periodic boundary data for an integrable model of stimulated raman scattering long time asymptotic behavior we study the long time asymptotic behavior of the solution to the initial boundary value ibv problem in the quarter plane x 0 t 0 for nonlinear integrable equations of stimulated raman scattering we consider the case of zero initial condition and periodic boundary data p e i t using the steepest descent method for oscillatory matrix riemann hilbert problems we show that the solution of the ibv problem has different asymptotic behavior in different regions the solution takes the form of a plane wave of finite amplitude when 0 2 t for the ibv problem with nonzero initial condition and the same periodic boundary data the solution to this problem is qualitatively similar to that of this study with the only difference that the solitons of finite amplitude can appear in the region x 2 t

long time behavior of the solution to the mkdv equation with step like initial data we consider the modified korteweg de vries equation on the line the initial data is the pure step function i e q x 0 cr for x 0 and q x 0 cl for x cr 0 are arbitrary real numbers long time behavior of the solution to the mkdv equation in the case cl cr 0 and t was studied recently in kotlyarov and minakov 2010 j math phys 51 093506 where the structure of the compression wave was obtained in the form of a modulated elliptic wave the goal of this paper is to study the asymptotic behavior of the solution of the initial value problem as t i e we study the long time dynamics of the rarefaction wave using the steepest descent method and the so called g function mechanism we deform the original oscillatory matrix riemann hilbert problem to the explicitly solvable model forms and show that the solution of the initial value problem has a different asymptotic behavior in different regions of the xt plane in the regions x 6c2rt the main term of asymptotics of the solution is equal to cl and cr respectively in the region the asymptotics of the solution tends to an influence of the dispersion is also studied the second term of the asymptotics is obtained in the region x 6c2rt where the background constant cr is perturbed by the self similar vanishing wave

homogenization of the acoustic transmission through a perforated layer the paper deals with homogenized transmission conditions imposed on an interface plane separating two halfspaces occupied by an acoustic medium the conditions are obtained as the two scale homogenization limit of a standard acoustic problem imposed on the layer perforated by a sieve like obstacle with a periodic structure both the characteristic scale of the perforations and the layer thickness are parametrized by e 0 the limit model involving some homogenized coefficients governs the interface discontinuity of the acoustic pressure associated with the two halfspaces and the magnitude of the transverse acoustic velocity this novel approach allows for the treatment of complicated designs of perforations and presents an alternative to the usual description of acoustic impedance which relies on a rough averaging of the quasi experimental data

modulated elliptic wave and asymptotic solitons in a shock problem to the modified korteweg de vries equation we study the long time asymptotic behavior of the cauchy problem for the modified korteweg de vries equation with an initial function of the step type this function rapidly tends to zero as and to some positive constant c as in 1989 khruslov and kotlyarov have found khruslov and kotlyarov 1989 inverse problems 5 1075 88 that for a large time the solution breaks up into a train of asymptotic solitons located in the domain is a constant the number n of these solitons grows unboundedly as in 2010 kotlyarov and minakov have studied temporary asymptotics of the solution of the cauchy problem on the whole line kotlyarov and minakov 2010 j math phys 51 093506 and have found that in the domain this solution is described by a modulated elliptic wave we consider here the modulated elliptic wave in the domain our main result shows that the modulated elliptic wave also breaks up into solitons which are similar to the asymptotic solitons in khruslov and kotlyarov 1989 inverse problems 5 1075 88 but differ from them in phase it means that the modulated elliptic wave does not represent the asymptotics of the solution in the domain the correct asymptotic behavior of the solution is given by the train of asymptotic solitons given in khruslov and kotlyarov 1989 inverse problems 5 1075 88 however in the asymptotic regime as in the region we can watch precisely a pair of solitons with numbers n one of them is the asymptotic soliton while the other soliton is generated from the elliptic wave their phases become closer to each other for a large n i e these solitons are also close to each other this result gives the answer on a very important question about matching of the asymptotic formulas in the mentioned region where the both formulas are well defined thus we have here a new and previously unknown mechanism 5 35 of matching of the asymptotics of the solution in the adjacent regions

the low frequency spectrum of small helmholtz resonators we analyse the spectrum of the laplace operator in a complex geometry representing a small helmholtz resonator the domain is obtained from a bounded set r n by removing a small obstacle e of size e 0 the set e essentially separates an interior domain e inn the resonator volume from an exterior domain e out but the two domains are connected by a thin channel for an appropriate choice of the geometry we identify the spectrum of the laplace operator it coincides with the spectrum of the laplace operator on but contains an additional eigenvalue e 1 we prove that this eigenvalue has the behaviour e v e l e a e where v e is the volume of the resonator l e is the length of the channel and a e is the area of the cross section of the channel this justifies the well known frequency formula hr c 0 a l v for helmholtz resonators where c 0 is the speed of sound

