symmetric duality for a class of multiobjective fractional programming problems this paper is concerned with symmetric duality for a class of nondifferentiable multiobjective fractional programming problems two weak duality theorems and two strong duality theorems are proved discussion on some special cases shows that results in this paper extend previous work in this area

extremal problems on the set of nonnegative definite matrices abstract an optimization problem of minimizing a real valued function of certain elements of a symmetric matrix subject to this matrix being nonnegative definite is considered optimality conditions are proposed the duality result of olkin and pukelsheim 1982 is extended to a wide class of such problems applications are discussed

generalized theory of diffusive stresses associated with the time fractional diffusion equation and nonlocal constitutive equations for the stress tensor abstract the theory of diffusive stresses based on the time fractional diffusion equation with the liouville caputo derivative is discussed the diffusion process is characterized by the chemical potential tensor and the concentration tensor eliminating the chemical potential tensor and the concentration tensor from the constitutive equations for the stress tensor the space time nonlocal equations for the mean stress and the deviatoric stress are obtained with the kernel being the wright function

theories of thermal stresses based on space time fractional telegraph equations the generalized telegraph equations with time and space fractional derivatives are considered the corresponding theories of thermal stresses are formulated the proposed theories interpolate the classical thermoelasticity the theory of lord and shulman thermoelasticity without energy dissipation of green and naghdi and theories of fractional thermoelasticity proposed earlier the fundamental solution to the nonhomogeneous space time fractional telegraph equation as well as the corresponding thermal stresses are obtained in the axisymmetric case

minimax and symmetric duality for a class of multiobjective variational mixed integer programming problems abstract in this paper we formulate a pair of multiobjective variational mixed integer programs for arbitrary cones under the separability and partial invexity assumptions on the functions involved we establish the weak strong converse and self duality theorems related to efficient solution

symmetric duality for multiobjective fractional variational problems with generalized invexity the concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems weak strong and converse duality theorems are proved under generalized invexity assumptions a close relationship between these problems and multiobjective fractional symmetric dual problems is also presented

duality for multiobjective variational problems abstract wolfe and mond weir type duals for multiobjective variational problems are formulated under convexity assumptions on the functions involved weak and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems a close relationship between these variational problems and nonlinear multiobjective programming problems is also indicated

models and methods for the analysis of correlation coefficients abstract the normal distribution plays a very prominant role in statistics and in multivariate analysis the multinormal model is even more dominant than in the classical univariate or bivariate situations in this paper we show that the assumption of continuous multinormal observations can be relaxed in various ways for continuous multivariate analysis most of the existing large sample theory can be applied without assuming multivariate normality we also develop several discrete multinormal models the first one is the classical pearson model which results from discreticizing multinormal variables the second one is inspired by correspondence analysis and the third one by loglinear analysis the models are presented in terms of correlation coefficients and applied to the spearman model of factor analyses using an example from political science

symmetric duality for multiobjective variational problems abstract a mond weir type symmetric dual for a multiobjective variational problem is formulated weak and strong duality theorems under generalized convexity assumptions are proved for properly efficient solutions under an additional condition on the kernel function that occurs in the formulation of the problems a self duality theorem is proved a close relationship between these variational problems and symmetric dual nonlinear multiobjective programming problems is also incorporated

taylor series approach to fuzzy multiobjective linear fractional programming this paper presents the use of a taylor series for fuzzy multiobjective linear fractional programming problems fmolfp the taylor series is a series expansion that a representation of a function in the proposed approach membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a taylor series are unified thus the problem is reduced to a single objective practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach

least squares approximation of an improper correlation matrix by a proper one an algorithm is presented for the best least squares fitting correlation matrix approximating a given missing value or improper correlation matrix the proposed algorithm is based upon a solution for mosier s oblique procrustes rotation problem offered by ten berge and nevels a necessary and sufficient condition is given for a solution to yield the unique global minimum of the least squares function empirical verification of the condition indicates that the occurrence of non optimal solutions with the proposed algorithm is very unlikely a possible drawback of the optimal solution is that it is a singular matrix of necessity in cases where singularity is undesirable one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be where is an arbitrary small positive constant finally it may be desirable to weight the squared errors of estimation differentially a generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting the generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way

second order f α ρ d convexity and duality in multiobjective programming a class of second order f a r d convex functions and their generalizations is introduced using the assumptions on the functions involved weak strong and strict converse duality theorems are established for a second order mond weir type multiobjective dual

symmetric duality for the multiobjective fractional variational problem with partial invexity a symmetric dual problem for a class of multiobjective fractional variational problems is first formulated under partial invexity assumptions on the functions involved dual theorems are proved through a parametric approach to related properly efficient solutions of the primal and dual problems finally self dual and related problems are considered

symmetric duality for multiobjective fractional variational problems involving cones in this paper a pair of multiobjective fractional variational symmetric dual problems over cones is formulated weak strong and converse duality theorems are established under generalized f convexity assumptions moreover self duality theorem is also discussed

symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear symmetric dual variational problems for the single objective problems our problems become the symmetric dual pair of i smart and b mond j math anal appl 152 1990 536 545 under invexity assumptions we establish the weak strong converse and self duality theorems for our variational problems by using the concept of efficiency also we give the static case of our symmetric duality results

symmetric duality with invexity in variational problems abstract weak and strong duality results are established under invexity hypotheses for symmetric dual variational problems without positivity constraints self dual problems and static symmetric dual programs are included as special cases

multi objective decision making model under fuzzy random environment and its application to inventory problems in this paper we concentrate on developing a fuzzy random multi objective model about inventory problems by giving some definitions and discussing some properties of fuzzy random variable we design a method of solving solution sets of fuzzy random multi objective programming problems these are applied to numerical inventory problems in which all inventory costs purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers the exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates by comparing the results with those from the fuzzy multi objective models we believe that the proposed fuzzy random multi objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life

weakly efficient solutions and pseudoinvexity in multiobjective control problems abstract in this paper we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem called w kt pseudoinvexity and w fj pseudoinvexity we prove that all kuhn tucker or fritz john points are weakly efficient solutions if and only if these conditions are fulfilled we relate weakly efficient solutions to optimal solutions of weighting control problems we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

efficient solutions in v kt pseudoinvex multiobjective control problems a characterization in this paper we introduce a new condition on functionals involved in a multiobjective control problem for which we define the v kt pseudoinvex control problem we prove that a v kt pseudoinvex control problem is characterized so that a kuhn tucker point is an efficient solution we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

robust estimation of dispersion matrices and principal components abstract this paper uses monte carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components the estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and m estimation the m estimators stand up exceptionally well they and the multivariate trimming procedure are especially effective at estimating the principal components including a near singularity however the m estimators can break down relatively easily when the dimensionality is large and the outliers are asymmetric with missing data the element wise approach becomes more attractive

symmetric duality for invex multiobjective fractional variational problems we introduce a symmetric dual for multiobjective fractional variational problems under certain invexity assumptions we establish weak strong and converse duality theorems as well as self duality relations the paper includes an extension of previous symmetric duality results for the static case obtained by weir to the dynamic case

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems