the poisson kernel for drinfeld modular curves in an earlier work t 1 the author described a technique for constructing rigid analytic modular forms on the p adic upper half plane by means of an integral transform a poisson kernel in this paper we apply these methods to the study of rigid analytic modular forms on the upper half plane over a complete local field k of characteristic p arising out of the theory of drinfeld modules d these modular forms first studied by goss see gol go2 are in many ways analogous to the classical modular forms for sl2 z for a brief but effective introduction to the theory of these characteristic p modular forms see the introduction to gekeler s paper gekl also useful is gekeler s book gek2 we establish three main results first of all we show that if k is the function field of a complete geometrically irreducible curve c over the finite field lfq with q elements k is a completion of k f is an arithmetic subgroup of gl2 k and u is a measure on pi coming from a harmonic cocycle of weight n for i see definition 1 below then

generators of fuzzy dynamical systems abstract in some previous papers dumitrescu 1983 1993 1995 an ergodic theory for fuzzy dynamical systems has been proposed the entropy of a fuzzy dynamical system has been defined it has proven dumitrescu and barbu 1985 dumitrescu 1995 that this entropy is an isomorphism invariant in this paper we define the generators of a fuzzy dynamical system using this notion a fuzzy version of kolmogorov sinai theorem kolmogorov 1958 sinai 1959 is given

connectives for fuzzy partitions abstract the fuzzy intersection and union are defined by means of a certain pair t s of non strict archimedean operators dual with respect to a strict negation having the same additive generator as t we prove that the equivalence between the butnariu s definition and the ruspini s one concerning the fuzzy partitions holds if and only if the connectives for fuzzy operations are t and s

i fuzzy equivalence relations and i fuzzy partitions a t fuzzy equivalence relation is a fuzzy binary relation on a set x which is reflexive symmetric and t transitive for a t norm t recently mesiar et al r mesiar b reusch h thiele fuzzy equivalence relations and fuzzy partitions j multi valued logic soft comput 12 2006 167 181 have generalised the t norm t to any general conjunctor c and investigated the minimal assumptions required on such operations called duality fitting conjunctors such that the fuzzification of the equivalence relation admits any value from the unit interval and also the one one correspondence between the fuzzy equivalence relations and fuzzy partitions is preserved in this work we conduct a similar study by employing a related form of c transitivity viz i transitivity where i is an implicator we show that although every i fuzzy equivalence relation can be shown to be a c fuzzy equivalence relation there exist c fuzzy equivalence relations that are not i fuzzy equivalence relations and hence these concepts are not equivalent most importantly we show that the class of duality fitting implicators i is much richer than the residuals of the duality fitting conjunctors in the study of mesiar et al we also show that the i fuzzy partitions have a constant wise structure

the entropy of fuzzy dynamical systems general scheme and generators in this paper some fuzzy modifications of the kolmogorov sinaj entropy are studied we introduce the general scheme which includes the mentioned entropies finally the kolmogorov sinaj theorem on generators is proved for special cases

entropy of a fuzzy process abstract using an additive fuzzy measure 1 in 5 a general concept of entropy of a fuzzy partition has been considered this concept is used to define the entropy of a fuzzy process in this paper some properties of this entropy are summarized these results could be used to build a fuzzy ergodic theory in a further paper the entropy of a measure preserving transformation of a fuzzy measure space will be studied

p adic l functions and p adic periods of modular forms let e be an elliptic curve which is defined over q and has stable reduction modulo a given prime p assuming that e is modular one can associate to e a p adic l function lp e s see mz swd a v vi mz t t for its construction in various cases this function is defined by a certain interpolation property and is analytic for sezp in this paper we will assume that e has split multiplicative reduction at p under this assumption the interpolation property implies that lp e 1 0 we will prove a formula for ep e 1 which was discovered experimentally by mazur tate and teitelbaum mz t t by tate s p adic urfiformization theory there is a p adic integer q epzp which we refer to as the tate period for e and a p adic analytic isomorphism

entropy of fuzzy dynamical systems abstract entropy of a finite fuzzy partition had been defined dumitrescu 1983 1993 using an additive fuzzy measure butnariu 1983 in this paper we define the independence of fuzzy partitions with respect to a fuzzy measure some properties concerning the entropy of independent fuzzy partitions are proved this concept of independence is also relevant for the study of the entropy of a fuzzy process dumitrescu 1993 we prove some new results concerning the entropy of a fuzzy process the fuzzy measure preserving transformations dumitrescu 1993 may be related with the fuzzy ergodic theory the main problem in ergodic theory is to build the isomorphism invariants kolmogorov s 1958 transformation entropy is such an invariant in this paper we define the entropy of a fuzzy dynamical system we prove that this entropy is an isomorphism invariant

