lower bounds for the perron root of a nonnegative matrix abstract new lower bounds frequently better than previous bounds and readily computable for the perron root r a of a nonnegative matrix a are obtained the theoretical comparison of new bounds with the known ones is supplemented with two numerical examples

migrative uninorms and nullnorms over t norms and t conorms in this paper the notions of migrative uninorms and nullnorms over a fixed t norm t and over a fixed t conorm s are introduced and studied all cases when the uninorm u lies in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations of u and t and for all possible combinations of u and s a similar study is done for nullnorms

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

local discontinuous galerkin methods for nonlinear schrodinger equations in this paper we develop a local discontinuous galerkin method to solve the generalized nonlinear schrodinger equation and the coupled nonlinear schrodinger equation l 2 stability of the schemes are obtained for both of these nonlinear equations numerical examples are shown to demonstrate the accuracy and capability of these methods

a sequence of lower bounds for the spectral radius of nonnegatfve matrices abstract we present a sequence of progressively better lower bounds for the s pectral radius of a nonnegative matrix each element of the sequence is a function of the spectral radius of the geometric symmetrization of a power of the matrix as defined by schwenk each element provides a better approximation to the spectral radius than the elements in the sequences provided by other authors

the solution of nonlinear schrodinger equations using orthogonal spline collocation abstract an orthogonal spline collocation semidiscretization previously applied in the numerical solution of the cubic schrodinger equation is extended to the solution of schrodinger equations which possess general power nonlinearities and nonlinear terms that contain derivatives the accuracy of the method is examined as well as its ability to conserve approximations to certain invariants associated with the theoretical solution the results of numerical experiments are presented in which the integration in time is performed using a routine from a software library particular attention is paid to the value and limitations of conservation as an indicator of accuracy

difference schemes for solving the generalized nonlinear schrodinger equation this paper studies finite difference schemes for solving the generalized nonlinear schrodinger gnls equationiut uxx q u 2 u f x t u a new linearlized crank nicolson type scheme is presented by applying an extrapolation technique to the real coefficient of the nonlinear term in the gnls equation several schemes including crank nicolson type schemes hopscotch type schemes split step fourier scheme and pseudospectral scheme are adopted for solving three model problems of gnls equation which arise from many physical problems withq s s2 q s ln 1 s andq s 4s 1 s respectively the numerical results demonstrate that the linearized crank nicolson scheme is efficient and robust

the semiclassical limit of the defocusing nls hierarchy we establish the semiclassical limit of the one dimensional defocusing cubic nonlinear schrodinger nls equation complete integrability is exploited to obtain a global characterization of the weak limits of the entire nls hierarchy of conserved densities as the field evolves from reflectionless initial data under all the associated commuting flows consequently this also establishes the zero dispersion limit of the modified korteweg de vries equation that resides in that hierarchy we have adapted and clarified the strategy introduced by lax and levermore to study the zero dispersion limit of the korteweg de vries equation expanding it to treat entire integrable hierarchies and strengthening the limits obtained a crucial role is played by the convexity of the underlying log determinant with respect to the times associated with the commuting flows c 1999 john wiley sons inc

exact solution for nonlinear schrodinger equation by he s frequency formulation in this work we apply he s frequency formulation to search for the solution to nonlinear schrodinger equation three examples are given and the solutions obtained are in good accordance with wazwaz s solution abdul majid wazwaz a study on linear and nonlinear schrodinger equations by the variational iteration method chaos solitons fractals 37 4 2008 1136 1142 it is shown that he s frequency formulation is of utter straightforward and effective

on some classes of nullnorms and h pseudo homogeneity abstract nullnorms are aggregation functions which generalize t norms and t conorms for each nullnorm there exists an annihilator element such that below it the function behaves like a t conorm and above it like a t norm in this paper we study some classes of nullnorms which naturally arise from well known classes of t norms and t conorms such as idempotent archimedean cancellative positive and nilpotent t norms and t conorms we also present the concept of h pseudo homogeneous nullnorm and we study when these classes of nullnorms fullfill it

a numerical method for two dimensional schrodinger equation using collocation and radial basis functions in this paper we propose a numerical scheme to solve the two dimensional 2d time dependent schrodinger equation using collocation points and approximating the solution using multiquadrics mq and the thin plate splines tps radial basis function rbf the scheme works in a similar fashion as finite difference methods the results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme

a sequence of upper bounds for the perron root of a nonnegative matrix abstract we present a sequence of progressively better upper bounds for the perron root of a nonnegative matrix each element in the sequence is a function of the perron root of the arithmetic symmetrization of a power of the matrix the results complement those of szyld based on the geometric symmetrization of a power of the matrix

