sufficiency and duality in nonsmooth multiobjective optimization involving generalized f α π d type i functions in this paper new classes of generalized f a p d type i functions are introduced for a nonsmooth multiobjective programming problem based upon these generalized functions sufficient optimality conditions are established weak strong and strict converse duality theorems are also derived for wolfe and mond weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems

fully automatic clustering system in this paper the fully automatic clustering system facs is presented it is a technique for clustering and vector quantization whose objective is the automatic calculation of the codebook of the right dimension the desired error or target being fixed at each iteration facs tries to improve the setting of the existing codewords and if necessary some elements are removed from or added to the codebook in order to save on the number of computations per iteration greedy techniques are adopted it has been demonstrated from a heuristic point of view that the number of the codewords determined by facs is very low and that the algorithm quickly converges toward the final solution

optimal adaptive k means algorithm with dynamic adjustment of learning rate adaptive k means clustering algorithms have been used in several artificial neural network architectures such as radial basis function networks or feature map classifiers for a competitive partitioning of the input domain this paper presents an enhancement of the traditional k means algorithm it approximates an optimal clustering solution with an efficient adaptive learning rate which renders it usable even in situations where the statistics of the problem task varies slowly with time this modification is based on the optimality criterion for the k means partition stating that all the regions in an optimal k means partition have the same variations if the number of regions in the partition is large and the underlying distribution for generating input patterns is smooth the goal of equalizing these variations is introduced in the competitive function that assigns each new pattern vector to the appropriate region to evaluate the optimal k means algorithm the authors first compare it to other k means variants on several simple tutorial examples then the authors evaluate it on a practical application vector quantization of image data

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

a general theory of fuzzy topological spaces abstract this paper presents a unification of different approaches to fuzzy topology originated from the early works of c l chang b hutton u hohle r lowen a sostak and l n stout

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

minimax partial distortion competitive learning for optimal codebook design the design of the optimal codebook for a given codebook size and input source is a challenging puzzle that remains to be solved the key problem in optimal codebook design is how to construct a set of codevectors efficiently to minimize the average distortion a minimax criterion of minimizing the maximum partial distortion is introduced in this paper based on the partial distortion theorem it is shown that minimizing the maximum partial distortion and minimizing the average distortion will asymptotically have the same optimal solution corresponding to equal and minimal partial distortion motivated by the result we incorporate the alternative minimax criterion into the on line learning mechanism and develop a new algorithm called minimax partial distortion competitive learning mmpdcl for optimal codebook design a computation acceleration scheme for the mmpdcl algorithm is implemented using the partial distance search technique thus significantly increasing its computational efficiency extensive experiments have demonstrated that compared with some well known codebook design algorithms the mmpdcl algorithm consistently produces the best codebooks with the smallest average distortions as the codebook size increases the performance gain becomes more significant using the mmpdcl algorithm the robustness and computational efficiency of this new algorithm further highlight its advantages

efficiency through variational like inequalities with lipschitz functions in this work first we introduce several notions of invexity and pseudoinvexity for a locally lipschitz function by means of the generalized jacobian we study relationships between these concepts in particular the implications between preinvexity and invexity next we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite dimensional non necessarily pareto vector optimization problems with locally lipschitz objective functions through solutions of vector variational like inequality problems these conditions are stated via the generalized jacobian and under pseudoinvexity hypotheses and they show that a vector optimization problem can be reformulated as a vector variational like inequality problem this work extends and improves several previous papers where the objective function of the vector optimization problem is assumed to be differentiable or being locally lipschitz the authors consider the componentwise subdifferential based on the clarke s generalized gradients of the components of the objective function throughout the paper some simple examples are given in order to illustrate the main concepts and results

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

on optimality conditions for multiobjective optimization problems in topological vector space abstract in this paper we are concerned with a differentiable multiobjective programming problem in topological vector spaces an alternative theorem for generalized k subconvexlike mappings is given this permits the establishment of optimality conditions in this context several generalized fritz john conditions in line to those in hu and ling y hu c ling the generalized optimality conditions of multiobjective programming problem in topological vector space j math anal appl 290 2004 363 372 are obtained and in the presence of the generalized slater s constraint qualification the karush kuhn tucker necessary optimality conditions

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

non differentiable minimax fractional programming with generalized α univexity in this paper we study a non differentiable minimax fractional programming problem under the assumption of generalized a univex function in this paper we extend the concept of a invexity m a noor on generalized preinvex functions and monotonicities j inequalities pure appl math 5 2004 1 9 and pseudo a invexity s k mishra m a noor on vector variational like inequality problems j math anal appl 311 2005 69 75 to a univexity and pseudo a univexity from a view point of generalized convexity we also introduce the concept of strict pseudo a univex and quasi a univex functions we derive karush kuhn tucker type sufficient optimality conditions and establish weak strong and converse duality theorems for the problem and its three different form of dual problems the results in this paper extend a few known results in the literature

on minimax fractional optimality conditions with invexity abstract under different forms of invexity conditions sufficient kuhn tucker conditions and three dual models are presented for the minimax fractional programming

second order symmetric duality in multiobjective programming involving generalized cone invex functions abstract in this paper cone second order pseudo invex and strongly cone second order pseudo invex functions are defined a pair of mond weir type second order symmetric dual multiobjective programs is formulated over arbitrary cones weak strong and converse duality theorems are established under aforesaid generalized invexity assumptions a second self duality theorem is also given by assuming the functions involved to be skew symmetric

hemivariational like inequalities in this paper we introduce and consider a new class of variational inequalities known as the hemivariational like inequalities it is shown that the hemivariational like inequalities include hemivariational inequalities variational like inequalities and the classical variational inequalities as special cases the auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational like inequalities under mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

controlling the magnification factor of self organizing feature maps the magnification exponents occurring in adaptive map formation algorithms like kohonen s self organizing feature map deviate for the information theoretically optimal value 1 as well as from the values that optimize e g the mean square distortion error 1 3 for one dimensional maps at the same time models for categorical perception such as the perceptual magnet effect which are based on topographic maps require negative magnification exponents 0 we present an extension of the self organizing feature map algorithm which utilizes adaptive local learning step sizes to actually control the magnification properties of the map by change of a single parameter maps with optimal information transfer with various minimal reconstruction errors or with an inverted magnification can be generated analytic results on this new algorithm are complemented by numerical simulations

a characterization of pseudoinvexity for the efficiency in non differentiable multiobjective problems duality abstract we prove that in order for the kuhn tucker or fritz john points to be efficient solutions it is necessary and sufficient that the non differentiable multiobjective problem functions belong to new classes of functions that we introduce here kt pseudoinvex ii or fj pseudoinvex ii respectively we illustrate it by examples these characterizations generalize recent results given for the differentiable case we study the dual problem and establish weak strong and converse duality results

on variational problems characterization of solutions and duality in this paper we introduce a new class of pseudoinvex functions for variational problems using this new concept we obtain a necessary and sufficient condition for a critical point of the variational problem to be an optimal solution illustrated with an example also weak strong and converse duality are established

a note on invex problems with nonnegative variable we provide sufficient optimality conditions involving invexity for mathematical programming problems with nonnegative variable we also show that upon certain assumptions on the scaling function these problems are convex transformable hence certain associated convex problems should be solved some applications are shown

symmetric duality for a class of nonlinear fractional programming problems abstract a pair of symmetric dual nonlinear fractional programming problems is presented and duality theorems are established under pseudoinvexity pseudoincavity and invexity incavity respectively type assumptions on the kernel function special cases are particularly discussed to show that this paper extends some work appeared in this area

preordered sets valued in a gl monoid let m l be a gl monoid an m valued preordered set is an l subset endowed with a reflexive and m transitive l relation it is essentially a category enriched in a quantaloid generated by m this paper presents a study of m valued preordered sets with emphasis on symmetrization and the cauchy completion the main result states that symmetrization and the cauchy completion of m valued preordered sets commute up to a natural isomorphism

existence and iterative approximations of solutions for mixed quasi variational like inequalities in banach spaces abstract in this paper we introduce and investigate a new class of mixed quasi variational like inequalities in reflexive banach spaces by applying a minimax inequality due to ding tan and a lemma due to chang we establish some existence and uniqueness results of solution for the mixed quasi variational like inequality next by using a kkm theorem due to fan and an auxiliary principle technique due to cohen we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms our results extend improve and unify several known results in the literature