analytical solutions of the space time fractional telegraph and advection diffusion equations abstract the aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non uniform large scale magnetic field by studying the fractional telegraph equation and the fractional advection diffusion equation analytical solutions of the space time fractional telegraph equation and space time fractional advection diffusion equation are obtained by use of the caputo fractional derivative and the laplace fourier technique the solutions are given in terms of fox s h function as an illustration they are applied to the case of solar energetic particles

integration on cal h _p times cal h and arithmetic applications this article describes a conjectural p adic analytic construction of global points on modular elliptic curves points which are defined over the ring class fields of real quadratic fields the resulting conjectures suggest that the classical heegner point construction and the theory of complex multiplication on which it is based should extend to a variety of contexts in which the underlying field is not a cm field

conditional fuzzy entropy of fuzzy dynamical systems abstract entropy of fuzzy dynamical systems has been investigated as an isomorphism invariant in dumitrescu 1995 13 in this paper we will introduce a new invariant called the conditional fuzzy entropy of fuzzy dynamical systems with respect to a finite fuzzy partition and an invariant sub algebra which is an extension of fuzzy entropy on fuzzy dynamical systems this new invariant possesses some basic properties such as power rule fuzzy version of abramov rokhlin entropy additive formula and generating sequence

on the topological entropy on the space of fuzzy numbers in the main result of this article we prove that the topological entropies of a given interval map and its zadeh s extension fuzzification to the space of fuzzy numbers i e the space of fuzzy sets with connected cuts are the same this result is in contrast with our previous result which claimed that the topological entropy of the zadeh s extension significantly increases for a majority of simple interval maps in addition we prove some properties of the limit sets of trajectories that are generated by iterating the fuzzy set valued function on connected fuzzy sets for instance we specify the shapes of the possible limit sets furthermore the presented topics are studied for set valued induced discrete dynamical systems the main results are proved with a variational principle that describes the relations between topological entropy and measure theoretical entropy

solutions of the space time fractional cattaneo diffusion equation abstract the object of this paper is to present the exact solution of the fractional cattaneo equation for describing anomalous diffusion the classical cattaneo model has been generalised to the space time fractional cattaneo model the method of the joint laplace and fourier transform is used in deriving the solution the solutions of the fractional cattaneo equation are obtained under integral and series forms in terms of the h functions finally the fractional order moments are also investigated

the generalized cattaneo equation for the description of anomalous transport processes the cattaneo equation which describes a diffusion process with a finite velocity of propagation is generalized to describe anomalous transport three possible generalizations are proposed each one supported by a different scheme continuous time random walks non local transport theory and delayed flux force relation the properties of these generalizations are studied in both the long time and the short time regimes in the long time limit we recover the mean square displacement which is characteristic for these anomalous processes as expected the short time behaviour is modified in comparison to generalized diffusion equations

the information content of fuzzy relations and fuzzy rules based on different emphases some general information content measures of fuzzy relations are given distinguished from the measures related to fuzzy relations proposed before these measures try to estimate the information conveyed by multiple domain fuzzy relations without preassigned probability distribution since fuzzy rules can be fully captured by fuzzy relations from an input universe to an output universe the information content of fuzzy rules can be easily measured by the information content of fuzzy relations proposed by us however there also exists a difference between fuzzy relations and fuzzy rules rules especially classification rules always have a direction from the antecedent and consequent while relations do not have direction based on this difference some general measures for the information content of fuzzy rules are proposed in practice these measures can do well in the evaluation and selection of fuzzy rules finally the measures of the information content of fuzzy rules are used to evaluate the stability and sensitivity of fuzzy implication operators in fuzzy control

on fuzzy entropy and topological entropy of fuzzy extensions of dynamical systems the goal of this paper is to establish connections between two entropy concepts namely the fuzzy entropy of a fuzzy set which appears in fuzzy set theory and the topological entropy of zadeh s extensions of continuous maps defined on metric compact spaces which is a topological dynamics concept we develop several concepts that allow us to simultaneously address the two entropy concepts except for stating several basic properties we are partially capable of specifying in which classes of fuzzy sets dynamically complex behavior can appear by using these instruments such instruments are necessary for a proper understanding of the behavior of fuzzy systems generated from crisp discrete dynamical systems

p adic periods and modular symbols of elliptic curves of prime conductor under certain assumptions we prove a conjecture of mazur and tate describing a relation between the modular symbol attached to an elliptic curve with split multiplicative reduction atp and itsp adic period we generalize this relation to modular forms of weight 2 with coefficients not necessarily in

