efficient computation of the hutchinson metric between digitized images the hutchinson metric is a natural measure of the discrepancy between two images for use in fractal image processing an efficient solution to the problem of computing the hutchinson metric between two arbitrary digitized images is considered the technique proposed here based on the shape of the objects as projected on the digitized screen can be used as an effective way to establish the error between the original and the possibly compressed decoded image to test the performance of our method we apply it to compare pairs of fractal objects as well as to compare real world images with the corresponding reconstructed ones

existence of positive solutions of superlinear second order neumann boundary value problem abstract in this paper we consider the neumann boundary value problem p t u t q t u t f t u t t 0 1 u 0 u 1 0 where p c 1 0 1 p t 0 q c 0 1 q t 0 f c 0 1 by using topological degree theory we investigate the existence of nontrivial solutions in particular we prove the existence of positive solutions provided that q t 0

monotone methods for higher order partial difference equations abstract a nonlinear difference equation of the order n m in two independent variables nx myu x y u together with appropriate initial and periodic boundary conditions is considered several comparison results for these problems are established these results are then used to provide sufficient conditions for the convergence of monotone iterative methods numerical illustrations dwelling upon the importance of our results are also included

fuzzy topological vector spaces topological generation and normability abstract increasing awareness of the utility of fuzzy systems in modeling real life situations necessitates a thorough understanding of fuzzy topological vector spaces in this paper the first of several to follow on this topic the generation of a fuzzy vector topology from an ordinary vector topology on a vector space is discussed also obtained is a condition for the fuzzy normability of a fuzzy vector topology induced by a family of fuzzy seminorms finally an example indicating that the earlier mentioned condition is only sufficient is given

fuzzy topological vector spaces over r in this paper the concepts of fuzzy vector fuzzy vector space and fuzzy topological vector space are investigated a topology called sendograph topology which is compatible with the algebraic structure is given

on the existence and uniqueness for higher order periodic boundary value problems abstract this paper discusses the existence and uniqueness for the n th order periodic boundary value problem l n u t f t u t 0 t 2 u i 0 u i 2 i 0 1 n 1 where l n u t u n t i 0 n 1 a i u i t is an n th order linear differential operator n 2 and f 0 2 r r is continuous in the case that l n has an even order derivative we present some new spectral conditions for the nonlinearity f t u to guarantee the existence and uniqueness these spectral conditions allow f t u to be a superlinear growth and are the extension for the spectral separation condition presented recently in y li existence and uniqueness for higher order periodic boundary value problems under spectral separation conditions j math anal appl 322 2 2006 530 539

positive solutions of neumann problems with singularities abstract in this paper we study the existence of positive solutions to second order singular equations with neumann boundary conditions the proof of the main result relies on a nonlinear alternative principle of leray schauder together with a truncation technique

multiplicity of positive solutions to second order neumann boundary value problems with impulse actions abstract this paper deals with existence theorems for single and multiple positive solutions to a kind of neumann boundary value problems with impulse actions the proof of the main results relies on a nonlinear alternative principle of leray schauder type and a well known fixed point theorem in cones the impulses are not restricted to be monotonous in the results obtained by us

iterative algorithms of domain decomposition for the solution of a quasilinear elliptic problem this paper deals with iterative algorithms for domain decomposition applied to the solution of a quasilinear elliptic problem two iterative algorithms are examined the first one is the schwarz alternating procedure and the second algorithm is suitable for parallel computing convergence results are established in the two domain and multidomain decomposition cases some issues of parallel implementation of these algorithms are discussed

on local bases of fuzzy topological vector spaces abstract in this paper the relations between neighborhood base introduced by warren and quasi coincidence neighborhood base introduced by pu and liu in fuzzy topological spaces are studied the characterizations of these two kind of local bases for fuzzy topological vector spaces are further discussed moreover we prove a necessary and sufficient condition for a family of fuzzy sets in a vector space to be the q prebase of a ql type fuzzy topological vector space

solvability of three point boundary value problems for second order differential equations with deviating arguments the monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi solutions