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

multi symplectic runge kutta collocation methods for hamiltonian wave equations a number of conservative pdes like various wave equations allow for a multi symplectic formulation which can be viewed as a generalization of the symplectic structure of hamiltonian odes we show that gauss legendre collocation in space and time leads to multi symplectic integrators i e to numerical methods that preserve a symplectic conservation law similar to the conservation of symplecticity under a symplectic method for hamiltonian odes we also discuss the issue of conservation of energy and momentum since time discretization by a gauss legendre method is computational rather expensive we suggest several semi explicit multi symplectic methods based on gauss legendre collocation in space and explicit or linearly implicit symplectic discretizations in time

nested bounds for the perron root of a nonnegative matrix abstract it is well known that for a nonnegative matrix a the smallest row sum r a and the largest row sum r a provide lower and upper bounds respectively for the perron root of a these bounds are generalized for a partitioned nonnegative matrix a the new bounds are better than r a and r a and they can be further improved by a refinement of the partition known monotonicity and convergence properties of r a and r a are generalized for the new bounds

symplectic and multi symplectic methods for the nonlinear schrodinger equation the hamiltonian and the multi symplectic formulations of the nonlinear schrodinger equation are considered for the multi symplectic formulation a new six point difference scheme which is equivalent to the multi symplectic preissman integrator is derived numerical experiments are also reported c 2002 elsevier science ltd all rights reserved

a wavelet operational method for solving fractional partial differential equations numerically fractional calculus is an extension of derivatives and integrals to non integer orders and a partial differential equation involving the fractional calculus operators is called the fractional pde they have many applications in science and engineering however not only the analytical solution existed for a limited number of cases but also the numerical methods are very complicated and difficult in this paper we newly establish the simulation method based on the operational matrices of the orthogonal functions we formulate the operational matrix of integration in a unified framework by using the operational matrix of integration we propose a new numerical method for linear fractional partial differential equation solving in the method we 1 use the haar wavelet 2 establish a lyapunov type matrix equation and 3 obtain the algebraic equations suitable for computer programming two examples are given to demonstrate the simplicity clarity and powerfulness of the new method

on the relationships between the orders induced by uninorms and nullnorms abstract in this paper some relationships between the orders induced by uninorms and nullnorms are discussed some relations between the sets admitting some incomparability w r t those orders are investigated also some relationships between the algebraic structures obtained from those orders are determined

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

on additive generators of overlap functions in this paper we introduce the notion of additive generator pair for overlap functions we also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its generator pair in particular given a continuous and positive t norm t we analyze the overlap functions which are obtained by the distortion of t by a pseudo automorphism showing that the additive generator pair of such overlap function may be given in terms of the considered pseudo automorphism and the additive generator of t finally we also consider the influence of the migrativity homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective additive generator pairs

biorthogonal multiwavelets on the interval for numerical solutions of burgers equation to numerically solve the burgers equation in this paper we propose a general method for constructing wavelet bases on the interval 0 1 derived from symmetric biorthogonal multiwavelets on the real line in particular we obtain wavelet bases with simple structures on the interval 0 1 from the hermite cubic splines in comparison with all other known constructed wavelets on the interval 0 1 our constructed wavelet bases on the interval 0 1 from the hermite cubic splines not only have good approximation and symmetry properties with extremely short supports but also employ a minimum number of boundary wavelets with a very simple structure these desirable properties make them to be of particular interest in numerical algorithms our constructed wavelet bases on the interval 0 1 are then used to solve the nonlinear burgers equation our method is based on the finite difference formula combined with the collocation method therefore our proposed numerical scheme in this paper is abbreviated as mfdcm mixed finite difference and collocation method some numerical examples are provided to demonstrate the validity and applicability of our proposed method which can be easily implemented to produce a desired accuracy

a quadratic b spline finite element method for solving nonlinear schrodinger equation a numerical solution of the nonlinear schrodinger nls equation is obtained by using the quadratic b spline finite element method test problems concerning motion birth and bound states of solitons of the nlg equation are studied to evaluate the method results are compared with various numerical methods

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

numerical study of time splitting spectral discretizations of nonlinear schrodinger equations in the semiclassical regimes in this paper we study the performance of time splitting spectral approximations for general nonlinear schrodinger equations nls in the semiclassical regimes where the planck constant varepsilon is small the time splitting spectral approximation under study is explicit unconditionally stable and conserves the position density in l 1 moreover it is time transverse invariant and time reversible when the corresponding nls is extensive numerical tests are presented for weak strong focusing defocusing nonlinearities for the gross pitaevskii equation and for current relaxed quantum hydrodynamics the tests are geared towards the understanding of admissible meshing strategies for obtaining correct physical observables in the semiclassical regimes furthermore comparisons between the solutions of the nls and its hydrodynamic semiclassical limit are presented

