fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

spectrum localizations for matrix operators on l p spaces we investigate localization of spectra of infinite matrices that can act as linear operators from the banach space l p 1 p to itself to that end we propose a method that is based on generalization of a strict diagonal dominance of infinite matrices that is adapted to l p and l q norms results are illustrated with several examples and some interesting applications are discussed

eigenvalues for infinite matrices this paper is concerned with the problem of determining the location of eigenvalues for diagonally dominant infinite matrices upper and lower bounds for eigenvalues are established for tridiagonal matrices a numerical procedure for improving the bounds is given and the approximation of the eigenvectors is also discussed the techniques are illustrated for the solution of the well known mathieu s equation

comparing the commutative and non commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices abstract let y be the variety of skew symmetric n n matrices of rank r in paper we construct a full faithful embedding between the derived category of a non commutative resolution of y constructed earlier by the authors and the derived category of the classical springer resolution of y

character formula for infinite dimensional unitarizable modules of the general linear superalgebra the fock space of m p bosonic and n q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm p n q its tensor powers decompose into direct sums of infinite dimensional irreducible highest weight glm p n q modules we obtain an explicit decomposition of any tensor power of this fock space into irreducibles and develop a character formula for the irreducible glm p n q modules arising in this way

a note on the conditional probability of fuzzy subsets of a continuous domain abstract the notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets the definition is motivated by considering a possible mechanism by which an intelligent agent could extend set theoretic operations to fuzzy sets this same mechanism also suggests an alternative definition for the conditional probability of fuzzy sets it is noted that this definition is probability possibility consistent and it is shown that in the case where the probability distribution on the domain has a density function then the conditional probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g this result is used to develop an analytical method for calculating conditional probabilities of fuzzy subsets of the reals where the membership functions of f and g and the density function are continuous piecewise linear functions such a method has applications to the development of a general semantic unification in fril

the approximation method for two stage fuzzy random programming with recourse in this paper a new class of fuzzy random optimization problem called two stage fuzzy random programming or fuzzy random programming with recourse frpr problem is first presented then its deterministic equivalent programming problem is characterized because the frpr problems include fuzzy random variable parameters with an infinite support they are inherently infinite dimensional optimization problems that can rarely be solved directly therefore an approximation approach to the fuzzy random variables with infinite supports by finitely supported ones is proposed which results in finite dimensional frpr problems after that this paper is devoted to establishing the conditions under which the objective value optimal objective value and minimizers of such finite dimensional frpr problem can be shown to converge to the objective value respectively optimal objective value and minimizers of the original infinite dimensional frpr problem

fuzzy random programming with equilibrium chance constraints to model fuzzy random decision systems this paper first defines three kinds of equilibrium chances via fuzzy integrals in the sense of sugeno then a new class of fuzzy random programming problems is presented based on equilibrium chances also some convex theorems about fuzzy random linear programming problems are proved the results provide us methods to convert primal fuzzy random programming problems to their equivalent stochastic convex programming ones so that both the primal problems and their equivalent problems have the same optimal solutions and the techniques developed for stochastic convex programming can apply after that a solution approach which integrates simulations neural network and genetic algorithm is suggested to solve general fuzzy random programming problems at the end of this paper three numerical examples are provided since the equivalent stochastic programming problems of the three examples are very complex and nonconvex the techniques of stochastic programming cannot apply in this paper we solve them by the proposed hybrid intelligent algorithm the results show that the algorithm is feasible and effectiveness

on the double points of a mathieu equation abstract for a mathieu equation with parameter q the eigenvalues can be regarded as functions of the variable q our aim is to find q when adjacent eigenvalues of the same type become equal yielding double points of the given mathieu equation the problem reduces to an equivalent eigenvalue problem of the form b x x where b is an infinite tridiagonal matrix a method is developed to locate the first double eigenvalue to any required degree of accuracy when q is an imaginary number computational results are given to illustrate the theory for the first double eigenvalue numerical results are given for some subsequent double points

quasi finite modules for lie superalgebras of infinite rank we classify the quasi finite irreducible highest weight modules over the infinite rank lie superalgebras gl and d and determine the necessary and sufficient conditions for such modules to be unitarizable the unitarizable irreducible modules are constructed in terms of fock spaces of free quantum fields and explicit formulae for their formal characters are also obtained by investigating howe dualities between the infinite rank lie superalgebras and classical lie groups