feedforward artificial neural networks for solving discrete multiple criteria decision making problems decision making involves choosing some course of action among various alternatives in almost all decision making problems there are several criteria for judging possible alternatives the main concern of the decision maker dm is to fulfill his conflicting goals while satisfying the constraints of the system in this paper we present an adaptive feedforward artificial neural network af ann approach to solve discrete multiple criteria decision making mcdm problems the af ann is used to capture and represent the dm s preferences and then to select the most desirable alternative the af ann can adjust and improve its representation as more information from the dm becomes available we begin with the assumption that an af ann topology is given i e specific numbers of nodes and links are predetermined to adjust the parameters of the af ann we present an iterative learning algorithm consisting of two steps a generating a direction and b a one dimensional search along that direction we then present a methodology to obtain the most appropriate af ann topology and set its parameters the procedure starts with a small number of nodes and links and then adaptively increases the number of nodes and links until the proper topology is obtained furthermore when the set of training patterns alternatives with their associated evaluations by the dm changes the af ann model can adapt itself by re training or expanding the existing model some illustrative examples are presented to solve discrete mcdm problems by an af ann we show how to incorporate basic properties of efficiency concavity and convexity into the af ann we formulate the mcdm problems and use the af ann to rank the set of discrete alternatives where each alternative is associated with a set of conflicting and noncommensurate criteria we present a method for solving discrete mcdm problems through af anns which consists of a formulating and assessing the utility function by eliciting information from the dm and then training the af ann and b ranking a rating alternatives by using the trained af ann model some computational experiments are presented to show the effectiveness of the method

generalized polynomial decomposable multiple attribute utility functions for ranking and rating multiple criteria discrete alternatives1all rights reserved this study or parts thereof may not be reproduced in any form without the written permission of the authors 1 this paper describes a class of nonlinear polynomial functions which are far more complex than linear and additive functions and other types of well known utility functions although the assessment of such nonlinear polynomial functions may require more time and possibly more cognitive burden the advantage of using more complex and nonlinear functions is that more complex preferential behaviors can be represented and hence a larger set of decision problems can be solved in this paper we develop a generalized decomposable multiattribute utility function gdmauf for representing the decision maker s dm s preferential behavior we show that any polynomial function can be represented by the gdmauf and that such a function can be assessed to represent the dm s behavioral preferences or so called the utility function our approach is based on the use of holistic responses numerical rankings and rating of alternatives from which we assess the gradients of the dm s unknown utility function from assessed gradients we then construct a generalized decomposable multiattribute utility function that mimics and represent the dm s preferential behavior this assessed generalized decomposable multiattribute utility function can be used directly to rank and rate all alternatives without any further interaction from the dm we also demonstrate that the generalized utility function gdmauf is more general and flexible than some other well known utility structures such as additive multiplicative multilinear quasi concave and quasi convex the underlying assumptions for gdmauf are that it is differentiable and that it can be expressed in a polynomial form some classes extensions and properties of the generalized utility function are explored to simplify its assessment several examples and experimental results are provided

a combined tchebycheff aspiration criterion vector interactive multiobjective programming procedure in this paper we combine the tchebycheff method of steuer and choo with wierzbicki s aspiration criterion vector method in order to form an improved procedure for interactive multiple objective programming the combined procedure is sensible because the tchebycheff and aspiration criterion vector methods possess complementary distinguishing characteristics solve similar optimization problems to probe the nondominated set and share a similar computer user interface in the early iterations tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search in later iterations aspiration criterion vector probes might be used to pinpoint a final solution computational experience is reported showing the improved effectiveness of the combined procedure when employed in this fashion when compared against the tchebycheff and aspiration criterion vector methods run separately

shape optimization of an acoustic horn the shape of an acoustic horn is optimized with respect to its ability to provide impedance matching to the surrounding air the resulting minimization problem is solved using a bfgs quasi newton algorithm the wave propagation is modeled by a finite element approximation of the helmholtz equation and the necessary objective function gradient is calculated from the solution of the associated adjoint equation local solutions to the optimization problem corresponding to irregular horn contours are avoided by using a filtering technique that applies smoothing to the design updates and the gradient the method converges fast to a smooth solution and the resulting horn has good impedance properties throughout the entire frequency band of interest

