mixed perfectly matched layers for direct transient analysis in 2d elastic heterogeneous media abstract we are concerned with elastic waves arising in plane strain problems in an elastic semi infinite arbitrarily heterogeneous medium specifically we discuss the development of a new mixed displacement stress formulation for forward elastic wave simulations in perfectly matched layer pml truncated heterogeneous media to date most pml formulations split the displacement and stress fields resulting in non physical components for each field in this work we favor unsplit schemes primarily for the relative ease by which the resulting forms can be incorporated into existing codes the ease by which the resulting semi discrete forms can be integrated in time and the ease by which they can be used in adjoint formulations arising in inverse problems contrary to most past and current developments we start by following classical lines and apply complex coordinate stretching to the governing equations in the frequency domain while retaining both displacements and stress quantities as unknowns with the aid of auxiliary variables the resulting mixed form is rendered second order in time thereby allowing the use of standard time integration schemes we report on numerical simulations demonstrating the stability and efficacy of the approach

the clebsch gordan coefficients for the two parameter quantum algebra sup q 2 in the lowdin shapiro approach the structure of the irreducible representations of the two parameter quantum algebra sup q 2 is studied the projection operators for this algebra are constructed in the lowdin shapiro form the explicit analytical expressions for the sup q 2 clebsch gordan coefficients are obtained with the help of these projection operators there are clear perspectives to elaborate the theory of tensor operators universal r matrix 6j 9j symbols etc for the sup q 2 algebra using the same tools

a p q oscillator realization of two parameter quantum algebras it is noted that the study of a quantum algebra sup q 2 with two independent deformation parameters p q leads to a p q oscillator realization for it the analysis is extended to the p q analogues of su 1 1 osp 2 1 and the centreless virasoro algebra the standard single parameter q deformations are obtained in the limit p q

application of the perfectly matched layer pml absorbing boundary condition to elastic wave propagation a method is presented for application of the perfectly matched layer pml absorbing boundary condition abc to the p sv velocity stress finite difference method the pml consists of a nonphysical material containing both passive loss and dependent sources that provides active absorption of fields it has been used in electromagnetic applications where it has provided excellent results for a wide range of angles and frequencies in this work numerical simulations are used to compare the pml and an optimal second order elastic abc peng and toksoz j acoust soc am 95 733 745 1994 reflection factors are used to compare angular performance for continuous wave illumination snapshots of potentials are used to compare performance for broadband illumination these comparisons clearly demonstrate the superiority of the pml formulation within the pml there is a 60 increase in the number of unknowns per grid cell relative to the velocity stress formulation however the high quality of the pml abc allows the use of a smaller grid which can result in a lower overall computational cost

the q laplace operator and q harmonic polynomials on the quantum vector space the aim of this paper is to study q harmonic polynomials on the quantum vector space generated by q commuting elements x1 x2 xn they are defined as solutions of the equation qp 0 where p is a polynomial in x1 x2 xn and the q laplace operator q is determined in terms of q derivatives the projector hm am hm is constructed where am and hm are the spaces of homogeneous of degree m polynomials and q harmonic polynomials respectively by using these projectors a q analog of classical associated spherical harmonics is constructed they constitute an orthonormal basis of hm a q analog of separation of variables is given representations of the nonstandard q deformed algebra uq son which plays the role of the rotation group so n in the case of classical harmonic polynomials on the spaces hm are explicitly constructed

improved finite element methods for elastic waves abstract in this work we develop finite element methods for exterior problems of time harmonic elastic waves we employ dtn exterior boundary conditions on an artificial boundary to obtain a well posed equivalent problem in a bounded region that is suitable for domain based computation galerkin galerkin least squares and galerkin gradient least squares finite element methods are presented in acoustic wave problems the galerkin least squares method counters the numerical difficulties that result from employing the galerkin method but proves to be insufficient for elastic waves a specialization of the galerkin gradient least squares method to problems of elastic waves yields good results numerical tests validate these conclusions

