on the completion of fuzzy metric spaces this paper discusses the completion of a fuzzy metric space in the sense of kaleva and seikkala that is modeled by a pair of two place functions l and r previous work on this question is based on l min r max under the condition that l and r are a generic class of two place functions we characterize the completable fuzzy metric space and show that the corresponding completion is uniquely determined up to isometry furthermore we point out that with more conditions on r including on r max the completion of each fuzzy metric space exists and is unique up to isometry this improves the corresponding result of kaleva the completion of fuzzy metric spaces j math anal appl 109 1985 194 198

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

entire functions that share one value with one or two of their derivatives we prove two uniqueness theorems for entire functions of finite order that share one finite value with one or two of their derivatives

growth and poles of meromorphic solutions of some difference equations abstract this paper is devoted to studying the growth property and the pole distribution of meromorphic solutions f of some complex difference equations with all coefficients being rational functions or of growth s r f we find the lower bound of the lower order or the relation between lower order and the convergence exponent of poles of meromorphic solutions of such equations

on some results of analysis for fuzzy metric spaces abstract a necessary and sufficient condition for a fuzzy metric space to be complete is given we prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable uniform limit theorem is generalized to fuzzy metric spaces

the radial oscillation of entire solutions of complex differential equations abstract this paper is devoted to studying the radial oscillation of solutions of linear differential equations f a z f b z f f z where a z b z and f z are transcendental entire functions with some added conditions on coefficients we show that there exists some close relation between the borel directions of solutions and that of f z and also obtain some estimates of growth of solutions in the angular domains

coupled coincidence point results for compatible mappings in partially ordered fuzzy metric spaces coupled fixed point problems have attracted much attention in recent times in this paper we establish coupled coincidence point and coupled fixed point results in the context of fuzzy metric spaces the two mappings considered here are assumed to be compatible hadzic type t norm is used by an application of the coincidence point theorem in fuzzy metric spaces a corresponding result is obtained in metric spaces the main theorem of this paper is illustrated with an example our work extends some existing results

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

on the question of whether f e zf b z f 0 can admit a solution f 0 of finite order on montre que si b z est soit i une fonction entiere transcendante d ordre 1 soit ii un polynome de degre impair alors toute solution f 0 de l equation f e z f b z f 0 est d ordre infini on obtient un resultat partiel quand b z est un polynome de degre pair

entire functions that have the same fixed points with their first derivatives let f be a nonconstant entire function and let k 2 be an integer we denote by ef z z c f z z counting multiplicities the set consisting of all the fixed points of f this paper proves that if f and f have the same fixed points namely ef z ef z and if f k z z whenever f z z then f f

partial quasi metrics in this article we introduce and investigate the concept of a partial quasi metric and some of its applications we show that many important constructions studied in matthews s theory of partial metrics can still be used successfully in this more general setting in particular we consider the bicompletion of the quasi metric space that is associated with a partial quasi metric space and study its applications in groups and bck algebras

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

finite order solutions of linear differential equations in the unit disc abstract necessary and sufficient conditions for the analytic coefficients of the complex linear differential equation f k a k 1 z f k 1 a 1 z f a 0 z f a k z are found such that all solutions satisfy f lim sup r 1 log t r f log 1 r moreover estimates for the number of linearly independent solutions of maximal growth are found in terms of the growth of the coefficients in addition sufficient conditions for the coefficients such that the zero sequence z n of any non trivial solution f of with a k 0 satisfies 1 z n 1 are found several non trivial examples are given in order to show that the established results are in a sense sharp

completeness in probabilistic quasi uniform spaces abstract in this paper we give a kind of cauchy completeness in probabilistic quasi uniform space by using pair filters and prove that this kind of cauchy completeness is equivalent to the completeness of induced probabilistic uniform space introduced by hohle we also give a characterization of cauchy completeness by lawvere completeness then we study the completion of probabilistic quasi uniform space and show that each t 0 separated probabilistic quasi uniform space has a t 0 cauchy completion finally in probabilistic quasi metric space we study the relationship between the completeness of induced quasi uniform space and the completeness of probabilistic quasi metric space

