irreducible calibrated representations of periplectic brauer algebras and hook representations of the symmetric group abstract we construct an infinite tower of irreducible calibrated representations of periplectic brauer algebras on which the cup cap generators act by nonzero matrices as representations of the symmetric group these are exterior powers of the standard representation i e hook representations our approach uses the recently defined degenerate affine periplectic brauer algebra which plays a role similar to that of the degenerate affine hecke algebra in representation theory of the symmetric group we write formulas for the representing matrices in the basis of jucys murphy eigenvectors and we completely describe the spectrum of these representations the tower formed by these representations provides a new non semisimple categorification of pascal s triangle along the way we also prove some basic results about calibrated representations of the degenerate affine periplectic brauer algebra

introduction to matrix analytic methods in stochastic modeling preface part i quasi birth and death processes 1 examples part ii the method of phases 2 ph distributions 3 markovian point processes part iii the matrix geometric distribution 4 birth and death processes 5 processes under a taboo 6 homogeneous qbds 7 stability condition part iv algorithms 8 algorithms for the rate matrix 9 spectral analysis 10 finite qbds 11 first passage times part v beyond simple qbds 12 nonhomogeneous qbds 13 processes skip free in one direction 14 tree processes 15 product form networks 16 nondenumerable states bibliography index

preinvexity and φ 1 convexity of fuzzy mappings through a linear ordering the preinvexity prequasiinvexity 1 convexity and 1 quasiconvexity of fuzzy mappings are defined based on a linear ordering on the set of fuzzy numbers characterizations for these fuzzy mappings are obtained the local global minimum properties of real valued preinvex functions and 1 convex functions are extended to preinvex fuzzy mappings and 1 convex fuzzy mappings respectively it is also proved that every strict local minimizer of a prequasiinvex fuzzy mapping is a strict global minimizer and that every strict local minimizer of a 1 quasiconvex fuzzy mapping is a strict global minimizer

convex fuzzy mapping and operations of convex fuzzy mappings convex and concave fuzzy mappings are considered in this paper based on the seminal work of nanda and kar on the definition of convex fuzzy mapping the operations of convex fuzzy mapping are established some of the important concepts such as positively homogeneous infimal convolution right scalar multiplication and convex hull are introduced and the corresponding theorems are demonstrated by using the parametric representation of fuzzy numbers

global optimization using q gradients abstract the q gradient vector is a generalization of the gradient vector based on the q derivative we present two global optimization methods that do not require ordinary derivatives a q analog of the steepest descent method called the q g method and a q analog of the conjugate gradient method called the q cg method both q g and q cg are reduced to their classical versions when q equals 1 these methods are implemented in such a way that the search process gradually shifts from global in the beginning to almost local search in the end moreover gaussian perturbations are used in some iterations to guarantee the convergence of the methods to the global minimum in a probabilistic sense we compare q g and q cg with their classical versions and with other methods including cma es a variant of controlled random search and an interior point method that uses finite difference derivatives on 27 well known test problems in general the q g and q cg methods are very promising and competitive especially when applied to multimodal problems

tabu search applied to global optimization abstract a new algorithm called enhanced continuous tabu search ects is proposed for the global optimization of multiminima functions it results from an adaptation of combinatorial tabu search which aims to follow as close as possible glover s basic approach in order to cover a wide domain of possible solutions our algorithm first performs the diversification it locates the most promising areas by fitting the size of the neighborhood structure to the objective function and its definition domain when the most promising areas are located the algorithm continues the search by intensification within one promising area of the solution space the efficiency of ects is thoroughly tested by using a set of benchmark multimodal functions of which global and local minima are known ects is compared to other published versions of continuous tabu search and to some alternative algorithms like simulated annealing we point out two main advantages of ects first its principle is rather basic directly inspired from combinatorial tabu search secondly it shows a good performance for functions having a large number of variables more than 10

irreducible characters of general linear superalgebra and super duality we develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra including all the finite dimensional modules by directly relating the problem to the classical kazhdan lusztig theory furthermore we prove that certain parabolic bgg categories over the general linear algebra and over the general linear superalgebra are equivalent we also verify a parabolic version of a conjecture of brundan on the irreducible characters in the bgg category of the general linear superalgebra

some properties of geodesic semi e convex functions abstract in this paper we introduce a new class of functions called geodesic semi e convex functions and discuss some of their properties

invex and generalized convex fuzzy mappings in this paper we introduce the concepts of pseudo convexity invexity and pseudo invexity for fuzzy mappings of one variable based on the notion of differentiability proposed by goetschel and voxman 4 and investigate the relationship between convex fuzzy mappings preinvex fuzzy mappings and these classes of fuzzy mappings we shall prove that pseudo convex fuzzy mappings and invex fuzzy mappings are pseudo invex and that a differentiable convex resp preinvex fuzzy mapping is pseudo convex resp invex in addition sufficient optimality conditions are obtained for pseudo convex invex and pseudo invex fuzzy mappings

