a fusion approach for managing multi granularity linguistic term sets in decision making the aim of this paper is to present a fusion approach of multi granularity linguistic information for managing information assessed in different linguistic term sets multi granularity linguistic term sets together with its application in a decision making problem with multiple information sources assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and or semantic in this context a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives first the fusion of the multi granularity linguistic performance values is carried out in order to obtain collective performance evaluations in this step on the one hand the multi granularity linguistic information is made uniform using a linguistic term set as the uniform representation base the basic linguistic term set on the other hand the collective performance evaluations of the alternatives are obtained by means of an aggregation operator being fuzzy sets on the basic linguistic term set second the choice of the best alternative s from the collective performance evaluations is performed to do that a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of possibility theory applied to fuzzy sets on the basic linguistic term set then a choice degree may be applied on the preference relation in order to rank the alternatives

a schur horn theorem for symplectic eigenvalues abstract let x and y be positive n vectors we show that there exists a 2 n 2 n positive definite real matrix whose symplectic spectrum is y and the symplectic spectrum of whose diagonal is x if and only if x is weakly supermajorised by y

boundary effects on localized structures in spatially extended systems abstract we present a general method of analyzing the influence of finite size and boundary effects on the dynamics of localized solutions of non linear spatially extended systems the dynamics of localized structures in infinite systems involve solvability conditions that require projection onto a goldstone mode our method works by extending the solvability conditions to finite sized systems by incorporating the finite sized modifications of the goldstone mode and associated nonzero eigenvalue we apply this method to the special case of non equilibrium domain walls under the influence of dirichlet boundary conditions in a parametrically forced complex ginzburg landau equation where we examine exotic nonuniform domain wall motion due to the influence of boundary conditions

around a multivariate schmidt spitzer theorem given an arbitrary complex valued infinite matrix infmata a ij i 1 dotsc infty j 1 dotsc infty and a positive integer n we introduce anaturally associated polynomial basis pol

real zeros of 2f1 hypergeometric polynomials we use a method based on the division algorithm to determine all the values of the real parameters b and c for which the hypergeometric polynomials 2f 1 n b c z have n real simple zeros furthermore we use the quasi orthogonality of jacobi polynomials to determine the intervals on the real line where the zeros are located

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

symmetry and bifurcations of momentum mappings the zero set of a momentum mapping is shown to have a singularity at each point with symmetry the zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function the proof uses the kuranishi theory of deformations among the applications it is shown that the set of all solutions of the yang mills equations on a lorentz manifold has a singularity at any solution with symmetry in the sense of a pure gauge symmetry similarly the set of solutions of einstein s equations has a singularity at any solution that has spacelike killing fields provided the spacetime has a compact cauchy surface

contiguous relations of hypergeometric series the 15 gauss contiguous relations for 2f1 hypergeometric series imply that any three 2f1 series whose corresponding parameters differ by integers are linearly related over the field of rational functions in the parameters we prove several properties of coefficients of these general contiguous relations and use the results to propose effective ways to compute contiguous relations we also discuss contiguous relations of generalized and basic hypergeometric functions and several applications of them

entropy of credibility distributions for fuzzy variables this paper deals with the degree of uncertainty associated with fuzzy variables based on the notion of credibility measure a definition of entropy is formulated from an information theoretical view and its properties are investigated finally some comments are given on the construction of alternative definitions of entropy and axiomatic characterization

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

an improved multiobjective differential evolution based on pareto adaptive dominance and orthogonal design abstract evolutionary multiobjective optimization has become a very popular topic in the last few years since the 1980s various evolutionary approaches that are capable of searching for multiple solutions simultaneously in a single run have been developed to solve multiobjective optimization problems mops however to find a uniformly distributed near complete and near optimal pareto front in a small number of fitness function evaluations nffes is a challenging task for any multiobjective optimization evolutionary algorithm moea in this paper we present an improved differential evolution algorithm to mops that combines several features of previous evolutionary algorithms in a unique manner it is characterized by a employing the orthogonal design method with quantization technique to generate the initial population b adopting an archive to store the nondominated solutions and employing the new pareto adaptive dominance method to update the archive at each generation c storing the extreme points and inserting them into the final archive in order to remedy one of the limitations of dominance the loss of the extreme points in the final archive and d using a hybrid selection mechanism in which a random selection and an elitist selection are alternated in order to allow using the archive solution to guide the search towards the pareto optimal front experiments have been conducted on a number of unconstrained real valued artificial functions of two and three objectives the results prove the efficiency of our approach with respect to the quality of the approximation of the pareto optimal front and the considerable reduction of nffes in these test problems by examining the selected performance metrics our approach is found to be statistically competitive with five state of the art moeas in terms of keeping the diversity of the individuals along the tradeoff surface finding a well approximated pareto optimal front and reducing the computational effort

