the existence and uniqueness of solution to wavelet collocation the study of the numerical solutions of pdes with wavelet collocation has yielded a number of substantial results however the existence and uniqueness of solution has not been discussed yet in this paper the existence and uniqueness of solution to wavelet collocation for elliptic equations is established and discussed moreover wavelet collocation is applied to numerical example to examine its appropriateness according to numerical example and analysis it is seen that the existence and uniqueness of solution of this paper is feasible and the new theory is meaningful for developing wavelet collocation

coincidence of extendible vector valued ideals with their minimal kernel abstract we provide coincidence results for vector valued ideals of multilinear operators more precisely if a is an ideal of n linear mappings we give conditions for which the equality a e 1 e n f a min e 1 e n f holds isometrically as an application we obtain in many cases that the monomials form a schauder basis of the space a e 1 e n f several structural and geometric properties are also derived using this equality we apply our results to the particular case where a is the classical ideal of extendible or pietsch integral multilinear operators similar statements are given for ideals of vector valued homogeneous polynomials

turbulence amalgamation and generic automorphisms of homogeneous structures we study topological properties of conjugacy classes in polish groups with emphasis on automorphism groups of homogeneous countable structures we first consider the existence of dense conjugacy classes the topological rokhlin property we then characterize when an automorphism group admits a comeager conjugacy class answering a question of truss and apply this to show that the homeomorphism group of the cantor space has a comeager conjugacy class answering a question of akin hurley and kennedy finally we study polish groups that admit comeager conjugacy classes in any dimension in which case the groups are said to admit ample generics we show that polish groups with ample generics have the small index property generalizing results of hodges hodkinson lascar and shelah and arbitrary homomorphisms from such groups into separable groups are automatically continuous moreover in the case of oligomorphic permutation groups they have uncountable cofinality and the bergman property these results in particular apply to automorphism groups of many stable 0 categorical structures and of the random graph in this connection we also show that the infinite symmetric group s has a unique non trivial separable group topology for several interesting groups we also establish serre s properties fh and fa

extension of vector valued integral polynomials abstract we study the extendibility of integral vector valued polynomials on banach spaces we prove that an x valued pietsch integral polynomial on e extends to an x valued pietsch integral polynomial on any space f containing e with the same integral norm this is not the case for grothendieck integral polynomials they do not always extend to x valued grothendieck integral polynomials however they are extendible to x valued polynomials the aron berner extension of an integral polynomial is also studied a canonical integral representation is given for domains not containing l 1

solving second kind fredholm integral equations by periodic wavelet galerkin method in this paper we use the periodized daubechies wavelets based galerkin method pwgm to solve linear nonlinear and singular fredholm integral equations of the second kind a main advantage of the present pwgm over the existing wavelet galerkin methods lies in that the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations therefore the computational cost is low whereas the accuracy is high after discretization the linear and nonlinear integral equations is converted into a system of linear and nonlinear equations respectively and for the linear case the matrix can be converted into a sparse and symmetrical one by fast wavelet transform fwt numerical experiments show that the pwgm has a good degree of accuracy

extendible polynomials on banach spaces abstract we are concerned with the following question when can a polynomial p e x e and x are banach spaces be extended to a banach space containing e we prove that the polynomials that are extendible to any larger space are precisely those which can be extended to c b e if x is complemented in its bidual and l b e in general we also show that the extendibility is a property that is preserved by aron berner extensions and composition with linear operators we construct a predual of the space of extendible polynomials for the case that x is a dual space

integral mappings between banach spaces abstract we consider the classes of grothendieck integral g integral and pietsch integral p integral linear and multilinear operators see definitions below and we prove that a multilinear operator between banach spaces is g integral resp p integral if and only if its linearization is g integral resp p integral on the injective tensor product of the spaces together with some related results concerning certain canonically associated linear operators as an application we give a new proof of a result on the radon nikodym property of the dual of the injective tensor product of banach spaces moreover we give a simple proof of a characterization of the g integral operators on c k x spaces and we also give a partial characterization of p integral operators on c k x spaces

a collocation method to find solutions of linear complex differential equations in circular domains in this study we introduce a collocation approach for solving high order linear complex differential equations in circular domain by using collocation points defined in a circular domain and bessel functions of the first kind this method transforms the linear complex differential equations into a matrix equation the matrix equation corresponds to a system of linear equations with the unknown bessel coefficients proposed method gives the analytic solution when the exact solutions are polynomials numerical examples are given to demonstrate the validity and applicability of the technique and the comparisons are made with existing results the results obtained from the examples demonstrate the efficiency and accuracy of the present work all of the numerical computations have been computed on computer using a code written in matlab