coherent families of weight modules of lie superalgebras and an explicit description of the simple admissible sl n 1 1 modules abstract let g be a classical lie superalgebra of type i we introduce coherent families of weight g modules with bounded weight multiplicities and establish a correspondence between cuspidal and highest weight submodules of these families by extending mathieu s work ann inst fourier 50 2000 537 this enables us to reduce the description of the g 0 module structure of arbitrary simple weight g modules with bounded weight multiplicities to the g 0 module structure of highest weight modules with bounded weight multiplicities we then construct tensor coherent families for g sl n 1 1 which yield an explicit description of the g 0 structure of an arbitrary simple weight module with bounded weight multiplicities in particular we show that for g sl n 1 1 the maximal length of an indecomposable g 0 submodule of a simple weight module with bounded multiplicities equals 5

a new hybrid algorithm of scatter search and nelder mead algorithms to optimize joint economic lot sizing problem this paper introduces a hybrid algorithm of nelder mead and scatter search algorithms called ssnm numerical results for some known test problems with varying dimensions from 2 to 100 variables prove its great performance for a bounded or constrained problem this paper also has a considerable contribution to the joint economic lot sizing jels problem literature this problem is considered for a two stage supply chain with price sensitive demand for geometric geometric then equal size and optimal shipment policies solution procedures are also developed which use the ssnm algorithm in their steps these models and solution procedures are novel in the jels literature it introduces a new hybrid algorithm of nelder mead and scatter search algorithms the new algorithm is able to find global optimal solution of constrained problems it considers joint economic lot sizing problem with price sensitive demand it models lot sizing problem for three shipment policies that were not modeled yet it develops solution procedures based on the new algorithm to solve the models

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

principles of scatter search scatter search is an evolutionary method that has been successfully applied to hard optimization problems the fundamental concepts and principles of the method were first proposed in the 1970s based on formulations dating back to the 1960s for combining decision rules and problem constraints in contrast to other evolutionary methods like genetic algorithms scatter search is founded on the premise that systematic designs and methods for creating new solutions afford significant benefits beyond those derived from recourse to randomization it uses strategies for search diversification and intensification that have proved effective in a variety of optimization problems this paper provides the main principles and ideas of scatter search and its generalized form path relinking we first describe a basic design to give the reader the tools to create relatively simple implementations more advanced designs derive from the fact that scatter search and path relinking are also intimately related to the tabu search ts metaheuristic and gain additional advantage by making use of ts adaptive memory and associated memory exploiting mechanisms capable of being tailored to particular contexts these and other advanced processes described in the paper facilitate the creation of sophisticated implementations for hard problems that often arise in practical settings due to their flexibility and proven effectiveness scatter search and path relinking can be successfully adapted to tackle optimization problems spanning a wide range of applications and a diverse collection of structures as shown in the papers of this volume

finite dimensional representations of periplectic lie superalgebras abstract we study categories of finite dimensional modules over the periplectic lie superalgebras and obtain a bgg type reciprocity in particular we prove that these categories have only finitely many blocks we also compute the characters for irreducible modules over periplectic lie superalgebras of ranks 2 and 3 and obtain explicit description of the blocks for ranks 2 3 and 4

a ph ph n c c state dependent queuing model for metro station corridor width design abstract metro station corridor width design considering demand fluctuation as well as the randomness and state dependence of service time is an urgent concern and a complicated random planning issue this paper confirms the accuracy of phase type distribution ph fitting for passenger arrival intervals and service times with randomness and state dependence in metro station corridors a ph ph n c c state dependent queuing model is thus established by a finite level dependent quasi birth death qbd process the existing m g n c c m g 1 c and d d 1 c models are proved to be special cases of the ph ph n c c model through theoretical derivation and the precision of the proposed model is analyzed through simulation tests the quantitative relationship between the level of service los and the corridor width is established based on the proposed model a total of 81 experiments are designed to compare the calculations between the proposed model and the m g n c c m g 1 c and d d 1 c models comparison results demonstrate that 1 the value of effective width of the ph ph n c c queuing model is higher than those of the m g n c c m g 1 c and d d 1 c models 2 the real area occupied per person in the corridor of the ph ph n c c queuing model is mostly proximate to the designed los whereas those of the m g n c c m g 1 c and d d 1 c models fail to meet the designed los and 3 the performance measures of the ph ph n c c queuing model enjoy high performance width elasticity and are significantly improved compared with those of the m g n c c m g 1 c and d d 1 c models

some properties of semi e convex functions abstract in this paper we show that theorems 4 2 4 3 and 4 6 in youness j optim theory appl 102 1999 439 450 are incorrect by giving some counterexamples we introduce a new class of semi e convex function and discuss some its basic properties

