated for deriving the fundamental solution to the heat conduction equation or to the schrodinger equation on an infinite line with the like source in particular for the heat conduction equation on an infinite line with the source a nontrivial counterpart is found namely a spectral problem with point interaction which possesses the same integrated heat kernel while the local heat kernels fundamental solutions in these spectral problems are different

random walk with a hop over site a novel approach to tagged diffusion and its applications we study on a d dimensional hypercubic lattice a random walk which is homogeneous except for one site instead of visiting this site the walker hops over it with arbitrary rates the probability distribution of this walk and the statistics associated with the hop overs are found exactly this analysis provides a simple approach to the problem of tagged diffusion i e the movements of a tracer particle due to the diffusion of a vacancy applications to vacancy mediated disordering are given through two examples

rate distortion constrained subband video coding this paper introduces a subband video coding algorithm for operation over a continuum of rates from very low to very high the key elements of the system are statistical rate distortion constrained motion estimation and compensation multistage residual quantization high order statistical modeling and arithmetic coding the method is unique in that it provides an improved mechanism for dynamic spatial and temporal coding motion vectors are determined in a nontraditional way using a rate distortion cost criterion this results in a smoother and more consistent motion field relative to that produced by conventional block matching algorithms control over the system computational complexity and performance may be exercised easily

explicit propagators for a random walker and unidirectionality on linear chains abstract explicit propagators are given for a diffusing particle motor moving on a linear chain of either infinity or finite length with reflecting ends each chain contains a number of thermally accessible barriers and or potential wells active sites all particle interactions with its environment are considered to be short range and are described by repulsive attractive delta function potentials by employing perturbation expansion closed analytical expressions for the spatio temporal evolution of the probability density function of the motor are derived and are valid up to second order with respect to the expansion parameter u which denotes the strength of interaction between motor and active sites the mean displacement for two different chains is calculated indicating in both cases that the organization of the motion is done through the interplay of interaction intensities and their positions

explicit derivation of the propagator for a dirac delta potential an explicit derivation of the propagator is given for a particle in a dirac delta potential lambda delta x by making a direct application of a variational technique followed by a systematic use of laplace transforms although the solution of the corresponding schrodinger equation has been known for years the solution of the propagator has been obtained only recently

global optimality conditions and optimization methods for quadratic assignment problems abstract in this paper some global optimality conditions for general quadratic 0 1 programming problems with linear equality constraints are discussed and then some global optimality conditions for quadratic assignment problems qap are presented a local optimization method for qap is derived according to the necessary global optimality conditions a global optimization method for qap is presented by combining the sufficient global optimality conditions the local optimization method and some auxiliary functions some numerical examples are given to illustrate the efficiency of the given optimization methods

boundary conditions in path integrals from point interactions for the path integral of the one dimensional dirac particle a proposal is given of how to implement point interactions and boundary conditions in the path integral the starting point is a path integral formulation of a dirac particle in one dimension the implementation of a point interaction yields by means of a perturbation expansion the corresponding green function for a relativistic particle in the non relativistic limit several cases can be distinguished depending on which of the four possibilities of the point interaction has been chosen by a proper combination of the various possibilities of implementing the point interaction the whole range of the four parameter family of boundary conditions for point interactions can be exploited in the relativistic case as well as in the non relativistic limit in addition making the strength of the point interaction infinitely repulsive yields boundary conditions at finite points on the real line in particular dirichlet and neumann boundary conditions emerge the method is illustrated with some examples

