points de croissance des processus de levy et theorie generale des processus we prove a conjecture of j bertoin a levy process has increase times if and only if the integral is finite where g and h are the distribution functions of the minimum and the maximum of the levy process killed at an independent exponential time the if part of the statement had been obtained before by r doney our proof uses different techniques from potential theory and the general theory of processes and is self contained our results also show that if p x t 0 1 2 for all t small enough then the process does not have increase times

realizability of algebraic galois extensions by strictly commutative ring spectra we discuss some of the basic ideas of galois theory for commutative s algebras originally formulated by john rognes we restrict our attention to the case of finite galois groups and to global galois extensions we describe parts of the general framework developed by rognes central roles are played by the notion of strong duality and a trace mapping constructed by greenlees and may in the context of generalized tate cohomology we give some examples where algebraic data on coefficient rings ensures strong topological consequences we consider the issue of passage from algebraic galois extensions to topological ones by applying obstruction theories of robinson and goerss hopkins to produce topological models for algebraic galois extensions and the necessary morphisms of commutative s algebras examples such as the complex k theory spectrum as a ko algebra indicate that more exotic phenomena occur in the topological setting we show how in certain cases topological abelian galois extensions are classified by the same harrison groups as algebraic ones and this leads to computable harrison groups for such spectra we end by proving an analogue of hilbert s theorem 90 for the units associated with a galois extension

simultaneous kummer congruences and mathbb e _ infty e orientations of ko and tmf building on results of ando hopkins and rezk we show the existence of uncountably many mathbb e infty string orientations of real k theory ko and of topological modular forms tmf generalizing the hat a resp the witten genus furthermore the obstruction to lifting an mathbb e infty string orientations from ko to tmf is identified with a classical iwasawa theoretic condition the common key to all these results is a precise understanding of the classical kummer congruences imposed for all primes simultaneously this result is of independent arithmetic interest

inversion de l espace et du temps des processus de levy stables we proove a new duality relation between stable levy processes with index open image in new window and those with index open image in new window this duality appears to be the trajectorial version of the duality of zolotarev which concerns one dimensional stable laws we give an application of this result to the behaviour of the paths at small and large times of the process conditioned to stay positive

adaptive fuzzy multilevel median filter a modified multilevel median filter mlmf incorporating the fuzzy associative memory fam system is proposed in this correspondence the modified method the adaptive fuzzy multilevel median filter afmmf overcomes some disadvantages common to most of the conventional mlmf experimental results demonstrated that the performance of the afmmf is superior to that of conventional mlmf in dealing with short line like noise while preserving edges

adaptive multistage median filter an adaptive multistage median filter is proposed for preserving the details of images it is shown that this filter can smooth noise more efficiently than the multistage median filter

genetic based fuzzy hybrid multichannel filters for color image restoration abstract on the design of multichannel filters especially in color image restoration it is not easy to simultaneously achieve three objectives noise attenuation chromaticity retention and edges or details preservation in this paper we propose a new class of multichannel filters called genetic based fuzzy hybrid multichannel gfhm filters to reach these three objectives simultaneously the design of gfhm filters is mainly based on human concept heuristic rules and genetic algorithms because the human concept can be readily and efficiently expressed by fuzzy implicative rules gfhm filters can take the useful characteristics of filtering behavior of three filters a vector median a vector directional and an identity filter since genetic algorithms possess the global searching capability for an optimal solution they are able to effectively optimize gfhm filters to improve the filtering performance in color image restoration applications extensive simulation results illustrate that gfhm filters not only achieve these three objectives but also possess the robust and the adaptive capability moreover these simulation results also demonstrate that the performance of gfhm filters outperforms that of other proposed filtering techniques