laurent determinants and arrangements of hyperplane amoebas abstract we study amoebas associated with laurent polynomials and obtain new results regarding the number and structure of the connected components of the complement of the amoeba we also investigate the associated laurent determinant in the case of a hyperplane arrangement we perform explicit computations leading to a closed formula for the laurent determinant

a competitive and cooperative co evolutionary approach to multi objective particle swarm optimization algorithm design multi objective particle swarm optimization mopso is an optimization technique inspired by bird flocking which has been steadily gaining attention from the research community because of its high convergence speed on the other hand in the face of increasing complexity and dimensionality of today s application coupled with its tendency of premature convergence due to the high convergence speeds there is a need to improve the efficiency and effectiveness of mopso in this paper a competitive and cooperative co evolutionary approach is adapted for multi objective particle swarm optimization algorithm design which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co evolution of competing and cooperating species the competitive and cooperative co evolution model helps to produce the reasonable problem decompositions by exploiting any correlation interdependency between components of the problem the proposed competitive and cooperative co evolutionary multi objective particle swarm optimization algorithm ccpso is validated through comparisons with existing state of the art multi objective algorithms using established benchmarks and metrics simulation results demonstrated that ccpso shows competitive if not better performance as compared to the other algorithms

quadratic and cubic transformations and zeros of hypergeometric polynomials in this paper we consider the location of the zeros of the hypergeometric polynomials that lie in either the quadratic or the cubic class where each of these classes is determined by a necessary and sufficient condition due to kummer we show that the zeros of most polynomials in these classes can be specified by simple applications of the results proved in recent papers of driver and duren

convex analysis on cartan subspaces in 1937 von neumann 31 gave a famous characterization of unitarily invariant matrix norms that is norms f on cp q satisfying f uxv f x for all unitary matrices u and v and matrices x in cp q his result states that such norms are those functions of the form g where the map x cp q 7 x r has components the singular values 1 x 2 x p x of x assuming p q and g is a norm on rp invariant under sign changes and permutations of components furthermore he showed the respective dual norms satisfy

heckman kostant and steinberg formulas for symplectic manifolds abstract let m be a compact symplectic manifold on which a compact connected lie group k acts in a hamiltonian fashion in part i we derive a formula for j m which generalizes the heckman formula for co adjoint orbits here j is the moment map associated with the action of k on m and m the liouville measure on m in part ii we derive a quantum analogue of this formula which extends to the symplectic setting classical multiplicity formulas of kostant and steinberg

hypergeometric polynomials are optimal with any integer convex polytope p subset mathbb r n we associate a multivariate hypergeometric polynomial whose set of exponents is mathbb z n cap p this polynomial is defined uniquely up to a constant multiple and satisfies a holonomic system of partial differential equations of horn s type we prove that under certain nondegeneracy conditions any such polynomial is optimal in the sense of 7 i e that the topology of its amoeba 13 is as complex as it could possibly be using this we derive optimal properties of several classical families of multivariate hypergeometric polynomials

a hybrid tabu search branch bound approach to solving the generalized assignment problem a new approach for solving the generalized assignment problem gap is proposed that combines the exact branch bound approach with the heuristic strategy of tabu search ts to produce a hybrid algorithm for solving gap the algorithm described uses commercial software to solve sub problems generated by the ts guiding strategy the ts approach makes use of the concept of referent domain optimisation and introduces novel add drop strategies in addition the linear programming relaxation of gap that forms part of the branch bound approach is itself helpful in suggesting which variables might take binary values computational results on benchmark test instances are presented and compared with results obtained by the standard branch bound approach and also several other heuristic approaches from the literature the results show the new algorithm performs competitively against the alternatives and is able to find some new best solutions for several benchmark instances

real algebraic curves the moment map and amoebas in this paper we prove the topological uniqueness of maximal arrangements of a real plane algebraic curve with respect to three lines more generally we prove the topological uniqueness of a maximally arranged algebraic curve on a real toric surface we use the moment map as a tool for studying the topology of real algebraic curves and their complexiflcations