generalized fuzzy linear programming for decision making under uncertainty feasibility of fuzzy solutions and solving approach in this study a generalized fuzzy linear programming gflp method is developed for dealing with uncertainties expressed as fuzzy sets the feasibility of fuzzy solutions of the gflp problem is investigated a stepwise interactive algorithm sia based on the idea of design of experiment is then advanced to solve the gflp problem this sia method was implemented through i discretizing membership grade of fuzzy parameters into a finite number of a cut levels ii converting the gflp model into an interval linear programming ilp submodel under every a cut level iii solving the ilp submodels through an interactive algorithm and obtaining the associated interval solutions iv acquiring the membership functions of fuzzy solutions through statistical regression methods a simple numerical example is then proposed to illustrate the solution process of the gflp model through sia a comparison between the solutions obtained though sia and monte carlo method is finally conducted to demonstrate the robustness of the sia method the results indicate that the membership functions for decision variables and objective function are reasonable and robust

eigenvalues of the laplacian on an elliptic domain the importance of eigenvalue problems concerning the laplacian is well documented in classical and modern literature finding the eigenvalues for various geometries of the domains has posed many challenges which include infinite systems of algebraic equations asymptotic methods integral equations etc in this paper we present a comprehensive account of the general solutions to helmholtz s equations defined on simply connected regions using complex variable techniques we consider boundaries of the form zz f z z or its inverse z z g zz to illustrate the theory we reduce the problem on elliptic domains to equivalent linear infinite algebraic systems where the coefficients of the infinite matrix are known polynomials of the eigenvalues we compute truncations of the infinite system for numerical values these values are compared to approximate values and some inequalities available in literature

howe duality and combinatorial character formula for orthosymplectic lie superalgebras we study the howe dualities involving the reductive dual pairs o d spo 2m 2n and sp d osp 2m 2n on the super symmetric tensor of cd cm n we obtain complete decompositions of this space with respect to their respective joint actions we also use these dualities to derive a character formula for these irreducible representations of spo 2m 2n and osp 2m 2n that appear in these decompositions

kostant homology formulas for oscillator modules of lie superalgebras abstract we provide a systematic approach to obtain formulas for characters and kostant u homology groups of the oscillator modules of the finite dimensional general linear and ortho symplectic superalgebras via howe dualities for infinite dimensional lie algebras specializing these lie superalgebras to lie algebras we recover in a new way formulas for kostant homology groups of unitarizable highest weight representations of hermitian symmetric pairs in addition two new reductive dual pairs related to the above mentioned u homology computation are worked out

spectral properties of diagonally dominant infinite matrices ii abstract this paper is concerned with the problem of determining the location of eigenvalues for diagonally dominant unbounded infinite matrix operators acting on l p for some 1 p the results are established using the continuity in the generalized sense of a family of closed operators a 0 1

remarks on classical invariant theory a uniform formulation applying to all classical groups simultaneously of the first fundamental theory of classical invariant theory is given in terms of the weyl algebra the formulation also allows skew symmetric as well as symmetric variables examples illustrate the scope of this formulation

dual pairs and tensor categories of modules over lie algebrasgl and w1 abstract we introduce a tensor category o resp o of certain modules of gl with nonnegative resp nonpositive integral central charges with the usual tensor product we also introduce a tensor category o f consisting of certain modules overgl n for alln we show that the tensor categories o and o fare semisimple abelian and all equivalent to each other we give a formula to decompose a tensor product of two modules and obtain a reciprocity law in each of these categories we also introduce a tensor category o wof certain modules over w 1 with nonnegative integral central charges we show that o wis semisimple abelian and give an explicit formula to decompose a tensor product of two modules in o w

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

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

reliability estimation and design with insufficient data based on possibility theory early in the engineering design cycle it is difficult to quantify product reliability or compliance to performance targets because of insufficient data or information for modeling the uncertainties design decisions are therefore based on fuzzy information that is vague imprecise qualitative linguistic or incomplete the uncertain information is usually available as intervals with lower and upper limits in this work the possibility theory is used to assess design reliability with incomplete information the possibility theory can be viewed as a variant of fuzzy set theory the formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures a computationally efficient and accurate hybrid global local optimization approach is subsequently described for calculating the confidence level of fuzzy response the method combines the advantages of the commonly used vertex and discretization methods subsequently the possibility theory is used in design a possibility based design optimization method is proposed where all design constraints are expressed in a possibilistic way it is shown that the method gives a conservative solution compared with all conventional reliability based designs obtained with different probability distributions finally a general possibility based design optimization method which handles a combination of random and possibilistic design variables is presented several numerical examples demonstrate the application of possibility theory in design

young diagrammatic methods for the representation theory of the classical groups of type bn cn dn since the appearance of the celebrated article the classical groups of weyl 7 numerous influences have occurred in the representation theory of the classical groups especially it has become folklore that the facts in this field should be expressed only in terms of young diagrams the aim of this paper is one of the realizations of this principle a classical model of our approach is the results for gl n which are known as littlewood richardson coefficients and the kostka coefficients these two coefficients can be stated in the combinatorial manner using only young diagrams independently of the rank n of gl n we generalize these results to the other classical groups over c namely we give explicit formulas to decompose the tensor product of two irreducible representations into irreducible constituents also we have obtained an interesting relationship linking the irreducible characters of sp and so which we call duality relation between the representations of sp and so as for explicit formulas for the multiplicities of weights in the form of polynomials in the rank n we refer to 3

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

an iterative method with truncation for infinite linear systems abstract for the infinite linear system tx v where t is an infinite uniformly strictly diagonally dominant matrix and x and v are infinite vectors sufficient conditions are imposed on t and v for the existence and uniqueness of a bounded solution the system is rewritten as x ax b which is first iterated and then truncated to a finite system convergence of the solution of the resulting system to that of the original system is established and explicit error bounds are determined examples are given to illustrate the computation

with central charge n we study representations of the central extension of the lie algebra of differential operators on the circle the algebra we obtain complete and specialized character formulas for a large class of representations which we call primitive these include all quasi finite irreducible unitary representations we show that any primitive representation with central chargen has a canonical structure of an irreducible representation of the with the same central charge and that all irreducible representations of with central chargen arise in this way we also establish a duality between integral modules of and finite dimensional irreducible modules ofgl n and conjecture their fusion rules

the first fundamental theorem of invariant theory for the orthosymplectic super group we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

character and dimension formulae for queer lie superalgebra closed formulae are constructed for the characters and dimensions of the finite dimensional simple modules of the queer lie superalgebra mathfrak q n this is achieved by refining brundan s algorithm for computing simple mathfrak q n characters

u cohomology formula for unitarizable modules over general linear superalgebras abstract the u cohomology groups with coefficients in infinite dimensional irreducible unitarizable highest weight modules are introduced for the general linear superalgebra the corresponding cohomology groups associated with a large class of infinite dimensional irreducible unitarizable representations known as the oscillator representations are computed explicitly results lead to a more detailed understanding of the character formula for such modules derived in an earlier publication using other methods

portfolio selection based on upper and lower exponential possibility distributions in this paper two kinds of possibility distributions namely upper and lower possibility distributions are identified to reflect experts knowledge in portfolio selection problems portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems it can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution in addition a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems a numerical example of a portfolio selection problem is given to illustrate our proposed approaches

possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems abstract in this paper several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems interval and triangular possibility distributions are used to express the non interactive cases between the fuzzy decision variables and exponential possibility distributions are used to represent the interrelated cases possibilistic linear programming problems based on exponential possibility distributions become non linear optimization problems in order to solve optimization problems easily algorithms for obtaining center vectors and distribution matrices in sequence are proposed by the proposed algorithms the possibility distribution of fuzzy decision variables can be obtained

foundational contributions of k asai and h tanaka to fuzzy optimization the first researchers to publish an operationalization of the bellman and zadeh s original approach to decision making in a fuzzy environment 1 were h tanaka and k asai in their 1973 article 2 which was published in english in 1974 3 these two researchers developed many fundamental theories and methods including novel concepts of fuzzy operations research 4 with their collaborators they went beyond the original proposal for fuzzy optimization set forth by bellman zadeh they are important founders of fuzzy optimization this paper gives an overview of their great contributions to fuzzy optimization

