using triangular orthogonal functions for solving fredholm integral equations of the second kind the present work proposes a method for solving fredholm integral equations this is demonstrated by using a complementary pair of orthogonal triangular functions set derived from the well known block pulse functions set the operational matrices for integration product of two triangular functions and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of fredholm integral equation to the solution of algebraic equations illustrative examples are included to show the high accuracy of the estimation and to demonstrate validity and applicability of the method

fixed point theorems of rothe and altman types about convex power condensing operator and application in this paper fixed point theorems of rothe and altman types about convex power condensing operator are given and applied to the differential equation of one order with integral boundary conditions in abstract space

positive solutions of nth order impulsive boundary value problems with integral boundary conditions in banach spaces abstract by using the fixed point theory for strict set contraction operator this paper investigates the existence of positive solutions for a class of n th order impulsive boundary value problems with integral boundary conditions in banach spaces moreover we offer some interesting discussion of the associated boundary value problems since the technique to deal with n th order bvp is completely different from that of previous papers the expression of the associated integral equation is simpler than that of relevant papers and upper and lower bounds for these positive solutions also are given our work is new

impulsive boundary value problems with integral boundary conditions and one dimensional p laplacian abstract by using the classical fixed point index theorem for compact maps some sufficient conditions for the existence of multiple positive solutions for a class of second order impulsive differential equations with p laplacian and integral boundary conditions are established which are the complement of previously known results meanwhile the existence of many solutions is also studied

positive solutions for a class of boundary value problems on time scales by obtaining intervals of the parameter l this paper is concerned with the existence and nonexistence of positive solution of the second order nonlinear dynamic equation on time scales p t x d t q t x t lw t f t x ax r a bx d r a 0 cx b dx d b 0 for t a b t where t is a time scale a 0 c 0 b 0 d 0 with a c 0 the arguments are based upon fixed point theorems in a cone

on existence theorems of positive solutions to nonlinear singular differential equations abstract suppose i f t u 0 1 0 0 is continuous and is increasing on u ii there exists a function g 1 0 g b b and g b b 2 is integrable on 1 such that f t bu g b f t u t u 0 1 0 consider the singular boundary value problem u t f t u t 0 0 t 1 u 0 au u 1 0 then a necessary and sufficient condition for eq to have c 0 1 positive solutions is that 0 0 1 s 1 s f s 1 d s a necessary and sufficient condition for eq to have c 1 0 1 positive solutions is that 0 0 1 f s 1 s d s also the uniqueness iterative methods and computational methods of c 1 0 1 positive solutions have been studied our nonlinearity may be singular at t 0 and or t 1

numerical computational method in solving fredholm integral equations of the second kind by using coifman wavelet in this paper we bring three theorems that enable us to approximate the solution of ferdholm integral equations of the second kind then we use coifman wavelets or coiflets as scaling functions for projection that satisfied the conditions of theorems for approximation also we use this projection to convert the integral equation to a galerkin system which is the most important of the expansion methods for solving linear integral equations finally by using numerical examples we show that our estimation have a good degree of accuracy

expansion method for linear integral equations by cardinal b spline wavelet and shannon wavelet as bases for obtain galerkin system in this paper we apply the b spline and shannon wavelets bases for approximation the solution of linear integral equations of the second kind then by this wavelet bases we construct galerkin system which is important the expansion methods in solving linear integral equations at the end for showing efficiency of this method we use numerical examples

a singular boundary value problem for the one dimensionalp laplacian abstract the singular boundary value problem formula is studied in this paper whereg s s p 2s p 1 the singularity may appear atu 0 and att 0 ort 1 and the functionfmay be discontinuous the authors prove that for anyp 1 and for any positive nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions the above mentioned problem has a unique solution also the properties of the solution are discussed in the paper

numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation numerical solution of linear integral equations by means of the sinc collocation method based on the double exponential transformation abbreviated the de transformation is considered we first apply the method to the volterra integral equation of the second kind and then to the volterra equation of the first kind this method is also applied to the fredholm integral equation of the second kind for the volterra equations we employed a formula for numerical indefinite integration developed by muhammad and mori obtained by applying the de transformation incorporated into the sinc expansion of the integrand while for the fredholm equation we employed the conventional de transformation for definite integrals an error analysis of the method is given and in every case a convergence rate of o exp cn logn for the error is established where n is a parameter representing the number of terms of the sinc expansion also the condition of the matrix of the main system of linear equations is watched through an estimate of the condition number returned by the program numerical examples show the convergence rate mentioned above and confirm the high efficiency of the present method

solving integral and differential equations by the aid of non uniform haar wavelets a modification of the haar wavelet method for which the stepsize of the argument is variable is proposed to establish the efficiency of the method three test problems for which exact solution is known are considered computer simulations show clear preference of the suggested method compared with the haar wavelet method of a constant stepsize

a novel semi analytical approach for solving nonlinear volterra integro differential equations in this work we present an efficient semi analytical method based on the taylor series for solving nonlinear volterra integro differential equations namely the differential transform method dtm the dtm provides a recursive relation for the coefficients of the taylor series that is derived from the given equations we provide a new recursive relation for the nonlinear volterra integro differential equations with complex nonlinear kernels since the dtm is based on the taylor series it is difficult to obtain accurate approximate solutions in a large domain to overcome this difficulty the standard dtm is applied in each subdomain called the multistage differential transform method msdtm we also present an convergence analysis for the proposed method to demonstrate the efficiency of the proposed method several numerical examples are performed and support the results in our analysis

exact number of solutions for a class of two point boundary value problems with one dimensional p laplacian abstract in this paper exact number of solutions are obtained for the one dimensional p laplacian in a class of two point boundary value problems the interesting point is that the nonlinearity f is general form f u g u h u meanwhile some properties of the solutions are given in details the arguments are based upon a quadrature method

an efficient numerical scheme for a nonlinear integro differential equations with an integral boundary condition nonlinear functional integro differential equations with an integral boundary condition is appeared in chemical engineering underground water flow and population dynamics phenomena and other field of physics and mathematical chemistry so this paper presents a powerful numerical approach based on an iterative technique and sinc quadrature to estimate a solution for this equation then convergence of this technique is discussed by preparing a theorem which guarantees the applicability of that finally some numerical examples are given to confirm efficiency and accuracy of the numerical scheme

using rationalized haar wavelet for solving linear integral equations the main purpose of this paper is to demonstrate that using rationalized haar wavelet for solving linear fredholm integral equation of the second kind we convert the integral equation to a system of linear equations and by using numerical examples we show our estimation have a good degree of accuracy

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

cellular algebras and cartan matrices abstract let a be a finite dimensional algebra over a field k and let c be the cartan matrix of a usually the eigenvalues of c being integers do not imply the semisimplicity of a however we prove that a cellular algebra a is semisimple if and only if det c 1 and all eigenvalues of c are integers moreover we use cartan matrices to classify the cellular algebras with the property that the determinant of the cartan matrix equals a given prime p and all eigenvalues are integers we also give a classification of cellular nakayama algebras with integral eigenvalues of their cartan matrices finally we show that if a is a cellular algebra then its trivial extension t a is also a cellular algebra in particular if a non simple connected cellular algebra a is quasi hereditary then the cartan matrix of t a has at least one non integral eigenvalue the main tool used in this paper is the well known perron frobenius theory on non negative matrices

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian p x t q t f t x t x t 0 t 0 1 subject to one of the following boundary conditions p x 0 p x 0 0 p x 1 p x 1 0 or x 0 g1 x 0 0 x 1 g2 x 1 0 where p s s p 2s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions the interesting point is the nonlinear term f is involved with the first order derivative explicitly

a comparative study of numerical integration based on haar wavelets and hybrid functions a quadrature rule based on uniform haar wavelets and hybrid functions is proposed to find approximate values of definite integrals the wavelet based algorithm can be easily extended to find numerical approximations for double triple and improper integrals the main advantage of this method is its efficiency and simple applicability error estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method

transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations abstract using a new method for dealing with the impulse term of second impulsive differential equations we are concerned with determining values of for which there exist positive solutions of the following boundary value problems in the form of x t f t x t 0 t j t t k x t k x t k c k x t k k 1 2 n a x 0 b x 0 a x 1 b x 1 0 1 h s x t d t where 0 is a positive parameter c k is a real sequence with c k 1 k 1 2 n the dependence of positive solution x t on the parameter is also studied i e lim x or lim x 0 the proof of our main result is based upon transformation techniques and fixed point theories this is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique

a unified approach to some two point three point and four point boundary value problems with caratheodory functions this paper deals with boundary value problems formula and formula wherea b 0 0 aandbare given real numbers gis a continuous strictly increasing function withg r r andfis a caratheodory function satisfying a nagumo condition the problems have solutions if and only if there exist a lower solutionxand an upper solutionyandx t y t for alla t b

on the solution of a nonlinear integral equation on the basis of a fixed point technique and cubic b spline scaling functions in this paper we apply the fixed point method to solve some nonlinear functional volterra integral equations which appear in many physical chemical and biological problems in each iteration of this method cubic semi orthogonal compactly supported b spline wavelets are used as basis functions to approximate the solution also the convergence of this numerical method is investigated and some examples are presented to show the accuracy and convergence of the method

the iterated galerkin method for linear integro differential equations abstract the iterated galerkin method of i h sloan which yields superconvergence for the approximate solution of integral equations is generalized to get similar results for the larger class of integro differential equations two approaches are investigated to obtain superconvergence in different norms moreover some additional aspects are discussed

positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and i i satisfy i i 0 0 i 1 n 2 i 1 and i 1 n 2 i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

positive solutions for a class of boundary value problem with integral boundary conditions in banach spaces this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problem of second order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators the nonexistence of a positive solution is also studied

existence and nonexistence results of impulsive first order problem with integral boundary condition abstract this paper is concerned with a first order impulsive boundary value problem ibvp for short with integral boundary condition and depending on a parameter we obtain the existence and nonexistence results of positive solutions for the ibvp when the nonlinear term and the impulses satisfy different requirements of superlinearity and sublinearity and the parameter lies in some intervals

a new estimator of the uniqueness in factor analysis a closed form estimator of the uniqueness unique variance in factor analysis is proposed it has analytically desirable properties consistency asymptotic normality and scale invariance the estimation procedure is given through the application to the two sets of emmett s data and holzinger and swineford s data the new estimator is shown to lead to values rather close to the maximum likelihood estimator

positive solutions for singular systems of three point boundary value problems this paper investigates the following singular systems of nonlinear second order three point boundary value problems u f t v email protected 0 1 v g t u email protected 0 1 u 0 v 0 0 u 1 email protected h v 1 email protected h where email protected 0 1 0 email protected 1 f and g may be singular at t 0 and or t 1 under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression two examples are then presented to demonstrate the application of our main results

the numerical solution of the non linear integro differential equations based on the meshless method this article investigates the numerical solution of the nonlinear integro differential equations the numerical scheme developed in the current paper is based on the moving least square method the moving least square methodology is an effective technique for the approximation of an unknown function by using a set of disordered data it consists of a local weighted least square fitting valid on a small neighborhood of a point and only based on the information provided by its n closet points hence the method is a meshless method and does not need any background mesh or cell structures the error analysis of the proposed method is provided the validity and efficiency of the new method are demonstrated through several tests

second order boundary value problems with integral boundary conditions abstract in this paper we investigate the existence of positive solutions of nonlocal second order boundary value problems with integral boundary conditions

on sinc discretization for systems of volterra integral algebraic equations abstract integral algebraic equations iaes are coupled systems of volterra integral equations of the first and second kind which naturally arise in many applications in mathematical physics in this paper we solve the iaes of index 1 by sinc collocation discretization and prove that the discrete solutions converge to the true solutions of the iaes exponentially the discrete solutions are determined by linear systems which can be effectively solved by suitable iteration methods numerical examples are given to illustrate the effective performance of our method

borelic pairs for stratified algebras abstract we determine all values of the parameters for which the cell modules form a standard system for a class of cellular diagram algebras including partition brauer walled brauer temperley lieb and jones algebras for this we develop and apply a general theory of finite dimensional algebras with borelic pairs the theory is also applied to give new uniform proofs of the cellular and quasi hereditary properties of the diagram algebras and to construct quasi hereditary 1 covers in the sense of rouquier with exact borel subalgebras in the sense of konig another application of the theory leads to a proof that auslander dlab ringel algebras admit exact borel subalgebras

