algebraic and topological results on lifting properties in residuated lattices we define lifting properties for universal algebras which we study in this general context and then particularize to various such properties in certain classes of algebras next we focus on residuated lattices in which we investigate lifting properties for boolean and idempotent elements modulo arbitrary as well as specific kinds of filters we give topological characterizations to the lifting property for boolean elements and several properties related to it many of which we obtain by means of the reticulation

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

some weaker versions of topological residuated lattices abstract the aim of this paper is to investigate some weaker versions of topological residuated lattices which are para topological residuated lattices continuous para topological residuated lattices continuous para topological residuated lattices continuous and para topological residuated lattices continuous respectively this paper mainly focuses on the latter two para topological residuated lattices we prove the independence of these para topological residuated lattices by using their algebraic properties moreover we establish the correspondence between algebraic properties and topologies in a residuated lattice l i e there is an injective mapping from m e q l i e q l a e q l c o n l resp to m t r l l i t r l l a t r l l t r l l resp finally some interactions between the topologies and algebraic properties in para semi topological residuated lattices are studied

nonlinear 0 1 programming i linearization techniques any real valued nonlinear function in 0 1 variables can be rewritten as a multilinear function we discuss classes of lower and upper bounding linear expressions for multilinear functions in 0 1 variables for any multilinear inequality in 0 1 variables we define an equivalent family of linear inequalities this family contains the well known system of generalized covering inequalities as well as other linear equivalents of the multilinear inequality that are more compact i e of smaller cardinality in a companion paper 7 we discuss dominance relations between various linear equivalents of a multilinear inequality and describe a class of algorithms for multilinear 0 1 programming based on these results

convergences of subgradients of sequences of convex functions abstract let f n n 1 be a sequence of proper lower semicontinuous convex functions on a banach space a condition ensuring the strong convergence of their subgradients is given

nonlinear 0 1 programming ii dominance relations and algorithms a nonlinear 0 1 program can be restated as a multilinear 0 1 program which in turn is known to be equivalent to a linear 0 1 program with generalized covering g c inequalities in a companion paper 6 we have defined a family of linear inequalities that contains more compact smaller cardinality linearizations of a multilinear 0 1 program than the one based on the g c inequalities in this paper we analyze the dominance relations between inequalities of the above family in particular we give a criterion that can be checked in linear time for deciding whether a g c inequality can be strengthened by extending the cover from which it was derived we then describe a class of algorithms based on these results and discuss our computational experience we conclude that the g c inequalities can be strengthened most of the time to an extent that increases with problem density in particular the algorithm using the strengthening procedure outperforms the one using only g c inequalities whenever the number of nonlinear terms per constraint exceeds about 12 15 and the difference in their performance grows with the number of such terms

topology on bl algebras in this paper by using a special family of filters on a bl algebra l we construct a topology on l show that l is a topological bl algebra find the closure of any subsets of l and obtain some conditions under which that l is a hausdorff space also we prove some theorems about connected components of this topological space and use them to construct a quotient semitopological bl algebras finally we introduce the concept of complete bl algebra and attempt to construct a complete bl algebra from l

asymptotic properties of the quadratic assignment problem for the general quadratic assignment problem as well as for a planar version of this problem we extend earlier work by burkard and fincke to prove that the ratio of the maximal to the minimal solution value converges to 1 almost surely in fact any solution value can almost surely be written asymptotically as a simple explicitly given function of the problem size theoretical analysis and computational experiments reveal the convergence to be relatively fast

on random quadratic bottleneck assignment problems the relative error between best and worst solution of quadratic bottleneck assignment problems with cost coefficientsdijpq aipbjq is considered whereaip is either arbitrarily given or corresponds to a distance in the plane it is shown that the relative error is bounded by a function m tending to zero with probability tending to one asm provided the data are uniformly distributed this implies that any algorithm for the above mentioned problems yields asymptotically an arbitrarily small relative error with probability tending to one

partial extensions of attouch s theorem with applications to proto derivatives of subgradient mappings attouch s theorem which gives on a reflexive banach space the equivalence between the mosco epi convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients has many important applications in convex optimization in particular generalized derivatives have been defined in terms of the epi convergence or graph convergence of certain difference quotient mappings and attouch s theorem has been used to relate these various generalized derivatives these relations can then be used to study the stability of the solution mapping associated with a parameterized family of optimization problems we prove in a hilbert space several partial extensions of attouch s theorem to functions more general than convex these functions are called primal lower nice furthermore we use our extensions to derive a relationship between the second order epi derivatives of primal lower nice functions and the proto derivative of their associated subgradient mappings

ranking scalar products to improve bounds for the quadratic assignment problem abstract the eigenvalue bound for the quadratic assignment problem qap is successively improved by considering a set of k best scalar products related to the qap an efficient procedure is proposedto find such a set of k best scalar products a class of qaps is described for which this procedure in general improves existing lower bounds and at the same time generates good suboptimal solutions the method leaves the user with a large flexibility in controlling the quality of the bound however since the method is sensitive to input data it should only be used in combination with other bounding rules

a heuristic for quadratic boolean programs with applications to quadratic assignment problems abstract a heuristic for quadratic boolean programs is presented computational tests with quadratic assignment problems qap showed that it finds very good suboptimal solutions in moderate time and behaves computationally stable in the appendix a fortran program for qap is listed which improves an earlier code published by burkard and derigs

a thermodynamically motivated simulation procedure for combinatorial optimization problems abstract exchange algorithms are an important class of heuristics for hard combinatorial optimization problems as e g salesman problems or quadratic assignment problems in kirkpatrick s and cerny s exchange algorithms for the travelling salesman problem and placement problem they propose to perform an exchange not only if the objective function value decreases by this exchange but also in certain cases if the objective function value increases an exchange increasing the objective function value is performed stochastically depending on the size of the increment computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach suboptimal solutions differing 1 2 from the best known solutions are obtained by a simple program in short time by starting this program several times with different starting values all known minimal objective function values were reached thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions

spectral analysis and the dynamic response of complex networks the eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior in particular the spectral density ensuremath rho ensuremath lambda of this matrix reveals important network characteristics random networks follow wigner s semicircular law whereas scale free networks exhibit a triangular distribution in this paper we show that the spectral density of hierarchical networks follows a very different pattern which can be used as a fingerprint of modularity of particular importance is the value ensuremath rho 0 related to the homeostatic response of the network it is maximum for random and scale free networks but very small for hierarchical modular networks it is also large for an actual biological protein protein interaction network demonstrating that the current leading model for such networks is not adequate

on equivalent forms of fuzzy logic systems nm and imtl the nilpotent minima are important t norms in fuzzy logic and fuzzy reasoning two interesting formal systems nilpotent minimum logic nm and l based on nilpotent minima have been proposed and have been intensively studied in this paper their equivalence is pointed out moreover coincidence of two related algebraic structures nm and r0 algebras is also proved in addition we give an equivalent form of involutive monoidal t norm based logic imtl

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

an extension of attouch s theorem and its application to second order epi differentiation of convexly composite functions in 1977 hedy attouch established that a sequence of closed proper convex functions epi converges to a convex function if and only if the graphs of the subdierentials converge in the mosco sense to the subdifferential of the limiting function and roughly speaking there is a condition that fixes the constant of integration we show that the theorem is valid if instead one considers functions that are the composition of a closed proper convex function with a twice continuously differentiable mapping in addition a constraint qualification is imposed

stone like representation theorems and three valued filters in r0 algebras nilpotent minimum algebras nilpotent minimum algebras nm algebras are algebraic counterpart of a formal deductive system where conjunction is modeled by the nilpotent minimum t norm a logic also independently introduced by guo jun wang in the mid 1990s such algebras are to this logic just what boolean algebras are to the classical propositional logic in this paper by introducing respectively the stone topology and a three valued fuzzy stone topology on the set of all maximal filters in an nm algebra we first establish two analogues for an nm algebra of the well known stone representation theorem for a boolean algebra which state that the boolean skeleton of an nm algebra is isomorphic to the algebra of all clopen subsets of its stone space and the three valued skeleton is isomorphic to the algebra of all clopen fuzzy subsets of its three valued fuzzy stone space respectively then we introduce the notions of boolean filter and of three valued filter in an nm algebra and finally we prove that three valued filters and closed subsets of the stone space of an nm algebra are in one to one correspondence and boolean filters uniquely correspond to closed subsets of the subspace consisting of all ultrafilters

on para quasi topological mv algebras abstract in this paper the notions of para quasi semi topological mv algebras are defined and their related properties are studied also topologies with which an mv algebra can be a para semi topological mv algebra are obtained clearly a topological mv algebra is a para quasi semi topological mv algebra but the converse is not true as shown by an example in addition we study ideals and filters in para quasi topological mv algebras and we show that a quasitopological mv algebra is a topological mv algebra if the ideal 0 or equivalently the filter 1 is open

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined