an application of convergence acceleration methods it is pointed out that certain convergence acceleration methods can be applied to sequences of driving point conductances obtained by solving hallen s equation numerically five easily applied methods are considered and all seem to greatly improve convergence reasons for having confidence in the resulting extrapolations are discussed

optimum lopsided binary trees binary search trees with costs and respectively on the left and right edges lopsided search trees are considered the exact shape minimum worst case cost and minimum average cost of lopsided trees of n internal nodes are determined for nonnegative and the costs are both roughly log p n 1 where p is the unique real number in the interval 1 2 satisfying 1 p 1 p 1 search procedures are given that come within a small additive constant of the lower bounds almost optimum algorithms for the lopsided case of unbounded searching are also obtained some extensions to nonconstant costs are briefly sketched

analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions abstract the localized method of fundamental solutions lmfs is an efficient meshless collocation method that combines the concept of localization and the method of fundamental solutions mfs the resultant system of linear algebraic equations in the lmfs is sparse and banded and thus drastically reduces the storage and computational burden of the mfs in the lmfs the moving least square mls approximation based on fundamental solutions is used to construct approximate solution at each node in this paper this fundamental solutions based mls approximation named as an augmented mls amls approximation is generalized to any point in the computational domain computational formulas theoretical properties and error estimates of the amls approximation are derived then taking laplace equation as an example this paper sets up a framework for the theoretical error analysis of the lmfs finally numerical results are presented to verify the efficiency and theoretical results of the amls approximation and the lmfs convergence and comparison researches are conducted to validate the accuracy convergence and efficiency

generalized finite difference method for solving stationary 2d and 3d stokes equations with a mixed boundary condition abstract in the present work a generalized finite difference method gfdm a meshless method based on taylor series approximations is proposed to solve stationary 2d and 3d stokes equations to overcome the troublesome pressure oscillation in the stokes problem a new simple formulation of boundary condition for the stokes problem is proposed this numerical approach only adds a mixed boundary condition the projections of the momentum equation on the boundary outward normal vector to the stokes equations without any other change to the governing equations the proposed formulation can be easily discretized by the gfdm the gfdm is evolved from the taylor series expansions and moving least squares approximation and the derivative expressed of unknown variables as linear combinations of function values of neighboring nodes numerical examples are utilized to verify the feasibility of the proposed gfdm scheme not only for the stokes problem but also for more involved and general problems such as the poiseuille flow the couette flow and the navier stokes equations in low reynolds number regime moreover numerical results and comparisons show that using the gfdm to solve the proposed formulation of the stokes equations is more accurate than the classical formulation of the pressure poisson equation

coding with digits of unequal cost at present optimal coding for a noiseless digital channel with digits of unequal cost requires solving a large linear programming problem much simpler procedures give codes resembling shannon s 1948 and huffman s that are found close to optimal in tests with typical sources and channels

solving parabolic and hyperbolic equations by the generalized finite difference method classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics an evolution of the method of finite differences has been the development of generalized finite difference gfd method that can be applied to irregular grids of points in this paper the extension of the gfd to the explicit solution of parabolic and hyperbolic equations has been developed for partial differential equations with constant coefficients in the cases of considering one two or three space dimensions the convergence of the method has been studied and the truncation errors over irregular grids are given different examples have been solved using the explicit finite difference formulae and the criterion of stability this has been expressed in function of the coefficients of the star equation for irregular clouds of nodes in one two or three space dimensions the numerical results show the accuracy obtained over irregular grids this paper also includes the study of the maximum local error and the global error for different examples of parabolic and hyperbolic time dependent equations