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

solving volterra integral equations of the second kind by wavelet galerkin scheme in this paper we apply the wavelet galerkin method to obtain approximate solutions to linear volterra integral equations vies of the second kind daubechies wavelets are used to find such approximations in this approach we introduce some new connection coefficients and discuss their properties and propose algorithms to evaluate them these coefficients can be computed just once and applied for solving every linear vie of the second kind convergence and error analysis are discussed and numerical examples illustrate the efficiency of the method

polynomials and holomorphic functions on a compact sets in banach spaces abstract in this paper we study the behavior of holomorphic mappings on a compact sets motivated by the recent work of aron caliskan garcia and maestre 2016 we give several conditions on the holomorphic mappings and on the banach operator ideal a under which a compact sets are preserved appealing to the notion of tensor stability for operator ideals we first address the question in the polynomial setting then we define a radius of a b compactification that permits us to tackle the analytic case our approach for instance allows us to show that the image of any p r compact set under any holomorphic function defined on any open set of a banach space is again p r compact

polynomials with an integral representation abstract we introduce a large class of polynomials between banach spaces which admit an integral representation this class coincides with the class of integral polynomials in the scalar valued case but it is larger in the vector valued case by comparing this class with other well known classes we obtain characterizations of banach spaces containing no copy of c 0 of grothendieck spaces and of l spaces among some other results we show that a polynomial has an integral representation if and only if it admits an orthogonally additive extension to c b e moreover if the range space is complemented in its bidual every polynomial with an integral representation is extendible to every superspace

bilinear ideals in operator spaces abstract we introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces in particular we study the bilinear ideals n of completely nuclear i of completely integral and e of completely extendible bilinear mappings we also consider the multiplicatively bounded bilinear mappings mb and its symmetrization smb we prove some basic properties of them one of which is the fact that i is naturally identified with the ideal of linear completely integral mappings on the injective operator space tensor product

graph theoretic structure of maps of the cantor space abstract in this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of spaces h 0 1 n and c 0 1 n the space of homeomorphisms and the space of self maps of the cantor space respectively using our methods we give characterizations which determine when two homeomorphisms of the cantor space are conjugate to each other we also give a new characterization of the comeager conjugacy class of the space h 0 1 n the existence of this class was established by kechris and rosendal and a specific element of this class was described concretely by akin glasner and weiss our characterization readily implies many old and new dynamical properties of elements of this class for example we show that no element of this class has a li yorke pair implying the well known glasner weiss result that there is a comeager subset of h 0 1 n each element of which has topological entropy zero our analogous investigation in c 0 1 n yields a surprising result there is a comeager subset of c 0 1 n such that any two elements of this set are conjugate to each other by an element of h 0 1 n our description of this class also yields many old and new results concerning dynamics of a comeager subset of c 0 1 n

an approximate method for solving a class of weakly singular volterra integro differential equations abstract in this paper we present a new approach to resolve linear and nonlinear weakly singular volterra integro differential equations of first or second order by first removing the singularity using taylor s approximation and then transforming the given first or second order integro differential equations into an ordinary differential equation such as the well known legendre degenerate hypergeometric euler or abel equations in such a manner that adomian s asymptotic decomposition method can be applied which permits convenient resolution of these equations some examples with closed form solutions are studied in detail to further illustrate the proposed technique and the results obtained demonstrate this approach is indeed practical and efficient

ordered structures and large conjugacy classes abstract this article is a contribution to the following problem does there exist a polish non archimedean group equivalently automorphism group of a fraisse limit that is extremely amenable and has ample generics as fraisse limits whose automorphism groups are extremely amenable must be ordered i e equipped with a linear ordering we focus on ordered fraisse limits we prove that automorphism groups of the universal ordered boron tree and the universal ordered poset have a comeager conjugacy class but no comeager 2 dimensional diagonal conjugacy class we formulate general conditions implying that there is no comeager conjugacy class comeager 2 dimensional diagonal conjugacy class or non meager 2 dimensional topological similarity class in the automorphism group of an ordered fraisse limit we also provide a number of applications of these results

numerical solution of nonlinear fredholm integral equations of the second kind using haar wavelets in this work we present a computational method for solving nonlinear fredholm integral equations of the second kind which is based on the use of haar wavelets error analysis is worked out that shows efficiency of the method finally we also give some numerical examples

polynomial characterization of l spaces it is shown that given an index m a banach space e is an l space if and only if every 1 dominated m homogeneous polynomial on e is integral this extends a result for linear operators due to stegall and retherford