monotone iterative method for the second order three point boundary value problem with upper and lower solutions in the reversed order abstract this article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order the sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method meantime the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given some results of previous literature are extended and improved a numerical example is also included to illustrate the effectiveness of the proposed results

existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order abstract this paper studies the existence and uniqueness of solutions of second order three point boundary value problems with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution

on the pumping effect in a pipe tank flow configuration with friction abstract we provide sufficient conditions for the existence and the asymptotic stability of periodic positive solutions for a pipe tank flow configuration the model is a nonlinear ordinary second order differential equation with a singularity containing the second power of the derivative of the unknown function and with a linear term representing friction in this way we complement previous results obtained by g propst in 2006

nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems this paper deals with the solvability of the nonlinear operator equations in normed spaces yx egx j where dp is a linear map with possible nontrivial kernel applications are given to the existence of periodic solutions for the thirdorder scalar differential equation x ax bx cx g t x p t under various conditions on the interaction of g t x x with spectral contigurations of a b and c

linearized domain decomposition approaches for nonlinear boundary value problems abstract linearized schwarz domain decomposition approaches for nonlinear boundary value problems of the form u f x u u subject to dirichlet boundary conditions are proposed and analyzed in the presence of subsolutions and supersolutions we construct a globally convergent linear monotone iteration suitable for implementation in a distributed computing environment these iterations provide an alternative to the typical locally convergent approach of discretizing and solving the resulting non linear algebraic equations using a newton iteration the work also extends previous results obtained in the case where f has no dependence on the derivative of the solution the schwarz iteration is first proposed and studied in detail on two subdomains the result is then generalized to an arbitrary number of subdomains both alternating and parallel schwarz iterations are analyzed numerical results are provided to demonstrate the theory and the utility of the proposed iterations

monotone method for second order periodic boundary value problems in recent years there has been an extensive study of the existence of periodic solutions l s 11 14 151 in 8 111 the existence of solutions of first and second order pbvp period boundary value problems has been obtained by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems lyapunovschmidt method which provide conditions that are easily verifiable and which covers previous known results of other authors as a constructive method for obtaining extremal solutions of initial and boundary value problems the monotone iterative procedure has been employed by several researchers 5 7 11 13 151 the objective of this paper is to employ this useful technique for second order pbvp to obtain the minimal and maximal solutions as limits of monotone iterates our method can be used to study semilinear parabolic initial boundary value problems and other problems at resonance

a constructive monotone iterative method for second order bvp in the presence of lower and upper solutions this paper concerns the monotone approximations of solutions of boundary value problems such as u f t u u 0 u 0 u 1 0 we consider linear iterative scheme in case f is lipschitz in u and satisfies a one sided lipschitz condition in u the initial approximations are lower and upper solutions which can be ordered one way a email protected we also consider the periodic and the dirichlet problems

the kantorovich metric for probability measures on the circle in this paper we show that there exists an analytic expression for the kantorovich distance between probability measures on the circle previously such an expression was only known for measures supported on the real line in the case that the measures are discrete this formula enables us to show that the kantorovich distance can be computed in linear time this is important for applications in particular in pattern recognition where this distance is used for texture analysis as another application we see that the analytic expression found allows us to solve a minimal matching problem in linear time for which so far only n log n algorithms were known

iterated function systems and the global construction of fractals iterated function systems i f ss are introduced as a unified way of generating a broad class of fractals these fractals are often attractors for i f ss and occur as the supports of probability measures associated with functional equations the existence of certain p balanced measures for i f ss is established and these measures are uniquely characterized for hyperbolic i f ss the hausdorff besicovitch dimension for some attrac tors of hyperbolic i f ss is estimated with the aid of p balanced measures what appears to be the broadest framework for the exactly computable moment theory of p balanced measures that of linear i f ss and of probabilistic mixtures of iterated riemann surfaces is presented this extensively generalizes earlier work on orthogonal polynomials on julia sets an example is given of fractal reconstruction with the use of linear i f ss and moment theory

monotone method for the neumann problem with lower and upper solutions in the reverse order this work is devoted to the study of the existence and approximation of solutions of the problem u f t u u u a u b 0 in the presence of lower and upper solutions in the reverse order to this end we prove anti maximum principles for the nonlinear operator u 2k u email protected