on characterizations of preinvex fuzzy mappings several characterizations about preinvex fuzzy mapping are obtained in this paper firstly an equivalent condition of preinvex fuzzy mapping is established under certain conditions furthermore the necessary and sufficient conditions for differentiable and twice differentiable preinvex fuzzy mapping are provided by using the given equivalent condition of preinvex fuzzy mapping finally a new proof of some known important conclusions is offered these results generalize and improve some known results

the center of a simple p type lie superalgebra we describe the center of a simple lie superalgebra of type p n the description is based on the notion of anticenter

subexponential asymptotics of the stationary distributions of m g 1 type markov chains this paper studies the subexponential asymptotics of the stationary distribution of an m g 1 type markov chain we provide a sufficient condition for the subexponentiality of the stationary distribution the sufficient condition requires only the subexponential integrated tail of level increments on the other hand the previous studies assume the subexponentiality of level increments themselves and or the aperiodicity of the g matrix therefore our sufficient condition is weaker than the existing ones we also mention some errors in the literature

the general linear supergroup and its hopf superalgebra of regular functions abstract the structure of the hopf superalgebra b of regular functions on the general linear supergroup is developed and applied to study the representation theory of the supergroup it is shown that the general linear supergroup can be reconstructed from b in a way reminiscent of the tannaka krein theory a borel weil type realization is also obtained for the irreducible integrable representations as a side result on the structure of b schur superalgebras are introduced and are shown to be semi simple over the complex field with the simple ideals determined explicitly

pseudolinear fuzzy mappings two classes of fuzzy mappings called pseudolinear and pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo convex and pseudo invex fuzzy mappings first some characterizations of pseudolinear and pseudolinear fuzzy mappings are obtained then characterizations of the solution sets of pseudolinear and pseudolinear fuzzy programs are derived

generalized convexity in fuzzy vector optimization through a linear ordering in this article we study efficiency and weakly efficiency in fuzzy vector optimization after formulating the problem we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized hukuhara differentiability pseudoinvexity i and pseudoinvexity ii we prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem we give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex i and ii moreover we present some examples to illustrate the results lastly we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models

finding local optima of high dimensional functions using direct search methods this paper focuses on a subclass of box constrained non linear optimization problems we are particularly concerned with settings where gradient information is unreliable or too costly to calculate and the function evaluations themselves are very costly this encourages the use of derivative free optimization methods and especially a subclass of these referred to as direct search methods the thrust of our investigation is twofold first we implement and evaluate a number of traditional direct search methods according to the premise that they should be suitable as local optimizers when used in a metaheuristic framework second we introduce a new direct search method based on scatter search designed to remedy the lack of a good derivative free method for solving problems of high dimensions our new direct search method has convergence properties comparable to those of existing methods in addition to being able to solve larger problems more effectively

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

on the structure of weight modules given any simple lie superalgebra g we investigate the structure of an arbitrary simple weight 0 module we introduce two invariants of simple weight modules the shadow and the small weyl group generalizing results of fernando and futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a levi subsuperalgebra then we classify the cuspidal levi subsuperalgebras of all simple classical lie superalgebras and of the lie superalgebra w n most of them are simply levi subalgebras of go in which case the classification of all finite cuspidal representations has recently been carried out by one of us mathieu our results reduce the classification of the finite simple weight modules over all classical simple lie superalgebras to classifying the finite cuspidal modules over certain lie superalgebras which we list explicitly

a path relinking approach with ejection chains for the generalized assignment problem the generalized assignment problem is a classical combinatorial optimization problem known to be np hard it can model a variety of real world applications in location allocation machine assignment and supply chains the problem has been studied since the late 1960s and computer codes for practical applications emerged in the early 1970s we propose a new algorithm for this problem that proves to be more effective than previously existing methods the algorithm features a path relinking approach which is a mechanism for generating new solutions by combining two or more reference solutions it also features an ejection chain approach which is embedded in a neighborhood construction to create more complex and powerful moves computational comparisons on benchmark instances show that the method is not only effective in general but is especially effective for types d and e instances which are known to be very difficult

graded tensor calculus we develop a graded tensor calculus corresponding to arbitrary abelian groups of degrees and arbitrary commutation factors the standard basic constructions and definitions like tensor products spaces of multilinear mappings contractions symmetrization symmetric algebra as well as the transpose adjoint and trace of a linear mapping are generalized to the graded case and a multitude of canonical isomorphisms is presented moreover the graded versions of the classical lie algebras are introduced and some of their basic properties are described

