diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions the three dimensional problem of diffraction of a skew incident plane wave by a wedge with anisotropic impedance boundary conditions is explicitly solved by the probabilistic random walk method the problem is formulated in terms of two certain components of the electric and magnetic fields which satisfy independent helmholtz equations but are coupled through the first order boundary conditions the solution is represented as a superposition of the geometric waves that are completely determined by elementary methods and of the waves diffracted by the apex of the wedge the diffracted field is explicitly represented as the mathematical expectation computed over the trajectories of a two state random motion which runs in a complex space and switches states under the control of stochastic equations determined by the problem s geometry and by the boundary conditions

on a higher order secant method in this paper we carry out a modification of the classical secant method our goal is to accelerate the convergence until order two but without using any derivative two convergence theorems are presented finally some numerical experiments are analyzed

diffraction of a normally incident plane wave at a wedge with identical tensor impedance faces diffraction of a normally incident plane wave by a wedge with identical tensor impedance faces is studied and an exact solution is obtained by reducing the original problem to two decoupled and already solved ones a uniform asymptotic solution then follows from the exact one and agrees excellently with numerical results due to the method of parabolic equation

arbitrarily oriented perfectly conducting wedge over a dielectric half space diffraction and total far field complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field in this paper we describe a complete procedure to study this problem with possible developments in radar technologies like gpr antenna development or electromagnetic compatibility tips near substrates the diffraction of an incident plane wave by a perfectly conducting pec wedge over a dielectric half space is studied using generalized wiener hopf equations gwhes and the solution is obtained using analytical and numerical analytical approaches that reduce the wiener hopf wh factorization to integral equations ies the mathematical aspects are described in a unified and consistent theory for angular and layered region problems the proposed procedure is valid for the general case and the paper focuses on e polarization at normal incidence the solutions are given in terms of geometrical uniform theory of diffraction gtd utd diffraction coefficients and total far fields for engineering applications this paper presents several numerical test cases that show the validity of the proposed method

a probabilistic look at the wiener hopf equation existence uniqueness and asymptotic properties of solutions z to the wiener hopf integral equation z x z x int infty xz x y f dy x ge 0 are discussed by purely probabilistic methods involving random walks supermartingales coupling the hewitt savage 0 1 law ladder heights and exponential change of measure

diffraction at skew incidence by an anisotropic impedance wedge in electromagnetism theory a new class of canonical cases an original mathematical approach for the diffraction of an electromagnetic skew incident wave by a wedge allows us to reduce such a problem to new elementary functional equations using this method we present an exact analytical solution with closed form expressions for a class of wedge of any angle with a certain type of anisotropic boundary condition which does not require any field component to vanish on the faces we thereby consider the important case where the principal axes of anisotropy are along and normal to the edge the relative impedance matrix attached to each face being diagonal with its determinant equal to unity

a new technique to obtain derivative free optimal iterative methods for solving nonlinear equations abstract a new technique to obtain derivative free methods with optimal order of convergence in the sense of the kung traub conjecture for solving nonlinear smooth equations is described the procedure uses steffensen like methods and pade approximants some numerical examples are provided to show the good performance of the new methods

numerical calculation of the diffraction coefficients for an arbitrary shaped perfectly conducting cone a method for numerical calculation of the diffraction coefficients for electromagnetic diffraction by arbitrarily shaped perfectly conducting cones is proposed the approach makes an extensive use of the analytic formulas of smyshlyaev in combination with further developments including a use of the potential theory adapted to the laplace beltrami operator on a subdomain of unit sphere this reduces the problem to a fredholm integral equation on the closed curve of the unit sphere defining the cone s geometry which can be solved numerically this strategy permits us to implement a numerical code for calculation of the diffraction coefficients for cones of rather general cross sections results of sample calculations for the circular and elliptic cones are given