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

realizations of su 1 1 and uq su 1 1 and generating functions for orthogonal polynomials positive discrete series representations of the lie algebra su 1 1 and the quantum algebra uq su 1 1 are considered the diagonalization of a self adjoint operator the hamiltonian in these representations and in tensor products of such representations is determined and the generalized eigenvectors are constructed in terms of orthogonal polynomials using simple realizations of su 1 1 uq su 1 1 and their representations these generalized eigenvectors are shown to coincide with generating functions for orthogonal polynomials the relations valid in the tensor product representations then give rise to new generating functions for orthogonal polynomials or to poisson kernels in particular a group theoretical derivation of the poisson kernel for meixner pollaczek and al salam chihara polynomials is obtained

intertwiners of uq sl 2 representations and the vector valued big q jacobi transform linear operators r are introduced on tensor products of evaluation modules of uq sl 2 obtained from the complementary and strange series representations the operators r satisfy the intertwining condition on finite linear combinations of the canonical basis elements of the tensor products infinite sums associated with the action of r on six pairs of tensor products are evaluated for two pairs the sums are related to the vector valued big q jacobi transform of the matrix elements defining the operator r in one case the sums specify the action of r on the irreducible representations present in the decomposition of the underlying indivisible sum of uqsl 2 tensor products in both cases bilinear summation formulae for the matrix elements of r provide a generalization of the unitarity property corresponding results are given for the remaining pairs

an order based algorithm for minimum dominating set with application in graph mining abstract dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set we propose a new order based randomised local search rlso algorithm to solve minimum dominating set problem in large graphs experimental evaluation is presented for multiple types of problem instances these instances include unit disk graphs which represent a model of wireless networks random scale free networks as well as samples from two social networks and real world graphs studied in network science our experiments indicate that rlso performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search the order based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices in addition we propose a multi start variant of rlso that is suitable for solving the minimum weight dominating set problem the application of rlso in graph mining is also briefly demonstrated

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

two dimensional axisymmetric numerical simulation of supercritical phase conjugation of ultrasound in active solid media in the present study a two dimensional axisymmetric numerical model is developed for supercritical parametric phase conjugation of ultrasound in a solid active element of cylindrical shape and finite length the pseudospectral time domain algorithm pstd is used owing to its efficiency to model large scale problems pstd solves elastic wave equation in time dependent heterogeneous isotropic and axisymmetric anisotropic solids using ffts for high order approximation of the spatial differential operator on staggered grid and a fourth order adams bashforth time integrator in order to truncate the computational domain absorbing boundary conditions are introduced with complex frequency shifted perfectly matched layers this procedure is highly effective at absorbing signals of long time signature the free surface of the active ceramic rod is introduced through the method of images a systematic study of the influence of lateral limitations of the active medium on parametric wave phase conjugation of sound

the complementary operators method applied to acoustic finite difference time domain simulations the complementary operators method com has recently been introduced as a mesh truncation technique for open domain radiation problems in electromagnetics the com entails the construction of two solutions that employ absorbing boundary conditions abcs with complementary behavior i e the reflection coefficients associated with the two abcs are exactly opposite each other the average of these solutions then yields a new solution in which the errors caused by artificial reflections from the termination of grid are nearly eliminated in this work com is introduced for the finite difference time domain fdtd solution of acoustics problems the development of com is presented in terms of higdon s absorbing boundary operators but generalization to non higdon operators is straightforward the effectiveness of com in comparison to other absorbing boundary conditions is demonstrated with numerical experiments in two and three dimensions

finite difference computation of head related transfer function for human hearing modeling the head related transfer function hrtf is a key to many applications in spatial audio to understand and predict the effects of head geometry and the surrounding environment on the hrtf a three dimensional finite difference time domain model 3d fdtd has been developed to simulate acoustic wave interaction with a human head a perfectly matched layer pml is used to absorb outgoing waves at the truncated boundary of an unbounded medium an external source is utilized to reduce the computational domain size through the scattered field total field formulation this numerical model has been validated by analytical solutions for a spherical head model the 3d fdtd code is then used as a computational tool to predict the hrtf for various scenarios in particular a simplified spherical head model is compared to a realistic head model up to about 7 khz the hrtf is also computed for a realistic head model in the presence of a wall it is demonstrated that this 3d fdtd model can be a useful tool for spatial audio applications