genetic and nelder mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions abstract a hybrid method combining two algorithms is proposed for the global optimization of multiminima functions to localize a promising area likely to contain a global minimum it is necessary to well explore the whole search domain when a promising area is detected the appropriate tools must be used to exploit this area and obtain the optimum as accurately and quickly as possible both tasks are hardly performed through only one method we propose an algorithm using two processes each one devoted to one task global metaheuristics such as simulated annealing tabu search and genetic algorithms gas are efficient to localize the best areas on the other hand local search methods are classically available in particular the hill climbing e g the quasi newton method and the nelder mead simplex search ss therefore we worked out an hybrid method called continuous hybrid algorithm cha performing the exploration with a ga and the exploitation with a nelder mead ss to evaluate the efficiency of cha we implemented a set of benchmark functions and compared our results to the ones supplied by other competitive methods

casimir elements of e lie algebras the classical framework for investigating the casimir elements of a lie algebra is generalized to the case of an e lie algebra l we construct the standard l module isomorphism of the e symmetric algebra of l onto its enveloping algebra and we introduce the harish chandra homomorphism in case the generators of l can be written in a canonical two index form we construct the associated standard sequence of casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module

a solution procedure for the discrete time cost and quality tradeoff problem using electromagnetic scatter search abstract decisions concerning a project s expedition traditionally involved considerations regarding time and cost tradeoff it was recently suggested that the quality of a project should also be taken into considerations in this paper we propose a meta heuristic solution procedure for the discrete time cost and quality tradeoff problem this problem involves the scheduling of project activities in order to minimize the total cost of the project while maximizing the quality of the project and also meeting a given deadline we apply a so called electromagnetic scatter search to solve this problem in this process we initially generate a population of feasible solutions in so doing we use frequency memory to well sample the feasible region a number of these solutions are then selected and improved locally the improved solutions are then combined to generate new set of solutions the combination process utilizes attraction repulsion mechanisms borrowed from the electromagnetism theory the whole process is stopped when no significant improvement in the set of solutions are observed the validity of the proposed solution procedure is demonstrated and its applicability is tested on a randomly generated large and complex problem having 19 900 activities

a multi objective quantity discount and joint optimization model for coordination of a single buyer multi vendor supply chain supply chain management is concerned with the coordination of different parts of the production system companies have realized that they must closely collaborate with the suppliers of their strategic components or products recently developing integrated inventory models for the supplier selection problem has attracted a significant amount of attention amongst researchers in these models some incentives are required from the vendors to motivate the buyer to change his her policies to the policy which is optimal for the entire system quantity discount policies are used as common incentives in the literature however the literature on this problem does not incorporate quantity discount into the coordination model this paper develops a multi objective mixed integer nonlinear programming model to coordinate the system of a single buyer and multiple vendors under an all unit quantity discount policy for the vendors due to the complexity of the problem two well known meta heuristic algorithms are proposed to solve the problem an illustrative example is given to show the behavior of the model results obtained from solving the sample problems show good performance of the proposed algorithms in finding the optimal solutions

preinvex fuzzy mappings abstract in this paper we introduce the concepts of preinvex fuzzy mappings quasi preinvex fuzzy mappings and invex sets by modifying the concepts proposed by noor we also give two characterization theorems for preinvex fuzzy mappings and present some new results for preinvex fuzzy mappings strictly preinvex fuzzy mappings and quasi preinvex fuzzy mappings

affine periplectic brauer algebras we formulate nazarov wenzl type algebras p over cap d for the representation theory of the periplectic lie superalgebras p n we establish an arakawa suzuki type functor to provide a connec

continuous optimization via simulation using golden region search simulation optimization so is a class of mathematical optimization techniques in which the objective function can only be numerically evaluated through simulation in this paper a new so approach called golden region gr search is developed for continuous problems gr divides the feasible region into a number of sub regions and selects one region in each iteration for further search based on the quality and distribution of simulated points in the feasible region and the result of scanning the response surface through a metamodel monte carlo experiments show that the gr method is efficient compared to three well established approaches in the literature we also prove the asymptotic convergence in probability to a global optimum for a large class of random search methods in general and gr in particular

on invex fuzzy mappings and fuzzy variational like inequalities in this paper we first show the need for introducing invex fuzzy mappings after that we show that the concept of invex fuzzy mapping previously given by wu and xu are very restrictive and the examples presented there are not correct then we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping finally we show that the results obtained by wu and xu on the relationship between fuzzy variational like inequalities and fuzzy optimization problems are still valid using these new concepts

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

some aspects of scatter search in the flow shop problem abstract the flow shop scheduling problem with the makespan criterion is a certain strongly np hard case from the domain of or this problem having simple formulation contrasting with its troublesome complex and time consuming solution methods is ideal for testing the quality of advanced combinatorial optimization algorithms although many excellent approximate algorithms for the flow shop problem have been provided up till now in the literature some theoretical and experimental problems associated with an algorithm s activity still remain unexamined in this paper we provide a new view on the solution space and the search process relying upon it we are proposing the new approximate algorithm which applies some properties of neighborhoods refers to the big valley phenomenon uses some elements of the scatter search as well as the path relinking technique this algorithm shows up to now unprecedented accuracy obtainable within a short time on a pc which has been confirmed in a wide variety of computer tests good properties of the algorithm remain scalable if the size of instances increases

the z2 graded schouten nijenhuis bracket and generalized super poisson structures the super or z2 graded schouten nijenhuis bracket is introduced using it new generalized super poisson structures are found which are given in terms of certain graded skew symmetric contravariant tensors of even order the corresponding super jacobi identities are expressed by stating that these tensors have a zero super schouten nijenhuis bracket with themselves 0 as a particular case we provide the linear generalized super poisson structures which can be constructed on the dual spaces of simple superalgebras with a non degenerate killing metric the su 3 1 superalgebra is given as a representative example