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

diffraction by a plane sector the problem of diffraction by a perfectly reflecting screen occupying an infinite sector of the equatorial plane is addressed by the random walk method the solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen the diffracted field is explicitly represented as the mathematical expectation of a specified functional on trajectories of the random motion the radial component of which runs in a complex space while the two dimensional angular component remains real valued the numerical results confirm the efficiency of the random walk approach to the analysis of diffraction by wedge shaped screens of arbitrary angles

steffensen type methods for solving non linear equations families of steffensen type methods for solving non linear equations are obtained one family consists of second order method involving no derivatives while other consists of third order methods involving only the first derivatives also a derivative free third order method is provided the theory is supported by an example comparing the existing methods with the present one

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

probabilistic approach to the lame equations of linear elastostatics abstract a probabilistic approach to systems of partial differential equations is developed on the basis of the well known feynman kac and bismut formulas providing explicit probabilistic representations of the solutions and of their derivatives of scalar differential equations some numerical examples are also included in particular the lame equations of elastostatics are solved and the results are compared with some known exact analytic solutions to demonstrate the efficiency of the approach

wiener hopf analysis of the em diffraction by an impedance discontinuity in a planar surface and by an impedance half plane the wiener hopf technique is used to solve two canonical problems the first problem considered is the electromagnetic em diffraction by a planar surface with an impedance discontinuity two part surface of an arbitrarily polarized plane wave obliquely incident to the axis of the two dimensional objects the second problem considers the em diffraction by a half plane with equal impedances on both sides the solutions obtained are cast in a matrix notation which is useful for diffraction problems the exact formal solutions are expressed in terms of integrals which can be asymptotically evaluated uniform asymptotic expressions are obtained where the presence of the geometrical optics go poles as well as the surface wave poles near the saddle point are fully taken into account several numerical examples are presented and it is shown that the solutions are continuous across the shadow boundaries of the go and surface wave fields

a monte carlo solution method for linear elasticity a probabilistic method is proposed and implemented to solve linear elasticity problems the method called walk on the boundary method wbm uses the same governing equations as the boundary element method unlike in finite element and boundary element methods wbm does not require any meshing also error estimates for wbm are easier to obtain than in finite element and boundary element methods furthermore wbm obtains a point solution at a specific point of interest instead of a full field solution as in finite element and boundary element methods wbm is developed for general traction boundary value problems in antiplane shear plane strain and 3d elasticity numerical implementations are performed for three example problems 1 antiplane shear problem with a centrally located circular hole being loaded by uniformly applied traction 2 plane strain problem with centrally located circular hole being loaded by uniform tension and 3 3d elasticity problem with a centrally located spherical cavity being loaded by uniform tension results from the three example problems compared favorably with results from the analytical and finite element solution three critical issues associated with the wbm for linear elasticity are pointed out for its further improvement

a path integral time domain method for electromagnetic scattering a new full wave time domain formulation for the electromagnetic field is obtained by means of a path integral the path integral propagator is derived via a state variable approach starting with maxwell s differential equations in tensor form a numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed an absorbing boundary condition is demonstrated for the one dimensional 1 d case it is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the nyquist limit two numerical points per wavelength as a consequence the calculated fields are not subject to numerical dispersion other advantages in comparison to presently popular time domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods

probabilistic solutions of the helmholtz equation solutions of the schrodinger and helmholtz equations are represented as mathematical expectations of functionals on paths in a complex space formulas obtained for the helmholtz equation appear as direct improvements of the ray method approximations to the exact solution presented numerical results confirm the efficiency of the suggested description of wave propagation phenomena

stochastic process leading to wave equations in dimensions higher than one stochastic processes are proposed whose master equations coincide with classical wave telegraph and klein gordon equations similar to predecessors based on the goldstein kac telegraph process the model describes the motion of particles with constant speed and transitions between discreet allowed velocity directions a new ingredient is that transitions into a given velocity state depend on spatial derivatives of other states populations rather than on populations themselves this feature requires the sacrifice of the single particle character of the model but allows to imitate the huygens principle and to recover wave equations in arbitrary dimensions