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

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

a lower bound for the perron root of a nonnegative matrix ii abstract this paper is a continuation of an earlier one by the author we obtain a new lower bound for the perron root r a of a nonnegative n n matrix a we show that for a with at least one principal submatrix of order two with different diagonal entries and with at least one positive off diagonal entry the bound is at least as good as the one from 7 and we determine a class of nonnegative matrices for which it is essentially better we also show that not every nonnegative square matrix is similar to a nonnegative square matrix with identical diagonal entries

sequences of bounds for the spectral radius of a positive operator abstract in 1992 szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix a based on the geometric symmetrization of powers of a in 1998 tasci and kirkland proved a companion result by giving a sequence of upper bounds for the spectral radius of a based on the arithmetic symmetrization of powers of a in this note we extend both results to positive operators on l 2 spaces

haar wavelet method for nonlinear integro differential equations abstract a numerical method for solving nonlinear integral equations based on the haar wavelets is presented the method is applicable for volterra integral equations and integro differential equations it can be used also for solving boundary value problems of ordinary differential equations the efficiency of the proposed method is tested with the aid of four examples high accuracy even for a small number of collocation points is stated

tight bounds on the spectral radius of asymmetric nonnegative matrices abstract for an arbitrary asymmetric nonnegative n n matrix a we identify a pair of symmetric matrices whose largest eigenvalues bound the spectral radius of a furthermore we show that these bounding matrices are best possible by characterizing matrices a which attain equality with either the upper or the lower bounding matrix the lower bound may be extended to some matrices with negative entries provided they have no negative cycles

on time splitting spectral approximations for the schrodinger equation in the semiclassical regime in this paper we study time splitting spectral approximations for the linear schrodinger equation in the semiclassical regime where the planck constant e is small in this regime the equation propagates oscillations with a wavelength of o e and finite difference approximations require the spatial mesh size h o e and the time step k o e in order to obtain physically correct observables much sharper mesh size constraints are necessary for a uniform l2 approximation of the wave function the spectral time splitting approximation under study will be proved to be unconditionally stable time reversible and gauge invariant it conserves the position density and gives uniform l2 approximation of the wave function for k o e and h o e extensive numerical examples in both one and two space dimensions and analytical considerations based on the wigner transform even show that weaker constraints e g k independent of e and h o e are admissible for obtaining correct observables finally we address the application to nonlinear schrodinger equations and conduct some numerical experiments to predict the corresponding admissible meshing strategies

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

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

archimedean overlap functions the ordinal sum and the cancellation idempotency and limiting properties abstract overlap functions are a particular type of aggregation functions given by increasing continuous commutative bivariate functions defined over the unit square satisfying appropriate boundary conditions overlap functions are applied mainly in classification problems image processing and in some problems of decision making based on some kind of fuzzy preference relations in which the associativity property is not strongly required moreover the class of overlap functions is reacher than the class of t norms concerning some properties like idempotency homogeneity and mainly the self closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap functions this flexibility of overlap functions increases their applicability the aim of this papers is to introduce the concept of archimedean overlap functions presenting a study about the cancellation idempotency and limiting properties and providing a characterization of such class of functions the concept of ordinal sum of overlap functions is also introduced providing constructing representing methods of certain classes of overlap functions related to idempotency cancellation limiting and archimedean properties

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

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

perron root bounding for nonnegative persymmetric matrices the eigenvalue problem for a symmetric persymmetric matrix can be reduced to two symmetric eigenvalue problems of lower order in this paper we find in which of these problems the perron root of a nonnegative symmetric persymmetric matrix lies this is applied to bound the perron root of such class of matrices

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

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

solving the generalized nonlinear schrodinger equation via quartic spline approximation this paper is concerned with a new conservative finite difference method for solving the generalized nonlinear schrodinger gnls equation iut uxx f u 2 u 0 the numerical scheme is constructed through the semidiscretization and an application of the quartic spline approximation central difference and extrapolation formulae are used for approximating the neumann boundary conditions introduced both continuous and discrete energy conservation and the stability property are investigated the numerical method provides an efficient and reliable way for computing long time solitary solutions given by the gnls equation numerical examples are given to demonstrate our conclusions

some further results on weighted sharing three values and brosch s theorem using the notion of weighted sharing of values we prove two uniqueness theorems which improve the results proved by t c alzahary t c alzahary weighted sharing three values and brosch s theorem j math anal appl 323 2006 8 25 t c alzahary on a result of ueda concerning unicity of meromorphic functions kodai math j 30 2007 140 146 under a weaker hypothesis

an algorithm of diagonal transformation for perron root of nonnegative irreducible matrices abstract it is always to use diagonal transformation for the estimation of nonnegative matrix s perron root however it is invalid for some matrices or a long distance of bounds generated sometimes so the application of this method is limitation therefore in this paper a condition of a diagonal transformation is researched and a new method is proposed for nonnegative irreducible matrices this method can be used for all nonnegative irreducible matrices and its convergence is proved in theory it is convenient to compute by this method and it is easy to get the precision you wanted it is proved by numerical testing that this method is valid and efficient

some notes on the partial orders induced by a uninorm and a nullnorm in a bounded lattice abstract in this paper an equivalence on the class of nullnorms on a bounded lattice is discussed some relationships between the u and v partial orders are investigated a necessary and sufficient condition making a bounded lattice also a lattice w r t the v partial order is given moreover the relation between the algebraic structures related to the u and v partial orders is studied

numerical approximation of quadratic observables of schrodinger type equations in the semi classical limit we apply wigner transform techniques to the analysis of difference methods for schrodinger type equations in the case of a small planck constant in this way we are able to obtain sharp conditions on the spatial temporal grid which guarantee convergence for average values of observables as the planck constant tends to zero the theory developed in this paper is not based on local and global error estimates and does not depend on whether caustics develop or not numerical test examples are presented to help interpret the theory

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

symplectic methods for the ablowitz ladik discrete nonlinear schrodinger equation using several kinds of coordinate transformations we standardize the noncanonical symplectic structure of the ablowitz ladik model a l model of nonlinear schrodinger equation nlse then we employ some symplectic scheme to simulate the solitons motion and test the evolution of the discrete invariants of the a l model and also the conserved quantities of the original nlse in comparison with a higher order non symplectic scheme applied directly to the a l model we show the overwhelming superiorities of the symplectic method we also compare the implementation of the same symplectic scheme to different standardized hamiltonian systems resulting from different coordinate transformations and show that the symmetric coordinate transformation improves the numerical results obtained via the asymmetric one in preserving the invariants of the a l model and the original nlse

comparison theorems for weak splittings of bounded operators comparison theorems for weak splittings of bounded operators are presented these theorems extend the classical comparison theorem for regular splittings of matrices by varga the less known result by wo nicki and the recent results for regular and weak regular splittings of matrices by neumann and plemmons elsner and lanzkron rose and szyld the hypotheses of the theorems presented here are weaker and the theorems hold for general banach spaces and rather general cones hypotheses are given which provide strict inequalities for the comparisons it is also shown that the comparison theorem by alefeld and volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators

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

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

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

numerical solution of first kind fredholm integral equations with wavelets galerkin method wgm and wavelets precondition in this paper we use orthogonal wavelets as basis in projection methods for obtaining numerical solution of the fredholm integral equations of the first kind fk1 if this basis has the mra property then we show that the projection methods specially wgm must be convergent at the end for showing efficiency of method we use some examples

on pseudo homogeneous triangular norms triangular conorms and proper uninorms in this paper quasi homogeneous t norms are generalized and then pseudo homogeneous t norms are introduced and characterized it is shown that only some particular strict t norms and the minimum t norm t m are pseudo homogeneous the concepts of pseudo homogeneous t conorms and proper uninorms are given as well different from t norms only the maximum t conorm s m is pseudo homogeneous and any proper uninorm is not pseudo homogeneous

dispersion relation equation preserving fdtd method for nonlinear cubic schrodinger equation in this study we aim to solve the cubic nonlinear schrodinger cnls equation by the method of fractional steps over a time step from t n to t n 1 the linear part of the schrodinger equation is solved firstly through four time integration steps in this part of the simulation the explicit symplectic scheme of fourth order accuracy is adopted to approximate the time derivative term the second order spatial derivative term in the linear schrodinger equation is approximated by centered scheme the resulting symplectic and space centered difference scheme renders an optimized numerical dispersion relation equation in the second part of the simulation the solution of the nonlinear equation is computed exactly thanks to the embedded invariant nature within each time increment the proposed semi discretized difference scheme underlying the modified equation analysis of second kind and the method of dispersion error minimization has been assessed in terms of the spatial modified wavenumber or the temporal angular frequency resolution several problems have been solved to show that application of this new finite difference scheme for the calculation of one and two dimensional schrodinger equations can deemed conserve hamiltonian quantities and preserve dispersion relation equation dre

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

a spectrum of compromise aggregation operators for multi attribute decision making in many decision making problems a number of independent attributes or criteria are often used to individually rate an alternative from an agent s local perspective and then these individual ratings are combined to produce an overall assessment now in cases where these individual ratings are not in complete agreement the overall rating should be somewhere in between the extremes that have been suggested however there are many possibilities for the aggregated value given this this paper systematically explores the space of possible compromise operators for such multi attribute decision making problems specifically we axiomatically identify the complete spectrum of such operators in terms of the properties they should satisfy and show the main ones that are widely used namely averaging operators uninorms and nullnorms represent only three of the nine types we identify for each type we then go onto analyse their properties and discuss how specific instances can actually be developed finally to illustrate the richness of our framework we show how a wide range of operators are needed to model the various attitudes that a user may have for aggregation in a given scenario bidding in multi attribute auctions