symmetric positive solutions of boundary value problems with integral boundary conditions under conditions weaker than those used by ma we establish various results on the existence and nonexistence of symmetric positive solutions to fourth order boundary value problems with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in a cone our results improve and extend that obtained in h ma symmetric positive solutions for nonlocal boundary value problems of fourth order nonlinear anal 68 2008 645 651 we illustrate our results by one example which cannot be handled using the existing results

fixed points of generalized e concave generalized e convex operators and their applications in this paper we present the definitions of generalized e concave operators and generalized e convex operators which are the generalizations of e concave operators and e convex operators respectively without compactness or continuity assumption of generalized e concave operators and generalized e convex operators we have proved the existence uniqueness and monotone iterative techniques of their fixed points our results are even new to e concave operators and e convex operators finally we apply the results to the singular boundary value problems for second order differential equations

on the quasi heredity and the semi simplicity of cellular algebras abstract some simpler homological characterizations of quasi hereditary algebras inside the class of cellular algebras are presented in terms of cell modules moreover some new criteria for the semi simplicity of cellular algebras are given by using the cohomology groups of cell modules and simple modules

multiple positive solutions to a three point boundary value problem with p laplacian abstract sufficient conditions are obtained that guarantee the existence of at least two positive solutions for the equation g u t a t f u 0 subject to boundary conditions by a simple application of a new fixed point theorem due to avery and henderson

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

numerical solution of two dimensional elliptic pdes with nonlocal boundary conditions in the present paper two numerical methods are analyzed for the solution of two dimensional poisson equation with two different types of nonlocal boundary conditions the first numerical method is a collocation method based on haar wavelet whereas the second numerical method is a meshless method based on different types of radial basis functions rbfs a two point boundary condition and an integral boundary condition are the two types of nonlocal boundary conditions considered in the present work for the collocation method based on haar wavelet a new approach is formulated which involves the approximation of a fourth order mixed derivative by a haar expansion which is integrated subsequently to get wavelet approximation of the solution for the meshless method based on rbfs the algorithm is implemented using two different splitting schemes with and without shape parameter splitting for numerical solution of the model the comparative analysis of the meshless methods with and without shape parameter splitting scheme is performed between themselves as well as with the haar wavelet accuracy and efficiency wise performance is confirmed through application of the algorithms on the benchmark tests

near optimality of the sinc approximation near optimality of the sinc approximation is established in a variety of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity

a necessary and sufficient condition for positive solutions for fourth order multi point boundary value problems with p laplacian abstractinthispaper weconsidertheexistenceofpositivesolutionsforaclassofsingularfourth order p laplacianequationwithmulti point boundary conditions by means of a monotone iterative technique a necessary and suf cient condition for the existence of apseudo c 3 0 1 positive solution is established also the existence and uniqueness of the pseudo c 3 0 1 positive solution theiterative sequence of the solution and an error estimation for the pseudo c 3 0 1 positive solution are obtained c 2007 elsevier ltd all rights reserved msc 34b15 34b25keywords necessary and suf cient condition p laplacian pseudo c 3 0 1 positive solutions cone 1 introductionin this paper we consider the existence of positive solutions for the singular fourth order multi point boundaryvalue problem with p laplacian p u 00 t 00 f 0 1u 0 m x 2i 1 a i u u 1 0 u 00 0 m x 2i 1 b u 00 u 00 1 0 1 1 where p t t p 2 t p 2 0 a i b i i

a generalization of kristofs theorem on the trace of certain matrix products kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form x 1 hat gamma 1 x 2 hat gamma 2 cdots x n hat gamma n where the matrices hat gamma i are diagonal and fixed and thex i vary unrestrictedly and independently over the set of orthonormal matrices the theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints the present paper contains a generalization of kristof s theorem to the case where thex i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank the generalized theorem contains the schwarz inequality as a special case various examples from the psychometric literature illustrating the practical use of the generalized theorem are discussed