on the numerical solution of linear and nonlinear volterra integral and integro differential equations abstract sinc bases are developed to approximate the solutions of linear and nonlinear volterra integral and integro differential equations properties of these sinc bases and some operational matrices are first presented these properties are then used to reduce the integral and integro differential equations to systems of linear or nonlinear algebraic equations numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems the examples include convolution type singular as well as singularly perturbed problems

taylor polynomial solutions of nonlinear volterra fredholm integral equations the kanwal and liu method for the solution of fredholm integral equations is applied to certain nonlinear volterra fredholm integral equations in addition examples that illustrate the pertinent features of the method are presented and the results of study are discussed

wavelet galerkin method for numerical solution of nonlinear integral equation in this paper the continues legendre wavelets constructed on the interval 0 1 are used to solve the nonlinear volterra and fredholm integral equation of the second kind the nonlinear part of the integral equation is approximated by legendre wavelets and the nonlinear integral equation is reduced to a system of nonlinear equations numerical examples illustrates the pertinent features of the method

numerical solution of the mixed volterra fredholm integro differential multi term equations of fractional order abstract this paper aims to introduce two effective numerical approaches for solving the mixed volterra fredholm integro differential equation of fractional order and multi order with initial values despite the fact that the second approach transfers the integro differential equations into a system of algebraic equations through the usage of operational matrices these problems can be transferred to a system of algebraic equations by expanding the solution s highest order derivative through the block pulse functions bpfs this is done by using the generalized operational matrices of bpfs for differentiation along with the fractional calculus properties in the first scheme in which convergence of the solution obtained has been shown in the following the accuracy and applicability of two proposed approaches will be compared by some relevant numerical examples for which the exact solution is known

generic automorphisms of homogeneous structures let g be a permutation group on the set usually we take n o we seek a notion of genericity for members of g the idea is that a member of g should be generic if it is in some sense typical we argue that the following is the correct definition suppose that g is endowed with a metric so that it becomes a complete metric space it follows that the baire category theorem holds and we may use the notions of meagre and comeagre sets

new algorithms for the numerical solution of nonlinear fredholm and volterra integral equations using haar wavelets two new algorithms based on haar wavelets are proposed the first algorithm is proposed for the numerical solution of nonlinear fredholm integral equations of the second kind and the second for the numerical solution of nonlinear volterra integral equations of the second kind these methods are designed to exploit the special characteristics of haar wavelets in both one and two dimensions formulae for calculating haar coefficients without solving the system of equations have been derived these formulae are then used in the proposed numerical methods in contrast to other numerical methods the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations the methods are validated on test problems and numerical results are compared with those from existing methods in the literature

taylor polynomial solution of high order nonlinear volterra fredholm integro differential equations in this paper a taylor method is developed to find an approximate solution for high order nonlinear volterra fredholm integro differential equation numerical examples presented to illustrate the accuracy of the method

duality in spaces of nuclear and integral polynomials abstract we study the spaces of nuclear and integral vector valued polynomials and their duals we prove that if e is asplund p n ne f p i ne f isometrically for any banach space f we describe p n ne f as a subspace of p ne f in terms of weak star continuous polynomials we show that p w ne f p c ne f when e has the approximation property

comparative experiment on the numerical solutions of hammerstein integral equation arising from chemical phenomenon in this paper efficient numerical techniques have been proposed to solve nonlinear hammerstein integral equation arising from chemical phenomenon the following integral equation forms the basis for the conductor like screening model for real solvent which appeared in chemical phenomenon our aim is to solve the hammerstein nonlinear integral equation s r t ln p s exp e i n t s r t d where r is the gas constant t is the temperature and the term e i n t denotes the interaction energy expression for the segments with screening charge density and respectively the molecular interaction in solvent is p s and the chemical potential of the surface segments is described by s which is to be determined this cosmo rs integral equation has been solved by bernstein collocation method haar wavelet method and sinc collocation method these methods reduce the integral equation to nonlinear system of algebraic equations and then this algebraic system has been solved numerically by newton s method comparison has been done for these methods illustrative examples have been discussed to demonstrate the validity and applicability of bernstein collocation method haar wavelet method and sinc collocation method

harmonic wavelet method towards solution of the fredholm type integral equations of the second kind periodic harmonic wavelets phw were applied as basis functions in solution of the fredholm integral equations of the second kind two equations were solved in order to find out advantages and disadvantages of such choice of the basis functions it is proved that phw satisfy the properties of the multiresolution analysis