a stabilized mlpg method for steady state incompressible fluid flow simulation in this paper the meshless local petrov galerkin mlpg method is extended to solve the incompressible fluid flow problems the streamline upwind petrov galerkin supg method is applied to overcome oscillations in convection dominated problems and the pressure stabilizing petrov galerkin pspg method is applied to satisfy the so called babuska brezzi condition the same stabilization parameter t t s u p email protected p s p g is used in the present method the circle domain of support linear basis and fourth order spline weight function are applied to compute the shape function and bubnov galerkin method is applied to discretize the pdes the lid driven cavity flow backward facing step flow and natural convection in the square cavity are applied to validate the accuracy and feasibility of the present method the results show that the stability of the present method is very good and convergent solutions can be obtained at high reynolds number the results of the present method are in good agreement with the classical results it also seems that the present method which is a truly meshless is very promising in dealing with the convection dominated problems

a generalized element free galerkin method for stokes problem abstract a generalized element free galerkin gefg method is developed in this paper for solving stokes problem in primitive variable form to obtain stable numerical results for both velocity and pressure extended terms are only introduced into the approximate space of velocity in a special way as that in the generalized finite element method theoretical analysis shows that the gefg method implies a stabilized formulation similar to that in the variational multiscale element free galerkin vmefg method numerical results show the efficiency of the present method and reveal that both computational errors and cpu times of the present method are less than those of the vmefg and the finite element methods

a stabilized and coupled meshfree meshbased method for the incompressible navier stokes equations part ii coupling in part i of this work meshfree galerkin methods have been used for the approximation of the incompressible navier stokes equations in eulerian or arbitrary lagrangian eulerian formulation the problem of stabilization of meshfree methods is addressed there analogously in the meshbased context the finite element method is frequently used in similar stabilized formulations for the simulation of flow problems in order to combine the advantages of both methods different coupling techniques are examined in this part of the work standard coupling approaches are modified in order to fulfill the requirements for a reliable stabilization found in part i of this work the resulting stabilized and coupled meshfree meshbased flow solver employs the comparatively costly meshfree galerkin method only where it is needed i e in areas of the domain where a mesh is difficult to maintain and the efficient meshbased finite element method in the rest of the domain this enables the solution of complex flow problems as thus involving large deformations of the physical domain and or moving and rotating obstacles

on the application of numerical methods to hallen s equation the so called hallen integral equation for the current on a finite linear antenna center driven by a delta function generator takes two forms depending on the choice of kernel the two kernels are usually referred to as the exact and the approximate or reduced kernel with the approximate kernel the integral equation has no solution nevertheless the same numerical method is often applied to both forms of the integral equation in this paper the behavior of the numerical solutions thus obtained is investigated and the similarities and differences between the two numerical solutions are discussed the numerical method is galerkin s method with pulse functions we first apply this method to the two corresponding forms of the integral equation for the current on a linear antenna of infinite length in this case the method yields an infinite toeplitz system of algebraic equations in which the width of the pulse basis functions enters as a parameter the infinite system is solved exactly for nonzero pulse width the exact solution is then developed asymptotically for the case where the pulse width is small when the asymptotic expressions for the case of the infinite antenna are used as a guide for the behavior of the solutions of the finite antenna the latter problem is greatly facilitated for the approximate kernel the main results of this paper carry over to a certain numerical method applied to the corresponding equation of the pocklington type

solving second order non linear elliptic partial differential equations using generalized finite difference method the generalized finite difference method gfdm has been proved to be a good meshless method to solve several linear partial differential equations pde s wave propagation advection diffusion plates beams etc the gfdm allows us to use irregular clouds of nodes that can be of interest for modelling non linear elliptic pde s this paper illustrates that the gfd explicit formulae developed to obtain the different derivatives of the pde s are based on the existence of a positive definite matrix that it is obtained using moving least squares approximation and taylor series development also it is shown that in 2d a regular neighbourhood of eight nodes can be regarded as a generalization of a classical finite difference formula with a sixth order truncation error this paper shows the application of the gfdm to solving different non linear problems including applications to heat transfer acoustics and problems of mass transfer

more efficient algorithms and analyses for unequal letter cost prefix free coding there is a large literature devoted to the problem of finding an optimal min cost prefix free code with an unequal letter cost encoding alphabet of size while there is no known polynomial time algorithm for solving it optimally there are many good heuristics that all provide additive errors to optimal the additive error in these algorithms usually depends linearly upon the largest encoding letter size this paper was motivated by the problem of finding optimal codes when the encoding alphabet is infinite because the largest letter cost is infinite the previous analyses could give infinite error bounds we provide a new algorithm that works with infinite encoding alphabets when restricted to the finite alphabet case our algorithm often provides better error bounds than the best previous ones known

