non self adjoint zakharov shabat operator with a potential of the finite asymptotic values i direct spectral and scattering problems the zakharov and shabat equation for the scattering problem is studied the estimates analytical properties and asymptotic expansions of the jost solution are presented for a general class of the potentials q x not vanishing at infinity the existence of the similarity transformation is also shown for q x vanishing at infinity the continuous part of the spectrum doubly degenerates however nonvanishing finite asymptotic values of q x dissolve the degeneracy completely the expansion theorem is given in c 0 2 r and for a class of q x we prove that the zakharov and shabat equation yields a non self adjoint spectral operator in the hilbert space in the sense of dunford and schwartz

extension theorems of continuous random linear operators on random domains abstract the central purpose of this paper is to prove the following theorem let u be a complete probability space b a normed linear space over the scalar field k e 2 b a separable random domain with linear subspace values and gr e k a continuous random linear operator where gr e x b x e denotes the graph of e then there exists a continuous random linear operator b k such that x x x e and sup x x b x 1 sup x x e x 1 for each in for the case where e is not separable a result similar to the above stated theorem is also given which generalizes and improves many previous results on random generalizations of the hahn banach theorem

random strict convexity and random uniform convexity in random normed modules abstract based on the analysis of stratification structure on random normed modules we first present random strict convexity and random uniform convexity in random normed modules then we establish their respective relations to classical strict and uniform convexity in the process some known important results concerning strict convexity and uniform convexity of lebesgue bochner function spaces can be obtained as a special case of our results further we also give their important applications to the theory of random conjugate spaces as well as best approximation finally we conclude this paper with some remarks showing that the study of geometry of random normed modules will also motivate the further study of geometry of probabilistic normed spaces

on the vectoral ekeland s variational principle and minimal points in product spaces abstract phelps 13 noticed that the scalar ekeland s variational principle evp is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order attouch and riahi 1 showed that evp is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions taking these into account gopfert and tammer 6 7 established a maximal point theorem in a product space the aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial evp

a study of boundedness in probabilistic normed spaces abstract it was shown in lafuerza guillen rodriguez lallena and sempi 1999 8 that uniform boundedness in a serstnev pn space v named boundedness in the present setting of a subset a v with respect to the strong topology is equivalent to the fact that the probabilistic radius r a of a is an element of d here we extend the equivalence just mentioned to a larger class of pn spaces namely those pn spaces that are topological vector spaces briefly tv spaces but are not serstnev pn spaces we present a characterization of those pn spaces whether they are tv spaces or not in which the equivalence holds then a characterization of the archimedeanity of triangle functions of type t l is given this work is a partial solution to a problem of comparing the concepts of distributional boundedness d bounded in short and that of boundedness in the sense of associated strong topology

a study of boundedness in probabilistic normed spaces probabilistic normed spaces have been redefined by alsina schweizer and sklar we give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity

on almost surely bounded semigroups of random linear operators menger proposed transferring the probabilistic notions of quantum mechanics to the underlying geometry following menger s idea the notion of random metric spaces is a random generalization of that of metric spaces and also plays an important role in the study of random operator equations the main difficulty of this article is to work out a skill to give a property peculiar to a special semigroup of random operators which is not involved in the classical case subsequently some random operators equations are studied in particular we discuss the schrodinger type random equation which considerably generalizes the corresponding result in the sense of skorohod

jacobians with group actions and rational idempotents abstract the object of this paper is to prove some general results about rational idempotents for a finite group g and deduce from them geometric information about the components that appear in the decomposition of the jacobian variety of a curve with g action we give an algorithm to find explicit primitive rational idempotents for any g as well as for rational projectors invariant under any given subgroup these explicit constructions allow geometric descriptions of the factors appearing in the decomposition of a jacobian with group action from them we deduce the decomposition of any prym or jacobian variety of an intermediate cover in the case of a jacobian with g action in particular we give a necessary and sufficient condition for a prym variety of an intermediate cover to be such a factor

separation and duality in locally l 0 convex modules motivated by financial applications we study convex analysis for modules over the ordered ring l0 of random variables we establish a module analogue of locally convex vector spaces namely locally l0 convex modules in this context we prove hyperplane separation theorems we investigate continuity subdifferentiability and dual representations of fenchel moreau type for l0 convex functions from l0 modules into l0 several examples and applications are given

the algebraic structure of finitely generated l0 f k modules and the helly theorem in random normed modules abstract let k be the scalar field of real numbers or complex numbers and l 0 f k the algebra of equivalence classes of k valued random variables defined on a probability space f p in this paper we first characterize the algebraic structure of finitely generated l 0 f k modules and then combining the recently developed separation theorem in random locally convex modules we prove the helly theorem in random normed modules with the countable concatenation property under the framework of random conjugate spaces at the same time a simple counterexample shows that it is necessary to require the countable concatenation property