summary of sinc numerical methods sinc approximation methods excel for problems whose solutions may have singularities or infinite domains or boundary layers this article summarizes results obtained to date on sinc numerical methods of computation sinc methods provide procedures for function approximation over bounded or unbounded regions encompassing interpolation approximation of derivatives approximate definite and indefinite integration solving initial value ordinary differential equation problems approximation and inversion of fourier and laplace transforms approximation of hilbert transforms and approximation of indefinite convolutions the approximate solution of partial differential equations and the approximate solution of integral equations methods for constructing conformal maps and methods for analytic continuation indeed sinc are ubiquitous for approximating every operation of calculus

clustered common factor exploration in factor analysis the factor analysis fa model does not permit unique estimation of the common and unique factor scores this weakness is notorious as the factor indeterminacy in fa luckily some part of the factor scores can be uniquely determined thus as a whole they can be viewed as a sum of determined and undetermined parts the paper proposes to select the undetermined part such that the resulting common factor scores have the following feature the rows i e individuals of the common factor score matrix are as well classified as possible into few clusters the clear benefit is that we can easily interpret the factor scores simply by focusing on the clusters the procedure is called clustered common factor exploration ccfe an alternating least squares algorithm is developed for ccfe it is illustrated with real data examples the proposed approach can be viewed as a parallel to the rotation techniques in fa they exploit another fa indeterminacy the rotation indeterminacy which is resolved by choosing the rotation that transforms the loading matrix into the most interpretable one according to a pre specified criterion in contrast to the rotational indeterminacy the factor indeterminacy is utilized to achieve well clustered factor scores by ccfe to the best of our knowledge such an approach to the fa interpretation has not been studied yet

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations haar wavelet operational matrix has been widely applied in system analysis system identification optimal control and numerical solution of integral and differential equations in the present paper we derive the haar wavelet operational matrix of the fractional order integration and use it to solve the fractional order differential equations including the bagley torvik ricatti and composite fractional oscillation equations the results obtained are in good agreement with the existing ones in open literatures and it is shown that the technique introduced here is robust and easy to apply

quadrature rules for numerical integration based on haar wavelets and hybrid functions in this paper haar wavelets and hybrid functions have been applied for numerical solution of double and triple integrals with variable limits of integration this approach is the generalization and improvement of the methods siraj ul islam et al 2010 9 where the numerical methods are only applicable to the integrals with constant limits apart from generalization of the methods 9 the new approach has two major advantages over the classical methods based on quadrature rule i no need of finding optimum weights as the wavelet and hybrid coefficients serve the purpose of optimal weights automatically ii mesh points of the wavelets algorithm are used as nodal values instead of considering the n nodes as unknown roots of polynomial of degree n the new methods are more efficient the novel methods are compared with existing methods and applied to a number of benchmark problems accuracy of the methods are measured in terms of absolute errors

multiple positive solutions for first order nonlinear impulsive integro differential equations in a banach space by using the fixed point index theory the author obtains the existence of two positive solutions for a boundary value problem of first order nonlinear impulsive integro differential equations on an infinite interval with an infinite number of impulsive times in a real banach space

collocation method for linear and nonlinear fredholm and volterra integral equations a collocation procedure is developed for the linear and nonlinear fredholm and volterra integral equations using the globally defined b spline and auxiliary basis functions the solution is collocated by cubic b spline and then the integral equation is approximated by the 5 points gauss turan quadrature formula with respect to the legendre weight function combination of these two approaches is the main idea of this paper to reduce the cost of computation and complexity the error analysis of proposed numerical method is studied theoretically numerical results are given to illustrate the efficiency of the proposed method the results are compared with the results obtained by other methods to verify that this method is accurate and efficient

double exponential formulas for numerical indefinite integration in this paper we derive a formula for indefinite integration of analytic functions over 1 s where 1 s 1 by means of the double exponential transformation and the sinc method the integrand must be analytic on 1 x 1 but may have a singularity at the end points x 1 the error of the formula behaves approximately as exp c1n logc2n where n is the number of function evaluations of the integrand this error term shows a much faster convergence to zero when n becomes large than that of the known formula by haber also we derive efficient double exponential formulas for numerical evaluation of indefinite integrals over 0 s 0 s and over s s several numerical examples indicate high efficiency of the formulas