localized states in the generalized swift hohenberg equation the swift hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable wealth of stable spatially localized states the presence of these states is related to a phenomenon called homoclinic snaking numerical computations are used to illustrate the changes in the localized solution as it grows in spatial extent and to determine the stability properties of the resulting states the evolution of the localized states once they lose stability is illustrated using direct simulations in time i introduction ever since the observation that the subcritical complex ginzburg landau equation exhibits stable spatially localized states 1 there has been considerable interest in the properties of these states the presence of these states has important consequences for other systems described by partial differential equations on the line since the ginzburg landau equation describes the behavior of such systems near bifurcation from the trivial state of the system specifically the complex ginzburg landau equation describes the evolution of a long wavelength oscillatory instability as well as oscillatory instabilities at finite wavelength in systems with broken reflection symmetry in contrast near a steady state bifurcation with finite wavelength the evolution of the instability is described by the real ginzburg landau equation and this equation possesses only unstable spatially localized states it is of interest therefore to examine what happens to these unstable states at larger amplitude where the real ginzburg landau equation no longer provides an adequate description of the system in this paper we show that the localized states can become stable at such amplitudes and indeed that there is a large multiplicity of coexisting stable localized states under very general conditions we are able to relate the existence of these states to a phenomenon sometimes called homoclinic snaking that is well known from the theory of reversible systems with 1 1 resonance and use this theory to construct a large number of such states the stability properties of these states are also determined and the evolution of nonstationary localized states is studied by numerical integration in time it is an interesting fact that closely related phenomena have already been described in several areas involving pattern formation the theory was originally developed in the context of water waves where localized states have been studied by moving into a reference frame of the waves and converting the problem into an ordinary differential equation ode the resulting localized states are called solitary waves and in some cases turn out to be solitons kirchgassner 2 has pioneered a successful approach to this type of problem that led to a number of advances in this area specifically the ode is viewed as a dynamical system in space and localized states are sought as homoclinic orbits connecting the trivial state to itself whether such orbits are possible depends in part on the stability properties of the trivial state eigenvalues with positive real part indicate that a nontrivial state can grow from x while eigenvalues with negative real part indicate that such a state may return under appropriate conditions back to the trivial state as x the spectrum of the linearization about the trivial state is influenced by spatial symmetries of the system in many cases and in particular in the case considered here the ode is reversible as a result the bifurcations that are encountered as a parameter is increased are nongeneric in the present case the spatial dynamics of the system near the trivial state turn out to be described by the reversible 1 1 resonance the unfolding of this resonance has been worked out in detail by iooss and peroueme 3 and can be used to understand the appearance of a variety of homoclinic orbits in this system and hence of localized states with different spatial structure

fuzzy matchmaking in e marketplaces of peer entities using datalog we present an approach to matchmaking in electronic marketplaces of peer entities which mixes in a formal and principled way datalog fuzzy sets and utility theory in order to determine the most promising matches between prospective counterparts the use of datalog ensures the scalability of our approach to large marketplaces while fuzzy logic provides a neat connection with logical specifications and allows to model soft constraints and how well they could be satisfied by an agreement noteworthy is that our approach takes into account in the peer to peer matchmaking also preferences of each counterpart and their utilities this allows to rule out of the match list those counteroffers that although seemingly appealing for the buyer would probably lead to failure due to contrasting preferences of the seller and paves the way to the actual negotiation stage

on the normalization of interval and fuzzy weights the normalization of interval and fuzzy weights is often necessary in multiple criteria decision analysis mcda under uncertainty especially in analytic hierarchy process ahp with interval or fuzzy judgements the existing normalization methods based on interval arithmetic and fuzzy arithmetic are found flawed and need to be revised this paper presents the correct normalization methods for interval and fuzzy weights and offers relevant theorems in support of them numerical examples are examined to show the correctness of the proposed normalization methods and their differences from those existing normalization methods

note on on the normalization of interval and fuzzy weights this paper shows by an example that lemma 2 in wang and elhag on the normalization of interval and fuzzy weights fuzzy sets and systems 157 2006 2456 2471 is false and presents the modified lemma and the correct proof of theorem 5

stokes matrices poisson lie groups and frobenius manifolds the purpose of this paper is to point out and then draw some consequences of the fact that the poisson lie group g dual to g gln c may be identified with a certain moduli space of meromorphic connections over the unit disc having an irregular singularity at the origin g will be fully described in sect 2 the key feature of this point of view is that there is a holomorphic map g g from the dual of the lie algebra to the group g for each choice of diagonal matrix a0 with distinct eigenvalues the irregular type this map is essentially the riemann hilbert map or de rham morphism for such connections we will call it the monodromy map it is generically a local analytic isomorphism the main result is

a taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi criteria tsp the difficulty to solve multiple objective combinatorial optimization problems with traditional techniques has urged researchers to look for alternative better performing approaches for them recently several algorithms have been proposed which are based on the ant colony optimization metaheuristic in this contribution the existing algorithms of this kind are reviewed and a proposal of a taxonomy for them is presented in addition an empirical analysis is developed by analyzing their performance on several instances of the bi criteria traveling salesman problem in comparison with two well known multi objective genetic algorithms

lie algebraic aspects of the finite nonperiodic toda flows in this paper we review various aspects of nonperiodic full and tridiagonal toda flow theory in particular we consider gradient structures in the dynamics and geometry of these systems and we compare and contrast a number of formulations of the nonperiodic toda equations we describe the structure of these systems on general semisimple lie algebras in the case of the full kostant asymmetric toda flow we describe some of the background behind its integrability and explain the role of noncommutative integrability in its qualitative behavior we describe the relationship between the asymmetric toda flows and the symmetric and indefinite toda flows and show how one may conjugate from the full kostant toda flows to the full symmetric toda flows via a poisson map we describe briefly related toda systems such as nonabelian toda and the peakon flows

fuzzy multiobjective modeling and optimization for one shot multiattribute exchanges with indivisible demand the modern economy involves a variety of marketplaces and the internet has led to the development of a new efficient marketplace the one shot multiattribute exchange it is an important decision problem for a matchmaker or broker to achieve the optimal trade matching in one shot multiattribute exchanges however to the best of our knowledge there has been little work on this issue under fuzzy environments this paper proposes an optimal matching approach for one shot multiattribute exchanges with simultaneous fuzzy information and indivisible demand considerations first we employ fuzzy set theory to represent the traders orders with fuzzy information and then put forward a calculation method of the matching degree based on the improved fuzzy information axiom second on the basis of the matching degree we construct a fuzzy multiobjective programming model for one shot multiattribute exchanges with indivisible demand afterward the credibility measure is introduced to convert the model into a crisp one the crisp model belongs to a class of multiobjective nonlinear general assignment problems and has np hard complexity in order to solve the crisp model effectively we develop a problem specified metaheuristic algorithm i e multiobjective discrete differential evolution finally we conduct comprehensive computational experiments on numerical examples to illustrate the application and performance of the proposed model and algorithm

algebraic a hypergeometric functions we formulate and prove a combinatorial criterion to decide if an a hypergeometric system of differential equations has a full set of algebraic solutions or not this criterion generalises the so called interlacing criterion in the case of hypergeometric functions of one variable

zeros of ultraspherical polynomials and the hilbert klein formulas abstract the orthogonality of the ultraspherical polynomials cn z for 1 2 ensures that all of their zeros are in the interval 1 1 in a previous paper driver and duren indag math 11 2000 43 51 we have shown that when 1 2 to 1 n in particular the pattern of migration from the interval 1 1 to the imaginary axis serves to confirm and explain the classical formulas of hilbert and klein for the number of zeros of cn z lying in each of the real intervals 1 1 1 and 1

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

amoebas of genus at most one abstract the amoeba of a laurent polynomial f c z 1 1 z n 1 is the image of its zero set v f under the log absolute value map understanding the space of amoebas i e the decomposition of the space of all polynomials say with given support or newton polytope with regard to the existing complement components is a widely open problem in this paper we investigate the class of polynomials f whose newton polytope new f is a simplex and whose support a contains exactly one point in the interior of new f amoebas of polynomials in this class may have at most one bounded complement component we provide various results on the space of these amoebas in particular we give upper and lower bounds in terms of the coefficients of f for the existence of this complement component and show that the upper bound becomes sharp under some extremal condition we establish connections from our bounds to purbhoo s lopsidedness criterion and to the theory of a discriminants finally we provide a complete classification of the space of amoebas for the case that the exponent of the inner monomial is the barycenter of the simplex newton polytope in particular we show that the set of all polynomials with amoebas of genus 1 is path connected in the corresponding space of amoebas which proves a special case of the question on connectivity for general newton polytopes stated by h rullgard

when is a pure state of three qubits determined by its single particle reduced density matrices using techniques from symplectic geometry we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one particle reduced density matrices exactly when their ordered spectra belong to the boundary of the so called kirwan polytope otherwise the states with given reduced density matrices are parameterized up to local unitary equivalence by two real variables given inevitable experimental imprecision this means that already for three qubits a pure quantum state can never be reconstructed from single particle tomography we moreover show that the knowledge of the reduced density matrices is always sufficient if one is given the additional promise that the quantum state is not convertible to the greenberger horne zeilinger state by stochastic local operations and classical communication and discuss generalizations of our results to an arbitrary number of qubits

