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

characterizing completable fuzzy metric spaces recently we showed the existence of a fuzzy metric space in the sense of george and veeramani which is not completable fuzzy sets and systems 130 2002 399 here we present an internal characterization of those fuzzy metric spaces that are completable some applications are derived and some illustrative examples are given

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

curve arclength in fuzzy metric spaces abstract in the paper an arclength notion of continuous curves in fuzzy metric spaces is proposed and some arclength properties are studied including invariance additivity continuity and boundedness it turns out that these arclength properties imply the corresponding ones in metric spaces

an identification theorem for the completion of the hausdorff fuzzy metric abstract we prove that given a fuzzy metric space in the sense of kramosil and michalek the completion of its hausdorff fuzzy metric space is isometric to the hausdorff fuzzy metric space of its completion when the hausdorff fuzzy metrics are defined on the respective collections of non empty closed subsets as a consequence we deduce the corresponding result for metric spaces by using the standard fuzzy metric an application to the extension of multivalued mappings and some illustrative examples are also given

fast evaluation of gaunt coefficients recursive approach solution of electromagnetic multisphere scattering problems involves the determination of a large number of gaunt coefficients that are connected with definite integrals of products of three associated legendre functions this paper presents general recursion formulae cycling a single index for the gaunt coefficient with the use of the recursive scheme gaunt coefficients of either low or high degree and order can be evaluated accurately and expeditiously

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

on fuzzy pseudo metric spaces this paper attempts to endow the fuzzy pseudo metric in the sense of george and veeramani with many valued topological structures it is shown that george and veeramani s fuzzy pseudo metric can be characterized by a family of compatible ordinary pseudo metrics called pseudo metric chain in this paper then two kinds of many valued topological structures fuzzifying topology and fuzzifying uniformity are generated by this fuzzy pseudo metric and their properties are also investigated

numerical integration of functions with a sharp peak at or near one boundary using mo bius transformations abstract a class of coordinate transformations depending on a single parameter is studied as quadrature tool working rules for the choice of the parameter are proposed numerical tests for the method are presented they show that these coordinate transformations when combined with gauss legendre quadrature rules are well suited for the numerical integration of functions possessing a sharp peak at or near one boundary of the interval of integration a method to combine the transformations with automatic quadrature routines is also proposed it seems to be useful for the numerical evaluation of integrals with the same kind of integrand behavior

the numerical evaluation of very oscillatory infinite integrals by extrapolation recently the author has given two modifications of a nonlinear extrapolation method due to levin and sidi which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity in this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and increasingly rapid oscillatory behavior at infinity the new method is applied to a number of complicated integrals among them the solution to a problem in viscoelasticity some convergence results for this method are presented

gromov hausdorff convergence of non archimedean fuzzy metric spaces we introduce the notion of the gromov hausdorff fuzzy distance between two non archimedean fuzzy metric spaces in the sense of kramosil and michalek basic properties involving convergence and the fuzzy version of the completeness theorem are presented we show that the topological properties induced by the classic gromov hausdorff distance on metric spaces can be deduced from our approach

the hd and hd methods for accelerating the convergence of three center nuclear attraction and four center two electron coulomb integrals over b functions and their convergence properties abstract three center nuclear attraction and four center two electron coulomb integrals over slater type orbitals are required for ab initio and density functional theory dft molecular structure calculations they occur in many millions of terms even for small molecules and require rapid and accurate evaluation the b functions are used as a basis set of atomic orbitals these functions are well adapted to the fourier transform method that allowed analytical expressions for the integrals of interest to be developed rapid and accurate evaluation of these analytical expressions is now made possible by applying the hd and hd methods for accelerating the convergence of the semi infinite oscillatory integrals the convergence properties of the new methods are analysed the numerical results section shows the high predetermined accuracy and the substantial gain in the calculation times obtained using the new methods

embedding meshes into crossed cubes crossed cubes are important variants of hypercubes in this paper we consider embeddings of meshes in crossed cubes the major research findings in this paper are 1 for any integer n 1 a 2x2 n 1 mesh can be embedded in the n dimensional crossed cube with dilation 1 and expansion 1 2 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded in the n dimensional crossed cube with dilation 1 and expansion 2 the obtained results are optimal in the sense that the dilations of the embeddings are 1 the embedding of the 2x2 n 1 mesh is also optimal in terms of expansion because it has the smallest expansion 1