directional decomposition heuristic for a linear machine cell location problem abstract a machine cell itself can be treated as a machine and the location of such a cell in a linear line configuration reflects an analogy to the machine location problem thus the problem addressed here is a one dimensional equidistant machine cell location problem that considers jobs with sequenced operations and the number of machine cells equals the number of locations that are equally spaced in a linear layout it is always desirable to achieve a cell assignment that minimizes the total inter cell flows and thus the total inter cell flow costs this assignment problem can be formulated as a quadratic assignment problem the optimal solution to which is usually prohibitive since it is a non deterministically polynomial hard problem and a heuristic procedure is justifiably called for in this research many of the investigations involved in seeking an improved location assignment in heuristics are repeated from one search to another each branch of the search requires re computation of all inter cell flows though only some of them have been changed from the previous one such a search mechanism requires considerable computation time thus making the algorithm inefficient this problem can be overcome by directionally decomposing the inter cell flows and incrementally computing them based on the directional decomposition of these flows a directional search is implemented in the heuristic in order to reduce the repetitiveness occurring in the traditional search both the partitioning procedure and the directional decomposition heuristic proposed here are demonstrated through examples and the performance measures indicate the superiority of the heuristic over the existing methods

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

effect of a forbidden site on a d dimensional lattice random walk we study the effect of a single excluded site on the diffusion of a particle undergoing a random walk in a d dimensional lattice the determination of the characteristic function allows us to find explicitly the asymptotical behaviour of physical quantities such as the particle average position drift x t and the mean square deviation x 2 t x 2 t in contrast to the one dimensional case where x t diverges at infinite times x t t 1 2 and where the diffusion constant d is changed due to the impurity the effects of the latter are shown to be much less important in higher dimensions for d 2 x t is simply shifted by a constant and the diffusion constant remains unaltered although dynamical corrections logarithmic for d 2 still occur finally the continuum space version of the model is analysed it is shown that d 1i s the lower dimensionality above which all the effects of the forbidden site are irrelevant

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

a new car following model with the consideration of anticipation optimal velocity abstract in this paper a new anticipation optimal velocity model aovm is proposed by considering anticipation effect on the basis of the full velocity difference model fvdm for car following theory on single lane the linear stability condition is derived from linear stability analysis starting and braking process is investigated for the car motion under a traffic signal which shows that the results accord with empirical traffic values especially aovm can avoid the disadvantage of the unrealistically high deceleration appearing in fvdm furthermore numerical simulation shows that aovm might avoid the disadvantage of negative velocity and headway that occur at small sensitivity coefficients in the fvdm since the anticipation effect is taken into account in aovm which means that collision disappears with the consideration of an appropriate anticipation parameter

applications of δ function perturbation to the pricing of derivative securities in the recent econophysics literature the use of functional integrals is widespread for the calculation of option prices in this paper we extend this approach in several directions by means of function perturbations first we show that results about infinitely repulsive function are applicable to the pricing of barrier options we also introduce functional integrals over skew paths that give rise to a new european option formula when combined with function potential we propose accurate closed form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable

random walks on lattices the problem of visits to a set of points revisited a general method is outlined for calculating the statistical properties of the number of visits to a set of points in a random walk in illustrative examples known results and new results are easily derived

generalized random walk algorithm for the numerical modeling of complex diffusion processes a generalized form of the random walk algorithm to simulate diffusion processes is introduced unlike the usual approach at a given time all the particles from a grid node are simultaneously scattered using the bernoulli repartition this procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations we prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles as an example simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested 2003 elsevier science b v all rights reserved

path integrals for potential problems with δ function perturbation the author presents several examples of potential problems with a function perturbation by means of path integrals the idea is to sum a perturbation series expansion resulting in an energy dependent green function g e the energy levels en of the perturbed problem are determined by the equation one dimensional case ig v a a en gamma where g v is the green function of the unperturbed problem gamma is the strength of the potential and a its location in r in d dimensional radial problems with a spherically shaped delta function located at r a this equation changes into ig v l a a en ad 1 where l denotes the angular momentum number

time dependent propagator with point interaction we compute the time dependent schrodinger propagator with a point interaction in dimension n or 3 including the new cases of n 2 and the most general interaction supported by a point for n 1 we also give the small time asymptotics for n or 3 the case n 2 has the peculiarity of involving logarithmic terms in the expansion