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

a monotone method for constructing extremal solutions to second order periodic boundary value problems abstract in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u t f t u u t t 0 2 u 0 u 2 u 0 u 2 in the presence of an upper solution and a lower solution with

on linear monotone iteration and schwarz methods for nonlinear elliptic pdes the schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each subdomain in this paper proofs of convergence of some schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method also known as the method of subsolutions and supersolutions are given in particular an additive schwarz method for scalar as well some coupled nonlinear pdes are shown to converge to some solution on finitely many subdomains even when multiple solutions are possible in the coupled system case each subdomain pde is linear decoupled and can be solved concurrently with other subdomain pdes these results are applicable to several models in population biology

a numerical approach to nonlinear two point boundary value problems for odes in this paper we propose a numerical approach to solve some problems connected with the implementation of the newton type methods for the resolution of the nonlinear system of equations related to the discretization of a nonlinear two point bvps for odes with mixed linear boundary conditions by using the finite difference method

the monotone method for periodic differential equations with the non well ordered upper and lower solutions in this paper we consider the following periodic problem x t g t x t x t a e t a b x a x b x a x b the unique solution is obtained by constructing an auxiliary periodic system with bounded solutions and proving these bounds to be equal in which case they are the expected unique solution

a positive operator approach to the neumann problem for a second order ordinary differential equation abstract in this paper the solvability of the second order neumann problem u t cu t f t u t 0 qquad u 0 a u r b is studied we suppose that there is a lower solution and an upper solution in the reversed order and we obtain optimal conditions infto assure the existence of a solution lying between and

on the sign of the green s function associated to hill s equation with an indefinite potential abstract in this note we give a l p criterium for the positiveness of the green s function of the periodic boundary value problem x a t x 0 x 0 x t x 0 x t with and indefinite potential a t moreover we prove that such green s function is negative provided a t belongs to the image of a suitable periodic ricatti type operator

a monotone method for constructing extremal solutions to fourth order periodic boundary value problems in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problemu 4 t f t u t u t email protected 0 email protected u 0 u email protected u 0 u email protected u 0 u email protected u 0 u email protected in the presence of an upper solution b and a lower solution a with b a

domain decomposition approaches for mesh generation via the equidistribution principle moving mesh methods based on the equidistribution principle are powerful techniques for the space time adaptive solution of evolution problems solving the resulting coupled system of equations namely the original pde and the mesh pde however is challenging in parallel we propose in this paper several schwarz domain decomposition algorithms for this task we then study in detail the convergence properties of these algorithms applied to the nonlinear mesh pde in one spatial dimension we prove convergence for classical transmission conditions and optimal and optimized variants for the generation of steady equidistributing grids a classical parallel schwarz algorithm is presented and analyzed for the generation of time dependent moving equidistributing grids we conclude our study with numerical experiments

a neural network to compute the hutchinson metric in fractal image processing the hutchinson metric is a natural measure of the discrepancy between two images for use in fractal image processing a neural network is described which can quickly calculate this metric by combining this with the architecture previously described by the author for implementing the markov operator of an iterated function system ifs on a neural network a fast method is obtained for determining the distance between a target image and the invariant measure of a trial ifs this has obvious applications to barnsley s fractal image compression scheme

separation of fuzzy normed linear spaces abstract this paper deals with hausdorff separation axiom for fuzzy topological spaces the necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated properties of separated and non separated fuzzy norms along with examples are studied separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterised separation of quotient fuzzy semi norm is studied