diffraction of a normally incident plane wave by an impedance wedge with its exterior bisected by a semi infinite impedance sheet this paper reports an application of a previously proposed procedure to diffraction of a normally incident arbitrarily polarized plane electromagnetic wave by a canonical structure which consists of a wedge with different face impedances and a semi infinite impedance sheet bisecting the exterior of the wedge the use of the sommerfeld malyuzhinets technique converts the original boundary value problem into a system of linear equations for two coupled spectral functions eliminating one of them we get a second order difference equation for the other spectral function from this function and the boundary condition on the upper wedge face we construct an even and in the basic strip regular new spectral function then we transform the second order equation into a simpler one by means of a generalized malyuzhinets function spl chi sub spl phi spl alpha and express the solution to the latter in an integral form with help of the so called s integrals solving a fredholm equation of the second kind for points on the imaginary axis of the complex plane which follows from the integral representation enables one to compute the sought for function the second spectral function is obtained via its dependence upon the first one we present a first order uniform asymptotic solution as well as numerical results

novel solutions of the helmholtz equation and their application to diffraction this paper presents a series of novel representations for the solutions of the helmholtz equation in a broad class of wedge like domains including those with curvilinear non flat faces these repr

wiener hopf solution for impenetrable wedges at skew incidence a new wiener hopf approach for the solution of impenetrable wedges at skew incidence is presented mathematical aspects are described in a unified and consistent theory for angular region problems solutions are obtained using analytical and numerical analytical approaches several numerical tests from the scientific literature validate the new technique and new solutions for anisotropic surface impedance wedges are solved at skew incidence the solutions are presented considering the geometrical and uniform theory of diffraction coefficients total fields and possible surface wave contributions

random walk approach to wave propagation in wedges and cones two and three dimensional helmholtz equations in wedge shaped and conical domains are addressed by the random walk method the solutions of the dirichlet problems in such domains are represented as mathematical expectations of specified functionals on trajectories of multidimensional random motions whose radial components run in a complex space while the angular components remain real valued this technique is applied to the sommerfeld problem of diffraction by a semi infinite screen which is explicitly solved here in the probabilistic form the numerical results confirm the efficiency of the random walk approach to the analysis of wave propagation

a general multisegment artificial neural network architecture for the efficient evaluation of electromagnetic plane wave wedge diffraction a multisegment artificial neural network ann is proposed as an interpolation technique for the evaluation of the electromagnetic field diffracted at the edge of anisotropic impedance wedges under plane wave illumination at oblique incidence multisegmentation is needed as the high frequency wedge diffracted field is characterized by a number of discontinuities at the shadow boundaries of the geometrical optics and surface wave fields the proposed approach is applied as a test case to the problem of an anisotropic impedance right angled wedge illuminated by a skewly incident plane wave some exact analytical solutions valid for specific surface impedance tensors are used to obtain numerical data for the ann training phase as well as to show the interpolation capabilities of the implemented ann nevertheless the proposed ann structure is general and can be trained with data obtained from other available solutions analytical perturbative numerical valid for more general wedge configurations eventually leading to a single software tool encompassing all of them and providing accurate approximations of the wedge diffracted field in a relatively short time comparable to that of a closed form analytical solution

a probabilistic approach to the two dimensional navier stokes equations we turn the navier stokes equations for a 2 dimensional viscous incompressible fluid into a system of functional integrals in the trajectory space of a suitable diffusion process using probabilistic techniques as girsanov s transformation and bismut elworthy formula we prove the existence of a unique global solution of this system in a constructive way

a class of steffensen type methods with optimal order of convergence abstract in this paper a family of steffensen type methods of fourth order convergence for solving nonlinear smooth equations is suggested in the proposed methods a linear combination of divided differences is used to get a better approximation to the derivative of the given function each derivative free member of the family requires only three evaluations of the given function per iteration therefore this class of methods has efficiency index equal to 1 587 kung and traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2 d 1 where d is the number of functional evaluations per step the new class of methods agrees with this conjecture for the case d 3 numerical examples are made to show the performance of the presented methods on smooth and nonsmooth equations and to compare with other ones