the discretized harmonic oscillator mathieu functions and a new class of generalized hermite polynomials we present a general asymptotical solution for the discretized harmonic oscillator the corresponding schrodinger equation is canonically conjugate to the mathieu differential equation the schrodinger equation of the quantum pendulum thus in addition to giving an explicit solution for the hamiltonian of an isolated josephon junction or a superconducting single electron transistor sset we obtain an asymptotical representation of mathieu functions we solve the discretized harmonic oscillator by transforming the infinite dimensional matrix eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution the proposed ansatz defines a new class of generalized hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary hermite polynomials in the limit of vanishing coupling constant the polynomials become orthogonal as parts of the eigenvectors of a hermitian matrix and consequently the exponential part o

a class of fuzzy random optimization expected value models fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables this concept may be regard as an extension of both random variable and fuzzy variable in this paper the linearity of a scalar value expected value operator of fuzzy random variable is discussed and a fuzzy random simulation approach is suggested to evaluate the expected value of a fuzzy random variable in addition three types of fuzzy random expected value models are presented to model fuzzy random decision systems moreover a hybrid intelligent algorithm which incorporates simulation neural network and genetic algorithm is designed in order to solve general fuzzy random expected value models at the end of this paper the effectiveness of this algorithm is showed via three numerical examples

infinite dimensional lie superalgebras and hook schur functions making use of a howe duality involving the infinite dimensional lie superalgebra and the finite dimensional group gll of cw3 we derive a character formula for a certain class of irreducible quasi finite representations of in terms of hook schur functions we use the reduction procedure of to to derive a character formula for a certain class of level 1 highest weight irreducible representations of the affine lie superalgebra associated to the finite dimensional lie superalgebra these modules turn out to form the complete set of integrable modules of level 1 we also show that the characters of all integrable level 1 highest weight irreducible modules may be written as a sum of products of hook schur functions

a review of infinite matrices and their applications abstract infinite matrices the forerunner and a main constituent of many branches of classical mathematics infinite quadratic forms integral equations differential equations etc and of the modern operator theory is revisited to demonstrate its deep influence on the development of many branches of mathematics classical and modern replete with applications this review does not claim to be exhaustive but attempts to present research by the authors in a variety of applications these include the theory of infinite and related finite matrices such as sections or truncations and their relationship to the linear operator theory on separable and sequence spaces matrices considered here have special structures like diagonal dominance tridiagonal sign distributions etc and are frequently nonsingular moreover diagonally dominant finite and infinite matrices occur largely in numerical solutions of elliptic partial differential equations the main focus is the theoretical and computational aspects concerning infinite linear algebraic and differential systems using techniques like conformal mapping iterations truncations etc to derive estimates based solutions particular attention is paid to computable precise error estimates and explicit lower and upper bounds topics include bessel s mathieu equations viscous fluid flow simply and doubly connected regions digital dynamics eigenvalues of the laplacian etc also presented are results in generalized inverses and semi infinite linear programming

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

unitary representations of non compact supergroups we give a general theory for the construction of oscillator like unitary irreducible representations uirs of non compact supergroups in a super fock space this construction applies to all non compact supergroupsg whose coset spaceg k with respect to their maximal compact subsupergroupk is hermitean supersymmetric we illustrate our method with the example of su m p n q by giving its oscillator like uirs in a particle state basis as well as supercoherent state basis the same class of uirs can also be realized over the super hilbert spaces of holomorphic functions of az variable labelling the coherent states

sampling fuzzy discretization and signal reconstruction abstract the sampling theorem provides the condition under which a continuous time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time it gives a condition for the signal reconstruction problem the importance of this theorem pertains to the necessity of knowing when a continuous time signal is uniquely represented by its discrete version so that continuous time signals can be properly converted and handled by sampled data systems like digital computers the problem of the equivalence between either continuous time or discrete time signals and their fuzzy descriptions is analyzed here this encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled data systems such as fuzzy filters fuzzy models or fuzzy controllers a necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces furthermore a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed the discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning

singular value decomposition gersgorin sets abstract in this note we introduce the singular value decomposition gersgorin set sv a of an n n complex matrix a where n for n finite the set sv a is similar to the standard gersgorin set a in that it is a union of n closed disks in the complex plane and it contains the spectrum a of a however sv a is constructed using column sums of singular value decomposition matrix coefficients whereas a is constructed using row sums of the matrix values of a in the case n the set sv a is defined in terms of the entries of the singular value decomposition of a compact operator a on a separable hilbert space examples are given and applications are indicated