φ1 φ2 convex fuzzy mappings abstract the concepts of 1 2 convexity 1 b vexity and 1 convexity for fuzzy mappings are introduced through the so called fuzzy max order among fuzzy numbers we show that the class of 1 2 convex fuzzy mappings 1 b vex fuzzy mappings and 1 convex fuzzy mappings includes many well known classes of fuzzy mappings such as convex fuzzy mappings and preinvex fuzzy mappings as its subclasses we also give a characterization for 1 b vex fuzzy mappings by proposing the concept of 1 b vex sets in addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed

spherical indecomposable representations of lie superalgebras abstract we present a classification of all spherical indecomposable representations of classical and exceptional lie superalgebras we also include information about stabilizers symmetric algebras and borels for which sphericity is achieved in one such computation the symmetric algebra of the standard module of osp m 2 n is computed which in particular gives the representation theoretic structure of polynomials on the complex supersphere

scatter search with path relinking for the flexible job shop scheduling problem abstract the flexible job shop scheduling is a challenging problem due to its high complexity and the huge number of applications it has in real production environments in this paper we propose effective neighborhood structures for this problem including feasibility and non improving conditions as well as procedures for fast estimation of the neighbors quality these neighborhoods are embedded into a scatter search algorithm which uses tabu search and path relinking in its core to develop these metaheuristics we define a novel dissimilarity measure which deals with flexibility we conducted an experimental study to analyze the proposed algorithm and to compare it with the state of the art on standard benchmarks in this study our algorithm compared favorably to other methods and established new upper bounds for a number of instances

path relinking approach for multiple allocation hub maximal covering problem we consider the multiple allocation hub maximal covering problem mahmcp considering a serviced o d flow was required to reach the destination optionally passing through one or two hubs in a limited time cost or distance what is the optimal way to locate p hubs to maximize the serviced flows by designing a new model for the mahmcp we provide an evolutionary approach based on path relinking the computational experience of an ap data set was presented and a special application on hub airports location of chinese aerial freight flows between 82 cities in 2002 was introduced

new expressions for the eigenvalues of the invariant operators of the general linear and the orthosymplectic lie superalgebras we obtain expansions for the eigenvalues cp of the invariant operators casimir operators of the general linear and the orthosymplectic lie superalgebras in terms of products of suitably defined graded power sums pk the resulting expressions are closed and provide unified formulas for computing the cp s for those superalgebras as well as their corresponding lie algebras the formulas are remarkably simple to suggest that the power sums used in this text could play a more basic role in the understanding of the pattern of the expansion coefficients explicit illustrations are given for the various series for p 8

cohomology of lie superalgebras and their generalizations the cohomology groups of lie superalgebras and more generally of e lie algebras are introduced and investigated the main emphasis is on the case where the module of coefficients is nontrivial two general propositions are proved which help to calculate the cohomology groups several examples are included to show the peculiarities of the super case for l sl 1 2 the cohomology groups h1 l v and h2 l v with v a finite dimensional simple graded l module are determined and the result is used to show that h2 l u l with u l the enveloping algebra of l is trivial this implies that the superalgebra u l does not admit any nontrivial formal deformations in the sense of gerstenhaber garland s theory of universal central extensions of lie algebras is generalized to the case of e lie algebras

fuzzy preinvex functions in this paper we introduce the concept of fuzzy preinvex functions and invex sets these functions are more general than convex fuzzy functions and when differentiable are fuzzy invex some different types of fuzzy preinvexity functions are defined and their properties are studied it is proved that the minimum of the fuzzy preinvex functions on the invex sets can be characterized by variational like inequalities