an approach to multiple attribute decision making based on fuzzy preference information on alternatives this paper investigates the multiple attribute decision making madm problem with preference information on alternatives a new approach is proposed to solve the madm problem where the decision maker gives his her preference on alternatives in a fuzzy relation to reflect the decision maker s preference information an optimization model is constructed to assess the attribute weights and then to select the most desirable alternatives finally an example is used to illustrate the proposed approach

an interactive branch and bound algorithm for multiple criteria optimization we present a new interactive algorithm for multiple criteria optimization the algorithm is of the branch and bound type and differs from previous interactive algorithms in several ways first the field of application is wider because it applies to two important classes of multiple criteria decision problems those for which the feasible set is convex and those for which the feasible set is discrete secondly the algorithm does not require a great deal from the decision maker he is merely required to indicate his preference between two vectors whenever the algorithm so demands

computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths the acoustic modelling of automotive exhaust devices such as catalytic converters cc and diesel particulate filters dpf usually requires the use of multidimensional analytical and numerical techniques the presence of higher order modes and three dimensional waves in the expansion and contraction subdomains as well as sound propagation within the monolith capillary ducts can be considered through the finite element method fem although this approach is traditionally thought to be very time consuming with a view to overcome this limitation and to reduce the computational effort of the fem alternative modelling techniques are presented in the current work to speed up transmission loss calculations in exhaust devices incorporating monoliths these approaches are based on the point collocation technique and the mode matching method as shown in earlier studies the sound attenuation of an exhaust device incorporating a monolith can be properly predicted if the latter is replaced by a plane wave four pole transfer matrix providing a relationship between the acoustic fields at both sides of the monolithic region therefore this work combines the presence of multidimensional higher order modes in the expansion and contraction regions with one dimensional wave propagation within the capillary ducts of the central monolith the point collocation technique and the mode matching method are applied to the compatibility conditions of the acoustic fields at all the subdomain interfaces to couple the solutions of the wave equation in the corresponding exhaust device subcomponents for the particular case of rigid circular ducts bessel functions are considered as transversal pressure modes the computational efficiency and accuracy of the results associated with the two analytical modelling techniques presented here are assessed including the effect of the number of modes and collocation points as well as their location all the analytical approaches proposed in this work provide accurate predictions of the device attenuation performance and outperform the computational expenditure of a fe computation some differences are found however among the various analytical schemes in terms of computational speed and solution accuracy from the results presented here the mode matching method is the most efficient technique for the particular configurations under study mainly due to the possibility of exploiting the orthogonality properties of the transverse pressure modes analytical techniques are proposed to speed up tl calculations in exhaust devices with monoliths multidimensional sound propagation in the ducts is combined with plane waves in the capillaries the computational effort and accuracy of the analytical approaches is compared

approximating polynomial functions by feedforward artificial neural networks capacity analysis and design polynomial functions are used in many applications in this paper we address the capacity of feedforward artificial neural networks fanns in approximating polynomial functions instead of studying the capacity of a fann with infinitely available hidden nodes which was proved to be a universal approximator we provide the capacity results of a fann with finite hidden nodes in approximating polynomial functions first we show that there is a relationship between the capacity of a fann in approximating polynomial functions and the number of hidden nodes used in the fann then we describe a procedure to realize a fann in approximating polynomial functions two examples are given to show the procedure several experiments are reported which verifies that a fann with a certain number of hidden nodes has the capability in learning given polynomial functions an extension of the approach for solving multiple criteria decision making problems is discussed the experiments also show that the proposed algorithm for training a fann performs accurately

acoustic fluid flow through holes and permeability of perforated walls abstract we first study the unsteady incompressible fluid flow through a hole in a wall in the two and three dimensional cases in the first case a convolution relation is obtained between the fluid flux through the hole and the difference of pressure between the far regions on the two sides of the wall in the two dimensional case the pressure increases logarithmically with distance from the wall in a second part we study acoustic flow in a domain containing a wall with many small holes the distance between two contiguous holes is of order and the size of each hole e and e are two small parameters in the three dimensional case the critical behaviour appears for e 2 it is described by a convolution relation between the flow through the wall and the jump of pressure in the two dimensional case the critical behaviour appears if log e tends to a constant there is a differential relation between the flow through the wall and the jump of pressure

