efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane this paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance the solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary and the discussion of the paper is motivated by this application the paper starts by deriving representations as laplace type integrals of the solution and its first partial derivatives the evaluation of these integral representations by gauss laguerre quadrature is discussed and theoretical bounds on the truncation error are obtained specific approximations are proposed which are shown to be accurate except in the very near field for all angles of incidence and a wide range of values of surface impedance the paper finishes with derivations of partial results and analogous laplace type integral representations for the case of a point source

reflection of an acoustic line source by an impedance surface with uniform flow abstract an exact analytic solution is derived for the 2d acoustic pressure field generated by a time harmonic line mass source located above an impedance surface with uniform grazing flow closed form asymptotic solutions in the far field are also provided the analysis is valid for both locally reacting and nonlocally reacting impedances as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface the analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface the line source is found to excite surface waves on the impedance surface some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow the surface waves may be treated either correctly as unstable waves or artificially as stable waves enabling comparison with previous numerical or mathematical studies which make either of these assumptions the computer code for evaluating the analytic solution and far field asymptotics is provided in the supplementary material it is hoped this work will provide a useful benchmark solution for validating 2d numerical acoustic codes

the effect of structural elasticity on the efficiency of noise barriers the efficiency of noise barriers is usually estimated neglecting their elastic behaviour in this paper the total vibro acoustical response of simple barriers is considered a variational approach with a boundary element technique is used it is a generalization of an existing formalism developed for the study of two dimensional acoustical problems the case of straight and thin barriers is studied it is found that at low frequencies their vibrations can modify their insertion losses by several decibels

complex gaussian quadrature of oscillatory integrals we construct and analyze gauss type quadrature rules with complex valued nodes and weights to approximate oscillatory integrals with stationary points of high order the method is based on substituting the original interval of integration by a set of contours in the complex plane corresponding to the paths of steepest descent each of these line integrals shows an exponentially decaying behaviour suitable for the application of gaussian rules with non standard weight functions the results differ from those in previous research in the sense that the constructed rules are asymptotically optimal i e among all known methods for oscillatory integrals they deliver the highest possible asymptotic order of convergence relative to the required number of evaluations of the integrand

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

noncommutative poisson bialgebras abstract in this paper we introduce the notion of a noncommutative poisson bialgebra and establish the equivalence between matched pairs manin triples and noncommutative poisson bialgebras using quasi representations and the corresponding cohomology theory of noncommutative poisson algebras we study coboundary noncommutative poisson bialgebras which leads to the introduction of the poisson yang baxter equation a skew symmetric solution of the poisson yang baxter equation naturally gives a coboundary noncommutative poisson bialgebra rota baxter operators more generally o operators on noncommutative poisson algebras and noncommutative pre poisson algebras are introduced by which we construct skew symmetric solutions of the poisson yang baxter equation in some special noncommutative poisson algebras obtained from these structures

efficient computation of the sound fields above a layered porous ground an efficient computation of sound fields due to a monopole source placed above a porous layer is presented this paper examines an improved scheme whereby the steepest descent path is selected for the numerical evaluation of the sommerfeld integral along the steepest descent path a standard gaussian hermite quadrature can be used to calculate the sound fields effectively the suggested numerical scheme is accurate at all frequencies except in the very near field the proposed method is more numerically efficient than other computational schemes especially at long ranges and high source frequencies

convergence of iterates with errors of asymptotically quasi nonexpansive mappings and applications in this paper we consider a generalized iterative process with errors to approximate the common fixed points of two asymptotically quasi nonexpansive mappings a convergence theorem has been obtained which generalizes a known result this theorem has then been used to prove another convergence theorem which in turn generalizes a number of results

efficient calculation of two dimensional periodic and waveguide acoustic green s functions new representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane and for the green s function for sound propagation in the canyon formed by two infinitely high parallel rigid or sound soft walls and an impedance ground surface the infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a laplace type integral a pole subtraction technique is used to remove poles in the integrand which lie near the path of integration obtaining a smooth integrand more suitable for numerical integration and a specific numerical integration method is proposed numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types it is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts and for problems of scattering by periodic surfaces