dual exponential polynomials and linear differential equations abstract we study linear differential equations with exponential polynomial coefficients where exactly one coefficient is of order greater than all the others the main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient several examples illustrate our results and exhibit possibilities that can occur

fuzzy pseudometric spaces vs fuzzifying structures in this paper we apply the representation theorem established in mardones perez and de prada vicente 2012 12 to define and study the degree in which some topological type properties of fuzzy pseudometric spaces are fulfilled fuzzifying structures which appear naturally are also investigated and the relation between these structures and fuzzy pseudometric spaces is explored

a representation theorem for fuzzy pseudometrics in this paper we show that there exists a one to one correspondence between a certain class of fuzzy pseudometrics in the sense of kramosil and michalek and 0 1 indexed families of ordinary pseudometrics satisfying a property of lower semicontinuity the aforementioned bijection is proved to be independent of the t norm and it provides a representation theorem for a large class of fuzzy pseudometric spaces further the relations between the uniformities and topologies both generated by the fuzzy pseudometric and by the corresponding family of ordinary pseudometrics are also investigated

on the relationship between the lower order of coefficients and the growth of solutions of differential equations abstract some criteria for entire coefficients a z and b z are given in terms of the lower order forcing the solutions of f a z f b z f 0 to grow fast in the literature similar criteria have been published in terms of the usual order the case when the coefficient a z has an asymptotic growth t r a log m r a 0 1 outside of an exceptional set is also discussed previously laine wu 2000 and kim kwon 2001 have made use of this asymptotic growth in the case 1

an alternative characterization of probabilistic menger spaces with h type triangular norms abstract the class of h type triangular norms was introduced for the first time by had ic in 1978 in this paper a new characteristic property of the h type triangular norm is presented by virtue of this alternative characterization the continuity of quasi metrics and quasi norms is studied and some properties of the probabilistic menger spaces with this triangular norm are considered as applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given

std convergence in fuzzy metric spaces in this note we answer two recent questions posed by morillas and sapena 10 related to standard convergence in fuzzy metric spaces in the sense of george and veeramani the obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of cauchyness

on the radial distribution of julia sets of entire solutions of f n a z f 0 abstract this paper is devoted to studying the dynamical properties of solutions of f n a z f 0 where n 2 is an integer and a z is a transcendental entire function of finite order we find the lower bound on the radial distribution of julia sets of e z provided that e f 1 f 2 f n and f 1 f 2 f n is a solution base of such equations

meir keeler theorems in fuzzy metric spaces abstract in this paper we propose the concept of fuzzy meir keeler contractive mappings in fuzzy metric spaces which covers fuzzy contractive mappings and fuzzy h contractive mappings as special cases with the aid of the proposed concept we obtain some meir keeler type fixed point theorems the derived theorems improve and extend the corresponding ones developed by d mihet d wardowski and v gregori et al and an example in the end of the paper illustrates the validity of our results

finite order solutions of second order linear differential equations on considere l equation differentielle f a z f b z f 0 ou a z et b z sont des fonctions entieres on trouve des conditions sur a z et b z qui garantissent que chaque solution f 0 de l equation a un ordre fini

lattice valued preordered sets as lattice valued topological systems this paper provides variable basis lattice valued analogues of the well known results that the construct prost of preordered sets firstly is concretely isomorphic to a full concretely coreflective subcategory of the category top of topological spaces which employs the concept of the dual of the specialization preorder and secondly is non concretely isomorphic to a full coreflective subcategory of the category topsys of topological systems of s vickers which employs the spatialization procedure for topological systems dualizing these results one arrives at the similar properties of quasi pseudo metric spaces built over locales

factorial representations of path groups abstract the reduction of the energy representation of the group of mappings from i 0 1 s11 r or r into a compact semisimple lie group g is given for g su 2 the factoriality of the representation which is of type iii in the case i r is proved

an application of a representation theorem for fuzzy metrics to domain theory in this paper we study the interplay between fuzzy metric spaces and domain theory using the representation theorem established in mardones perez and de prada vicente 2012 12 we will prove that suitable restrictions of completeness in fuzzy metric spaces correspond to a structure of domain in the poset of formal balls endowed with appropriate orders

a note on compactness in a fuzzy metric space we study the compactness in a fuzzy metric space we also give a generalization of niemytzki tychonoff theorem for a fuzzy metric space

on the growth of solutions of a class of higher order linear differential equations with coefficients having the same order abstract in this paper the authors investigate the growth of solutions of a class of higher order linear differential equations f k a k 1 f k 1 a 0 f 0 when most coefficients in the above equations have the same order with each other and obtain some results which improve previous results due to k h kwon k h kwon nonexistence of finite order solutions of certain second order linear differential equations kodai math j 19 1996 378 387 and z x chen z x chen the growth of solutions of the differential equation f e z f q z f 0 sci china ser a 31 2001 775 784 in chinese z x chen on the hyper order of solutions of higher order differential equations chinese ann math ser b 24 2003 501 508 in chinese z x chen on the growth of solutions of a class of higher order differential equations acta math sci ser b 24 2004 52 60 in chinese z x chen c c yang quantitative estimations on the zeros and growth of entire solutions of linear differential equations complex var 42 2000 119 133

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

entire functions that share a polynomial with their derivatives abstract let f be a nonconstant entire function k and q be positive integers satisfying k q and let q be a polynomial of degree q this paper studies the uniqueness problem on entire functions that share a polynomial with their derivatives and proves that if the polynomial q is shared by f and f cm and if f k z q z 0 whenever f z q z 0 then f f we give two examples to show that the hypothesis k q is necessary

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

on limit directions of julia sets of entire solutions of linear differential equations abstract this paper is devoted to studying the limit directions of julia sets of solutions of f n a n 1 z f n 1 a 0 z f 0 where n 2 is an integer and a j z j 0 1 n 1 are entire functions of finite lower order with some additional conditions on coefficients we know that every non trivial solution f z of such equations has infinite lower order and prove that the limit directions of julia sets of f z must have a definite range of measure

hutton 0 1 quasi uniformities induced by fuzzy quasi metric spaces it is well known that given a probabilistic metric space menger space with continuous t norm t there is a hausdorff topology associated this association factorizes through strong uniformities or e l uniformities similarly any fuzzy metric space x m can be endowed with a hausdorff topology t m in the case of fuzzy quasi metric spaces a t 1 topology and again this association factorizes through quasi uniform spaces in this paper we associate to each fuzzy quasi metric space a hutton 0 1 quasi uniformity u m this allows us to give a factorization of the previous association via hutton 0 1 quasi uniformities it is also proved that the topology t m is exactly the image under lowen s functor i of the 0 1 topology induced by u m as a consequence we get a class of hutton 0 1 quasi uniformities which are probabilistic metrizable

on completable fuzzy metric spaces in this paper we construct a non completable fuzzy metric space in the sense of george and veeramani which allows to answer an open question related to continuity on the real parameter t in addition the constructed space is not strong non archimedean

multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces in recent times coupled tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions roldan et al showed a unified version of these results for nonlinear mappings in any number of variables which were not necessarily permuted or ordered introducing the notion of multidimensional coincidence point very recently choudhury et al proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of george and veeramani in this paper using the idea of coincidence point for nonlinear mappings in any number of variables we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with hadzic type t norms then we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied

irreducibility and reducibility for the energy representation of the group of mappings of a riemannian manifold into a compact semisimple lie group abstract the irreducibility of the energy representation of the group of smooth mappings from a riemannian manifold of dimension d 3 into a compact semisimple lie group is proven the nonequivalence of the representations associated with different riemann structures is also proven for d 3 the case d 2 is examined and irreducibility and nonequivalence results are also given the reducibility in the case d 1 is pointed out in this case the commutant contains a representation equivalent with the energy representation

the hausdorff fuzzy quasi metric removing the condition of symmetry in the notion of a fuzzy pseudo metric in kramosil and michalek s sense one has the notion of a fuzzy quasi pseudo metric then for each fuzzy quasi pseudo metric on a set x we construct a fuzzy quasi pseudo metric on the collection of all nonempty subsets of x called the hausdorff fuzzy quasi pseudo metric we investigate several properties of this structure and present several illustrative examples as well as an application to the domain of words the notion of hausdorff fuzzy quasi pseudo metric when quasi pseudo metric fuzziness is considered in the sense of george and veeramani is also discussed

classification and construction of quasisimple lie algebras abstract we study a class of possibly infinite dimensional lie algebras called the quasisimple lie algebras qsla s and generalizing semisimple and affine kac moody lie algebras they are characterized by the existence of a finite dimensional cartan subalgebra a non degenerate symmetric ad invariant killing form and nilpotent rootspaces attached to non isotropic roots we are then able to derive a classification theorem for the possible irreducible elliptic quasisimple root systems moreover we construct explicit realizations of some of them as untwisted and twisted current algebras generalizing the affine loop algebras

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

l valued bornologies on powersets in m abel and a ostak 2011 1 the concept of an l fuzzy bornology was introduced actually an l fuzzy bornology on a set x is a certain ideal in the family lx of l fuzzy subsets of a set x here we propose an alternative approach to fuzzification of the concept of bornology we define an l valued bornology on a set x as an l fuzzy subset b of the powerset 2x satisfying l valued analogues of the axioms of a bornology basic properties of l valued bornological spaces are studied our special interest concerns l valued bornologies induced by fuzzy metrics and relative compactness type l valued bornologies in changgoguen l topological spaces

fatou sets of entire solutions of linear differential equations abstract this paper is devoted to studying the dynamical properties of solutions of f a z f 0 where a z is an entire function of finite order with some added conditions on a z we prove that all the fatou components of e z are simply connected provided that e f 1 f 2 and f 1 f 2 are two linearly independent solutions of such equations

iterated function systems and attractors in the km fuzzy metric spaces fractal attractors are considered as invariant sets for contraction mappings in hyperspaces of the km fuzzy metric spaces using the properties of hausdorff fuzzy metrics several existence results of attractors are obtained for a finite family and a countable family of nonlinear contractions in particular unbounded invariant sets are also examined for the iterated function systems in km fuzzy metric spaces our results are generalizations in some aspects and analogous to their counterparts in usual metric spaces

fuzzifying topology induced by a strong fuzzy metric a construction of a fuzzifying topology induced by a strong fuzzy metric is presented properties of this fuzzifying topology in particular its convergence structure are studied our special interest is in the study of the relations between products of fuzzy metrics and the products of the induced fuzzifying topologies

on generalized fuzzy normed spaces and coincidence point theorems in this paper generalized fuzzy norms are defined on a set of objects endowed with a structure of linear space the relationships between these fuzzy norms and the fuzzy metrics and between these fuzzy norms and the topological structures on the base linear space are analyzed finally coincidence and fixed point theorems for mappings with values in fuzzy metric spaces and in such fuzzy normed spaces are proved

fixed point theorems in fuzzy metric spaces using property e a abstract we prove two common fixed point theorems for a pair of weakly compatible maps in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using e a property

linear differential equations with entire coefficients of p q order in the complex plane in this paper we firstly investigate the complex high order linear differential equations in which the coefficients are entire functions of p q order and obtain some results which improve and generalize some previous results in cao 2009 3 chen and yang 2000 4 heittokangas et al 2006 12 kinnunen 1998 17 tu and yi 2008 20

the order theoretic duality and relations between partial metrics and local equalities for a gl monoid l hohle introduced l valued sets to formalize the mathematical theory of identity and existence in monoidal logic for the purpose of analyzing deadlock situations in data flow networks the notion of partial metric space was proposed by matthews later on a lattice theoretic generalization of pseudo partial metric spaces extending the range of pseudo partial metrics to a value lattice v were studied under the name of v pseudo pmetric spaces referring to a gl monoid l and a dual gl monoid v we show that l valued sets are order theoretically dual to v pseudopmetric spaces and apply this duality to the representation of v pseudopmetric spaces and the determination of their various categorical properties in addition to this the present paper provides not only some new results about the representation of l valued sets and their categories but also some non trivial categorical connections between l valued sets and v pseudopmetric spaces

some remarks on representations of jet groups and gauge groups irreducible unitary representations of the three first jet or leibniz extensions gkm of a compact group g are studied focusing on the neighborhood of the trivial representation some associated irreducible unitary continuous tensor product representations of the gauge or current groups of mappings from a riemannian manifold into gkm are described

fuzzy quasi pseudometrics on algebraic structures abstract in this work we state a number of theorems about fuzzy quasi pseudometrizable algebraic structures our most useful results are 1 a fuzzy semitopological group whose topology is induced by a left invariant fuzzy quasi pseudometric then it is a fuzzy paratopological topological group 2 if the topology on a semigroup s is induced by an invariant fuzzy quasi pseudometric then s is a fuzzy topological semigroup and 3 the same conclusion is valid for a left invariant fuzzy quasi pseudometric on a monoid g such that the left translations are open and the right translations are continuous at the identity e of g by means of the standard fuzzy quasi pseudometric m d associated to a quasi pseudometric d our results apply in the case of semitopological groups semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes

representations of solutions of periodic second order linear differential equations on considere l equation y g z y h z y 0 a coefficients entiers periodiques arbitraires g z et h z de periode 0 et des solutions y z ayant la propriete que l exposant de convergence de la suite nulle est finie

fuzzy lipschitz maps and fixed point theorems in fuzzy metric spaces in this paper we introduce the notion of dilation and fuzzy lipschitz of a map from a fuzzy metric space into a fuzzy metric space and we prove continuity properties for such maps we also define the notion of the fuzzy lipschitz distance between two fuzzy metric spaces and show that two compact fuzzy metric spaces whose lipschitz distance is zero is fuzzy isometric to each other on the other hand we introduce the concept of minimal slope of a map between fuzzy metric spaces which is defined by the ratio of two fuzzy metrics and derive some properties on it and relations with the dilation in particular we show that if the dilation of a map from a fuzzy metric space which is complete in george and veeramani sense into itself is less than the minimal slope then the map must have a fixed point in case that a fuzzy metric space is considered in the sense of kramosil and michalek and that the completeness in the sense of grabiec the same result holds

the bicompletion of fuzzy quasi metric spaces extending the well known result that every fuzzy metric space in the sense of kramosil and michalek has a completion which is unique up to isometry we show that every km fuzzy quasi metric space has a bicompletion which is unique up to isometry and deduce that for each km fuzzy quasi metric space the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion

a new class of unitarizable highest weight representations of infinite dimensional lie algebras ii on donne les details rigoureux pour le probleme de classification on redemontre l unitarite de la representation exceptionnelle on considere les produits tensoriels et les problemes d integrabilite

linear differential equations with coefficients in weighted bergman and hardy spaces complex linear differential equations of the form with coefficients in weighted bergman or hardy spaces are studied it is shown for example that if the coefficient a j z of belongs to the weighted bergman space a 1 k j where a 0 for all j 0 k 1 then all solutions are of order of growth at most a measured according to the nevanlinna characteristic in the case when a 0 all solutions are shown to be not only of order of growth zero but of bounded characteristic conversely if all solutions are of order of growth at most a 0 then the coefficient aj z is shown to belong to a pj for all p j 0 1 k j and j 0 k 1 analogous results when the coefficients belong to certain weighted hardy spaces are obtained the non homogeneous equation associated to is also briefly discussed

growth of meromorphic solutions of linear difference equations abstract in this paper the authors continue to study the growth of meromorphic solutions of homogeneous or non homogeneous linear difference equations with entire coefficients and obtain some results which are improvement and extension of previous results in chiang and feng 2008 7 and laine and yang 2007 19 examples are also given to illustrate the sharpness of our results

the growth oscillation and fixed points of solutions of complex linear differential equations in the unit disc abstract we consider the complex differential equations of the form a k z f k a k 1 z f k 1 a 1 z f a 0 z f f z where a 0 0 a 1 a k and f are analytic functions in the unit disc d z c z 1 some results on the finite iterated order and the finite iterated convergence exponent of zero points in d of meromorphic analytic solutions are obtained the fixed points of solutions of differential equations are also investigated in this paper

a characterization of partial metrizability a characterization of partial metrizability is given which provides a partial solution to an open problem stated by kunzi in the survey paper non symmetric topology in proceedings of the szekszard conference bolyai soc math studies vol 4 1993 pp 303 338 problem 711 characterize those quasi uniformities having a countable base which are induced by a weighted quasi metric the characterization yields a powerful tool which establishes a correspondence between partial metrics and special types of valuations referred to as q valuations cf also theoret comput sci to appear the notion of a q valuation essentially combines the well known notion of a valuation with a weaker version of the notion of a quasi unimorphism i e an isomorphism in the context of quasi uniform spaces as an application we show that continuous directed complete partial orders dcpos are quantifiable in the sense of o neill in s andima et al eds proceedings of the 11th summer conference on general topology and applications annals of the new york academy of sciences vol 86 1997 pp 304 315 i e the scott topology and partial order are induced by a partial metric for algebraic dcpos the lawson topology is induced by the associated metric the partial metrization of general domains improves prior approaches in two ways the partial metric is guaranteed to capture the scott topology as opposed to e g smyth quasi uniformities reconciling domains with metric spaces lecture notes in computer science vol 298 springer berlin 1987 pp 236 253 bonsangue et al theoret comput sci 193 1998 1 flagg theoret comput sci to appear and flagg theoret comput sci 177 1 1997 1 which in general yield a coarser topology partial metric spaces are smyth completable and hence their smyth completion reduces to the standard bicompletion this type of simplification is advocated in smyth in g m reed a w roscoe r f wachter eds topology and category theory in computer science oxford university press oxford 1991 pp 207 229 our results extend smyth 1991 s scope of application from the context of 2 3 sfp domains to general domains the quantification of general domains solves an open problem on the partial metrizability of domains22pawel waszkiewicz communicated recently to the author that he obtained similar results independently a stronger result implying the quantifiability of general domains is reported in 23 o neill obtained the partial metrizability of algebraic domains in his thesis 29 stated in o neil 1997 and heckmann appl categor struct 1999 71 our proof of the quantifiability of domains is novel in that it relies on the central notion of a semivaluation schellekens the correspondence between partial metrics and semivaluations theoret comput sci to appear the characterization of partial metrizability is entirely new and sheds light on the deeper connections between partial metrics and valuations commented on in bukatin and shorina in m nivat ed foundations of software science and computation structures lecture notes in computer science vol 1378 springer berlin 1998 pp 125 139 based on schellekens the correspondence between partial metrics and semivaluations theoret comput sci to appear and our present characterization we conclude that the notion of a semi valuation is central in the context of quantitative domain theory since it can be shown to underlie the various models arising in the applications

entire functions that share a small function with their derivatives abstract let f be an entire function of finite order and a an entire function of order less than f s if f a and f a have the same zeros with the same multiplicities then f a c f a for some non zero constant c

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

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

topological stability for fuzzy expansive maps abstract we introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces we show some basic properties of fuzzy expansive homeomorphisms moreover we prove walters s theorem in the context of fuzzy metric spaces i e a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable

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