on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

fuzzy ψ contractive mappings in non archimedean fuzzy metric spaces this paper deals with some issues of fixed point theory involving fuzzy contractive mappings introduced by gregori and sapena we enlarge this class and prove a banach contraction theorem in m complete non archimedean fuzzy metric spaces under arbitrary t norms partially answering a question of gregori and sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 252

technical communique an equivalence result in linear quadratic theory we consider the zero endpoint infinite horizon lq problem we show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic riccati equation this result is shown without assuming positive definiteness of the state weighting matrix the feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback nash equilibria both in a deterministic and stochastic context

solving polynomial systems using a branch and prune approach this paper presents tt newton a branch and prune algorithm used to find all isolated solutions of a system of polynomial constraints tt newton can be characterized as a global search method which uses intervals for numerical correctness and for pruning the search space early the pruning in tt newton consists of enforcing at each node of the search tree a unique local consistency condition called box consistency which approximates the notion of arc consistency well known in artificial intelligence box consistency is parametrized by an interval extension of the constraint and can be instantiated to produce the hansen sengupta narrowing operator used in interval methods as well as new operators which are more effective when the computation is far from a solution tt newton has been evaluated on a variety of benchmarks from kinematics chemistry combustion economics and mechanics on these benchmarks it outperforms the interval methods we are aware of and compares well with textit state of the art continuation methods limitations of tt newton e g a sensitivity to the size of the initial intervals on some problems are also discussed of particular interest is the mathematical and programming simplicity of the method

necessary conditions for constant solutions of coupled riccati equations in nash games abstract the asymptotic behaviour of solutions as t for coupled matrix riccati equations occurring in open loop linear quadratic nash games is studied in this paper a general formula representing all possible solutions is given necessary conditions for constant real solutions are derived and an estimate for the rate of convergence is obtained two examples illustrate these results

short communication some remarks on fuzzy contractive mappings recently a new concept of fuzzy contraction in fuzzy metric spaces in the sense of george and veeramani wardowski 2013 5 has been introduced here we provide some comments to this paper

some properites of fuzzy metric spaces abstract we prove that the topology induced by any complete fuzzy metric space in the sense of george and veeramani is completely metrizable we also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete finally we generalize among other classical results the niemytzki tychonoff theorem to fuzzy metric spaces

homotopies exploiting newton polytopes for solving sparse polynomial systems this paper is concerned with the problem of finding all isolated solutions of a polynomial system the bkk bound defined as the mixed volume of the newton polytopes of the polynomials in the system is a sharp upper bound for the number of isolated solutions in mathbb c 0 n mathbb c 0 mathbb c backslash 0 of a polynomial system with a sparse monomial structure first an algorithm is described for computing the bkk bound following the lines of bernshtei n s proof the algorithmic construction of the cheater s homotopy or the coefficient homotopy is obtained the mixed homotopy methods can be combined with the random product start systems based on a generalized bezout number applications illustrate the effectiveness of the new approach

a new class of fuzzy contractive mappings and fixed point theorems abstract the main aim of this work is to unify different classes of fuzzy contractive mappings by introducing a new class of fuzzy contractive mappings called fuzzy z contractive mappings for this new class of mappings suitable conditions are framed to ensure the existence of fixed point in m complete fuzzy metric spaces in the sense of george and veeramani a comprehensive set of examples are presented to support the claim

on fuzzy ź contractive sequences and fixed point theorems in this paper we give a fixed point theorem in the context of fuzzy metric spaces in the sense of george and veeramani as a consequence of our result we obtain a fixed point theorem due to d mihet and generalize a fixed point theorem due to d wardowski also we answer in a positive way to a question posed by d wardowski and solve partially an open question on cauchyness and contractivity

on polynomial feedback nash equilibria for two player scalar differential games in this paper two player scalar differential games are thoroughly studied in the presence of polynomial dynamics and focusing on the notion of solution provided by polynomial feedback nash equilibria it is well known that such strategies are related to the solution of coupled partial differential equations namely the so called hamilton jacobi isaacs equations herein we firstly prove a somewhat negative result stating that for a generic choice of the parameters two player scalar polynomial differential games do not admit polynomial nash equilibria then we focus on the class of linear quadratic lq games and we propose an algorithm that by borrowing techniques from algebraic geometry allows to recast the problem of computing all stabilizing nash feedback strategies into that of finding the zero of a single polynomial function in a scalar variable this permits a comprehensive characterization in terms of number and values of the set of solutions to the associated game

contractive sequences in fuzzy metric spaces abstract in this paper we present an example of a fuzzy contractive sequence in the sense of d mihet which is not cauchy in a fuzzy metric space in the sense of george and veeramani to overcome this drawback we introduce and study a concept of strictly fuzzy contractive sequence then we also make an appropriate correction to lemma 3 2 of gregori and minana 2016 5

order invariant spectral properties for several matrices abstract the collections of m n by n matrices over a field such that the products in any of the m orders share a common similarity class resp spectrum trace are studied the spectral and trace order invariant properties are characterized and the similarity invariant one is related to them in several cases a complete explicit description is given in case m 3 and n 2

fuzzy contractive mappings and fixed points in fuzzy metric spaces in the paper we introduce a new concept of fuzzy contraction which is a generalization of a fuzzy contractive mapping initiated in the article v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 252 for this type of contraction the conditions guaranteeing the existence of fixed point in fuzzy m complete metric spaces in the sense of george and veeramani are established the result is supported by examples