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

replacing the finite difference methods for nonlinear two point boundary value problems by successive application of the linear shooting method abstract this paper studies numerical solution of nonlinear two point boundary value problems for second order ordinary differential equations first it establishes a connection between the finite difference method and the quasi linearization method we prove that using finite differences to discretize the sequence of linear differential equations arising from quasi linearization newton method on operator level leads to the usual iteration formula of the newton finite difference method from the provided derivation it can easily be inferred that such a relation holds also for the picard and the constant slope methods based on this result we propose a way of replacing the newton picard and constant slope finite difference methods by respective successive application of the linear shooting method this approach has a number of advantages it removes the necessity of solving systems of algebraic equations hence working with matrices altogether compared to the usual finite difference method with general solver it reduces the number of computational operations from o n 3 where n is the number of mesh points to only o n

existence and localization of solution for second order elliptic bvp in presence of lower and upper solutions without any order abstract we prove an existence and localization result for a solution of a second order elliptic equations with dirichlet and regular oblique derivative boundary conditions the main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behaviour of the right hand member of the equation

extremal solutions of second order nonlinear periodic boundary value problems we study a periodic boundary value problem for a nonlinear ordinary differential equation of second order when the nonlinearity is given by a caratheodory function we generalize the monotone iterative method to cover the fully nonlinear case

monotone methods for periodic solutions of second order scalar functional differential equations an iterative method is presented which starting from a lower or from an upper periodic solution provides a monotone sequence converging to a periodic solution of 1 with some restrictions on the growth off the method extends to functional differential equations of type 1 two numerical examples with an a posteriori error analysis are given

existence and uniqueness for higher order periodic boundary value problems under spectral separation conditions abstract this paper deals with the existence and uniqueness for the nth order periodic boundary value problem l n u t f t u t 0 t 2 u i 0 u i 2 i 0 1 n 1 where l n u t u n t i 0 n 1 a i u i t is an nth order linear differential operator and f 0 2 r r is continuous we present some spectral conditions for the nonlinearity f t u to guarantee the existence and uniqueness these spectral conditions are the generalization for nonresonance condition of duffing equation

a monotone method for constructing extremal solutions of second order scalar boundary value problems a monotone iterative method is given for the construction of extremal solutions to second order scalar boundary value problems starting from a pair of upper and lower solutions the fully nonlinear case is considered

fuzzy continuity of linear maps on vector spaces abstract this paper studies the fuzzy continuity of linear maps from one vector space into another through a simple characterization of fuzzy convergence of fuzzy points a fuzzy norm is defined on the set of all fuzzy continuous linear maps from a vector space into another convergence of a sequence of fuzzy continuous linear maps to a fuzzy continuous linear map is obtained it is observed that unlike in the ordinary case fuzzy normed topological vector spaces cannot be imbedded in their second duals

the monotone method for neumann functional differential equations with upper and lower solutions in the reverse order abstract in this paper we show that the monotone technique produces two monotone sequences that converge uniformly to extremal solutions of second order functional differential equations and laplacian equations with neumann boundary value conditions moreover we obtain existence results assuming upper and lower solutions in the reverse order

remarks on the lower and upper solutions method for second and third order periodic boundary value problems we study the solvability and the approximation of the solutions by monotone iteration of the second and third order periodic boundary value problems bvps u cu t u u 0 u email protected u 0 u email protected and email protected au bu t u u 0 u email protected u 0 u email protected u 0 u email protected in the presence of lower and upper solutions which may not satisfy the usual ordering condition to this end some maximum and antimaximum principles are stated and proved for certain linear differential operators naturally associated with the previously stated problems

an abstract framework in the numerical solution of boundary value problems for neutral functional differential equations we consider the numerical solution of boundary value problems for general neutral functional differential equations the problems are restated in an abstract form and then a general discretization of the abstract form is introduced and a convergence analysis of this discretization is developed

extremality and comparison results for discontinuous implicit third order functional initial boundary value problems extremality results are derived for implicit third order functional initial boundary value problems differential equations initial conditions and boundary conditions of problems may involve discontinuous nonlinearities

uniqueness comparison and existence results for third order initial boundary value problems abstract we derive maximum principles for a nonlinear third order differential operator and prove uniqueness comparison and existence results for different types of third order initial boundary value problems including existence results for functional problems

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when