lorentzian type soliton solutions of ac driven complex ginzburg landau equation abstract fractional transform solutions of modified complex ginzburg landau equation phase locked to a time dependent force have been found the reported solutions are necessarily of the lorentzian type containing trigonometric hyperbolic and pure cnoidal functions numerical simulations indicated that the periodic solutions and soliton solutions are quite stable against finite perturbations

scheduling flow shops using differential evolution algorithm this paper describes a novel optimization method based on a differential evolution exploration algorithm and its applications to solving non linear programming problems containing integer and discrete variables the techniques for handling discrete variables are described as well as the techniques needed to handle boundary constraints in particular the application of differential evolution algorithm to minimization of makespan flowtime and tardiness in a flow shop manufacturing system is given in order to illustrate the capabilities and the practical use of the method experiments were carried out to compare results from the differential evolution algorithm and the genetic algorithm which has a reputation for being very powerful the results obtained have proven satisfactory in solution quality when compared with genetic algorithm the novel method requires few control variables is relatively easy to implement and use effective and efficient which makes it an attractive and widely applicable approach for solving practical engineering problems future directions in terms of research and applications are given

multistable pulselike solutions in a parametrically driven ginzburg landau equation department of interdisciplinary studies faculty of engineering tel aviv university tel aviv 69978 israel dated february 8 2008 it is well known that pulse like solutions of the cubic complex ginzburg landau equation are un stable but can be stabilised by the addition of quintic terms in this paper we explore an alternativemechanism where the role of the stabilising agent is played by the parametric driver our analysis isbased on the numerical continuation of solutions in one of the parameters of the ginzburg landauequation the di usion coe cient c starting from the nonlinear schr odinger limit for which c 0 the continuation generates recursively a sequence of coexisting stable solutions with increasingnumber of humps the sequence converges to a long pulse which can be interpreted as a boundstate of two fronts with opposite polarities i introduction

hamiltonian 2 forms in kahler geometry ii global classification we present a classification of compact kahler manifolds admitting a hamiltonian 2 form which were classified locally in part i of this work this involves two components of independent interest the first is the notion of a rigid hamiltonian torus action this natural condition for torus actions on a kahler manifold was introduced locally in part i but such actions turn out to be remarkably well behaved globally leading to a fairly explicit classification up to a blow up compact kahler manifolds with a rigid hamiltonian torus action are bundles of toric kahler manifolds the second idea is a special case of toric geometry which we call orthotoric we prove that orthotoric kahler manifolds are diffeomorphic to complex projective space but we extend our analysis to orthotoric orbifolds where the geometry is much richer we thus obtain new examples of kahler einstein 4 orbifolds combining these two themes we prove that compact kahler manifolds with hamiltonian 2 forms are covered by blow downs of projective bundles over kahler products and we describe explicitly how the kahler metrics with a hamiltonian 2 form are parameterized we explain how this provides a context for constructing new examples of extremal kahler metrics in particular a subclass of such metrics which we call weakly bochner flat we also provide a self contained treatment of the theory of compact toric kahler manifolds since we need it and find the existing literature incomplete

evolution of nonsoliton and quasi classical wavetrains in nonlinear schro dinger and korteweg de vries equations with dissipative perturbations abstract nonlinear schrodinger equations with attraction and with repulsion nse and nse and the korteweg de vries equation perturbed by small dissipative terms are considered near the linear instability threshold where nonlinear and spatially nonuniform dissipations dominate explicit solutions expressing the local amplitude and occupation numbers of a nonsoliton dispersive wavetrain in terms of arbitrary initial data are obtained at sufficiently large times in the logarithmic approximation for nse the particular case of the wavetrain near the soliton birth threshold is also considered the influence of the dissipation on the evolution of a quasi classical strongly nonlinear wavetrain is studied it is demonstrated that for nse the dissipation can be taken into account within the framework of the eikonal approximation while for the nse a perturbation theory based on the inverse scattering transform is relevant

a multiplier adjustment method for the generalized assignment problem we describe a branch and bound algorithm for the generalized assignment problem in which bounds are obtained from a lagrangian relaxation with the multipliers set by a heuristic adjustment method the algorithm was tested on a large sample of small random problems and a number of large problems derived from a vehicle routing application computation times were reasonable in all cases and the branch and bound trees generated had nearly two orders of magnitude fewer nodes than for competing algorithms although comparison of running times on different machines is difficult the multiplier adjustment method appears to be about one order of magnitude faster than the best previously existing algorithms for this problem