electromagnetic diffraction by arbitrary angle impedance wedges the problem of the diffraction of a plane electromagnetic wave incident at an oblique angle on a wedge of arbitrary angle with general tensor impedance boundary conditions is solved using a semi an

diffraction of a plane wave by a circular cone with an impedance boundary condition we consider the boundary value problem for the helmholtz equation in a circular cone with an impedance boundary condition on its face a new approach for its solution is proposed the scheme of solution includes applying the kontorovich lebedev transform derivation of a second order difference equation in a strip of a complex variable and reduction of the latter to an integral equation of the convolution type with variable coefficients it is also shown that the equation is equivalent to a 2 2 matrix riemann hilbert problem with a discontinuous coefficient we analyze the behavior of the solution of the integral equation at the ends of the contour and construct an approximate solution using a collocation method the diffraction coefficient is found in terms of the solution of the integral equation numerical results for the diffraction coefficient and comparative analysis of the results for the impedance cone with the limiting cases of the acoustically soft and hard cones are reported a full high f

on a steffensen s type method and its behavior for semismooth equations abstract a generalization of steffensen s method is proposed our goal is to obtain similar convergence as newton s method but without to evaluate any derivative and without to have stability problems convergence analysis and numerical results for semismooth equations are presented

high order iterative methods without derivatives for solving nonlinear equations the new second order and third order iterative methods without derivatives are presented for solving nonlinear equations the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided finally some numerical experiments show the efficiency of the theoretical results for the above methods

two dimensional problems of diffraction by finite collinear structures two closely related problems of diffraction are solved by use of the probabilistic random walk method the first concerns diffraction by a boundary of a half space with a piecewise constant boundary impedance and the second solves the problem of diffraction by a finite segment with different impedances on its sides the solutions are represented as superpositions of predefined geometric fields with several diffracted fields which are explicitly represented as mathematical expectations of certain functionals along the trajectories of specified random motions running across multisheet analytic manifolds associated with the boundary conditions numerical examples confirm the feasibility of the solutions

the effect of test signal type and bandwidth on the categorical scaling of loudness recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth beyond the critical band affected loudness growth as wideband speech stimuli were judged to be significantly louder than narrow band speech at equivalent overall sound levels in this investigation similar loudness growth patterns were noted across category ratings for all test signal bandwidths in contrast loudness growth data obtained using an intelligible speech signal cox et al the american academy of audiology 1994a revealed loudness growth patterns for speech were fundamentally different than those obtained for tones implications for hearing aid fitting strategies are discussed recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth bey

wiener hopf splitting of a 2 x 2 matrix explicit expressions for the wiener hopf factors of a 2 x 2 matrix are determined in terms of a single scalar examples of the application to various matrices are given

random walk methods and wave diffraction this paper develops an approach to problems of wave diffraction that combines the physical clarity of the ray method with the versatility of direct numerical methods first it addresses scalar problems with general linear first order boundary conditions and then it considers problems formulated in adjacent domains with imposed interface conditions we start by following closely the scheme of the ray method but instead of looking for approximate expressions for the amplitudes of the liouville decomposition we obtain their exact representations as the mathematical expectations of some functionals on the space of brownian trajectories the obtained solutions provide direct improvements of the ray method approximations to the exact solutions and they are shown to admit efficient numerical evaluations

diffraction by a nonconvex polygon the probabilistic approach to wave propagation and diffraction is applied to a typical problem of diffraction by a nonconvex polygon the solution is obtained using a transparent technique that employs a floating coordinate system and it combines ideas from ray theory stochastic analysis and complex analysis the obtained solution is compatible with intuitive ideas about diffraction and it admits simple implementations

on one approach to an electromagnetic diffraction problem in a wedge shaped region an electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional equations by means of sommerfeld integrals anisotropic impedance boundary conditions are satisfied on the wedge s faces this system of functional equations is solved by regular perturbation method it is shown that for weak anisotropy the solution is presented by converging series which are neumann recurrent series for linear equations with contracting operators in a general case the problem is reduced to linear equations with compact operators the wave field asymptotic is computed for the region outside the vicinity of the edge of the wedge