double poisson algebras in this paper we develop poisson geometry for non commutative algebras this generalizes the bi symplectic geometry which was recently and independently introduced by crawley boevey etingof and ginzburg our quasi poisson brackets induce classical quasi poisson brackets on representation spaces as an application we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by crawley boevey and shaw carry a natural poisson structure

compatible lie brackets related to elliptic curve for the direct sum of several copies of sln a family of lie brackets compatible with the initial one is constructed the structure constants of these brackets are expressed in terms of functions associated with an elliptic curve the structure of casimir elements for these brackets is investigated a generalization of this construction to the case of vector valued functions is presented a different procedure for constructing compatible lie brackets based on the argument shift method for quadratic poisson brackets is discussed

on the solvability of second kind integral equations on the real line abstract this paper considers general second kind integral equations of the form s r k s t t dt s in operator form k k where the functions k and are assumed known with y the space of bounded continuous functions on r and k such that the mapping s k s from r to l1 r is bounded and continuous the function y is the solution to be determined conditions on a set w bc r l1 r are obtained such that a generalised fredholm alternative holds if w satisfies these conditions and i k k is injective for all k w then i k k is also surjective for all k w and moreover the inverse operators i k k 1 on y are uniformly bounded for k w the approximation of the kernel in the integral equation by a sequence kn converging in a weak sense to k is also considered and results on stability and convergence are obtained these general theorems are used to establish results for two special classes of kernels k s t s t z t and k s t s t s t t where l1 r z l r and bc r 0 r kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces the general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period

a conjugated infinite element method for half space acoustic problems many acoustic problems especially in environmental acoustics involve half space domains bounded by a plane subjected to normal admittance boundary conditions in the low frequency domain the numerical treatment of such problems usually relies on boundary element methods based on a particular green s function suited for the half admittance plane in the present paper an alternative hybrid finite infinite element scheme is proposed the method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges or faces the procedure is validated through comparisons with an available reference solution

on a mann type implicit iteration process for continuous pseudo contractive mappings abstract let k be a nonempty closed convex subset of a banach space e t k k a continuous pseudo contractive mapping suppose that n is a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the mann type implicit iteration process x n given by x n n x n 1 1 n t x n n 0 strongly and weakly converges to a fixed point of t respectively

scattering by infinite one dimensional rough surfaces we consider the dirichlet boundary value problem for the helmholtz equation in a non locally perturbed half plane this problem models time harmonic electromagnetic scattering by a one dimensional infinite rough perfectly conducting surface the same problem arises in acoustic scattering by a sound soft surface chandler wilde and zhang have suggested a radiation condition for this problem a generalization of the rayleigh expansion condition for diffraction gratings and uniqueness of solution has been established recently an integral equation formulation of the problem has also been proposed and in the special case when the whole boundary is both lyapunov and a small perturbation of a flat boundary the unique solvability of this integral equation has been shown by chandler wilde and ross by operator perturbation arguments in this paper we study the general case with no limit on surface amplitudes or slopes and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers as an important corollary we prove that for a variety of incident fields including the incident plane wave the dirichlet boundary value problem for the scattered field has a unique solution

renormalization in quantum field theory and the riemann hilbert problem i the hopf algebra structure of graphs and the main theorem this paper gives a complete selfcontained proof of our result announced in 6 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the riemann hilbert problem we shall first show that for any quantum field theory the combinatorics of feynman graphs gives rise to a hopf algebra which is commutative as an algebra it is the dual hopf algebra of the enveloping algebra of a lie algebra whose basis is labelled by the one particle irreducible feynman graphs the lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa the corresponding lie group g is the group of characters of we shall then show that using dimensional regularization the bare unrenormalized theory gives rise to a loop where c is a small circle of complex dimensions around the integer dimension d of space time our main result is that the renormalized theory is just the evaluation at z d of the holomorphic part of the birkhoff decomposition of we begin to analyse the group g and show that it is a semi direct product of an easily understood abelian group by a highly non trivial group closely tied up with groups of diffeomorphisms the analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title

a uniqueness result for scattering by infinite rough surfaces consider the dirichlet boundary value problem for the helmholtz equation in a non locally perturbed half plane with an unbounded piecewise lyapunov boundary this problem models time harmonic electromagnetic scattering in transverse magnetic polarization by one dimensional rough perfectly conducting surfaces a radiation condition is introduced for the problem which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi periodic and allows a variety of incident fields including an incident plane wave to be included in the results obtained we show in this paper that the boundary value problem for the scattered field has at most one solution for the case when the whole boundary is lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle

computing fresnel integrals via modified trapezium rules in this paper we propose methods for computing fresnel integrals based on truncated trapezium rule approximations to integrals on the real line these trapezium rules modified to take into account poles of the integrand near the real axis our starting point is a method for computation of the error function of complex argument due to matta and reichel j math phys 34 298 307 1956 and hunter and regan math comp 26 539 541 1972 we construct approximations which we prove are exponentially convergent as a function of n n the number of quadrature points obtaining explicit error bounds which show that accuracies of 10 15 10 15 uniformly on the real line are achieved with n 12 n 12 this confirmed by computations the approximations we obtain are attractive additionally in that they maintain small relative errors for small and large argument are analytic on the real axis echoing the analyticity of the fresnel integrals and are straightforward to implement

rapidly convergent two dimensional quasi periodic green function throughout the spectrum including wood anomalies we introduce a new methodology based on new quasi periodic green functions which converge rapidly even at and around wood anomaly configurations for the numerical solution of problems of scattering by periodic rough surfaces in two dimensional space as is well known the classical quasi periodic green function ceases to exist at wood anomalies the approach introduced in this text produces fast green function convergence throughout the spectrum on the basis of a certain finite differencing approach and smooth windowing of the classical green function lattice sum the resulting green function convergence is super algebraically fast away from wood anomalies and it reduces to an arbitrarily high user prescribed algebraic order of convergence at wood anomalies

strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings abstract suppose that k is a nonempty closed convex nonexpansive retract of a real uniformly convex banach space e let t 1 t 2 k e be two nonself asymptotically nonexpansive mappings with sequences k n l n 1 lim n k n 1 lim n l n 1 f t 1 f t 2 x k t 1 x t 2 x x respectively suppose x n is generated iteratively by x 1 k x n 1 p 1 n x n n t 1 p t 1 n 1 y n y n p 1 n x n n t 2 p t 2 n 1 x n n 1 where n and n are two real sequences in 1 for some 0 1 strong convergence theorems of x n to some q f t 1 f t 2 are obtained under conditions that one of t 1 and t 2 is completely continuous or demicompact and n 1 k n 1 n 1 l n 1 2 if e is real uniformly convex banach space satisfying opial s condition then weak convergence of x n to some q f t 1 f t 2 is obtained

convergence theorems for fixed points of uniformly quasi lipschitzian mappings in convex metric spaces abstract in this paper we consider an ishikawa type iteration process with errors to approximate the fixed point of two uniformly quasi lipschitzian mappings in convex metric spaces some results have been obtained which generalize and unify many important known results in recent literature

iterative algorithms for a new class of extended general nonconvex set valued variational inequalities abstract some new classes of extended general nonconvex set valued variational inequalities and the extended general wiener hopf inclusions are introduced by the projection technique equivalence between the extended general nonconvex set valued variational inequalities and the fixed point problems as well as the extended general nonconvex wiener hopf inclusions is proved then by using this equivalent formulation we discuss the existence of solutions of the extended general nonconvex set valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set valued variational inequalities we also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set valued variational inequalities the results presented in this paper extend and improve some known results from the literature

on the associative analog of lie bialgebras abstract an infinitesimal bialgebra is at the same time an associative algebra and coalgebra in such a way that the comultiplication is a derivation this paper continues the basic study of these objects with emphasis on the connections with the theory of lie bialgebras it is shown that non degenerate antisymmetric solutions of the associative yang baxter equation are in one to one correspondence with non degenerate cyclic 2 cocycles the associative and classical yang baxter equations are compared it is studied when a solution to the first is also a solution to the second necessary and sufficient conditions for obtaining a lie bialgebra from an infinitesimal one are found in terms of a canonical map that behaves simultaneously as a commutator and a cocommutator the class of balanced infinitesimal bialgebras is introduced they have an associated lie bialgebra several well known lie bialgebras are shown to arise in this way the construction of drinfeld s double from earlier work by the author in press in contemp math amer math soc providence for arbitrary infinitesimal bialgebras is complemented with the construction of the balanced double for balanced ones this construction commutes with the passage from balanced infinitesimal bialgebras to lie bialgebras

acoustic scattering by an inhomogeneous layer on a rigid plate the problem of scattering of time harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in r 2 is considered the density is assumed to be unity in the media within the layer the sound speed is assumed to be an arbitrary bounded measurable function the problem is modelled by the reduced wave equation with variable wavenumber in the layer and a neumann condition on the plate to formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced a generalization of the rayleigh expansion condition for diffraction gratings with the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate under additional assumptions on the wavenumber in the layer uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established general results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data

a fast two grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half plane we consider the numerical treatment of second kind integral equations on the real line of the form phi s psi s int infty infty k s t z t phi t dt s in mathbb r abbreviated k z in which l 1 z l and bc the space of bounded continuous functions on are assumed known and bc is to be determined we first derive sharp error estimates for the finite section approximation reducing the range of integration to a a via bounds on i k z 1 as an operator on spaces of weighted continuous functions numerical solution by a simple discrete collocation method on a uniform grid on is then analysed in the case whenz is compactly supported this leads to a coefficient matrix which allows a rapid matrix vector multiply via the fft to utilise this possibility we propose a modified two grid iteration a feature of which is that the coarse grid matrix is approximated by a banded matrix and analyse convergence and computational cost in cases wherez is not compactly supported a combined finite section and two grid algorithm can be applied and we extend the analysis to this case as an application we consider acoustic scattering in the half plane with a robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied our final result is that ifz related to the boundary impedance in the application takes values in an appropriate compact subsetq of the complex plane then the difference between s and its finite section approximation computed numerically using the iterative scheme proposed is c 1 khlog 1 kh 1 1 2 ka 1 2 in the interval a a 1 forkh sufficiently small wherek is the wavenumber andh the grid spacing moreover this numerical approximation can be computed in c 2 n logn operations wheren 2a h is the number of degrees of freedom the values of the constantsc 1 andc 2 depend only on the setq and not on the wavenumberk or the support ofz

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

the dtn nonreflecting boundary condition for multiple scattering problems in the half plane abstract the multiple dirichlet to neumann multiple dtn non reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half plane the multiple dtn map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries as opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half plane the adapted multiple dtn condition is simultaneously imposed in each of the artificial circular boundaries as a result the computational effort is significantly reduced a computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary fitted grids approximate solutions to problems involving two scatterers of arbitrary geometry are presented the proposed numerical method is validated by comparing the approximate and exact far field patterns for the scattering from a single and from two circular obstacles in the half plane

common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in a banach space in this paper we introduce a new two step iterative scheme for two asymptotically nonexpansive nonself mappings in a uniformly convex banach space weak and strong convergence theorems are established for the new two step iterative scheme in a uniformly convex banach space

application of the fourier pseudospectral time domain method in orthogonal curvilinear coordinates for near rigid moderately curved surfaces the fourier pseudospectral time domain method is an efficient wave based method to model sound propagation in inhomogeneous media one of the limitations of the method for atmospheric sound propagation purposes is its restriction to a cartesian grid confining it to staircase like geometries a transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries for applicability of this method near the boundaries the acoustic velocity variables are solved for their curvilinear components the performance of the curvilinear fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain the applicability of the curvilinear fourier pseudospectral time domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer with the proposed method accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained

strong and weak convergence theorems for asymptotically nonexpansive mappings abstract suppose k is a nonempty closed convex nonexpansive retract of a real uniformly convex banach space e with p as a nonexpansive retraction let t k e be an asymptotically nonexpansive nonself map with sequence kn n 1 1 limkn 1 f t x k tx x suppose xn n 1 is generated iteratively by x 1 k x n 1 p 1 n x n n t pt n 1 x n n 1 where n n 1 0 1 is such that 0 it is proved that i t is demiclosed at 0 moreover if n 1 kn2 1 x f t is proved if t is not assumed to be completely continuous but e also has a frechet differentiable norm then weak convergence of xn to some x f t is obtained

on the evaluation of highly oscillatory integrals by analytic continuation we consider the integration of one dimensional highly oscillatory functions based on analytic continuation rapidly converging quadrature rules are derived for a general class of oscillatory integrals with an analytic integrand the accuracy of the quadrature increases both for the case of a fixed number of points and increasing frequency and for the case of an increasing number of points and fixed frequency these results are then used to obtain quadrature rules for more general oscillatory integrals i e for functions that exhibit some smoothness but that are not analytic the approach described in this paper is related to the steepest descent method but it does not employ asymptotic expansions it can be used for small or moderate frequencies as well as for very high frequencies the approach is compared with the oscillatory integration techniques recently developed by iserles and norsett

the numerical solution of scattering by infinite rough interfaces based on the integral equation method in this paper we describe a nystrom integration method for the integral operator t which is the normal derivative of the double layer potential arising in problems of two dimensional acoustic scattering by infinite rough interfaces the hypersingular kernel and unbounded integral interval of t are the key difficulties by using a mollifier we separately deal with these two difficulties and propose its nystrom integration method furthermore we establish convergence of the method finally we apply the method to the scattering problem by infinite rough interfaces and carry out some numerical experiments to show the validity

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

the epsilon algorithm and related topics the epsilon algorithm is recommended as the best all purpose acceleration method for slowly converging sequences it exploits the numerical precision of the data to extrapolate the sequence to its limit we explain its connections with pade approximation and continued fractions which underpin its theoretical base then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector valued sequences and some related topics in this paper we consider the class of methods based on using generalised inverses of vectors and the formulation specifically includes the complex case wherever possible

general a monotone operators and perturbed iterations for nonlinear set valued relaxed cocoercive operator inclusion problems in this paper we introduce the notion of general a monotone operators in banach spaces study some properties of general a monotone operator and the new proximal mapping associated with the general a monotone operators by using alber s inequalities nalder s results and the new proximal mapping technique we also construct two new class of perturbed iterative algorithms with mixed errors for solving a new class of nonlinear set valued relaxed cocoercive operator inclusions and study applications of general a monotone operators to the approximation solvability of the nonlinear set valued relaxed cocoercive operator inclusion problems in banach spaces furthermore the general a monotone operators are illustrated by some examples the results presented in this paper improve and generalize the corresponding results on strongly monotone quasi variational inclusions and nonlinear implicit quasi variational inclusions

a wavenumber independent boundary element method for an acoustic scattering problem in this paper we consider the impedance boundary value problem for the helmholtz equation in a half plane with piecewise constant boundary data a problem which models for example outdoor sound propagation over inhomogeneous flat terrain to achieve good approximation at high frequencies with a relatively low number of degrees of freedom we propose a novel galerkin boundary element method using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that on each element the approximation space contains polynomials of degree nu multiplied by traces of plane waves on the boundary we prove stability and convergence and show that the error in computing the total acoustic field is cal o n nu 1 log 1 2 n where the number of degrees of freedom is proportional to n log n this error estimate is independent of the wavenumber and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity

a novel boundary integral formulation for three dimensional analysis of thin acoustic barriers over an impedance plane this article presents a three dimensional formulation for the analysis of acoustic barriers over an impedance plane as infinitely thin structures the barriers are therefore modeled as simple surfaces rather than volumetric structures using this approach the problems caused by near singular integrations and near degenerate systems of equations are averted and mesh generation is made easier a dual boundary element method is used in the analysis involving the simultaneous solution of standard and hypersingular boundary integral equations an optimization procedure is used to speed up the assembling of the system of equations increasing the applicability of the method to a wider range of frequencies

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

new iterative schemes for asymptotically quasi nonexpansive nonself mappings in banach spaces in this paper a new two step iterative scheme with errors is introduced for two asymptotically quasi nonexpansive nonself mappings several convergence theorems are established in real banach spaces and real uniformly convex banach spaces our theorems improve and extend the results due to thianwan s thianwan common fixed point of new iterations for two asymptotically nonexpansive nonself mappings in a banach space j comput appl math 224 2009 685 695 and many other papers

global existence and mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations abstract this paper deals with the first order nonlinear neutral delay differential equation d dt x t p t x t f t x 1 t x 2 t x n t 0 t t 0 where 0 p c t 0 r f c t 0 r n r and l c t 0 r with limt l t for l 1 2 n by using the banach fixed point theorem we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p construct some mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions seven examples are presented to illuminate the results obtained in this paper