diffusion in the presence of a pole from the continuous gaussian to a discrete lattice model abstract the continuous gaussian model with delta function potentials which has been used to describe the effects that interacting centers poles bring to the diffusion of a random walker provides an exact solution only in dimension d 1 its application in dimension d 2 is in need of introduction of cutoffs coming from the finite sizes of poles we therefore formulate an analogous discrete model in the d dimensional lattice space where no cutoffs or their regularization are necessary the discrete model is amenable to numerical treatment and the green s function its first moments and properties derived from them can be determined numerically to all dimensionalities in the one dimensional 1 d case in the presence of a single center the outcomes of the gaussian model are compared with the corresponding results of the discrete lattice model the possibility of extension of the lattice model to higher dimension permits the study of the two dimensional 2 d case too the intensities of interactions considered before to obtain positive values are extended to negative values in order to describe attractions also

overview of theoretical models for reaction rates there is enormous recent interest in the development of models for rate processes because rates are an almost universal characterization in the physical and biological sciences in this paper we provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the national institutes of health on may 6 8 1985 this review will focus on 1 the smoluchowski model for reaction rates together with its extension by onsager 2 first passage time formalism for discrete and continuous master equations and fokker planck equations 3 the kramers model and its extensions 4 diffusion in the presence of trapping centers

trapping of random walks on the line several features of the trapping of random walks on a one dimensional lattice are analyzed the results of this investigation are as follows 1 the correction term to the known asymptotic form for the survival probability ton steps is o 2n 1 3 where ln 1 c andc is the trap concentration 2 the short time form for the survival probability is found to be exp a c n1 2 wherea c is given in eq 21 3 the mean square displacement of a surviving random walker is found to go liken2 3for largen 4 when the distribution of trap free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn one such model is studied

explicit time dependent schrodinger propagators the authors compute explicitly the time dependent schrodinger and heat propagator for the potentials lambda 2m m 1 cosh2 lambda x a delta function potential several cases of periodic delta function potentials and a delta function potential in a square well they also discuss the semiclassical approximation for the delta function potential

a jointly optimized subband coder the mainstream approach to subband coding has been to partition the input signal into subband signals and to code those signals separately with optimal or near optimal quantizers and entropy coders a more effective approach however is one where the subband coders are optimized jointly so that the average distortion introduced by the subband quantizers is minimized subject to a constraint on the output rate of the subband encoder a subband coder with jointly optimized multistage residual quantizers and entropy coders is introduced and applied to image coding the high performance of the coder is attributed to its ability to exploit statistical dependencies within and across the subbands the efficiency of the multistage residual quantization structure and the effectiveness of the statistical modeling algorithm result in an attractive balance among the reproduction quality rate and complexity

one dimensional machine location problems in a multi product flowline with equidistant locations an assignment of machines to locations along a straight track is required to optimize material flow in many manufacturing systems the assignment of m unique machines to m locations along a linear material handling track with the objective of minimizing the total machine to machine material transportation cost is formulated as a quadratic assignment problem qap the distance matrix in problems involving equally spaced machine locations in one dimension is seen to possess some unique characteristics called amoebic properties since an optimal solution to a problem with large m is computationally intractable the qap is np hard a number of the amoebic properties are exploited to devise heuristics and a lower bound on the optimal solution computational results which demonstrate the performance of the heuristics and the lower bound are presented

localized partial traps in diffusion processes and random walks reaction diffusion equations in which the reaction is described by a sink term consisting of a sum of delta functions are studied it is shown that the laplace transform of the reactive green s function can be analytically expressed in terms of the green s function for diffusion in the absence of reaction moreover a simple relation between the green s functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained several applications are presented and the formalism is used to establish the relationship between the time dependent geminate recombination yield and the bimolecular reaction rate for diffusion influenced reactions finally an analogous development for lattice random walks is presented