application of fuzzy minimum cost flow problems to network design under uncertainty this paper deals with fuzzy quantities and relations in multi objective minimum cost flow problem when t norms and t conorms are available the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied to obtain the most optimistic and the most pessimistic satisficing solutions of this problem two polynomial time algorithms are introduced applying some network transformations to demonstrate the performance of this approach in actual substances network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem this scheme is applied on a pilot network for more description

rational semistandard tableaux and character formula for the lie superalgebra abstract a new combinatorial interpretation of the howe dual pair gl gl n acting on an infinite dimensional fock space is presented the character of a quasi finite irreducible highest weight representation of gl occurring in the fock space is realized in terms of certain bitableaux of skew shapes we study a general combinatorics of these bitableaux including the robinson schensted knuth correspondence and the littlewood richardson rule and then its dual relation with rational semistandard tableaux for gl n this result also explains other howe dual pairs g gl n where g is a lie superalgebra

the eigenvalue problem for infinite complex symmetric tridiagonal matrices with application abstract we consider an infinite complex symmetric not necessarily hermitian tridiagonal matrix t whose diagonal elements diverge to in modulus and whose off diagonal elements are bounded we regard t as a linear operator mapping a maximal domain in the hilbert space l2 into l2 assuming the existence of t 1 we consider the problem of approximating a given simple eigenvalue of t by an eigenvalue n of tn and nth order principal submatrix of t let x x 1 x 2 t be an eigenvector corresponding to assuming xtx 0 and f n 1 x n 1 x n 0 as n we show that there exists a sequence n of tn such that n f n 1 x n 1 1 o 1 x t x 0 where fn 1 represents the n n 1 element of t application to the following problems is included a solve jv z 0 for v given z 0 and b compute the eigenvalues of the mathieu equation fortunately the existence of t 1 need not be verified for these examples since we may show that t i with taken appropriately has an inverse

efficiencies of two stage systems with fuzzy data two stage dea data envelopment analysis models show the performance of individual processes and thus are more informative than the conventional one stage models for making decisions this paper extends this approach from deterministic to uncertain situations where the observations are represented by fuzzy numbers the extension principle is utilized to develop a pair of two level mathematical programs to calculate the lower and upper bounds of the a cut of the fuzzy efficiency by enumerating various values of a the membership functions of fuzzy efficiencies are constructed numerically it is found that the property of the system efficiency being equal to the product of the two process efficiencies which holds for the deterministic case also holds for the fuzzy case this property can be generalized to series systems with more than two processes an example of non life insurance companies in taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy

unitary highest weight representations of quantum general linear superalgebra fock space realisations of unitary highest weight representations of compact and noncompact real forms of the quantum general linear superalgebra uq glm n are constructed we decompose all tensor powers of the fock spaces into direct sums of irreducible unitary submodules for compact or noncompact real forms of the quantum superalgebra obtaining multiplicities of the irreducibles and also explicit formulae for their highest weight vectors a generalised howe duality of type uq glm n uq glk is also established which is used in the study of unitary representations and should also be of independent interest

identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters abstract we have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non interactive i e the possibilistic distribution of parameters is defined by minimum operators in this paper quadratic membership functions as defined by a celmi s are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems our method can be reduced to linear programming so that it is very easy to obtain the posssibilistic distribution of parameters

exponential stability of positive semigroups in banach spaces abstract the paper establishes a link between the stability of the semigroup e m t and the spectral radius of 1 m in ordered banach spaces on the one hand our result allows utilizing simple estimates for the eigenvalues of m in order to provide general conditions for the convergence of the successive approximation scheme for semilinear operator equations on the other hand this paper helps examining the stability of the semigroup e m t for those classes of matrices and m which lead to observable expressions for 1 m e g when m is a coupling applied to disjoint systems representing the novelty of the paper is in the development of an infinite dimensional framework where an absolute value function induced by a cone is introduced and a way to deal with the lack of global continuity of eigenvalues is presented

the spectral approximation of linear operators with applications to the computation of eigenelements of differential and integral operators we are concerned with the numerical solution of the eigenvalue problem t varphi lambda varphi varphi ne 0 where t is a linear operator in a bana ch space t may represent a bounded integral operator or a closed differential operator with bounded inverse the linear operator t and its approximation t n are defined in the same space perturbation theory is then a suitable framework for our problem we present in the first part a systematic study of the various notions of convergence t n to t which imply the convergence of the eigenvalues with preservation of the multiplicities the results are then applied to practical methods for integral and differential operators in the second part we present convergence rates analytic perturbation theory is used to refine on the computed eigenelements of an integral operator and to produce localization results on the eigenelements finally superconvergence results are discussed both for integral and differential operators