numerical solution of non linear fredholm integral equations by using multiwavelets in the petrov galerkin method in this paper we use the wavelet petrov galerkin wpg method for solving one of the most important cases in non linear fredholm integral equations which is called hammerstein equations we suppose that the trial space and the test space that are used in this method to be piecewise polynomials space also we use alpert s multiwavelets as the bases for these spaces such that the wavelet basis for the test space constructed from lower degree polynomials than the trial space finally for showing efficiency of this method we use some numerical examples

twin positive solutions for quasi linear multi point boundary value problems abstract in this paper we investigate two classes of quasi linear multi point boundary value problems with sign changing nonlinearity by applications of fixed point index theory sufficient conditions for the existence of twin positive solutions are established

explicit nearly optimal linear rational approximation with preassigned poles this paper gives explicit rational functions for interpolating and approximating functions on the intervals 1 1 0 oc and oc oc the rational functions are linear in the functions to be approximated and they have preassigned poles the error of approximation of these rationals is nearly as small as the error of best rational approximation with numerator and denominator polynomials of the same degrees regions of analyticity are described which make it possible to tell a priori the accuracy which we can expect from this type of rational approximation 1 introduction and summary in this paper we attempt to give a constructive affirmative answer to each of the following questions

recent developments of the sinc numerical methods abstract this paper gives a survey of recent developments of the sinc numerical methods a variety of sinc numerical methods have been developed by stenger and his school for a certain class of problems the sinc numerical methods have the convergence rates of o exp n with some 0 where n is the number of nodes or bases used in the methods recently it has turned out that the sinc numerical methods can achieve convergence rates of o exp n log n with some 0 for a smaller but still practically meaningful class of problems and that these convergence rates are best possible the present paper demonstrates these facts for two sinc numerical methods the sinc approximation and the sinc collocation method for two point boundary value problems

the double exponential transformation in numerical analysis the double exponential transformation was first proposed by takahasi and mori in 1974 for the efficient evaluation of integrals of an analytic function with end point singularity afterwards this transformation was improved for the evaluation of oscillatory functions like fourier integrals recently it turned out that the double exponential transformation is useful not only for numerical integration but also for various kinds of sinc numerical methods the purpose of the present paper is to review the double exponential transformation in numerical integration and in a variety of sinc numerical methods

periodic boundary value problems for a class of second order impulsive integro differential equations in banach spaces abstract this paper investigates periodic boundary value problems for a class of second order nonlinear impulsive integro differential equations of mixed type in a banach space by establishing a comparison result criteria on the existence of maximal and minimal solutions are obtained

existence of multiple positive solutions for one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value conditions p u 0 i 1 n 2 a i p u i u 1 i 1 n 2 b i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and a i b i satisfy a i b i 0 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem

multiple nonnegative solutions for second order impulsive differential equations we study the existence of single and multiple solutions to a second order impulsive equation with fixed moments our analysis relies on combining a nonlinear alternative of leray schauder type with krasnoselskii s fixed point theorem in a cone

haar wavelet collocation method for three dimensional elliptic partial differential equations a new collocation method based on haar wavelet is presented for numerical solution of three dimensional elliptic partial differential equations with dirichlet boundary conditions an important advantage of the method is that it can be applied to both linear as well as nonlinear problems the algorithm based on this new method is simple and can be easily implemented in any programming language experimental rates of convergence of the proposed method are calculated which are in agreement with theoretical results the proposed method is applied to several benchmark problems from the literature including linear and nonlinear elliptic problems as well as systems of elliptic partial differential equations the numerical experiments confirm the accuracy and diverse applicability of the method

numerical methods based on whittaker cardinal or sinc functions this paper summarizes the results known to date for using sine functions composed with other functions as bases for approximations in numerical analysis described in this paper are methods of interpolation and approximation of functions and their derivatives quadrature the approximate evaluation of transforms hilbert fourier laplace hankel and mellin and the approximate solution of differential and integral equations the methods have many advantages over classical methods which use polynomials as bases in addition all of the methods converge at an optimal rate if singularities on the boundary of approximation are ignored

on the quasi heredity of birman wenzl algebras abstract in this paper we consider the birman wenzl algebras over an arbitrary field and prove that they are cellular in the sense of graham and lehrer furthermore we determine for which parameters the birman wenzl algebras are quasi hereditary so the general theory of cellular algebras and quasi hereditary algebras applies to birman wenzl algebras as a consequence we can determine all irreducible representations of the birman wenzl algebras by linear algebra methods we prove also that the new hecke algebras induced from birman wenzl algebras are frobenius over a field but not always cellular

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

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

double positive solutions for a nonlinear four point boundary value problem with a p laplacian operator in this paper we study the existence of positive solutions for a nonlinear four point boundary value problem with a p laplacian operator by using a three functionals fixed point theorem in a cone the existence of double positive solutions for the nonlinear four point boundary value problem with ap laplacian operator is obtained this is different than previous results

a wavelet method for solving singular integral equation of mhd this paper presents haar wavelet approximation to solve a singular integral equation which has singularities on a diagonal of the domain r 1 1 x 1 1 the singularities arise basically due to modified bessel function k 0 which appears as a part of the kernel thus the integral equation is weakly logarithmically singular only the problem is solved considering all the singularities of the kernel and results are examined for approximations of different orders our interest to solve the problem using haar wavelet basis is due to its simplicity and efficiency in numerical approximation the results show convergence trend as mesh is refined comparison is made with some available results obtained earlier by partial consideration of the singularities

sinc approximation for numerical solution of integral equation arising in conductor like screening model for real solvent in this study we present the existence of solutions for some nonlinear integral equations known as hammerstein type which forms the basis for the conductor like screening model for real solvents cosmo rs by using the techniques of noncompactness measures we employ the basic fixed point theorems such as darbo s theorem to obtain the mentioned aim in banach algebra then this paper presents a powerful numerical approach based on the sinc approximation to solve the equation which forms the basis for the conductor like screening model for real solvents cosmo rs the approach is based on the recognition of the hammerstein integral equation for the determination of the chemical potential of a surface segment as a function of screening charge density then convergence of this technique is discussed by preparing a theorem which shows an exponential type convergence rate and guarantees the applicability of that

numerical solution of linear integral equations by using sinc collocation method a collocation procedure is developed for linear fredholm integral equations of the second kind using sinc basis functions the convergence rate of the method is o e k m numerical results are included to confirm the efficiency and accuracy of the method

optimality of the double exponential formula functional analysis approach in the light of the functional analysis theory we establish the optimality of the double exponential formula the argument consists of the following three ingredients 1 introduction of a number of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity 2 proof of the near optimality of the trapezoidal formula in each space introduced in 1 by showing the near equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum error norm of quadratures 3 nonexistence theorem for the spaces the characterizing decay rate of which is more rapid than the double exponential

positive solutions for nonhomogeneous boundary value problems in banach spaces abstract by using darbo fixed point theorem the existence and nonexistence of fixed point are obtained for the following integral operator t y t 0 1 g t s f s y s ds tv using these results we investigate the existence and nonexistence of positive solutions for second order nonhomogeneous local and nonlocal boundary value problems in banach spaces

some mathematical properties of the matrix decomposition solution in factor analysis a new factor analysis fa procedure has recently been proposed which can be called matrix decomposition fa mdfa all fa model parameters common and unique factors loadings and unique variances are treated as fixed unknown matrices then the mdfa model simply becomes a specific data matrix decomposition the mdfa parameters are found by minimizing the discrepancy between the data and the mdfa model several algorithms have been developed and some properties have been discussed in the literature notably by stegeman in comput stat data anal 99 189 203 2016 but as a whole mdfa has not been studied fully yet a number of new properties are discovered in this paper and some existing ones are derived more explicitly the properties provided concern the uniqueness of results covariances among common factors unique factors and residuals and assessment of the degree of indeterminacy of common and unique factor scores the properties are illustrated using a real data example

haar wavelet approximation for the solution of cubic nonlinear schrodinger equations abstract in this study haar wavelet collocation method is used for the numerical solution of 1d and 2d cubic nonlinear schrodinger equations with initial and dirichlet boundary conditions the space derivatives are estimated through haar wavelet collocation method whereas for time derivative we have used crank nicolson scheme the proposed method is implemented upon several test problems and the numerical results of these test problems establish that the proposed method is accurate