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

a perfectly matched layer for fluid solid problems application to ocean acoustics simulations with solid ocean bottoms a time domain legendre spectral element method is described for full wave simulation of ocean acoustics models i e coupled fluid solid problems in unbounded or semi infinite domains taking into account shear wave propagation in the ocean bottom the technique can accommodate range dependent and depth dependent wave speed and density as well as steep ocean floor topography for truncation of the infinite domain to efficiently absorb outgoing waves a fluid solid complex frequency shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique the complex stretching is rigorously taken into account in the derivation of the fluid solid matching condition inside the absorbing layer which has never been done before in the time domain two implementations are designed a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high order time schemes leading to reduced numerical dispersion and dissipation a topic of importance in particular in long range ocean acoustics simulations the method is validated for a two dimensional fluid solid pekeris waveguide and for a three dimensional seamount model which shows that the technique is accurate and numerically long time stable compared with widely used paraxial absorbing boundary conditions the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves

complexity of approximating bounded variants of optimization problems we study low degree graph problems such as maximum independent set and minimum vertex cover the goal is to improve approximation lower bounds for them and for a number of related problems like max b set packing min b set cover and max b dimensional matching b 3 we prove for example that it is np hard to achieve an approximation factor of 95 94 for max 3 dm and a factor of 48 47 for max 4 dm in both cases the hardness result applies even to instances with exactly two occurrences of each element

parameterized approximation algorithms for some location problems in graphs we develop efficient parameterized with additive error approximation algorithms for the connected r domination problem and the connected p center problem for unweighted and undirected graphs given a graph g we show how to construct a connected big r mathcal o mu big dominating set d with d le d efficiently here d is a minimum connected r dominating set of g and mu is our graph parameter which is the tree breadth or the cluster diameter in a layering partition of g additionally we show that a mathcal o mu approximation for the connected p center problem on g can be computed in polynomial time our interest in these parameters stems from the fact that in many real world networks including internet application networks web networks collaboration networks social networks biological networks and others and in many structured classes of graphs these parameters are small constants

representations of the cyclically symmetric q deformed algebra soq 3 an algebra homomorphism from the nonstandard q deformed cyclically symmetric algebra uq so3 to the extension uq sl2 of the hopf algebra uq sl2 is constructed not all irreducible representations of uq sl2 can be extended to representations of uq sl2 composing the homomorphism with irreducible representations of uq sl2 we obtain representations of uq so3 not all of these representations of uq so3 are irreducible reducible representations of uq so3 are decomposed into irreducible components in this way we obtain all irreducible representations of uq so3 when q is not a root of unity a part of these representations turns into irreducible representations of the lie algebra so3 when q 1 representations of the other part have no classical analog using the homomorphism it is shown how to construct tensor products of finite dimensional representations of uq so3 irreducible representations of uq so3 when q is a root of unity are constructed some of them are obtained from irreducible re

analysis of a cartesian pml approximation to acoustic scattering problems in r2 abstract in this paper we consider a cartesian pml approximation to solutions of acoustic scattering problems on an unbounded domain in r 2 the perfectly matched layer pml technique in a curvilinear coordinate system has been researched for acoustic scattering applications both in theory and computation our goal will be to extend the results of spherical cylindrical pml to pml in cartesian coordinates that is the well posedness of cartesian pml approximation on both the unbounded and truncated domains the exponential convergence of approximate solutions as a function of domain size is also shown we note that once the stability and convergence of the continuous truncated problem has been achieved the analysis of the resulting finite element approximations is then classical finally the results of numerical computations illustrating the theory and efficiency of the cartesian pml approach will be given

solutions of the quantum yang baxter equation with extra nonadditive parameters we present a systematic technique to construct solutions to the yang baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters these extra parameters enter the yang baxter equation in a similar way to the spectral parameter but in a non additive form we exploit the fact that quantum non compact algebras such as uq su 1 1 and type i quantum superalgebras such as uq gl 1 mod 1 and uq gl 2 mod 1 are known to admit non trivial one parameter families of infinite dimensional and finite dimensional irreps respectively even for generic q we develop a technique for constructing the corresponding spectral dependent r matrices as examples we work out the the r matrices for the three quantum algebras mentioned above in certain representations