unitary representations of nilpotent super lie groups we show that irreducible unitary representations of nilpotent super lie groups can be obtained by induction from a distinguished class of sub super lie groups these sub super lie groups are natural analogues of polarizing subgroups that appear in classical kirillov theory we obtain a concrete geometric parametrization of irreducible unitary representations by nonnegative definite coadjoint orbits as an application we prove an analytic generalization of the stone von neumann theorem for heisenberg clifford super lie groups

spectral enclosures for a class of block operator matrices abstract we prove new spectral enclosures for the non real spectrum of a class of 2 2 block operator matrices with self adjoint operators a and d on the diagonal and operators b and b as off diagonal entries one of our main results resembles gershgorin s circle theorem the enclosures are applied to j frame operators

quasifinite representations of classical lie subalgebras of w1 we show that there are precisely two up to conjugation anti involutions of the algebra of differential operators on the circle preserving the principal gradation we classify the irreducible quasifinite highest weight representations of the central extension d of the lie subalgebra of this algebra fixed by and find the unitary ones we realize them in terms of highest weight representations of the central extension of the lie algebra of infinite matrices with finitely many non zero diagonals over the algebra c u um 1 and its classical lie subalgebras ofb canddtypes character formulas forpositive primitiverepresentations of d including all the unitary ones are obtained we also realize a class of primitive representations of d in terms of free fields and establish a number of duality results between these primitive representations and finite dimensional irreducible representations of finite dimensional lie groups and supergroups we show that the vacuum modulevcof d carries a vertex algebra structure and establish a relationship betweenvcforc 12z and w algebras

super theta functions and the weil representation we show that the super theta function of levin 1987 is a matrix coefficient of the super heisenberg group

gershgorin s theorem for matrices of operators let a aij be an n n matrix of operators acting on the bannach space x x1 x2 xn endowed with the x norm gershgorin circle theorem extends to this setting gi aii aii and aii 1 1 j li jn aij then a i 1ngi moreover assume that j is a proper nonempty subset of 1 2 n if i jgj and i jgj are disjoint then there exist invariant subspaces y1 and y2 for a such that a y1 i jgiand a y2 i jgi where y1 i jxiand y2 i jxi the notion of minimal gershgorin sets that follows is one possible generalization of what varga studied in the scalar case for partitioned matrices he used a more refined generalization for any positive n dimensional vector x x1 xn the operator 1 x1 i 1 xn i a x1i xni ax is similar to a let gix a aii z z aii and aii z 1 1 j lj in xj xi aij the minimal gershgorin set g a is defined to be g a x 0 i angix a as in the scalar case it has the property that a b a b g a where a b bii bii aiifori 1 nand bij aij ifi j it is proved that if each xi is a hilbert space and each aii is normal i 1 n then g a a where g a denotes the boundary of g a it is worth remarking that the closure of a is necessary

the first fundamental theorem of invariant theory for the orthosymplectic supergroup we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

asymptotics of large eigenvalues for some discrete unbounded jacobi matrices abstract the aim of this paper is to find asymptotic formulas for eigenvalues of self adjoint discrete operators in l 2 n given by some infinite symmetric jacobi matrices the approach used to calculate an asymptotic behaviour of eigenvalues is based on method of diagonalization janas and naboko s lemma j janas s naboko infinite jacobi matrices with unbounded entries asymptotics of eigenvalues and the transformation operator approach siam j math anal 36 2 2004 643 658 and the rozenbljum theorem g v rozenbljum near similarity of operators and the spectral asymptotic behaviour of pseudodifferential operators on the circle russian trudy maskov mat obshch 36 1978 59 84 the asymptotic formulas are given with use of eigenvalues and determinants of finite tridiagonal matrices

upper and lower bounds for inverse elements of finite and infinite tridiagonal matrices abstract we give easily computable upper and lower bounds for the inverse elements of finite tridiagonal diagonally dominant matrices and we improve the well known upper bounds due to ostrowski the results are extended to infinite systems the theory is also applied to some earlier results and to the evaluation of bessel functions and mathieu functions by using their recurrence relations

principal agent problem in a fuzzy environment this paper studies implementation of a classical principal agent problem in which the agents characteristics are supposed to be unknown to the principal it is reasonable for us to employ fuzzy variables to denote these hidden characteristics since generally they are fuzzy by nature a fuzzy expected value model which aims to maximize the utility function of the principal under the incentive constraints is developed from the principal s point of view pontryagin maximum principle is adopted in this paper to find the optimal solutions to the fuzzy expected value model

spectral properties of diagonally dominant infinite matrices part i on etablit des theoremes de type gersgorin pour un operateur matriciel infini non borne diagonalement dominant a agissant sur l p pour 1 p

theorems on schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems abstract we firstly consider the block dominant degree for i ii block strictly diagonally dominant matrix and their schur complements showing that the block dominant degree for the schur complement of an i ii block strictly diagonally dominant matrix is greater than that of the original grand block matrix then as application we present some disc theorems and some bounds for the eigenvalues of the schur complement by the elements of the original matrix further by means of matrix partition and the schur complement of block matrix based on the derived disc theorems we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and the numerical example illustrates that the iteration can compute out the results faster

howe duality for quantum queer superalgebras abstract we establish a new howe duality between a pair of quantum queer superalgebras u q 1 q n u q q m the key ingredient is the construction of a non commutative analogue a q q n q m of the symmetric superalgebra s c m n m n with the use of quantum coordinate queer superalgebra it turns out that this superalgebra is equipped with a u q 1 q n u q q m supermodule structure that admits a multiplicity free decomposition we also show that the u q 1 q n u q q m howe duality implies the sergeev olshanski duality

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

modeling fuzzy multi period production planning and sourcing problem with credibility service levels a great deal of research has been done on production planning and sourcing problems most of which concern deterministic or stochastic demand and cost situations and single period systems in this paper we consider a new class of multi period production planning and sourcing problem with credibility service levels in which a manufacturer has a number of plants and subcontractors and has to meet the product demand according to the credibility service levels set by its customers in the proposed problem demands and costs are uncertain and assumed to be fuzzy variables with known possibility distributions the objective of the problem is to minimize the total expected cost including the expected value of the sum of the inventory holding and production cost in the planning horizon because the proposed problem is too complex to apply conventional optimization algorithms we suggest an approximation approach aa to evaluate the objective function after that two algorithms are designed to solve the proposed production planning problem the first is a pso algorithm combining the aa and the second is a hybrid pso algorithm integrating the aa neural network nn and pso finally one numerical example is provided to compare the effectiveness of the proposed two algorithms

unitary representations of super lie groups and applications to the classification and multiplet structure of super particles it is well known that the category of super lie groups slg is equivalent to the category of super harish chandra pairs shcp using this equivalence we define the category of unitary representations ur s of a super lie group we give an extension of the classical inducing construction and mackey imprimitivity theorem to this setting we use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical lie groups in particular of the super poincare groups in arbitrary dimension and signature finally we compare our results with those in the physical literature on the structure and classification of super multiplets

an information axiom based decision making approach under hybrid uncertain environments this paper aims to develop a decision making approach based on the information axiom under hybrid uncertain environments in these environments fuzziness and randomness co exist to model the hybrid uncertainties the design range and system range of an evaluation criterion are expressed as a fuzzy variable and a random variable respectively calculating the information contents for these criteria would involve integrals whose bounds are fuzzy variables to calculate these integrals an expected information content model eicm is proposed based upon the credibility theory to reflect the designer s risk appetite accurately the confidence levels are introduced and a credibility information content model cicm based on the chance constrains programming model is constructed two algorithms based on fuzzy simulation methods and genetic algorithm are developed for these two models finally a case study is illustrated to highlight the effectiveness and accuracy of the proposed approach

classification of irreducible super unitary representations of su p q n in this paper we classify all the irreducible super unitary representations ofsu p q n which can be integrated up to a unitary representation ofs u p q u n a lie group corresponding to the even part ofsu p q n note that a real form of the lie superalgebrasl m n which has non trivial superunitary representations is of the formsu p q n p q m orsu m r s r s n moreover we give an explicit realization for each irreducible super unitary representation using the oscillator representation of an orthosymplectic lie superalgebra

hook young diagrams with applications to combinatorics and to representations of lie superalgebras definition et etude des tableaux k l semi standards applications a la combinatoire et aux representations des superalgebres de lie des diagrammes de young a crochets