huffman coding with letter costs a linear time approximation scheme we give a polynomial time approximation scheme for the generalization of huffman coding in which codeword letters have nonuniform costs as in morse code where the dash is twice as long as the dot the algorithm computes a 1 epsilon approximate solution in time o n f epsilon log 3n where n is the input size

the mini mixed finite element for the stokes problem an experimental investigation abstract o h 3 2 superconvergence in pressure and velocity has been experimentally investigated for the two dimensional stokes problem discretized with the mini mixed finite element even though the classic mixed finite element theory for the mini element guarantees linear convergence for the total error recent theoretical results indicate that superconvergence of order o h 3 2 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured three directional triangular meshes the numerical experiments presented here suggest a more general validity of o h 3 2 superconvergence possibly to automatically generated and unstructured triangulations in addition the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise linear part of the computed velocity finding that the former is generally closer to the exact velocity whereas the latter conserves mass better

a novel dna sequence similarity calculation based on simplified pulse coupled neural network and huffman coding abstract a novel method for the calculation of dna sequence similarity is proposed based on simplified pulse coupled neural network s pcnn and huffman coding in this study we propose a coding method based on huffman coding where the triplet code was used as a code bit to transform dna sequence into numerical sequence the proposed method uses the firing characters of s pcnn neurons in dna sequence to extract features besides the proposed method can deal with different lengths of dna sequences first according to the characteristics of s pcnn and the dna primary sequence the latter is encoded using huffman coding method and then using the former the oscillation time sequence ots of the encoded dna sequence is extracted simultaneously relevant features are obtained and finally the similarities or dissimilarities of the dna sequences are determined by euclidean distance in order to verify the accuracy of this method different data sets were used for testing the experimental results show that the proposed method is effective

boundary conditions involving pressure for the stokes problem and applications in computational hemodynamics pressure driven flows typically occur in hydraulic networks e g oil ducts water supply biological flows microfluidic channels etc however stokes and navier stokes problems are most often studied in a framework where dirichlet type boundary conditions on the velocity field are imposed thanks to the simpler settings from the theoretical and numerical points of view in this work we propose a novel formulation of the stokes system with pressure boundary condition together with no tangential flow on a part of the boundary in a standard stokes functional framework using lagrange multipliers to enforce the latter constraint on velocity more precisely we carry out i a complete analysis of the formulation from the continuous to discrete level in two and three dimensions ii the description of our solution strategy iii a verification of the convergence properties with an analytic solution and finally iv three dimensional simulations of blood ow in the cerebral venous network that are in line with in vivo measurements and the presentation of some performance metrics with respect to our solution strategy

the generalized finite difference method for long time dynamic modeling of three dimensional coupled thermoelasticity problems abstract in this study a new framework for the efficient and accurate solutions of three dimensional 3d dynamic coupled thermoelasticity problems is presented in our computations the krylov deferred correction kdc method a pseudo spectral type collocation technique is introduced to perform the large scale and long time temporal simulations the generalized finite difference method gfdm a relatively new meshless method is then adopted to solve the resulting boundary value problems the gfdm uses the taylor series expansions and the moving least squares approximation to derive explicit formulae for the required partial derivatives of unknown variables the method thus is truly meshless that can be applied for solving problems merely defined over irregular clouds of points for problem with complicated geometries this paper also examines a new distance criterion for adaptive selection of nodes in the gfdm simulations preliminary numerical experiments show that the kdc accelerated gfdm methods are very promising for accurate and efficient long time and large scale dynamic simulations