topological modular forms with level structure the cohomology theory known as mathrm tmf for topological modular forms is a universal object mapping out to elliptic cohomology theories and its coefficient ring is closely connected to the classical ring of modular forms we extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them along the way we produce a natural way to restrict to the cusps providing multiplicative maps from mathrm tmf with level structure to forms of k theory in particular this allows us to construct a connective spectrum mathrm tmf 0 3 consistent with properties suggested by mahowald and rezk this is accomplished using the machinery of logarithmic structures we construct a presheaf of locally even periodic elliptic cohomology theories equipped with highly structured multiplication on the log etale site of the moduli of elliptic curves evaluating this presheaf on modular curves produces mathrm tmf with level structure

combination median filter a detail and structure preserving smoothing filter is introduced it is called the combination median filter as it uses directional median multilevel median and median filters to smooth different regions of the image the decision about the region is made by robust dixon s r test which is well known in statistics for outlier detection the threshold value of dixon s test can be kept constant as a result the filtering algorithm operates like a quasi nonadaptive filter and no computation of local statistics is involved some properties of the filter as well as detailed experimental results that demonstrate its superior performance are presented

representation of digital image by fuzzy neural network a multilayer feedforward fuzzy neural network fnn by which the predetermined fuzzy system can be realized is constructed to express a given two dimensional 2 d digital image it is shown that such a network is universal approximator the fnn approach provides us with the representation model of the 2 d discrete image in noise environment some given fuzzy numbers are employed to describe gray levels of a digital image and the deviation of corrupted image to its noise free one a class of fuzzy rules for removing impulse noise in degraded image are presented the corresponding fnn may work as a filter which improves the performances of median and rank conditioned rank selection filters especially such a filter may to a greatest extent maintain the fine structure of the image under the minimum mean absolute error criterion the membership functions of fuzzy numbers are adaptively adjusted and an optimal fnn for image representation is derived in noise environment simultaneously some real image examples are systemically analyzed to show that the fnn may result in higher quality global restoration

a robust approach to image enhancement based on fuzzy logic in this paper we propose a robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement i removing impulse noise ii smoothing out nonimpulse noise and iii enhancing or preserving edges and certain other salient structures we derive three different filters for each of the above three tasks using the weighted or fuzzy least squares ls method and define the criteria for selecting each of the three filters the criteria are based on the local context and they constitute the antecedent clauses of the fuzzy rules the overall result of the fuzzy rule based system is the combination of the results of the individual filters where each result contributes to the degree that the corresponding antecedent clause is satisfied this approach gives us a powerful and flexible image enhancement paradigm results of the proposed method on several types of images are compared with those of other standard techniques

power operations in elliptic cohomology and representations of loop groups the first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve the second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups the third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part

the sigma orientation is an h map in an earlier paper the authors constructed a natural map called the sigma orientation from the thom spectrum mu 6 to any elliptic spectrum mu 6 is an h ring spectrum and in this paper we show that if e c t is the elliptic spectrum associated to the universal deformation of a supersingular elliptic curve over a perfect field of characteristic p 0 then the sigma orientation is a map of h ring spectra

on wiener hopf factorisation and the distribution of extrema for certain stable processes it is shown that when the index 0 0 l alpha 1 k where l and k are integers darling s integral can be evaluated this leads to explicit formulas for a transform of the laplace transform of sup 0 leq t leq 1 x t and the wiener hopf factors of x t t geq 0

spl lscr m s filters for image restoration applications a new filtering architecture is proposed generalizing some previously introduced multilevel median filters an efficient design procedure for the new filtering architecture is demonstrated for image restoration application simulation results show a good noise rejection performance combined with a fine detail preservation capability

buildings elliptic curves and the k 2 local sphere we investigate a dense subgroup of the second morava stabilizer group given by a certain group of quasi isogenies of a supersingular elliptic curve in characteristic p the group acts on the bruhat tits building for gl2 through its action on the adic tate module this action has finite stabilizers giving a small resolution for the homotopy fixed point spectrum eh 2 hgal by spectra of topological modular forms here e2 is a version of morava e theory and gal gal

k 1 local topological modular forms we construct the witten orientation of the topological modular forms spectrum tmf in the k 1 local setting by attaching e cells to the bordism theory mo we also identify the ko homology of tmf with the ring of divided congruences