diffraction by a highly contrast transparent wedge the problem of a plane wave diffraction by a highly contrast transparent wedge of an arbitrary opening is studied with the aid of the sommerfeld integrals it is reduced to a system of coupled maliuzhinets equations by use of the theory of s integrals the system of functional equations is transformed to a system of linear equations in a banach space in the case of the high contrast of a material inside the wedge in comparison with that in the wedge s exterior the linear equations are solved by means of perturbation theory convergence of the corresponding neumann series is proved singularities of the integrands in the sommerfeld integrals are investigated application of the steepest descent method leads to the determination of the reflected transmitted and diffracted waves expressions for the diffraction coefficients are also represented

steffensen type methods for solving nonlinear equations in the present paper by approximating the derivatives in the well known fourth order ostrowski s method and in a sixth order improved ostrowski s method by central difference quotients we obtain new modifications of these methods free from derivatives we prove the important fact that the methods obtained preserve their convergence orders 4 and 6 respectively without calculating any derivatives finally numerical tests confirm the theoretical results and allow us to compare these variants with the corresponding methods that make use of derivatives and with the classical newton s method

diffraction of a plane wave by a sector with dirichlet or neumann boundary conditions the problems of diffraction by a screen occupying an infinite sector with dirichlet or neumann boundary conditions are addressed by the random walk method the solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen the diffracted field is explicitly represented as a mathematical expectation of a specified functional on trajectories of a random motion whose behavior is determined by the configuration of the problem and by the boundary conditions the numerical results confirm the efficiency of the random walk approach to the analysis of diffraction by wedge shaped screens of different angles

exact evaluation of the maliuzhinets half plane function the maliuzhinets half plane function psipi z has been used for many applications but its closed form has not been known in this communication we exactly evaluate a known integral representation of psipi z to formulate an exact closed form of the function which is expressed in terms of the dilogarithm function the exact formulation is numerically verified by comparing it with the results obtained by numerical integration of a integral representation of general maliuzhinets function a closed form of psipi 2 z is also obtained since it can be expressed in terms of psipi z

exact solution to diffraction problem by wedges with a class of anisotropic impedance faces oblique incidence of a plane electromagnetic wave this paper studies diffraction of an obliquely incident arbitrarily polarized plane electromagnetic wave by an anisotropic impedance wedge with an opening angle 2 spl phi between 0 and 2 spl pi and presents a closed form exact solution to a class of impedance wedge faces and the related uniform asymptotic solution uas on use of a unitary similarity transform the boundary conditions on the wedge faces is brought into a form which makes the exactly soluble class of impedance faces evident the exact solution is found with help of the sommerfeld malyuzhinets 1896 1958 technique a generalized malyuzhinets function spl chi sub spl phi and the so called s integrals a standard procedure yields therefrom the uas the exact solution agrees with known analytical results in special cases and the numerical results of uas are confirmed by that of parabolic equation method pem

two dimensional diffraction by a wedge with impedance boundary conditions the two dimensional problem of diffraction by a wedge with impedance boundary conditions on its faces is explicitly solved in a form that admits effective numerical simulation by simple perfectly scalable algorithms with unlimited capability for parallel processing the solution is represented as a superposition of the geometric field that is completely determined by elementary ray analysis and of the waves diffracted by the tip of the wedge the diffracted field is explicitly represented as a mathematical expectation of a specified functional on trajectories of a random motion determined by the configurations of the problem and by the boundary conditions the numerical results confirm the efficiency of this approach

some novel optimal eighth order derivative free root solvers and their basins of attraction we present two families of derivative free methods with eighth order convergence for solving nonlinear equations each method of the families requires four function evaluations per full iteration that means the families are optimal in the sense of the hypothesis of kung traub 1974 computational results and comparison including cpu time with existing methods confirm the efficient and robust character of new methods moreover the presented basins of attraction also confirm equal or better performance of the methods as compared to other established methods in literature