entropy of fuzzy partitions a general model abstract the entropy of fuzzy partitions with regard to a fuzzy measure is analyzed a general model based on pseudo arithmetical operations and g functions will be created the entropy of fuzzy partitions introduced by ruspini inform and control 15 1969 22 and dumitrescu j math anal appl 176 1993 359 is shown to be reasonable only up to an isomorphism

m equivalence entropy and f dynamical systems the present paper deals with the theory of entropy of f dynamical systems using the concept of atoms in a fuzzy algebra having introduced the notions of m equivalence and m refinement it is proved that entropy of an f dynamical system with respect to each m equivalence class is an m isomorphism invariant results proved in this paper include the corresponding classical results as particular cases

solitary wave solutions for time fractional third order modified kdv equation using two reliable techniques g g expansion method and improved g g expansion method abstract in the present paper we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics namely time fractional modified kdv equation by using g g expansion method and improved g g expansion method as a result new types of exact analytical solutions are obtained

fuzzy a algebras and conditional entropy the purpose of the present paper is to introduce and study the concept of conditional entropy of fuzzy sub algebras having finitely many atoms

degenerate and non degenerate convex decomposition of finite fuzzy partitions ii abstract in bezdek and harris 1979 an algorithm called minimax shortly mm algorithm for the convex decomposition of a fuzzy partition has been proposed in this paper another decomposition algorithm called miniminimax shortly mmm algorithm is considered a comparative study of these algorithms is done from this study we may conclude that 1 i the mm convex decomposition sequence is not lexicographically larger than any other convex decomposition 2 ii the conjecture from bezdek and harris 1979 concerning the length of the mm decomposition fails some properties of the spaces of fuzzy partitions are also given in part ii a theorem which states a necessary and sufficient condition for the existence of non degenerate convex decompositions is proved an algorithm for non degenerate convex decomposition of a fuzzy partition inspired by the constructive proof of this theorem is proposed this algorithm builds a positive path through the matrix representing a fuzzy partition the convergence of the algorithm and the monotony of the coefficients sequence in the convex decomposition are proved other two results the limited cardinality and the heredity property concerning this algorithm are also given

on hudetz entropy localization abstract in rahimi and riazi 2014 22 a type of entropy of continuous maps on compact metric spaces is defined via integrating a local entropy map this average entropy is represented in terms of the entropy in the sense of dumitrescu but the equality of these two types of entropy is left as an open problem in 22 in this paper we modify the problem stated in 22 by replacing the dumitrescu entropy by the hudetz entropy since in our case the two previous types of entropy take an infinite value and the problem stated in 22 reduces to a trivial equality then we conclude the paper by proving the equality of the modified average entropy and the hudetz entropy the key tool is a version of jaccob s theorem for the hudetz entropy

une base explicite de symboles modulaires sur les corps de fonctions modular symbols for the congruence subgroup gamma 0 mathfrak n of gl 2 mathbf f q t have been defined by teitelbaum they have a presentation given by a finite number of generators and relations in a formalism similar to manin s for classical modular symbols we completely solve the relations and get an explicit basis of generators when mathfrak n is a prime ideal of odd degree as an application we give a non vanishing statement for l functions of certain automorphic cusp forms for mathbf f q t the main statement also provides a key step for a result towards the uniform boundedness conjecture for drinfeld modules of rank 2

fuzzy measures and the entropy of fuzzy partitions abstract using an additive fuzzy measure a notion of the entropy of a finite fuzzy partition has been defined d dumitrescu on fuzzy partitions in itinerant seminar on functional equations approximation and convexity cluj napoca 1983 pp 57 60 d dumitrescu and m barbu fuzzy entropy and processes in itinerant seminar on functional equations approximation and convexity cluj napoca 1985 pp 71 74 this notion contains as a particular case a well known concept of entropy m a gil et al fuzzy sets and systems15 1985 65 78 h tanaka et al kybernetes5 1976 25 30 i j taneja bivariate entropies of finite partitions of fuzzy sets in preprints of second ifsa congress tokyo 1987 vol 2 pp 696 699 the aim of this paper is to review some basic properties of the considered entropy

fractional brownian motion fractional gaussian noise and tsallis permutation entropy abstract in this work we analyze two important stochastic processes the fractional brownian motion and fractional gaussian noise within the framework of the tsallis permutation entropy this entropic measure evaluated after using the bandt pompe method to extract the associated probability distribution is shown to be a powerful tool to characterize fractal stochastic processes it allows for a better discrimination of the processes than the shannon counterpart for appropriate ranges of values of the entropic index moreover we find the optimum value of this entropic index for the stochastic processes under study