a characterization for an l μ k topological module to admit enough canonical module homomorphisms let k be the scalar field of all real or complex numbers let a be a finite measure space and let l k be the algebra of the equivalence classes of all k valued measurable functions defined on a l k is a topological algebra over k when endowed with the topology of convergence locally in measure topological modules over this topological algebra l k briefly l k topological modules are an extensive class of topological modules which arise naturally in the course of the study of the theory of probabilistic normed spaces the purpose of this paper is to show that an arbitrary regular l k topological module admits enough canonical module homomorphisms if and only if all of its quasi free submodules of finite rank are complemented in the sense of topological modules

nonvanishing boundary condition for the mkdv hierarchy and the gardner equation a kac moody algebra construction for the integrable hierarchy containing the gardner equation is proposed solutions are systematically constructed by employing the dressing method and deformed vertex operators which take into account the nonvanishing boundary value problem for the modified korteweg de vries mkdv hierarchy explicit examples are given and besides the usual kdv like solitons our solutions contemplate the large amplitude table top solitons kinks dark solitons breathers and wobbles

supertransparent potentials for the dirac equation an extension of the classical darboux transformations is applied to the one dimensional dirac equation in order to construct von neumann wigner potentials allowing embedded eigenvalues these potentials lead to a novel type of scattering problem with a trivial s matrix composed of vanishing reflection coefficients and a trivial transmission coefficient related topics like the underlying symmetry of the dirac equation and the connection with positon solutions of nonlinear evolution equations are discussed

countable products of probabilistic normed spaces abstract countable products of probabilistic normed spaces are introduced and studied in particular a comparison is made with the analogous constructions for probabilistic metric spaces

probabilistic norms and convergence of random variables abstract we prove that the probabilistic norms of suitable probabilistic normed spaces induce convergence in probability l p convergence and almost sure convergence

research on some problems for nonlinear operators abstract in this paper we discuss some problems for nonlinear operators in the menger pn space meanwhile we prove existence theorems for the solution of an operator equation and obtain some new results by means of the theory of topological degree for the z p s space

nonlinear contraction theorems in probabilistic spaces abstract in this paper first we prove a common fixed point theorem in menger probabilistic metric spaces then we present a nonlinear contraction case of jungck s common fixed point theorem in menger probabilistic metric spaces finally we prove a common fixed point theorem for six self maps in a menger probabilistic metric space

the topological structure of a certain menger space in this paper we will reconsider the topological structure of menger probabilistic normed spaces briefly pn spaces under the t norm m we will prove that this topology is compatible with the topology induced by a countable and separating family of semi norms and hence the well known theorems of classical functional analysis such as the principle of uniform boundedness open mapping and closed graph theorems are valid in this context also we will meanwhile obtain a method by which one may construct easily a large class of pn spaces finally using this method we see that a certain subspace of bounded linear operators between pn spaces i e the class of strongly bounded linear operators has a natural pn structure

on jacobians with group action and coverings let s be a compact riemann surface and let h be a finite group it is known that if h acts on s then there is a h equivariant isogeny decomposition of the jacobian variety js of s called the group algebra decomposition of js with respect to h if s 1 rightarrow s 2 is a regular covering map then it is also known that the group algebra decomposition of js 1 induces an isogeny decomposition of js 2 in this article we deal with the converse situation more precisely we prove that the group algebra decomposition can be lifted under regular covering maps under appropriate conditions

ekelandʼs variational principle for an l 0 valued function on a complete random metric space abstract motivated by the recent work on conditional risk measures this paper studies the ekeland s variational principle for a proper lower semicontinuous and lower bounded l 0 valued function where l 0 is the set of equivalence classes of extended real valued random variables on a probability space first we prove a general form of ekeland s variational principle for such a function defined on a complete random metric space then we give a more precise form of ekeland s variational principle for such a local function on a complete random normed module finally as applications we establish the bishop phelps theorem in a complete random normed module under the framework of random conjugate spaces

a note on large automorphism groups of compact riemann surfaces abstract belolipetsky and jones classified those compact riemann surfaces of genus g admitting a large group of automorphisms of order g 1 for each 6 under the assumption that g 1 is a prime number in this article we study the remaining large cases namely we classify riemann surfaces admitting 5 g 1 and 6 g 1 automorphisms with g 1 a prime number as a consequence we obtain the classification of riemann surfaces admitting a group of automorphisms of order 3 g 1 with g 1 a prime number we also provide isogeny decompositions of their jacobian varieties

distance type and common fixed point theorems in menger probabilistic metric type spaces in this paper we introduce the concept of rt distance on a menger probabilistic metric type space further we prove some fixed point theorems in a complete menger probabilistic metric type space which generalizes some famous fixed point theorems

the bishop phelps theorem in complete random normed modules endowed with the e λ topology abstract in this paper we adopt a new approach so that we can prove that the bishop phelps theorem in complete random normed modules still holds under the e topology which solves an open problem posed in t x guo y j yang ekeland s variational principle for an l 0 valued function on a complete random metric space j math anal appl 389 2012 1 14

linear operators in finite dimensional probabilistic normed spaces in this paper we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete

darboux transformations for the korteweg de vries equation a darboux transformation converting the jost solution relating to the n 1 soliton solution of the kdv equation to that to the n soliton solution is shown to be written in the form of a pole expansion and is then found explicitly for arbitrary n multisoliton solutions of the kdv equation are thus generated in practice by algebraic recursive procedures

lattice solitary wave solutions of discrete nonlinear wave equations using a direct method it is shown that the real exponential approach to the solutions of nonlinear evolution and wave equations can also he applied to discrete systems as examples the lattice solitary wave and kink solutions of the discrete modified kdv dmkdv equation and some modified versions of this equation are derived using this approach

an explicit expression of the dark n soliton solution of the mkdv equation by means of the darboux transformation a darboux transformation is developed for generating dark multi soliton solutions of the mkdv equation the darboux matrices are found explicitly in recursive manner and a system of linear algebraic equations is derived for determining the dark n soliton solutions by means of the binet cauchy formula an explicit expression of the dark n soliton solution is obtained

on the normability of generalized serstnev pn spaces probabilistic normed spaces have been redefined by c alsina b schweizer and a sklar but even today whether the generalized serstnev pn space is normable or not is still an open question in this paper through applying kolmogorov s theorem we will give several sufficient conditions under which many generalized serstnev pn spaces are normable as the application of our results we will give two examples which are normable generalized serstnev pn space but not serstnev space

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

relations between some basic results derived from two kinds of topologies for a random locally convex module the purpose of this paper is to exhibit the relations between some basic results derived from the two kinds of topologies namely the e topology and the stronger locally l0 convex topology for a random locally convex module first we give an extremely simple proof of the known hahn banach extension theorem for l0 linear functions as well as its continuous variant then we give the relations between the hyperplane separation theorems in d filipovic m kupper n vogelpoth separation and duality in locally l0 convex modules j funct anal 256 2009 3996 4029 and a basic strict separation theorem in t x guo h x xiao x x chen a basic strict separation theorem in random locally convex modules nonlinear anal 71 2009 3794 3804 in the process we also obtain a very useful fact that a random locally convex module with the countable concatenation property must have the same completeness under the two topologies as applications of the fact we prove that most of the previously established principal results of random conjugate spaces of random normed modules under the e topology are still valid under the locally l0 convex topology which considerably enriches financial applications of random normed modules

non self adjoint zakharov shabat operator with a potential of the finite asymptotic values ii inverse problem the inverse spectral and scattering problem of the zakharov shabat zs operator is studied the similarity transformation between zs operators is examined when their potentials q x have the common nonvanishing asymptotic values q at the infinity the marchenko equation is derived from the parseval equation we give the necessary as well as the sufficient condition of the scattering data for the potential of the specified class

an alternative explicit construction of n soliton solutions in 1 1 dimensions using the special riemann problem technique of zakharov et al sov phys jetp 47 1017 1978 an explicit n step backlund transformation is derived for a class of 1 1 dimensional nonlinear evolution equations thus providing an alternative explicit expression of their n soliton solutions which no longer involves computations of the intermediate solutions nor leaves any expansion of n n determinants and their differentiation to be done

dynamical selection of critical exponents in renormalized field theories there are in general one or few fixed points that are accessible by the renormalization group flow they can be identified from the fixed point equations exceptionally an infinite family of fixed points exists parameterized by a scaling exponent itself a function of a nonrenormalizing parameter here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization group flow this dynamical selection takes place in systems with an attractive interaction v as in standard 4 theory but where the potential v at large goes to zero as e g the attraction by a defect

several nonlinear operator problems in the menger pn space abstract in this paper we investigate some nonlinear operator problems and the theory of topological degree meanwhile we obtain some new fixed point theorems in the m pn space

lacunary ideal convergence of multiple sequences in probabilistic normed spaces an ideal i is a family of subsets of positive integers n n which is closed under finite unions and subsets of its elements the aim of this paper is to study the notion of lacunary i convergence of double sequences in probabilistic normed spaces as a variant of the notion of ideal convergence also lacunary i limit points and lacunary i cluster points have been defined and the relation between them has been established furthermore lacunary cauchy and lacunary i cauchy lacunary i cauchy lacunary i convergent double sequences are introduced and studied in probabilistic normed spaces finally we provided example which shows that our method of convergence in probabilistic normed space is more general

interacting crumpled manifolds in this paper we study the effect of a interaction on a polymerized membrane of arbitrary internal dimension d depending on the dimensionality of the membrane and embedding space different physical scenarios are observed we emphasize the difference of polymers from membranes for the latter nontrivial contributions appear at the two loop level we also exploit a massive scheme inspired by calculations in fixed dimensions for scalar field theories despite the fact that these calculations are only amenable numerically we found that in the limit of d 2 each diagram can be evaluated analytically this property extends in fact to any order in perturbation theory allowing for a summation of all orders this is a novel and quite surprising result finally an attempt to go beyond d 2 is presented applications to the case of selfavoiding membranes are mentioned