secant methods for semismooth equations some generalizations of the secant method to semismooth equations are presented in the one dimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved moreover a new quadratically convergent method is proposed that requires two function values per iteration for the n dimensional cases we discuss secant methods for two classes of composite semismooth equations most often studied semismooth equations are of such form

a class of two step steffensen type methods with fourth order convergence abstract based on steffensen s method we derive a one parameter class of fourth order methods for solving nonlinear equations in the proposed methods an interpolating polynomial is used to get a better approximation to the derivative of the given function each member of the class requires three evaluations of the given function per iteration therefore this class of methods has efficiency index which equals 1 587 kung and traub conjectured an iteration using n evaluations of f or its derivatives without memory is of convergence order at most 2 n 1 the new class of fourth order methods agrees with the conjecture of kung traub for the case n 3 numerical comparisons are made to show the performance of the presented methods

a monte carlo method for solving the one dimensional telegraph equations with boundary conditions a monte carlo algorithm is derived to solve the one dimensional telegraph equations in a bounded domain subject to resistive and non resistive boundary conditions the proposed numerical scheme is more efficient than the classical kac s theory because it does not require the discretization of time the algorithm has been validated by comparing the results obtained with theory and the finite difference time domain fdtd method for a typical two wire transmission line terminated at both ends with general boundary conditions we have also tested transmission line heterogeneities to account for wave propagation in multiple media the algorithm is inherently parallel since it is based on monte carlo simulations and does not suffer from the numerical dispersion and dissipation issues that arise in finite difference based numerical schemes on a lossy medium this allowed us to develop an efficient numerical method capable of outperforming the classical fdtd method for large scale problems and high frequency signals

on random time and on the relation between wave and telegraph equations kac s conjecture relating the solution of wave and telegraph equations in higher dimensions through a poisson process driven random time is established through the concepts of stochastic calculus new expression is derived for the probability density function of the random time we demonstrate how the relationship between the solution of a lossy wave and that of a lossless wave equation can be exploited to derive some statistical identities relevance of the results presented to the study of pulse propagation in a dispersive medium characterized by a lorentz or drude model is discussed and new evolution equations for 2 d maxwell s equations are presented for the drude medium it is shown that the computational time required for updating the electric field using the stochastic technique is expected to go up as o t

a steffensen like method and its higher order variants for solving nonlinear equations we suggest a second order parametric steffensen like method which is derivative free and only uses two evaluations of the function in one step we also suggest a variant of the steffensen like method which is still derivative free and uses four evaluations of the function to achieve cubic convergence moreover a fast steffensen like method with super quadratic convergence and a fast variant of the steffensen like method with super cubic convergence are proposed by using a parameter estimation the error equations and asymptotic convergence constants are obtained for the discussed methods the numerical results and the basins of attraction support the proposed methods

numerical study of diffraction and slope diffraction at anisotropic impedance wedges by the method of parabolic equation space waves the method of parabolic equation pe has been successfully applied to the numerical determination of diffraction slope diffraction and multiple diffraction coefficients of scalar impedance wedges illuminated by a line source as a continuation this paper studies for the first time to the authors knowledge another important canonical problem for the uniform geometrical theory of diffraction utd namely diffraction and slope diffraction of an incident cylindrical wave at wedges with anisotropic impedance surfaces by using the same method for the diffracted fields the exact helmholtz equation is asymptotically approximated by the corresponding parabolic one it is proved that the sufficient conditions for the unique solution of the helmholtz equation also guarantee the uniqueness of the solution of the parabolic one the latter is then efficiently solved by using crank nicholson finite difference fd scheme due to the lack of exact solutions the pe results were compared to uniform asymptotic theory of diffraction uat ones for weak anisotropy and in this case very good agreement has been achieved the diffraction and slope diffraction behavior dependent upon the measure of the weakness of the anisotropy has been demonstrated by several examples