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

fuzzy galois connections on fuzzy sets abstract in fairly elementary terms this paper presents how the theory of preordered fuzzy sets more precisely quantale valued preorders on quantale valued fuzzy sets is established under the guidance of enriched category theory motivated by several key results from the theory of quantaloid enriched categories this paper develops all needed ingredients purely in order theoretic languages for the readership of fuzzy set theorists with particular attention paid to fuzzy galois connections between preordered fuzzy sets

sufficiency and duality in nondifferentiable multiobjective programming involving generalized type i functions abstract recently hachimi and aghezzaf defined generalized f d type i functions a new class of functions that unifies several concepts of generalized type i functions in this paper the generalized f d type i functions are extended to nondifferentiable functions by utilizing the new concepts we obtain several sufficient optimality conditions and prove mixed type and mond weir type duality results for the nondifferentiable multiobjective programming problem

infine functions and nonsmooth multiobjective optimization problems in this paper we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints equality and inequality to be an efficient or properly efficient solution we also obtain duality theorems for wolf type and mond weir type duals under the generalized invexity assumptions

nonsmooth invex functions and sufficient optimality conditions in this paper the various definitions of nonsmooth invex functions are gathered in a general scheme by means of the concept of k directional derivative characterizations of nonsmooth k invexity are derived as well as results concerning constrained optimization without any assumption of convexity of the k directional derivatives

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

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

the q norm complexity measure and the minimum gradient method a novel approach to the machine learning structural risk minimization problem this paper presents a novel approach for dealing with the structural risk minimization srm applied to a general setting of the machine learning problem the formulation is based on the fundamental concept that supervised learning is a bi objective optimization problem in which two conflicting objectives should be minimized the objectives are related to the empirical training error and the machine complexity in this paper one general q norm method to compute the machine complexity is presented and as a particular practical case the minimum gradient method mgm is derived relying on the definition of the fat shattering dimension a practical mechanism for parallel layer perceptron plp network training involving only quasi convex functions is generated using the aforementioned definitions experimental results on 15 different benchmarks are presented which show the potential of the proposed ideas

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

nondifferentiable multiobjective programming under generalized d univexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex strong pseudoinvex weak quasi invex weak pseudoinvex and strong quasi invex functions in aghezzaf and hachimi numer funct anal optim 22 2001 775 d invex functions in antczak europ j oper res 137 2002 28 and univex functions in bector et al univex functions and univex nonlinear programming proc admin sci assoc canada 1992 p 115 by utilizing the new concepts we derive a karush kuhn tucker sufficient optimality condition and establish mond weir type and general mond weir type duality results for the nondifferentiable multiobjective programming problem

preinvex functions and weak efficient solutions for some vectorial optimization problem in banach spaces in this work we introduce the notion of preinvex function for functions between banach spaces by using these functions we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities moreover we will show that this class of problems has the property that each local optimal solution is in fact global

multi objective infinite programming using the theory of abstract optimization problems in infinite dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi objective infinite programming problem sufficient conditions are given under invexity assumptions we generalize the notion of kkt invexity for the multi objective infinite problem and show that this notion is a necessary and sufficient condition for every vector kkt solution to be a weakly efficient solution moreover we develop a theorem of the alternative useful for proving some of our results