prefix codes equiprobable words unequal letter costs we consider the following variant of huffman coding in which the costs of the letters rather than the probabilities of the words are nonuniform given an alphabet of r letters em of nonuniform length find a minimum average length prefix free set of n codewords over the alphabet equivalently find an optimal r ary search tree with n leaves where each leaf is accessed with equal probability but the cost to descend from a parent to its i th child depends on i we show new structural properties of such codes leading to an o n log 2 r time algorithm for finding them this new algorithm is simpler and faster than the best previously known o nr min log n r time algorithm due to perl garey and even em j assoc comput mach 22 1975 pp 202 214

a dynamic programming algorithm for constructing optimal prefix free codes with unequal letter costs we consider the problem of constructing prefix free codes of minimum cost when the encoding alphabet contains letters of unequal length the complexity of this problem has been unclear for thirty years with the only algorithm known for its solution involving a transformation to integer linear programming we introduce a new dynamic programming solution to the problem it optimally encodes n words in o n sup c 2 time if the costs of the letters are integers between 1 and c while still leaving open the question of whether the general problem is solvable in polynomial time our algorithm seems to be the first one that runs in polynomial time for fixed letter costs

the universal current distribution near the end of a tubular antenna an asymptotic solution for the charge density and current near the end of a linear tubular antenna is obtained by means of the wiener hopf technique it is found that due to the charge repulsion effect the distributions of charge per unit length and of current within a distance of the order of the radius from the end are significantly different from the sinusoidal distributions that are the solutions from approximate theories furthermore the relative distributions are independent of the length of the antenna and of the frequency of operation

the generalized finite difference method for the inverse cauchy problem in two dimensional isotropic linear elasticity abstract in this study the generalized finite difference method gfdm was used to stably and accurately solve two dimensional 2d inverse cauchy problems in linear elasticity by using the navier equations in cauchy problems overdetermined boundary conditions are imposed on parts of the boundary whereas there are missing boundary conditions on some parts of the boundary in cauchy problems conventional numerical methods generally generate highly ill conditioned matrices and thus provide unstable numerical solutions moreover even if a slight noise is added in the boundary conditions numerical errors are evidently magnified the gfdm one of the most promising meshless methods and an extension of the classical finite difference method can avoid time consuming tasks of mesh generation and numerical quadrature the gfdm was applied in this study to stably solve the 2d cauchy problems in linear elasticity and four numerical examples are provided to illustrate the consistency and accuracy of the presented meshless numerical scheme moreover the stability of the presented scheme for inverse cauchy problems was proved by adding noise into the boundary conditions

application of the generalized finite difference method to solve the advection diffusion equation the study of the advection diffusion equation continues to be an active field of research the subject has important applications to fluid dynamics as well as many other branches of science and engineering this paper shows the application of the generalized finite difference method to solve the advection diffusion equation by the explicit method the convergence of the method has been studied and the truncation error over irregular grids is given an example has been solved using the explicit finite difference formulae and the criterion of stability

iterative methods for stokes flow under nonlinear slip boundary condition coupled with the heat equation abstract we study two iterative schemes for the finite element approximation of the heat equation coupled with stokes flow under nonlinear slip boundary conditions of friction type the iterative schemes are based on uzawa s algorithm in which we decouple the computation of the velocity and pressure from that of the temperature by means of linearization we derive some a priori estimates and prove convergence of these schemes the theoretical results obtained are validated by means of numerical simulations

a meshfree generalized finite difference method for surface pdes abstract in this paper we propose a novel meshfree generalized finite difference method gfdm approach to discretize pdes defined on manifolds derivative approximations for the same are done directly on the tangent space in a manner that mimics the procedure followed in volume based meshfree gfdms as a result the proposed method not only does not require a mesh it also does not require an explicit reconstruction of the manifold in contrast to some existing methods it avoids the complexities of dealing with a manifold metric while also avoiding the need to solve a pde in the embedding space a major advantage of this method is that all developments in usual volume based numerical methods can be directly ported over to surfaces using this framework we propose discretizations of the surface gradient operator the surface laplacian and surface diffusion operators possibilities to deal with anisotropic and discontinuous surface properties with large jumps are also introduced and a few practical applications are presented