a utd solution for the scattering by a wedge with anisotropic impedance faces skew incidence case asymptotic expressions for the fields scattered by an anisotropic impedance wedge at oblique incidence are derived in the context of the uniform geometrical theory of diffraction utd they are obtained by resorting to a perturbative approach considering the normal incidence case as the imperturbed configuration we observe that the limits of applicability of this approximate analytical solution extend far beyond those of standard perturbative approaches allowing us to account for deviations from the normal incidence case of 20 spl deg to 30 spl deg

cross modality matching and the loudness growth function for click stimuli loudness intensity functions for click stimuli were obtained from 30 adult listeners having normal n 10 flat n 10 or sloping n 10 high frequency cochlear hearing loss configurations the procedure of cross modality matching cmm between loudness and perceived line length r p hellman and c h meiselman j speech hear res 31 605 615 1988 j acoust soc am 88 2596 2606 1990 j acoust soc am 93 966 975 1993 was used to validate their loudness growth functions mean group loudness exponents were similar to those reported in recent investigations that utilized pure tone stimuli further supporting the validity and reliability of the cmm task as an estimate of the loudness growth function the results also suggest that the mean loudness function for clicks is similar to the function obtained with tonal stimuli at least for listeners with moderately impaired hearing or better moreover cmm produced less variability than the more conventional psychophysical methods of magnitude estimation and production for the groups with cochlear hearing loss toward direct application of the cmm technique in lieu of absolute exponential slope values the individually determined loudness growth function over a range of intensities should be compared to the normal mean functions for calculations of deviations

categorical loudness scaling and equal loudness contours in listeners with normal hearing and hearing loss this study describes procedures for constructing equal loudness contours elcs in units of phons from categorical loudness scaling cls data and characterizes the impact of hearing loss on these estimates of loudness additionally this study developed a metric level dependent loudness loss which uses cls data to specify the deviation from normal loudness perception at various loudness levels and as function of frequency for an individual listener with hearing loss cls measurements were made in 87 participants with hearing loss and 61 participants with normal hearing an assessment of the reliability of cls measurements was conducted on a subset of the data cls measurements were reliable there was a systematic increase in the slope of the low level segment of the cls functions with increase in the degree of hearing loss elcs derived from cls measurements were similar to standardized elcs international organization for standardization iso 226 2003 the presence of hearing loss decreased the vertical spacing of the elcs reflecting loudness recruitment and reduced cochlear compression representing cls data in phons may lead to wider acceptance of cls measurements like the audiogram that specifies hearing loss at threshold level dependent loudness loss describes deficit for suprathreshold sounds such information may have implications for the fitting of hearing aids

an optimal and efficient general eighth order derivative free scheme for simple roots abstract the main motivation of this study is to present an optimal scheme in a general way that can be applied to any existing optimal multipoint fourth order iterative scheme whose first substep employs steffensen s method or steffensen like method to further produce optimal eighth order iterative schemes a rational function approximation approach is used in the construction of proposed scheme in addition we also discussed the theoretical and computational properties of our scheme each member of the presented scheme satisfies the optimality conjecture for multipoint iterative methods without memory which was given by kung and traub in 1970 finally we also concluded on the basis of obtained numerical results that our methods have faster convergence in contrast to the existing methods of same order because they have minimum residual errors minimum error difference between two consecutive iterations and minimum asymptotic error constants corresponding to the considered test function

a steffensen type method of two steps in banach spaces with applications this paper is devoted to the analysis of a steffensen type of two steps with order of convergence at least three the main advantage of this method is that it does not need to evaluate any frechet derivative or any bilinear operator the method includes extra parameters in the divided difference in order to ensure a good approximation to the first derivative in each iteration we prove using recurrence relations a semilocal convergence result in banach spaces and do a detailed study of the domain of parameters associated to this result finally some numerical results including differentiable and nondifferentiable operators are presented special attention is paid in the approximation of solutions of boundary problems using the multiple shooting method and in the approximation of a nonlinear model related with image processing

on a two step optimal steffensen type method relaxed local and semi local convergence analysis and dynamical stability abstract in this paper we study on the local and semi local convergence and dynamic of an iterative optimal two step steffensen s method we study local convergence by using lipschitz conditions and continuity of differentiable function f we also obtain semi local convergence by using majorizing sequences by this approach we can obtain the convergence of the method by minimum of auxiliary sequences and few initial conditions moreover we analyze the stability of the method via julia sets and parameter planes that is a novelty for steffensen type methods we extend this method for obtaining the sign function of a matrix numerical examples are given to confirm our theoretical results

solution of a second order difference equation using the bilinear relations of riemann a recently proposed technique to solve a class of second order functional difference equations arising in electromagnetic diffraction theory is further investigated by applying it to a case of intermediate complexity the proposed approach is conceptually simple and relies on first obtaining well defined branched solutions to a pair of associated first order difference equations the construction of these branched expressions leads to an equation system whose solution requires relationships akin to riemann s bilinear relations for differentials of the first and third kinds their derivation necessitates the application of cauchy s theorem on riemann surfaces of in this particular instance genera one and three branch free solutions of the second order difference equation are then obtained by taking appropriate linear combinations of the branched solutions of the first order equations analysis and computation demonstrate that the resulting expressions have the desired analytical properties and recover known solutions in the appropriate limit

probabilistic computation of poiseuille flow velocity fields velocity fields for poiseuille flow through tubes having general cross section are calculated using a path integral method involving the first passage times of random walks in the interior of the cross sectional domain d of the pipe this method is applied to a number of examples where exact results are available and to more complicated geometries of practical interest these examples include a tube with fractal cross section and open channel flows the calculations demonstrate the feasibility of the probabilistic method for pipe flow and other applications having an equivalent mathematical description e g torsional rigidity of rods membrane deflection the example of flow through a fractal pipe shows an extended region of diminished flow velocity near the rough boundary which is similar to the suppressed vibration observed near the boundaries of fractal drums

several iterative methods with memory using self accelerators we derive new iterative methods with memory for approximating a simple zero of a nonlinear single variable function to this end we first consider several modifications on some existing optimal classes without memory in such a way that their extensions to cases with memory could obtain the higher efficiency index 12 1 4 1 86120 furthermore we construct our main method with memory using three self accelerators it is demonstrated that this new scheme possesses the very high efficiency index 7 23814 1 3 1 93438

the leading asymptotic term for the scattering diagram in the problem of diffraction by a narrow circular impedance cone the leading term for the scattering diagram in the scalar problem concerning the diffraction of a plane wave by a narrow circular impedance cone is obtained although up to now the problem cannot be solved in an explicit form its reduction to a non oscillating integral equation has been recently developed it is used here in order to determine formal asymptotics of the scattering diagram by means of a perturbation method

high frequency directed wave propagators a path integral derivation in this paper we derive an approximate high frequency green s function propagator for directed waves scattered in an inhomogeneous medium and governed by a standard parabolic wave equation the analysis is based on a path integral formalism incorporating the ray concept into an approximate description of the diffraction effects although this propagator was obtained earlier by using asymptotic expansions applied to the analysis of an appropriate differential equation the procedure based on the path integral technique is conceptually simpler and also clarifies the physical nature of the approximations performed in the derivation of the final result it is shown that the propagator obtained belongs to a family of well known straight line approximations all of them can be presented in the form of ordinary or paired fresnel transforms of a complex exponential coined here a radon hologram which encodes the scattering potential of the object applications of the high frequency propagators to solving both direct and inverse problems of wave scattering are briefly discussed

a class of optimal eighth order derivative free methods for solving the danchick gauss problem abstract a derivative free optimal eighth order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences its performance along with several other derivative free methods is studied on the specific problem of danchick s reformulation of gauss method of preliminary orbit determination numerical experiments show that such derivative free high order methods offer significant advantages over both the classical and danchick s newton approach