point collocation scheme in silencers with temperature gradient and mean flow this work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow three dimensional wave propagation is considered in silencer geometries with arbitrary but axially uniform cross section to reduce the computational requirements of a full multidimensional finite element calculation a method is developed combining axial and transversal solutions of the wave equation first the finite element method is employed in a two dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section mean flow as well as transversal temperature gradients and the corresponding thermal induced material heterogeneities are included in the model in addition an axially uniform temperature field is taken into account its value being the inlet outlet average a point collocation technique is then used to match the acoustic fields pressure and axial acoustic velocity at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes transmission loss predictions are compared favorably with a general three dimensional finite element approach offering a reduction in the computational effort sound attenuation in perforated dissipative silencers including temperature gradients and mean flow is computed a two dimensional finite element eigenvalue problem is solved for a silencer cross section with transversal thermal variations a point collocation scheme is presented to match the acoustic pressure and axial velocity at the silencer geometrical discontinuities a significant reduction in the computational requirements is obtained compared to a full three dimensional finite element approach

asymptotics of step like solutions for the camassa holm equation abstract we study the long time asymptotics of solution of the cauchy problem for the camassa holm equation with a step like initial datum by using the nonlinear steepest descent method and the so called g function approach we show that the camassa holm equation exhibits a rich structure of sharply separated regions in the x t half plane with qualitatively different asymptotics which can be described in terms of a modulated finite gap elliptic function and a finite number of solitons

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

a new riemann hilbert problem in a model of stimulated raman scattering the riemann hilbert problem proposed in 2 for the integrable stimulated raman scattering srs model was shown to be solvable under an additional condition the boundary data have to be chosen in such a way that a corresponding spectral problem has no spectral singularities in the general case it can be shown that a spectral singularity occurs at k 0 on the other hand the initial boundary value ibv problem for the srs equations is known to be well posed using pde techniques this has been established in 3 therefore it seems natural to try to find a new rh problem that is solvable in the presence of arbitrary spectral singularities the formulation of such a rh problem is the main aim of the paper then the solution of the nonlinear initial boundary value problem for the srs equations is expressed in terms of the solution of a linear problem which is the riemann hilbert problem for a sectionally analytic matrix function

bvp s with odd differences of gaps in boundary conditions for nth order ode s by matching solutions matching of solutions of boundary value problems plays an important role in interface problems we are concerned with the existence and uniqueness of solutions to boundary value problems on an interval a c for the nth order ordinary differential equation y n f x y y y n 1 for n 3 by matching solutions on a b with solutions on b c in this paper we consider a general case where the gap in boundary conditions at b is odd different monotonicity conditions on f are imposed for distinct cases that arise

long time asymptotics of the nonlinear schrodinger equation shock problem the long time asymptotics of two colliding plane waves governed by the focusing nonlinear schrodinger equation are analyzed via the inverse scattering method we find three asymptotic regions in space time a region with the original wave modified by a phase perturbation a residual region with a one phase wave and an intermediate transition region with a modulated two phase wave the leading order terms for the three regions are computed with error estimates using the steepest descent method for riemann hilbert problems the nondecaying initial data requires a new adaptation of this method a new breaking mechanism involving a complex conjugate pair of branch points emerging from the real axis is observed between the residual and transition regions also the effect of the collision is felt in the plane wave state well beyond the shock front at large times 2007 wiley periodicals inc

numerical modeling of the acoustic wave propagation across a homogenized rigid microstructure in the time domain homogenization of a thin micro structure yields effective jump conditions that incorporate the geometrical features of the scatterers these jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded this paper aims i to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain ii to inspect the validity of the homogenized problem when compared to the real one for this purpose we adapt an immersed interface method originally developed for standard jump conditions across a zero thickness interface doing so allows us to handle arbitrary shaped interfaces on a cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in an homogeneous medium numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

selecting subsets from the set of nondominated vectors in multiple objective linear programming in this paper we develop methods for selecting certain subsets from the set n of nondominated points for multiple objective linear programming problems one such subset is the set of a points x in n for which the maximum deviation of the objective function values c x from some ideal vector m is as small as possible this subset can be obtained as the set of nondominated points for a multiple objective problem that is considerably smaller than the original problem and the proposed method does not require that the set n be calculated explicitly the method is extended to obtain another subset of n called the trade off compromise set that has some interesting properties and that gives valuable information about possible trade offs amongst the objectives

nonessential objectives within network approaches for mcdm in gal and hanne eur j oper res 119 1999 373 the problem of using several methods to solve a multiple criteria decision making mcdm problem with linear objective functions after dropping nonessential objectives is analyzed it turned out that the solution does not need be the same when using various methods for solving the system containing the nonessential objectives or not in this paper we consider the application of network approaches for multicriteria decision making such as neural networks and an approach for combining mcdm methods called mcdm networks we discuss questions of comparing the results obtained with several methods as applied to the problem with or without nonessential objectives especially we argue for considering redundancies such as nonessential objectives as a native feature in complex information processing in contrast to previous results on nonessential objectives the current paper focuses on discrete mcdm problems which are also denoted as multiple attribute decision making madm