two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series two new classes of nonlinear transformations the d transformation to accelerate the convergence of infinite integrals and the d transformation to accelerate the convergence of infinite series are presented in the course of the development of these transformations two interesting asymptotic expansions one for infinite integrals and the other for infinite series are derived the transformations d and d can easily be applied to infinite integrals 0f t dt whose integrands f t satisfy linear differential equations of the form f t s m k 1p k t f k t and to infinite series s r 1f r w terms f r satisfy a linear difference equation of the form f r s m k 1p k r d kf r such that in both cases the p k have asymptotic expansions in inverse powers of their arguments in order to be able to apply these transformations successfully one need not know explicitly the differential equation that the integrand satisfies or the difference equation that the terms of the series satisfy mere knowledge of the existence of such a differential or difference equation and its order m is enough this broadens the areas to which these methods can be applied the connection between the d and d transformations with some known transformations in shown the use and the remarkable efficiency of the d and d transformations are demonstrated through several numerical examples the computational aspects of these transformations are described in detail

on completion of fuzzy metric spaces completions of fuzzy metric spaces in the sense of george and veeramani are discussed a complete fuzzy metric space y is said to be a fuzzy metric completion of a given fuzzy metric space x if x is isometric to a dense subspace of y we present an example of a fuzzy metric space that does not admit any fuzzy metric completion however we prove that every standard fuzzy metric space has an up to isometry unique fuzzy metric completion we also show that for each fuzzy metric space there is an up to uniform isomorphism unique complete fuzzy metric space that contains a dense subspace uniformly isomorphic to it

fuzzy quasi metrics for the sorgenfrey line we endow the set of real numbers with a family of fuzzy quasi metrics in the sense of george and veeramani which are compatible with the sorgenfrey topology although these fuzzy quasi metrics are not deduced explicitly from a quasi metric they possess interesting properties related to completeness for instance we prove that they are balanced and complete in the sense of doitchinov and that only one of them is right k sequentially complete we also observe that compatible fuzzy quasi metrics for the sorgenfrey line cannot be left weakly right k sequentially complete

fuzzy uniform structures and continuous t norms we introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces more exactly for each continuous t norm we prove that the category of all fuzzy uniform spaces in our sense and fuzzy uniformly continuous mappings is isomorphic to the category of uniform spaces and uniformly continuous mappings by means of a covariant functor moreover we also describe the inverse functor and then we discuss completeness and completion of these fuzzy uniform structures it follows from our results that each fuzzy uniform structure in our sense induces a hutton 0 1 uniformity and conversely each hutton 0 1 uniformity induces a fuzzy uniform structure in our sense

lower bounds for quartic anharmonic and double well potentials rigorous and remarkably accurate lower bounds to the lower eigenvalue spectrum of the schrodinger equation with quartic anharmonic and symmetric double well potentials of the form v a b ax2 2 bx4 b 0 are presented this procedure exploits some exactly soluble model potentials and appears to be of quite general utility

efficient evaluation of coulomb integrals the nonlinear d and transformations the two electron multicentre coulomb integrals constitute the rate limiting step of ab initio and density functional theory dft molecular structure calculations speed up can be achieved by limiting the number of integrals to evaluate analytically but these analytical evaluations remain rate limiting for large molecules here we apply the nonlinear d and transformations to evaluate coulomb integrals over b functions more rapidly than the alternative transformation methods to a given predetermined high accuracy

completeness of hutton 0 1 quasi uniform spaces this paper deals with completeness of hutton 0 1 quasi uniform spaces recently the first two authors j gutierrez garcia m a de prada vicente hutton 0 1 quasi uniformities induced by fuzzy quasi metric spaces fuzzy sets and systems 157 2006 755 766 have constructed a hutton 0 1 quasi uniformity induced by a fuzzy metric space in the sense of george and veeramani in this paper we define completeness of hutton 0 1 quasi uniform spaces as convergence of any stratified tight cauchy 0 1 filter our main result states the equivalence between completeness of any fuzzy metric space x m and completeness of the induced hutton 0 1 quasi uniformity u m also it is proved that the hutton 0 1 quasi uniform space x u m has in this context a kind of completion that is unique up to uniform isomorphism the obtained results come from an appropriate definition of cauchy l filter where l stands for a complete lattice with additional properties

efficient evaluation of vector translation coefficients in multiparticle light scattering theories vector addition theorems are a necessary ingredient in the analytical solution of electromagnetic multiparticle scattering problems these theorems include a large number of vector addition coefficients there exist three basic types of analytical expressions for vector translation coefficients stein s quart appl math 19 15 1961 cruzan s quart appl math 20 33 1962 and xu s j comput phys 127 285 1996 stein s formulation relates vector translation coefficients with scalar translation coefficients cruzan s formulas use the wigner 3jm symbol xu s expressions are based on the gaunt coefficient since the scalar translation coefficient can also be expressed in terms of the gaunt coefficient the key to the expeditious and reliable calculation of vector translation coefficients is the fast and accurate evaluation of the wigner 3jm symbol or the gaunt coefficient we present highly efficient recursive approaches to accurately evaluating wigner 3jm symbols and gaunt coefficients armed with these recursive approaches we discuss several schemes for the calculation of the vector translation coefficients using the three general types of formulation respectively our systematic test calculations show that the three types of formulas produce generally the same numerical results except that the algorithm of stein s type is less accurate in some particular cases these extensive test calculations also show that the scheme using the formulation based on the gaunt coefficient is the most efficient in practical computations

paths and cycles identifying vertices in twisted cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement the twisted cube is an important variation of the hypercube and preserves many of its desirable properties karpovsky et al introduced the concept of identifying codes to model fault detection in multiprocessor systems and honkala et al developed an identifying code by using cycles to identify the faulty processors in the hypercube in this paper we study the vertex identification problem on the twisted cube we first propose an interesting construction scheme to build paths and cycles and furthermore apply a minimum number of paths and cycles to identify the faulty processors of the twisted cube

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

embedding of meshes in mobius cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement mobius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices in this paper we consider embedding of meshes in mobius cubes the main results obtained in this paper are 1 for n 1 there exists a 2x2 n 1 mesh that can be embedded in the n dimensional mobius cube with dilation 1 and expansion 1 2 for n 4 there exists a 4x2 n 2 mesh that can be embedded in the n dimensional mobius cube with dilation 2 and expansion 1 3 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 0 type n dimensional mobius cube with dilation 1 4 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 1 type n dimensional mobius cube with dilation 2 results of 1 and 3 are optimal in the sense that the dilations of the embeddings are 1

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

a new algorithm for accurate and fast numerical evaluation of hybrid and three centre two electron coulomb integrals over slater type functions recently we developed a new algorithm for a fast and accurate numerical evaluation of three centre nuclear attraction integrals over slater type functions the results obtained were very satisfactory now it is shown that this new algorithm can also be applied to hybrid and three centre two electron coulomb integrals over slater type functions these integrals which are numerous are very difficult to evaluate to a high accuracy because of the presence of spherical bessel functions and hypergeometric series in the integrands we have proved that the integrands that occur in the analytic expressions of the integrals under consideration satisfy all the conditions to apply the approach the hypergeometric functions which occur in the semi infinite integrals can be expressed as a finite expansion and the semi infinite integrals involving the spherical bessel functions can be transformed into semi infinite integrals involving the simple sine function the numerical results obtained with linear and non linear systems illustrate clearly a further improvement of accuracy and a substantial reduction in calculation times comparisons with existing codes stop developed by bouferguene et al 1996 int j quantum chem 57 801 and adggstngint developed by rico et al 1997 comp phys commun 105 216 are listed

addition theorems for b functions and other exponentially declining functions in this paper addition theorems are derived for a special class of exponentially declining functions the so called b functions bmn l r e filter and e o steinborn phys rev a 18 1 1978 although these b functions have a relatively complicated analytical structure they nevertheless have some mathematical properties that are particularly advantageous in connection with multicenter problems also all the commonly occurring exponentially declining functions like for instance bound state hydrogen eigenfunctions and slater type functions can be expressed by simple finite sums of b functions consequently addition theorems for these functions can also be written down immediately the various addition theorems for b functions are derived by applying suitable generating differential operators to the well known addition theorem of the special b function bm l l which is that solution of the modified helmholtz equation that is irregular at the origin and regular at infinity e j weniger and e o

the hausdorff fuzzy metric on compact sets we propose a method for constructing a hausdorff fuzzy metric on the set of the nonempty compact subsets of a given fuzzy metric space in the sense of george and veeramani we discuss several important properties as completeness completion and precompactness some illustrative examples are given

embedding a family of disjoint 3d meshes into a crossed cube crossed cubes are an important class of hypercube variants this paper addresses how to embed a family of disjoint 3d meshes into a crossed cube two major contributions of this paper are 1 for n 4 a family of two disjoint 3d meshes of size 2x2x2 n 3 can be embedded in an n d crossed cube with unit dilation and unit expansion and 2 for n 6 a family of four disjoint 3d meshes of size 4x2x2 n 5 can be embedded in an n d crossed cube with unit dilation and unit expansion these results mean that a family of two or four 3d mesh structured parallel algorithms can be executed on a same crossed cube efficiently and in parallel our work extends the results recently obtained by fan and jia j fan x jia embedding meshes into crossed cubes information sciences 177 15 2007 3151 3160

an algorithm for a generalization of the richardson extrapolation process in this paper we present a recursive method designated the w m algorithm for implementing a generalization of the richardson extrapolation process that has been ntroduced in 8 compared to the direct solution of the linear systems of equations defining the extrapolation procedure this method requires a small number of arithmetic operations and very little storage the technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying the d transformation of 6 13 to power series in the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced which is similar to that given in 2 4 for solving the same problem a fortran program for the w m algorithm is also appended

the properties of sine spherical bessel and reduced bessel functions for improving convergence of semi infinite very oscillatory integrals the evaluation of three centre nuclear attraction integrals over b functions this paper focuses on the use of useful properties of sine spherical bessel and reduced bessel functions to simplify the application of the nonlinear d and transformations for accelerating the convergence of semi infinite very oscillatory integrals and to reduce the calculation times keeping a high predetermined accuracy three centre nuclear attraction integrals which are one of the most difficult type involved in density functional theory methods when using a basis set of b functions are evaluated using the new approach the numerical results show the efficiency of the new method compared with other alternatives

some questions in fuzzy metric spaces the george and veeramani s fuzzy metric defined by m x y t min x y t max x y t on 0 the set of non negative real numbers has shown some advantages in front of classical metrics in the process of filtering images in this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it as a consequence of this study we introduce throughout the paper some questions relative to fuzzy metrics also as another practical application we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples

fast evaluation of the gaunt coefficients addition theorems for vector spherical harmonics require the determination of the gaunt coefficients that appear in a linearization expansion of the product of two associated legendre functions this paper presents an algorithm for the efficient calculation of these coefficients through solving the most appropriate lower triangular linear system and derives all relevant recurrence relations needed in the calculation this algorithm is also applicable to the calculation of the clebsch gordan coefficients that are closely related to the gaunt coefficients and are frequently encountered in the quantum theory of angular momentum the new method described in this paper reduces the computing time to 1 compared to the existing formulation that is widely used this new method can be applied to the calculation of both low and high degree coefficients while the existing formulation works well only for low degrees

a comment on the completion of fuzzy metric spaces we argue that in some recent papers discussing the completion of fuzzy metric and fuzzy normed spaces proper credit is not given to earlier works on the subject

a technique for fuzzifying metric spaces via metric preserving mappings abstract in this paper we develop a new technique for constructing fuzzy metric spaces in the sense of george and veeramani from metric spaces and by means of the lukasievicz t norm in particular such a technique is based on the use of metric preserving functions in the sense of j dobos besides the new generated fuzzy metric spaces are strong and completable and if we add an extra condition they are principal appropriate examples of such fuzzy metric spaces are given in order to illustrate the exposed technique

new formulae for higher order derivatives and applications we present new formulae the slevinsky safouhi formulae i and ii for the analytical development of higher order derivatives these formulae which are analytic and exact represent the kth derivative as a discrete sum of only k 1 terms involved in the expression for the kth derivative are coefficients of the terms in the summation these coefficients can be computed recursively and they are not subject to any computational instability as examples of applications we develop higher order derivatives of legendre functions chebyshev polynomials of the first kind hermite functions and bessel functions we also show the general classes of functions to which our new formula is applicable and show how our formula can be applied to certain classes of differential equations we also presented an application of the formulae of higher order derivatives combined with extrapolation methods in the numerical integration of spherical bessel integral functions

three centre two electron coulomb and hybrid integrals evaluated using nonlinear d and bard transformations of the two electron integrals occuring in the molecular context the three centre coulomb and hybrid integrals are numerous and difficult to evaluate to high accuracy the analytical and numerical difficulties arise mainly from the presence of the spherical bessel function and hypergeometric series in these integrals the present work accelerates the convergence of these integrals by first manipulating the indices of the hypergeometric function and exploiting relationships to express this function as a finite expansion and exploiting the properties of bessel functions which satisfy second order linear differential equations this is a suitable form of the integrand to apply the nonlinear d due to d levin and a sidi and due to a sidi transformations the extensive numerical results section illustrates the accuracy and unprecedented efficiency of evaluation of these integrals

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

probabilistic metric spaces as enriched categories in this paper we investigate cauchy completeness and exponentiablity for quantale enriched categories paying particular attention to probabilistic metric spaces

on fuzzy uniformities induced by a fuzzy metric space abstract different types of fuzzy uniformities have been introduced in the literature standing out the notions due to hutton hohle and lowen the main purpose of this paper is to study several methods to endow a fuzzy metric space x m in the sense of george and veeramani with a probabilistic uniformity and with a hutton 0 1 quasi uniformity we will show the functorial behavior of these constructions as well as its relation with respect to lowen s functors and katsaras s functors which establish a relationship between the categories of probabilistic uniformities and hutton 0 1 quasi uniformities with the category of classical uniformities respectively furthermore we also study the fuzzy topologies associated with these fuzzy uniformities

a characterization of bicompletable fuzzy quasi metric spaces we obtain an internal characterization of those fuzzy quasi metric spaces that admit a fuzzy quasi metric bicompletion we also show that such a bicompletion is unique up to isometry

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 novel algorithm to embed a multi dimensional torus into a locally twisted cube this paper addresses how to embed a multi dimensional torus of maximal size of into an n dimensional locally twisted cube the major contribution of this paper is that for n 4 every k dimensional torus of size 2 s 1x2 s 2x x2 s k satisfying i 1 ks i n can be embedded into an n dimensional locally twisted cube with dilation 2 and unit expansion further an embedding algorithm can be constructed based on our embedding method and the time complexity of this algorithm is linear with respect to the size of the locally twisted cube the embedding is optimal in the sense that it has unit expansion

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

regular article efficient and rapid evaluation of three center two electron coulomb and hybrid integrals using nonlinear transformations among the two electron integrals occurring in the molecular context the three center coulomb and hybrid integrals are numerous and difficult to evaluate to high accuracy the analytical and numerical difficulties arise mainly from the presence of the spherical bessel function and hypergeometric series in these integrals the present work pursues the acceleration of convergence for three center two electron coulomb and hybrid integrals we have proven that the hypergeometric function can be expressed as a finite expansion and that the integrand involving this series and a product of bessel functions satisfies a linear differential equation with coefficients having a power series expansion in the reciprocal of the variable suitable for application of the nonlinear d and d transformations these transformations depend strongly on the order of the differential equation that the integrand of interest satisfies this work concentrates on reduction of this order to two exploiting properties of spherical and reduced bessel functions leading to greatly simplified calculations to evaluate the integrals precisely by reducing the order of linear systems to be solved it also avoids the long and difficult implementations of successive derivatives of the integrands the numerical results section illustrates clearly the reduction of the calculation time we obtained for a high predetermined accuracy

examples of fuzzy metrics and applications in this paper we present new examples of fuzzy metrics in the sense of george and veeramani the examples have been classified attending to their construction and most of the well known fuzzy metrics are particular cases of those given here in particular novel fuzzy metrics by means of fuzzy and classical metrics and certain special types of functions are introduced we also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection finally we give an application of this type of fuzzy metrics to color image processing we propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images obtaining promising results this application is also illustrative of how fuzzy metrics can be used in other engineering problems

constructing edge disjoint spanning trees in locally twisted cubes the use of edge disjoint spanning trees for data broadcasting and scattering problem in networks provides a number of advantages including the increase of bandwidth and fault tolerance in this paper we present an algorithm for constructing n edge disjoint spanning trees in an n dimensional locally twisted cube since the n dimensional locally twisted cube is regular with the common degree n the number of constructed trees is optimal

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