symmetric complex valued rbf receiver for multiple antenna aided wireless systems a nonlinear beamforming assisted detector is proposed for multiple antenna aided wireless systems employing complex valued quadrature phase shift keying modulation by exploiting the inherent symmetry of the optimal bayesian detection solution a novel complex valued symmetric radial basis function srbf network based detector is developed which is capable of approaching the optimal bayesian performance using channel impaired training data in the uplink case adaptive nonlinear beamforming can be efficiently implemented by estimating the system s channel matrix based on the least squares channel estimate adaptive implementation of nonlinear beamforming in the downlink case by contrast is much more challenging and we adopt a cluster variation enhanced clustering algorithm to directly identify the srbf center vectors required for realizing the optimal bayesian detector a simulation example is included to demonstrate the achievable performance improvement by the proposed adaptive nonlinear beamforming solution over the theoretical linear minimum bit error rate beamforming benchmark

generalized proper efficiency and duality for a class of nondifferentiable multiobjective variational problems withv invexity abstract a mond weir type dual for a class of nondifferentiable multiobjective variational problems in which every component of the objective function contains a term involving the square root of a certain positive semidefinite quadratic form is considered and various duality results viz weak strong and converse duality theorems are developed for conditionally properly efficient solutions these results are obtained under v invexity assumptions and its generalizations on objective and constraint functions this work extends many results on variational problems established earlier

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

diagonals between q distributors abstract for a small quantaloid q it is shown that the category of q distributors and diagonals is equivalent to a quotient category of the category of q interior spaces and continuous q distributors kan adjunctions induced by q distributors play a crucial role in establishing this equivalence

asymmetric clustering using the alpha beta divergence we propose the use of an asymmetric dissimilarity measure in centroid based clustering the dissimilarity employed is the alpha beta divergence ab divergence which can be asymmetrized using its parameters we compute the degree of asymmetry of the ab divergence on the basis of the within cluster variances in this way the proposed approach is able to flexibly model even clusters with significantly different variances consequently this method overcomes one of the major drawbacks of the standard symmetric centroid based clustering

optimality and duality in nondifferentiable multiobjective optimization involvingd type i and related functions abstract in this paper new classes of functions namely d type i d quasitype i and d pseudo type i are defined for a multiobjective nondifferentiable programming problem kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be a weak minimum for this problem two duals are formulated and various duality results are given by using the above defined classes of functions considering the concept of a weak minimum

fuzzy closure operators closure operators and closure systems play a significant role in both pure and applied mathematics in the framework of fuzzy set theory several particular examples of closure operators and systems have been considered e g so called fuzzy subalgebras fuzzy congruences fuzzy topology etc recently fuzzy closure operators and fuzzy closure systems themselves i e operators which map fuzzy sets to fuzzy sets and the corresponding systems of closed fuzzy sets have been studied by gerla et al see e g 3 4 6 7 as a matter of fact a fuzzy set a is usually defined as a mapping from a universe set x into the real interval 0 1 in the above mentioned works therefore the structure of truth values of the logic behind is fixed to 0 1 equipped usually with minimum as the operation corresponding to logical conjunction as it appeared recently in the investigations of fuzzy logic in narrow sense 9 10 i e fuzzy logic as a many valued logical calculus there are several logical calculi formalizing the intuitive idea of fuzzy reasoning which are complete with respect to the semantics over special structures of truth values among these structures the most general one is that of a residuated lattice it is worth noticing that residuated lattices introduced originally in 12 as an abstraction in the study of ideal systems of rings have been proposed as a suitable structure of truth values by goguen in 8 from this point of view the need for a general notion of a fuzzy closure concept becomes apparent the aim of this paper is to outline a general theory of fuzzy closure operators and fuzzy closure systems in the next section we introduce the necessary concepts in section 3 fuzzy closure operators and systems are

quantale valued dissimilarity abstract inspired by the theory of apartness relations of scott we establish a positive theory of dissimilarity valued in an involutive quantale q without the aid of negation it is demonstrated that a set equipped with a q valued dissimilarity is precisely a symmetric category enriched in a subquantaloid of the quantaloid of back diagonals of q interactions between q valued dissimilarities and q valued similarities which are equivalent to q valued equalities in the sense of hohle kubiak are investigated with the help of lax functors in particular it is shown that similarities and dissimilarities are interdefinable if q is a girard quantale with a hermitian and cyclic dualizing element

