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 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

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

classifying and counting fuzzy normal subgroups by a new equivalence relation abstract the main goal of this paper is to give an explicit formula for the number of fuzzy normal subgroups of some finite non abelian groups by using the new equivalence relation presented in fuzzy sets and systems 289 2016 113 121 precisely for a group g this new equivalence is induced by an action of the automorphism group a u t g associated with g on the lattice of fuzzy normal subgroups of g in fact this new equivalence relation generalizes the natural equivalence relation defined on the lattice of fuzzy normal subgroups

the wijsman topology of a fuzzy metric space we introduce and study the notions of lower wijsman topology upper wijsman topology and wijsman topology of a fuzzy metric space in the sense of kramosil and michalek in particular quasi uniformizability uniformizability quasi metrizability and metrizability of these topologies are discussed their relations with other hypertopologies are also analyzed corresponding results to the wijsman topology of a metric space are deduced from our approach with the help of the standard fuzzy metric

finite fuzzy topological spaces abstract we compute for the first time the number of fuzzy topologies defined on a finite set and having a small number of open sets certain cases where the number of open sets is large are also considered several well known results are obtained as corollaries the paper is ended by some questions for future investigations

distributivity in lattices of fuzzy subgroups the main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive we obtain a characterization of these groups which is similar to a well known result of group theory

on the number of fuzzy subgroups of finite abelian groups the main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group by using a similar method some important steps in counting the number of fuzzy subgroups of a finite elementary abelian p group are also made

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

on an equivalence of fuzzy subgroups ii this paper forms a sequel to the paper on an equivalence of fuzzy subgroups i here we determine the number of distinct equivalence classes of fuzzy subgroups of g z p 1 z p n where p 1 p 2 p n are distinct primes we introduce the notion of a keychain of a chain of length n 1 and index of a keychain in order to determine the number of fuzzy subgroups of g we achieve this by using induction on the index of a keychain

asymptotic option pricing under the cev diffusion abstract in finance many option pricing models generalizing the black scholes model do not have closed form analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions therefore asymptotic representation of options prices of various type has important practical implications in finance this paper presents asymptotic expansions of option prices in the constant elasticity of variance model as the parameter appearing in the exponent of the diffusion coefficient tends to 2 which corresponds to the well known black scholes model we use perturbation theory for partial differential equations to obtain the relevant results for european vanilla barrier and lookback options we make our application of perturbation theory mathematically rigorous by supplying error bounds

scaling studies of percolation phenomena in systems of dimensionality two to seven ii equation of state cluster statistics obtained by the monte carlo method for percolation processes in systems of dimensionality two to seven are analysed for the percolation analogue of the thermodynamic equation of state thus complementing the work of paper i on cluster numbers in particular we calculate the scaling functions for the analogues of the thermodynamic potentials and their derivatives and investigate their dependence on dimension d we are guided by the two exactly soluble limits of d 1 and the bethe lattice d a the scaling region where a good degree of data collapsing can be observed is investigated in terms of the two thermodynamic variables one of which is analogous to the temperature and the other to the magnetic field this region is found to be comparatively large and symmetrical in two dimensions but considerably smaller in higher dimensions in addition we find that the characteristic forms of the scaling functions are closely related to the thermodynamic stability conditions finally we analyse the logarithmic corrections to the scaled equation of state at the upper marginal dimension d 6 and a numerical demonstration of the significance of the logarithmic corrections is presented in terms of data collapsing

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

a metatheorem for deriving fuzzy theorems from crisp versions a metatheorem is developed that allows theorems containing references to crisp substructures to be reformulated to refer to fuzzy substructures theorems concerning fuzzy substructures in semigroups rings and lattices are derived in concise fashion from analogous theorems that concern crisp substructures the modularity of the lattice of fuzzy normal subgroups of a group is concisely derived from the modularity of its lattice of crisp normal subgroups the fundamental tool used is a function that represents the algebra of fuzzy subsets of a set as a subdirect product of copies of the algebra of crisp subsets

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

singular perturbations in option pricing after the celebrated black scholes formula for pricing call options under constant volatility the need for more general nonconstant volatility models in financial mathematics motivated numerous works during the 1980s and 1990s in particular a lot of attention has been paid to stochastic volatility models in which the volatility is randomly fluctuating driven by an additional brownian motion we have shown in derivatives in financial markets with stochastic volatility cambridge university press cambridge uk 2000 internat j theoret appl finance 13 2000 pp 101 142 that in the presence of a separation of time scales between the main observed process and the volatility driving process asymptotic methods are very efficient in capturing the effects of random volatility in simple robust corrections to constant volatility formulas from the point of view of pdes this method corresponds to a singular perturbation analysis the aim of this paper is to deal with the nonsmoothness of the payoff

stochastic volatility asymptotics of stock loans valuation and optimal stopping abstract a stock loan or equity security lending service is a loan which uses stocks as collateral the borrower has the right to repay the principal with interest and regain the stock or make no repayment and surrender the stock therefore the valuation of stock loan is an optimal stopping problem related to a perpetual american option with a negative effective interest rate the negative effective interest rate makes standard techniques for perpetual american option pricing failure using a fast mean reverting stochastic volatility model we applied a perturbation technique to the free boundary value problem for the stock loan price an analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion

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

clusters size degree distribution for bond percolation abstract to address some physical properties of percolating systems it can be useful to know the degree distributions in finite clusters along with their size distribution here we show that to achieve this aim for classical bond percolation one can use the q 1 limit of suitably modified q state potts model we consider a version of such model with the additional complex variables and show that its partition function gives the bond percolation s generating function for the size and degree distribution in the q 1 limit for the first time we derive this distribution analytically for bond percolation on bethe lattices and complete graph the possibility to expand the applications of present method to other clusters characteristics and to models of correlated percolation is discussed

counting the number of fuzzy subgroups of an abelian group of order pnqm abstract in this paper we determine the number of fuzzy subgroups of g z p n z q m where p q are distinct primes and n m are any two natural numbers first we represent the number of maximal chains of g as a summation through m involving certain binomial coefficients using this concise expression we propose a combinatorial formula for the number of fuzzy subgroups of g and verify it for specific values of m and n finally we sketch a proof for the general case

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

high temperature series expansions for the q state potts model on a hypercubic lattice and critical properties of percolation we present results for the high temperature series expansions of the susceptibility and free energy of the q state potts model on a d dimensional hypercubic lattice zd for arbitrary values of q the series are up to order 20 for dimension d 1 limit of these series we estimate the percolation threshold pc and critical exponent gamma for bond percolation in different dimensions we also extend the 1 d expansion of the critical coupling for arbitrary values of q up to order d 9

matching asymptotics in path dependent option pricing abstract the valuation of path dependent options in finance creates many interesting mathematical challenges among them are a large delta and gamma near the expiry leading to a big error in pricing those exotic options as well as european vanilla options also the higher order corrections of the asymptotic prices of the derivatives in some stochastic volatility models are difficult to be evaluated in this paper we use the method of matched asymptotic expansions to obtain more practical values of lookback and barrier option prices near the expiry our results verify that matching asymptotics is a useful tool for pde methods in path dependent option pricing

a new equivalence relation to classify the fuzzy subgroups of finite groups in this paper a new equivalence relation for classifying the fuzzy subgroups of finite groups is introduced and studied this generalizes the equivalence relation defined on the lattice of fuzzy subgroups of a finite group that has been used in our previous papers explicit formulas for the number of distinct fuzzy subgroups with respect to the new equivalence relation are obtained in some particular cases

field theoretic approaches to biconnectedness in percolating systems two field theoretic formulations for the percolation problem are presented from which the critical exponents describing the backbone of the infinite cluster at the percolation threshold are obtained at high spatial dimension d the order parameter exponent for the backbone beta 2 is given by beta 2 2 beta psi 2 nu where beta is the critical exponent for the density of the infinite cluster and psi 2 is a new crossover exponent in mean field theory psi 2 0 and for d 6 epsilon psi 2 2 epsilon 2 49 o epsilon 3 presumably psi 2 d is a smooth function of d for d d where numerical and theoretical work indicates that d is about 3 the result indicates that the fractal dimensionality of the backbone is given in terms of the percolation exponents as gamma nu psi 2

an extension of stone duality to fuzzy topologies and mv algebras abstract in this paper we introduce the concept of mv topology a special class of fuzzy topological spaces and prove a proper extension of stone duality to the categories of limit cut complete mv algebras and stone mv spaces namely zero dimensional compact hausdorff mv topological spaces then we describe the category of limit cut complete mv algebras and show that it is a completion namely a reflective subcategory with faithful reflection of the category of semisimple mv algebra last we compose our duality with other known ones thus obtaining new categorical equivalences and dualities involving categories of mv algebras

on the lattices of l topologies certain properties of the lattices of l topologies determined by the families of scott continuous functions for a given topological space are investigated the authors disprove certain known theorems on the above lattices and the correct results are provided using the concept of strict chain join generability in lattices