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

mixed boundary value problems for elliptic and parabolic differential equations of second order on considere les problemes aux valeurs limites mixtes suivants lu f 1 dans mu f 2 sur u f 3 sur avec l operateur elliptique et pu f 1 dans 0 t mu f 2 sur 0 t u f 3 sur 0 t 0 pour des operateurs p paraboliques pour des operateurs obliques generaux m et pour des domaines ou et se rencontrent a des angles arbitraires on montre l existence de solutions classiques quand les angles sont non nuls et f 3 est continue de holder

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

optimal holder regularity for mixed boundary value problems abstract we continue our study of mixed boundary value problems lu 1 in mu 2 on u 3 on for second order elliptic operators l and first order oblique operators m a best possible estimate of the regularity of u is proved under weak hypotheses on the coefficients of l and m

generalized stable models for financial asset returns a new model utilizing generalized stable distributions for financial asset returns is presented a comparison of fit to interest and exchange rate data is provided

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

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

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

new efficient estimators in rare event simulation with heavy tails this paper is concerned with the efficient simulation of p s n s in situations where s is large and s n is the sum of n i i d heavy tailed random variables x 1 x n the most efficient and simplest estimators introduced in the rare event simulation literature are those proposed by asmussen and kroese 2006 and asmussen and kortschak 2012 although the main techniques for facing the rare event problem are importance sampling and splitting the estimators of asmussen kortschak and kroese combine exchangeability arguments with conditional monte carlo to construct estimators whose relative errors go to 0 as s in this paper we decompose p s n s as the sum of p m n s and p s n s m ns is known in closed form and is asymptotically equivalent to p s n s we construct new efficient estimators of p s n s m n

comonotonic approximations for a generalized provisioning problem with application to optimal portfolio selection in this paper we discuss multiperiod portfolio selection problems related to a specific provisioning problem our results are an extension of dhaene et al 2005 14 where optimal constant mix investment strategies are obtained in a provisioning and savings context using an analytical approach based on the concept of comonotonicity we derive convex bounds that can be used to estimate the provision to be set up at a specified time in future to ensure that after having paid all liabilities up to that moment all liabilities from that moment on can be fulfilled with a high probability

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

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

the perron process applied to oblique derivative problems abstract the perron process has been used with great success to prove the solvability of the dirichlet problem for linear elliptic equations by elementary methods a modification of this process is used to give an elementary proof of the solvability of the regular oblique derivative problem for linear elliptic equations

skewness and asymmetry measures and orderings recent interest in skewness has tended to separate two aspects of the concept two distributions may be compared with respect to skewness or a distribution may be self compared that is the distributions of the random variables of x and x may be compared this paper uses the unification of these two aspects to attemp to complete a skewness structure of orderings that identifies the roles of various skewness and scale measures and enables classification of the skewness properties of any distribution the structure is also used to propose measures of asymmetry some skewness properties of the weibull and johnson systems are examined

the tricomi problem for a genuinely nonlinear lavrentiev bitsadze equation of mixed type abstract in this paper we consider the tricomi problem for a genuinely nonlinear lavrentiev bitsadze mixed type equation 2 u x 2 sgn y 1 u x 2 2 u y 2 0 whose coefficients depend on the first order derivative of an unknown function we prove the existence of a solution to this problem by a method which can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

harmonic analysis on quantum tori this paper is devoted to the study of harmonic analysis on quantum tori we consider several summation methods on these tori including the square fej r means square and circular poisson means and bochner riesz means we first establish the maximal inequalities for these means then obtain the corresponding pointwise convergence theorems in particular we prove the noncommutative analogue of the classical stein theorem on bochner riesz means the second part of the paper deals with fourier multipliers on quantum tori we prove that the completely bounded l p fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension finally we present the littlewood paley theory associated with the circular poisson semigroup on quantum tori we show that the hardy spaces in this setting possess the usual properties of hardy spaces as one can expect these include the quantum torus analogue of fefferman s h 1 bmo duality theorem and interpolation theorems our analysis is based on the recent developments of noncommutative martingale ergodic inequalities and littlewood paley stein theory

a fixed point theorem in probabilistic metric spaces and an application abstract the notion of a c contraction type multivalued mapping is introduced this notion is a generalization of the notion of c contraction introduced by t l hicks univ u novom sadu zb rad prirod mat fak ser mat 13 1983 63 72 a fixed point theorem for c contraction is proved an application on the existence of a random fixed point for random operator f m m where m d is a separable metric space and a m a measure space with a decomposable measure of nsa type is given

on fixed point theorems of gregori and sapena using the theory of countable extension of a t norm we prove in this paper that the fixed point theorem of gregori and sapena holds under more general conditions

boundary value problem for a nonlinear equation of mixed type abstract in this paper we consider the boundary value problem for a nonlinear lavrentiev bitsadze equation of mixed type 2 u x 2 sgn y 1 u x 2 2 u y 2 0 whose coefficients depend on the first order derivatives of unknown function above y 0 and below y 0 the equation becomes the nonlinear elliptic equation and nonlinear hyperbolic equation respectively this is different from the equation studied in chen 2011 9 we prove the existence of solution to the problem by the method which can be used to study more difficult problems for nonlinear equations of mixed type arising in gas dynamics

asymptotic stochastic dominance rules for sums of i i d random variables in this paper we deal with stochastic dominance rules under the assumption that the random variables are stable distributed the stable paretian distribution is generally used to model a wide range of phenomena in particular its use in several applicative areas is mainly justified by the generalized central limit theorem which states that the sum of a number of i i d random variables with heavy tailed distributions tends to a stable paretian distribution we show that the asymptotic behavior of the tails is fundamental for establishing a dominance in the stable paretian case moreover we introduce a new weak stochastic order of dispersion aimed at evaluating whether a random variable is more risky than another under condition of maximum uncertainty and a stochastic order of asymmetry aimed at evaluating whether a random variable is more or less asymmetric than another the theoretical results are confirmed by a financial application of the obtained dominance rules the empirical analysis shows that the weak order of risk introduced in this paper is generally a good indicator for the second order stochastic dominance

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