quantale valued preorders each divisible and unital quantale is associated with two quantaloids categories enriched over these two quantaloids can be regarded respectively as crisp sets endowed with fuzzy preorders and fuzzy sets endowed with fuzzy preorders this paper deals with the relationship between these two kinds of enriched categories this is a special case of the change base issue in enriched category theory two functors the forward globalization functor and the backward globalization functor that map a fuzzy set with a fuzzy preorder to a crisp set with a fuzzy preorder are considered it is shown that both of them preserve cocompleteness with respect to several classes of weights

minimax fractional programming under nonsmooth generalized f ρ θ d univexity abstract in this paper we are concerned with a nondifferentiable minimax fractional problem with inequality constraints we introduce a new class of generalized convex function that is nonsmooth generalized f d univex function in the framework of the new concept we derive kuhn tucker type sufficient optimality conditions and establish weak strong and converse duality theorems for the problem and its three different types of dual problems

a non commutative and non idempotent theory of quantale sets in fuzzy set theory non idempotency arises when the conjunction is interpreted by arbitrary t norms there are many instances in mathematics where set theory ought to be non commutative and or non idempotent the purpose of this paper is to combine both ideas and to present a theory of non commutative and non idempotent quantale sets among other things standard concepts like fuzzy preorders and fuzzy equivalence relations will be exhibited as special cases more specifically the category q set is investigated where q is an arbitrary involutive quantale objects quantale sets are pairs consisting of a set and a q valued equality with a suitable symmetry axiom three important properties of q set are shown it is complete cocomplete and has the epi extremal mono factorization property its subcategory s q set of separated quantale sets is reflective in q set and shares the same fundamental properties with q set in particular s q set is also a complete and cocomplete epi extremal mono category the objects of the category q set are interesting categories in their own right two categorical frameworks for objects of q set are exhibited first it is shown that q valued equalities arise from q valued preorders with self adjoint extents by symmetrization which leaves q valued equalities invariant here sets with quantale preorders are shown to be b categories with base b being a specific quantaloid the second approach is based on involutive quantaloids a combination of two well known things quantaloids and ordered categories with involution in this context quantale sets are precisely symmetric b categories w r t appropriately chosen quantaloid b with involution further the cauchy completion preserves the symmetry axiom for a large class of involutive quantales which include quantic frames our non commutative generalization of frames and all left continuous t norms there exist at least two monads on q set the singleton monad and quasi singleton monad which are of special interest for fuzzy set theory the kleisli category associated with the singleton monad is the non commutative and non idempotent analogue of higgs topos while the eilenberg moore category of the quasi singleton monad permits the internalization of lukasiewicz negation as truth arrow finally an application of quantale sets to c algebras is given and the change of base is treated

q closure spaces for a small quantaloid q a q closure space is a small category enriched in q equipped with a closure operator on its presheaf category we investigate q closure spaces systematically with specific attention paid to their morphisms and as preordered fuzzy sets are a special kind of quantaloid enriched categories in particular fuzzy closure spaces on fuzzy sets are introduced as an example by constructing continuous relations that naturally generalize continuous maps it is shown in the generality of the q version that the category of closure spaces and closed continuous relations is equivalent to the category of complete lattices and sup preserving maps

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

invexity and the kuhn tucker theorem abstract it is pointed out that type 1 invex functions are the most general class of functions relevant to necessary and sufficient conditions for kuhn tucker optimality in nonlinear programming linear programming duality is used to show an equivalence between the concept of invexity and the kuhn tucker conditions for optimality the invexity kernel and the lagrange multiplier y in the kuhn tucker theory are dual variables the kuhn tucker conditions are necessary conditions for optimality provided that certain constraint qualifications apply a particular result given here is that invexity in itself constitutes an appropriate constraint qualification

kt invex control problem abstract in this paper we introduce a new condition on functions of a control problem for which we define a kt invex control problem we prove that a kt invex control problem is characterized in order that a kuhn tucker point is an optimal solution we generalize optimality results of known mathematical programming problems we illustrate these results with examples

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments