arf numerical semigroups we introduce and study the concept of arf system of generators for an arf numerical semigroup this study allows us to arrange the set of all arf numerical semigroups in a binary tree and enables us to compute the arf closure of a given numerical semigroup

harmonic wavelet analysis a new harmonic wavelet is suggested unlike wavelets generated by discrete dilation equations whose shape cannot be expressed in functional form harmonic wavelets have the simple structure w x exp i4 pi x exp i2 pi x i2 pi x this function w x is concentrated locally around x 0 and is orthogonal to its own unit translations and octave dilations its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain rather than in the x domain an efficient implementation of a discrete transform using this wavelet is based on the fast fourier transform fft fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the fft the same process works backwards for the inverse transform

approximate travelling waves for generalized kpp equations and classical mechanics we consider the existence of approximate travelling waves of generalized kpp equations in which the initial distribution can depend on a small parameter which in the limit 0 is the sum of some functions or a step function using the method of elworthy truman 1982 we construct a classical path which is the backward flow of a classical newtonian mechanics with given initial position and velocity before the time at which the caustic appears by the feynman kac formula and the maruyama girsanov cameron martin transformation we obtain an identity from which with a late caustic assumption we see the propagation of the global wave front and the shape of the trough our theory shows clearly how the initial distribution contributes to the propagation of the travelling wave finally we prove a huygens principle for kpp equations on complete riemannian manifolds without cut locus with some bounds on their volume element in particular cartan hadamard manifolds

stabilized multilevel monte carlo method for stiff stochastic differential equations a multilevel monte carlo mlmc method for mean square stable stochastic differential equations with multiple scales is proposed for such problems that we call stiff the performance of mlmc methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the mlmc approach we show that by switching to explicit stabilized stochastic methods and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of mlmc methods the computational cost for stiff systems is significantly reduced while keeping the computational algorithm fully explicit and easy to implement numerical experiments on linear and nonlinear stochastic differential equations and on a stochastic partial differential equation illustrate the performance of the stabilized mlmc method and corroborate our theoretical findings

wavelet expansion based stochastic response of chain like mdof structures abstract this paper presents a wavelet expansion based approach for response determination of a chain like multi degree of freedom mdof structure subject to full non stationary stochastic excitations specifically the generalized harmonic wavelet ghw is first utilized as the expansion basis to solve the dynamic equation of structures via the galerkin treatment in this way a linear matrix relationship between the deterministic response and excitation can be derived further considering the ghw based representation of the stochastic processes a time varying power spectrum density psd relationship on a certain wavelet scale or frequency band between the excitation and response is derived finally pertinent numerical simulations including deterministic dynamic analysis and monte carlo simulations of both the response psd and the story drift based reliability are utilized to validate the proposed approach

some remarks on pythagorean real curve germs let k be a real closed field a real ap curve over k is a 1 dimensional excellent henselian local real domain with residue field k a 1 dimensional noetherian local ring is arf if emb dim b mult b for every local ring b infinitely near to a j lipman amer j math 93 1971 649 685 for n 1 the 2nth pythagoras number p2n of a commutative ring a is the least p 1 p such that any sum of 2nth powers in a is a sum of no more than p2nth powers in a a main purpose of this paper is to affirm the following conjectures proposed by ruiz j algebra 94 1985 no 1 126 144 let a be a real ap curve and let a be pythagorean i e p2 1 then i a is arf ii every local ring infinitely near to a is pythagorean actually the authors obtain a finer result for a real ap curve a the following assertions are equivalent 1 a is arf 2 a is pythagorean 3 p2n 1 for some n 4 p2n 1 for all n here 2 1 is exactly conjecture i and 1 2 reduces conjecture ii to the obvious fact that if a is arf every local ring infinitely near to a is arf too of course the result contains some additional insight into the study of pythagoras s numbers even of higher order of real curve germs

solving a continuous local access network design problem with a stabilized central column generation approach abstract in this paper we focus on a variant of the multi source weber problem in the multi source weber problem the location of a fixed number of concentrators and the allocation of terminals to them must be chosen to minimize the total cost of links between terminals and concentrators in our variant we have a third hierarchical level two categories of link costs and the number of concentrators is unknown to solve this difficult problem we propose several heuristics and use a new stabilized column generation approach based on a central cutting plane method to provide lower bounds

the coiflet galerkin method for linear volterra integral equations this paper deals with the application of the wavelet galerkin method based on coiflets as a basis for solving linear volterra integral equations vies the main contribution of this work is that some new connection coefficients are introduced and a suitable algorithm is developed for their solution once they have been computed they can be stored and applied to any linear vie the convergence properties of the coiflet galerkin method are analyzed some test examples are presented to illustrate the performance of the method with respect to the error norms and cpu time

poisson voronoi spanning trees with applications to the optimization of communication networks we define a family of random trees in the plane their nodes of level k k 0 m are the points of a homogeneous poisson point process k whereas their arcs connect nodes of level k and k 1 according to the least distance principle if v denotes the voronoi cell w r t k 1 with nucleus x where x is a point of k 1 then there is an arc connecting x to all the points of k that belong to v this creates a family of stationary random trees rooted in the points of m these random trees are useful to model the spatial organization of several types of hierarchical communication networks in relation to these communication networks it is natural to associate various cost functions with such random trees using point process techniques like the exchange formula between two palm measures and integral geometry techniques we show how to compute these average costs as functions of the intensity parameters of the poisson processes the formulas derived for the average value of these cost functions can then be exploited for parametric optimization purposes several applications to classical and mobile cellular communication networks are presented

a proximal cutting plane method using chebychev center for nonsmooth convex optimization an algorithm is developed for minimizing nonsmooth convex functions this algorithm extends elzinga moore cutting plane algorithm by enforcing the search of the next test point not too far from the previous ones thus removing compactness assumption our method is to elzinga moore s algorithm what a proximal bundle method is to kelley s algorithm instead of lower approximations used in proximal bundle methods the present approach is based on some objects regularizing translated functions of the objective function we propose some variants and using some academic test problems we conduct a numerical comparative study with elzinga moore algorithm and two other well known nonsmooth methods

a numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions abstract in this paper we use hat basis functions to solve the system of fredholm integral equations sfies and the system of volterra integral equations svies of the second kind this method converts the system of integral equations into a linear or nonlinear system of algebraic equations also we consider the order of convergence of the method and show that it is o h 2 application of the method on some examples show its accuracy and efficiency

stochastic volterra equations in banach spaces and stochastic partial differential equation abstract in this paper we study the existence uniqueness and large deviation estimate for stochastic volterra integral equations with singular kernels in 2 smooth banach spaces then we apply them to a large class of semilinear stochastic partial differential equations spde and obtain the existence of unique maximal strong solutions in the sense of sde and pde under local lipschitz conditions moreover stochastic navier stokes equations are also investigated

mean square numerical solution of random differential equations facts and possibilities this paper deals with the construction of numerical solutions of random initial value differential problems the random euler method is presented and the conditions for the mean square convergence are established numerical examples show that random euler method gives good results even if the sufficient convergence conditions are not satisfied

on the exact solution of large scale simple plant location problems abstract the simple plant location problem deals with the selection of facility sites from a set of possible locations with the intention of serving a given set of customers from the chosen locations the objective is to minimize the sum of the fixed charges for establishing the facilities and the transportation costs corresponding to the supply of the demands we show how to modify a primal dual version of erlenkotter s exact algorithm to get an improved procedure computational experience with large scale problems indicates that compared with erlenkotter s code an implementation of the modified algorithm is faster by more than one order of magnitude for real life problems with 1500 potential facility sites the increase of computational speed may even exceed the factor of 100

acute semigroups the order bound on the minimum distance and the feng rao improvements we introduce a new class of numerical semigroups which we call the class of acute semigroups and we prove that they generalize symmetric and pseudosymmetric numerical semigroups arf numerical semigroups and the semigroups generated by an interval for a numerical semigroup spl lambda spl lambda sub 0 i spl nu sub i 1 for all i spl ges m we prove that the only numerical semigroups for which the sequence spl nu sub i is always nondecreasing are ordinary numerical semigroups furthermore we show that a semigroup can be uniquely determined by its sequence spl nu sub i

euler schemes and large deviations for stochastic volterra equations with singular kernels in this paper an euler type approximation is constructed for stochastic volterra equation with singular kernels which provides an algorithm for numerical calculation then the large deviation estimates of small perturbation to equations of this type are obtained we finally apply them to sdes with the kernel of fractional brownian motion with hurst parameter h 0 1

convergence analysis of hybrid functions method for two dimensional nonlinear volterra fredholm integral equations abstract an interesting and computationally efficient scheme is proposed for solving a class of two dimensional nonlinear volterra fredholm integral equations the collocation method in conjunction with two dimensional hybrid functions is utilized to convert these types of equations to a nonlinear system of equations that can be solved numerically by the newton s method the major advantages of this method are simplicity of performing and favorable convergence rate for an approximate solution the convergence analysis of the hybrid functions and the error bound of the presented method are discussed in detail moreover some numerical experiments are provided to confirm our theoretical analysis

patterns on numerical semigroups we introduce the notion of pattern for numerical semigroups which allows us to generalize the definition of arf numerical semigroups in this way infinitely many other classes of numerical semigroups are defined giving a classification of the whole set of numerical semigroups in particular all semigroups can be arranged in an infinite non stabilizing ascending chain whose first step consists just of the trivial semigroup and whose second step is the well known class of arf semigroups we describe a procedure to compute the closure of a numerical semigroup with respect to a pattern by using the concept of system of generators associated to a pattern we construct recursively a directed acyclic graph with all the semigroups admitting the pattern

a computational method for solving stochastic ito volterra integral equations based on stochastic operational matrix for generalized hat basis functions abstract in this paper a new computational method based on the generalized hat basis functions is proposed for solving stochastic ito volterra integral equations in this way a new stochastic operational matrix for generalized hat functions on the finite interval 0 t is obtained by using these basis functions and their stochastic operational matrix such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution also the rate of convergence of the proposed method is considered and it has been shown that it is o 1 n 2 further in order to show the accuracy and reliability of the proposed method the new approach is compared with the block pulse functions method by some examples the obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method

solving volterra integral equations of the second kind by wavelet galerkin scheme in this paper we apply the wavelet galerkin method to obtain approximate solutions to linear volterra integral equations vies of the second kind daubechies wavelets are used to find such approximations in this approach we introduce some new connection coefficients and discuss their properties and propose algorithms to evaluate them these coefficients can be computed just once and applied for solving every linear vie of the second kind convergence and error analysis are discussed and numerical examples illustrate the efficiency of the method

a fast algorithm for constructing arf closure and a conjecture abstract in this article we give a fast and an easily implementable algorithm for computing the arf closure of an irreducible algebroid curve or a branch moreover we study the relation between the branches having the same arf closure and their regularity indices we give some results and a conjecture which are steps towards the interpretation of arf closure as a specific way of taming the singularity

optimal homotopy asymptotic method for solving nonlinear fredholm integral equations of second kind abstract the aim of this communication is to present the effectiveness of optimal homotopy asymptotic method oham for solving nonlinear fredholm integral equations of second kind here we consider the first second and third order fredholm integral equations of second kind comparisons are made with adomian decomposition method discrete adomian decomposition method homotopy perturbation method quasi interpolation method triangular functions method trapezoidal rule and simpson rule the results reveal that the oham is very effective simple and has close agreement with exact solutions

a numerical method for solving m dimensional stochastic ito volterra integral equations by stochastic operational matrix the multidimensional ito volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources in this paper we obtain a stochastic operational matrix of block pulse functions on interval 0 1 to solve m dimensional stochastic ito volterra integral equations by using block pulse functions and their stochastic operational matrix of integration m dimensional stochastic ito volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution we prove that the rate of convergence is o h furthermore a 95 confidence interval of the errors mean is made the results shows that the approximate solutions have a credible degree of accuracy

hybrid legendre polynomials and block pulse functions approach for nonlinear volterra fredholm integro differential equations this paper introduces an approach for obtaining the numerical solution of the nonlinear volterra fredholm integro differential nvfid equations using hybrid legendre polynomials and block pulse functions these hybrid functions and their operational matrices are used for representing matrix form of these equations the main characteristic of this approach is that it reduces nvfid equations to a system of algebraic equations which greatly simplifying the problem numerical examples illustrate the validity and applicability of the proposed method

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

an accelerated central cutting plane algorithm for linear semi infinite programming an algorithm for linear semi infinite programming is presented which accelerates the convergence of the central cutting plane algorithm first proposed in 4 compared with other algorithms the algorithm in 4 has the advantage of being applicable under mild conditions and of providing feasible solutions however its convergence has been shown to be rather slow in practical instances the algorithm proposed in this paper introduces a simple acceleration scheme which gives faster convergence as confirmed by several examples as well as an interval of prefixed length containing the optimum value it is also shown that the algorithm provides a solution of the dual problem and that it can be used for convex semi infinite programming too

wavelet galerkin method for numerical solution of nonlinear integral equation in this paper the continues legendre wavelets constructed on the interval 0 1 are used to solve the nonlinear volterra and fredholm integral equation of the second kind the nonlinear part of the integral equation is approximated by legendre wavelets and the nonlinear integral equation is reduced to a system of nonlinear equations numerical examples illustrates the pertinent features of the method

cubic b spline approximation for linear stochastic integro differential equation of fractional order abstract in this paper the cubic b spline collocation method is used for solving the stochastic integro differential equation of fractional order we show that stochastic integro differential equation of fractional order is equivalent to a modified stochastic integral equation then we apply the proposed method to obtain a numerical scheme of the modified stochastic integral equation using this method the problem solving turns into a linear system solution of equations also the convergence analysis of this numerical approach has been discussed in the end examples are given to test the accuracy and the implementation of the method the results are compared with the results obtained by other methods to verify that this method is accurate and efficient

an iterative numerical method for fredholm volterra integral equations of the second kind in this paper we propose a simple numerical method for approximating solutions of fredholm volterra integral equations of the second kind the method is based on picard iteration and uses a suitable quadrature formula under certain conditions we prove the existence and uniqueness of the solution and give error estimates for our approximations the paper concludes with numerical examples and a discussion of the approximations proposed

numerical approach for solving stochastic volterra fredholm integral equations by stochastic operational matrix in this paper we obtain stochastic operational matrix of block pulse functions on interval 0 1 to solve stochastic volterra fredholm integral equations by using block pulse functions and their stochastic operational matrix of integration the stochastic volterra fredholm integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution we prove that the rate of convergence is o h furthermore the results show that the approximate solutions have a good degree of accuracy

an efficient computational method for solving nonlinear stochastic ito integral equations because of the nonlinearity closed form solutions of many important stochastic functional equations are virtually impossible to obtain thus numerical solutions are a viable alternative in this paper a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of ito integration is proposed for solving nonlinear stochastic ito integral equations in large intervals in the proposed method a new technique for computing nonlinear terms in such problems is presented the main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples the obtained results reveal that the proposed method is very accurate and efficient as two useful applications the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem

on the complexity of some common geometric location problems given n demand points in the plane the p center problem is to find p supply points anywhere in the plane so as to minimize the maximum distance from a demand point to its respective nearest supply point the p median problem is to minimize the sum of distances from demand points to their respective nearest supply points we prove that the p center and the p median problems relative to both the euclidean and the rectilinear metrics are np hard in fact we prove that it is np hard even to approximate the p center problems sufficiently closely the reductions are from 3 satisfiability

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

harmonic wavelet method towards solution of the fredholm type integral equations of the second kind periodic harmonic wavelets phw were applied as basis functions in solution of the fredholm integral equations of the second kind two equations were solved in order to find out advantages and disadvantages of such choice of the basis functions it is proved that phw satisfy the properties of the multiresolution analysis