complementary basic matrices abstract we show that an n n matrix which has both subdiagonal and superdiagonal rank at most one even if we distribute the diagonal positions except the first and last completely between the subdiagonal and superdiagonal part then this matrix can be factorized into a product of n 1 matrices each consisting of a 2 2 principal submatrix in two consecutive rows and columns in all possible of the n 1 positions and completed by ones along the diagonal the converse is also true it is shown that the spectrum does not depend on the order of the factors

a numerical analysis of the nash strategy for weakly coupled large scale systems this note discusses the feedback nash equilibrium of linear quadratic n player nash games for infinite horizon large scale interconnected systems the asymptotic structure along with the uniqueness and positive semidefiniteness of the solutions of the cross coupled algebraic riccati equations cares is newly established via the newton kantorovich theorem the main contribution of this study is the proposal of a new algorithm for solving the cares in order to improve the convergence rate of the algorithm newton s method is combined with a new decoupling algorithm it is shown that the proposed algorithm attains quadratic convergence moreover it is shown for the first time that solutions to the cares can be obtained by solving the independent algebraic lyapunov equation ale by using the reduced order calculation

a polyhedral method for solving sparse polynomial systems a continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations we introduce mixed subdivisions of newton polytopes and we apply them to give a new proof and algorithm for bernstein s theorem on the expected number of roots this results in a numerical homotopy with the optimal number of paths to be followed in this homotopy there is one starting system for each cell of the mixed subdivision and the roots of these starting systems are obtained by an easy combinatorial construction

intrinsic products and factorizations of matrices we say that the product of a row vector and a column vector is intrinsic if there is at most one nonzero product of corresponding coordinates analogously we speak about intrinsic product of two or more matrices as well as about intrinsic factorizations of matrices since all entries of the intrinsic product are products of entries of the multiplied matrices there is no addition we present several examples together with important applications these applications include companion matrices and sign nonsingular matrices

some inheritance properties for complementary basic matrices abstract we say that the product of a row vector and a column vector is intrinsic if there is at most one non zero product of corresponding coordinates analogously we speak about intrinsic product of two or more matrices as well as about intrinsic factorizations of matrices since all entries of the intrinsic product are products of entries of the multiplied matrices there is no addition the class of complementary basic matrices cb matrices was recently introduced as matrices if of order n a g i 1 g i 2 g i n 1 where i 1 i 2 i n 1 is a permutation of 1 2 n 1 and the matrices g k k 1 n 1 have the form g k i k 1 c k i n k 1 for some 2 2 matrices c k it was observed that 1 independently of the permutation all such matrices with given c i s have the same spectrum though they do not form a similarity class 2 the classical companion matrix belongs to the class of cb matrices m fiedler a note on companion matrices linear algebra appl 372 2003 325 331 9 3 the multiplication of the g i s is intrinsic we explore connections between the 2 2 matrices c k and the resulting cb matrix g k in particular which properties are inherited from the c k to the g k we consider two situations for the ordinary real cb matrices and for the corresponding sign pattern matrices

on fuzzy contractive mappings in fuzzy metric spaces some results on fuzzy contractive mappings in v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 253 are extended to edelstein fuzzy contractive mappings some new results are obtained by modifying the notion of convergence in fuzzy metric spaces due to specific axiom gv 2 in fuzzy metric spaces in the sense of george and veeramani this convergence is frechet

solving the scalar feedback nash algebraic riccati equations an eigenvector approach in this note we present an algorithm to compute all solutions of the scalar algebraic riccati equations that play an important role in finding feedback nash equilibria of the scalar n player linear quadratic differential game we show that all appropriate solutions can be obtained by analyzing the eigenstructure of a related matrix

applying genetic algorithms for solving nonlinear algebraic equations solving of nonlinear algebraic equations is a prominent problem in science and engineering in this study the systems of these equations were solved using genetic algorithms three distinctive groups of the equations were studied a single nonlinear equation a simple set of nonlinear equations and a complex set of nonlinear equations in the two first cases the problem was converted into the unconstrained optimization problem with some simple mathematical relations then the genetic algorithm was used to solve the problem in the complex nonlinear equations the problem was changed into the constrained optimization problem and genetic algorithm in conjunction with augmented lagrangian function has been used to find the solution the proposed scheme has been evaluated with five benchmarks with different applications moreover the sensitivity analysis of the method to initial interval and size of population has been studied the results have a high precision and show good agreement in comparison with conventional methods

on fixed point theorems in fuzzy metric spaces we give fixed point theorems for complete fuzzy metric spaces in the sense of george and veeramani and also for kramosil and michalek s fuzzy metric spaces which are complete in grabiec s sense

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek

the solution set of the n player scalar feedback nash algebraic riccati equations we analyze the set of scalar algebraic riccati equations are that play an important role in finding feedback nash equilibria of the scalar n player linear quadratic differential game we show that in general there exist at most 2 sup n 1 solutions of the are that give rise to a nash equilibrium in particular we analyze the number of equilibria as a function of the autonomous growth parameter and present both necessary and sufficient conditions for the existence of a unique solution of the are

a numerical algorithm to find soft constrained nash equilibria in scalar lq games this paper provides a numerical algorithm to calculate all soft constrained nash equilibria in a regular scalar indefinite linear quadratic game the algorithm is based on the calculation of the eigenstructure of a certain matrix the analysis follows the lines of the approach taken by engwerda 2003 to calculate the solutions of a set of scalar coupled feedback nash algebraic riccati equations