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

generalization of preinvex and b vex fuzzy mappings a class of fuzzy mappings called b preinvex and strictly b preinvex fuzzy mappings is introduced by relaxing the definition of preinvexity of a fuzzy mapping similarly based on a notion of differentiability of fuzzy mappings different from the usual one the class of pseudo b vex b invex and pseudo b invex fuzzy mappings is defined as a generalization of pseudo convex invex and pseudo invex fuzzy mappings we prove that a strictly b vex or b preinvex fuzzy mapping has at most one global minimum point and that the class of b vex fuzzy mappings forms a subset of the class of quasi convex fuzzy mappings b vex resp b preinvex fuzzy mappings satisfy most of the basic properties of convex resp preinvex fuzzy mappings in addition characterizations and sufficient optimality conditions are obtained for b vex and b preinvex fuzzy mappings

accelerated tabu search for no wait flowshop scheduling problem with maximum lateness criterion abstract for the no wait flowshop scheduling problem with maximum lateness criterion properties are developed to speed up three kinds of basic operations generating candidate solutions i e the insertion of a new job into a partial sequence and the insertion and exchange neighborhood moves the properties reduce the time to evaluate a candidate from o nm to o 1 and simplify the implementation of the heuristics based on the basic operations by evaluating candidates before their generation the properties also reduce from o n 3 m to o n 2 the time complexity of well known neh heuristic and the complete evaluation of the insertion and exchange neighborhoods tabu search ts is applied to the considered problem since ts tries to find the best neighbor of the current solution in each iteration and therefore can much benefit from the speedups three different ways to use insertion and exchange neighborhoods are compared in ts computational experiments show that the speedups are more helpful as job number increases and all proposed ts algorithms are more effective and robust than the existing algorithms although two and single neighborhood ts algorithms are not significantly different two neighborhood ts algorithms are more preferable

super duality and irreducible characters of ortho symplectic lie superalgebras we formulate and establish a super duality which connects parabolic categories o for the ortho symplectic lie superalgebras and classical lie algebras of bcd types this provides a complete and conceptual solution of the irreducible character problem for the ortho symplectic lie superalgebras in a parabolic category o which includes all finite dimensional irreducible modules in terms of classical kazhdan lusztig polynomials

on fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings in this paper we first introduce the weakly invex fuzzy mappings based on weakly differentiable functions and discuss the relationships between several kinds of fuzzy generalized convex mappings then a kind of fuzzy weakly univex functions are introduced and some properties of them are investigated furthermore optimality and duality results are derived for a class of generalized convex optimization problems with fuzzy weakly univex functions

hybrid of the scatter search improved adaptive genetic and expectation maximization algorithms for phase type distribution fitting although a large number of different methods for establishing the fitting parameters of ph distributions to data traces ph fitting have been developed most of these approaches lack efficiency and numerical stability in the present paper a restricted class of ph distribution called the hyper erlang distribution herd is used to establish a maximum likelihood estimation model for data tracing to fit the parameters a hybrid algorithm based on the scatter search algorithm the improved adaptive genetic algorithm and the expectation maximization algorithm was developed to obtain the ssi thus g fit repeatedly has to test the number of states manually to achieve a satisfactory fitting effect b although setting range of the number of branches in g fit could mitigate the aforementioned deficiency the combinations of the number of phases per branch grow exponentially and c on ss iaga em can optimize the number of states and the number of phases automatically aside from being slightly faster than g fit for a small number of branches and is significantly faster for a large number of branches moreover in all tests ss iaga em can achieve the same fitting quality as g fit for the same number of states

laplace operators of infinite dimensional lie algebras and theta functions abstract until recently the generalized casimir operator constructed by kac kac v g 1974 funct anal appl 8 68 70 has been the only known element of the center of a completion of the enveloping algebra of a kac moody algebra it has been conjectured deodhar v v gabber o kac v g 1982 adv math 45 92 116 however that the image of the harish chandra homomorphism contains all theta functions defined on the interior of the complexified tits cone and hence separates the orbits of the weyl group developing the ideas of feigin and fuchs feigin b l fuchs d b 1983 dokl akad nauk sssr 269 1057 1060 i prove this conjecture another application of this method is the chevalley type restriction theorem for simple finite dimensional lie superalgebras

eigenvalues of casimir operators for the general linear the special linear and the orthosymplectic lie superalgebras the generators of the algebras under consideration can be written in a canonical two index form and hence the associated standard sequence of casimir elements can be constructed following the classical approach by perelomov and popov we obtain the eigenvalues of these casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions

invariant supersymmetric multilinear forms and the casimir elements of p type lie superalgebras the casimir elements of the p type lie superalgebras are investigated depending on the class of algebras under consideration either there do not exist any nontrivial casimir elements at all or else the casimir elements are highly degenerate basic to the investigation is a lemma about invariant supersymmetric multilinear forms on a finite dimensional module over a lie superalgebra some comments on the cartan subalgebras of a lie superalgebra are also included an appendix provides some information on multilinear algebra with e commuting scalars

grasp and path relinking for the matrix bandwidth minimization in this article we develop a greedy randomized adaptive search procedure grasp for the problem of reducing the bandwidth of a matrix this problem consists of finding a permutation of the rows and columns of a given matrix which keeps the nonzero elements in a band that is as close as possible to the main diagonal the proposed method may be coupled with a path relinking strategy to search for improved outcomes empirical results indicate that the proposed grasp implementation compares favourably to classical heuristics grasp with path relinking is also found to be competitive with a recently published tabu search algorithm that is considered one of the best currently available for bandwidth minimization

indecomposable representations of special linear lie superalgebras abstract the main result of this paper is a classification of finite dimensional representations of the lie superalgebras sl m 1 of supertraceless endomorphisms of the vector superspace of dimension m 1 the classification extends to the so called singly atypical blocks of the lie superalgebras sl m n but there exist wild representation type blocks as soon as bothmandnare 2

ph fitting of the arrival interval distribution of the passenger flow on urban rail transit stations the urban railway transit station is a type of stochastic service system the accurate description for the arrival interval distribution of the passenger flow with strong randomness is the basis of the planning design and operation of the urban rail transit stations however the existing fitting distributions are not accurate enough to satisfy the demand in practice although the famous phase type distribution ph has been proven to have the merits of high accuracy universality and analyticity it has too many parameters needed to be calibrated in this paper seven common distributions and hyper erlang distribution herd which is a dense subset of ph were applied to fit arrival interval distribution of the passenger flow of entrances and platforms on subway stations the comparative results indicated that herd achieves the highest accuracy on this basis the fitting parameters of herd were analysed finding that this distribution is required to determine two parameters and only related with variation coefficient possessing good practicability finally this paper puts forward a practical method to determine the two parameters of herd through the easy captured peak passenger flow volume and super peak coefficient during station planning and design stage this research provides a new alternative ph distribution for fitting passenger flow arrival interval distribution on urban rail transit stations

on fuzzy convexity and parametric fuzzy optimization abstract in this paper some different types of convexity and generalized convexity of fuzzy sets are defined and their properties are studied a general fuzzy nonlinear programming problem is formulated with application of the concept of convexity

on representations of the lie superalgebra p n abstract we introduce a new way to study representations of the lie superalgebra p n since the center of the universal enveloping algebra u acts trivially on all irreducible representations we suggest to study the quotient algebra u by the radical of u we show that u has a large center which separates typical finite dimensional irreducible representations we give a description of u factored by a generic central character using this description we obtain character formulae of generic infinite dimensional irreducible representations we also describe some geometric properties of the supervariety spec gr u in the coadjoint representation

a tower construction for the radical in brauer s centralizer algebras abstract in this paper we study the structure of the brauer centralizer algebras in the case that the multiplication constant x is a rational integer several authors have studied the structure of these algebras for generic values of x in particular hans wenzl showed that the brauer algebras can be obtained from jones basic construction and he used that fact to prove that the brauer algebras are semisimple when x is not a rational integer the tower construction is a method to study towers of semisimple algebras hence it does not apply in our case where the algebras in the tower eventually have radicals our first step in this paper is to modify the tower construction so that it does a simultaneous tower construction of the radicals and the semisimple quotients of a tower of algebras the rest of the paper is devoted to describing these constructions explicitly in the brauer algebra case one surprising corollary of this method is a connection between two seemingly distinct criteria for the simplicity of certain subrings of the brauer algebras it is possible to identify explicitly certain subrings of the brauer algebras which are the matrix rings corresponding to irreducible representations in the semisimple case in previous work these authors gave a combinatorial condition for simplicity of these individual matrix rings when x is a rational integer the tower construction gives a second algebraic condition for simplicity it is difficult to see why these two conditions are equivalent however the methods used in this paper make that clear

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

casimir invariants characteristic identities and tensor operators for strange superalgebras we define a class of super subalgebras of gl m n realized as the set of fixed points of a graded endomorphism of gl m n this class includes the superalgebras gp m and gq m related to the so called strange simple superalgebras p m and q m as well as osp m n general covariant contravariant and mixed tensor operators are defined for this class in terms of appropriate module homomorphisms traces of certain tensors give the usual sequence of casimir invariants for gp m these are shown to vanish identically while for gq m eigenvalues of the quadratic and cubic casimir invariants are derived in terms of highest weights and a polynomial characteristic identity is exhibited

a scatter search algorithm for the distributed permutation flowshop scheduling problem abstract the distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs distributed manufacturing is a common situation for large enterprises that compete in a globalized market the problem has two dimensions assigning jobs to factories and scheduling the jobs assigned to each factory despite being recently introduced this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature in this paper we present a scatter search ss method for this problem to optimize makespan ss has seldom been explored for flowshop settings in the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search a comprehensive computational campaign including 10 existing algorithms together with statistical analyses shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin moreover all 720 known best solutions for this problem are improved

a t norm embedding theorem for fuzzy sets it is well known that the class of upper semicontinuous normal convex fuzzy sets with compact supports can be embedded isometrically as a complete convex cone in a banach space we prove an analogous result for a subclass of fuzzy sets that is free from the normality limitation by exchanging the standard algebraic operations on fuzzy sets with operations based on strict t norms this allows us to investigate a new notion of fuzzy convexity that we call t convexity we show that the class of upper semicontinuous fuzzy t convex sets with nonempty compact supports can be embedded as a closed convex cone in a banach space this implies that fuzzy t convex sets satisfy the cancellation law we discuss a possible application of the embedding theorem in mathematical morphology

bethe subalgebras in affine birman murakami wenzl algebras and flat connections for q kz equations commutative sets of jucys murphy elements for affine braid groups of types were defined construction of r matrix representations of the affine braid group of type and its distinguished commutative subgroup generated by the type jucys murphy elements are given we describe a general method to produce flat connections for the two boundary quantum knizhnik zamolodchikov equations as necessary conditions for sklyanin s type transfer matrix associated with the two boundary multicomponent zamolodchikov algebra to be invariant under the action of the type jucys murphy elements we specify our general construction to the case of the birman murakami wenzl algebras bmw algebras for short as an application we suggest a baxterization of the dunkl cherednik elements in the double affine hecke algebra of type a

incorporating scatter search and threshold accepting in finding maximum likelihood estimates for the multinomial probit model this paper presents a procedure that incorporates scatter search and threshold accepting to find the maximum likelihood estimates for the multinomial probit mnp model scatter search widely used in optimization related studies is a type of evolutionary algorithm that uses a small set of solutions as the selection pool for mating and generating new solutions to search for a globally optimal solution threshold accepting is applied to the scatter search to improve computational efficiency while maintaining the same level of solution quality a set of numerical experiments based on synthetic data sets with known model specifications and error structures were conducted to test the effectiveness and efficiency of the proposed framework the results indicated that the proposed procedure enhanced performance in terms of likelihood function value and computational efficiency for mnp model estimation as compared to the original scatter search framework

continuous scatter search an analysis of the integration of some combination methods and improvement strategies scatter search is an evolutionary method that shares with genetic algorithms a well known evolutionary approach the employment of a combination method that combines the features of two parent vectors to form several offspring furthermore it uses improvement strategies to efficiently produce the local tuning of the solutions an important aspect concerning scatter search is the trade off between the exploration abilities of the combination method and the exploitation capacity of the improvement mechanism in this paper we deal with a continuous version of the scatter search which works directly with vectors of real components our objective is to study the balance between the reliability induced by the combination method and the accuracy levels provided by the improvement mechanism in continuous scatter search to do this we analyse two combination methods that may be applied to continuous scatter search 1 the blx a operator which is one of the most effective combination methods for real coded genetic algorithms and 2 the average combination method which is the classical combination method for continuous scatter search we investigate the interrelations that exist between

minimization by random search techniques we give two general convergence proofs for random search algorithms we review the literature and show how our results extend those available for specific variants of the conceptual algorithm studied here we then exploit the convergence results to examine convergence rates and to actually design implementable methods finally we report on some computational experience

necessary and sufficient conditions for fuzzy optimality problems in this paper we define a new minimum concept for fuzzy optimization problems more general than those that exist in the literature we find necessary optimality conditions based on a new fuzzy stationary point definition and we prove that these conditions are also sufficient under new fuzzy generalized convexity notions

lie groups and lie algebras with generalized supersymmetric parameters matrices with symmetric parameters the most general extension of supersymmetric parameters are investigated the superdeterminants of such matrices are defined lie groups consisting of these matrices and their lie algebras are studied

cohomology of generalized supergrassmannians and character formulae for basic classical lie superalgebras we use geometrical methods adapted from borel weil bott theory to compute the character of every finite dimensional simple module over a basic classical lie superalgebra the answer is given by a combinatorial algorithm in terms of weight and cap diagrams which were defined by brundan and stroppel for the general linear superalgebra ams subject classification 20g05 14f05

combining path relinking and genetic algorithms for the multiple level warehouse layout problem path relinking is a method to generate new solution by exploring trajectories that connect high quality solutions in this paper a class of new hybrid heuristics are proposed by combining a genetic algorithm and path relinking and applying these to a multiple level warehouse layout problem parallel and series combinations to integrate crossover and mutation operations of a genetic algorithm with path relinking are investigated we proposed position and sequence based path relinking methods to connect two solutions which are either elites or ones selected randomly extensive experiments are carried out to compare the performance of the new heuristics

eigenvalues of casimir operators for the general linear and orthosymplectic lie superalgebras a racah basis is introduced for the generators of these matrix superalgebras and explicit formulas are derived for eigenvalues of casimir operators in terms of the components of the highest weight the result contains as special cases the corresponding expressions for the general linear orthogonal and symplectic lie algebras

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed

automorphisms of toroidal lie superalgebras abstract we give a description of the algebraic group aut g of automorphisms of a simple finite dimensional lie superalgebra g over an algebraically closed field k of characteristic 0 which is obtained by viewing g as a module over a levi subalgebra of its even part as an application we give a detailed description of the group of automorphism of the k lie superalgebra g k r for a large class of commutative rings r