independent dominating set problem revisited an independent dominating set of a graph g is a subset d of v such that every vertex not in d is adjacent to at least one vertex of d and no two vertices in d are adjacent the independent dominating set ids problem asks for an independent dominating set with minimum cardinality first we show that the independent dominating set problem and the dominating set problem on cubic bipartite graphs are both np complete as an additional result we give an alternative and more direct proof for the np completeness of both the independent dominating set problem and the dominating set problem on at most cubic grid graphs next we show that there are fixed parameter tractable algorithms for the independent dominating set problem and the dominating set problem on at most cubic graphs which run in o 3 3028 k n and o 4 2361 k n time respectively moreover we consider the weighted independent dominating set problem on k graphs we show that the problem on 2 1 graphs is np complete we also show that the problem can be solved in linear time for 1 1 graphs and in polynomial time for 1 graphs for constant respectively

new results on maximum induced matchings in bipartite graphs and beyond the maximum induced matching problem is known to be apx hard in the class of bipartite graphs moreover the problem is also intractable in this class from a parameterized point of view i e it is w 1 hard in this paper we reveal several classes of bipartite and more general graphs for which the problem admits fixed parameter tractable algorithms we also study the computational complexity of the problem for regular bipartite graphs and prove that the problem remains apx hard even under this restriction on the other hand we show that for hypercubes a proper subclass of regular bipartite graphs the problem admits a simple solution

explicit finite element perfectly matched layer for transient three dimensional elastic waves the use of a perfectly matched layer pml model is an efficient approach toward the bounded domain modelling of wave propagation on unbounded domains this paper formulates a three dimensional pml for elastic waves by building upon previous work by the author and implements it in a displacement based finite element setting the novel contribution of this paper over the previous work is in making this finite element implementation suitable for explicit time integration thus making it practicable for use in large scale three dimensional dynamic analyses an efficient method of calculating the strain terms in the pml is developed in order to take advantage of the lack of the overhead of solving equations at each time step the pml formulation is studied and validated first for a semi infinite bar and then for the classical soil structure interaction problems of a square flexible footing on a i half space ii layer on a half space and iii layer on a rigid base numerical results for these problems demonstrate that the pml models produce highly accurate results with small bounded domains and at low computational cost and that these models are long time stable with critical time step sizes similar to those of corresponding fully elastic models copyright 2008 john wiley sons ltd

a nonreflecting boundary condition for discrete acoustic and elastic wave equations one of the nagging problems which arises in application of discrete solution methods for wave propagation calculations is the presence of reflections or wraparound from the boundaries of the numerical mesh these undesired events eventually override the actual seismic signals which propagate in the modeled region the solution to avoiding boundary effects used to be to enlarge the numerical mesh thus delaying the side reflections and wraparound longer than the range of times involved in the modeling obviously this solution considerably increases the expense of computation more recently nonreflecting boundary conditions were introduced for the finite difference method clayton and enquist 1977 reynolds 1978 these boundary conditions are based on replacing the wave equation in the boundary region by one way wave equations which do not permit energy to propagate from the boundaries into the numerical mesh this approach has been relatively successful except that its effectiveness degrades for event

semitotal domination new hardness results and a polynomial time algorithm for graphs of bounded mim width abstract a semitotal dominating set of a graph g with no isolated vertex is a dominating set d of g such that every vertex in d is within distance two of another vertex in d the minimum size t 2 g of a semitotal dominating set of g is squeezed between the domination number g and the total domination number t g semitotal dominating set is the problem of finding given a graph g a semitotal dominating set of g of size t 2 g in this paper we continue the systematic study on the computational complexity of this problem when restricted to special graph classes in particular we show that it is solvable in polynomial time for the class of graphs of bounded mim width by a reduction to total dominating set and we provide several approximation lower bounds for subclasses of subcubic graphs moreover we obtain complexity dichotomies in monogenic classes for the decision versions of semitotal dominating set and total dominating set finally we show that it is np complete to recognise the graphs such that t 2 g t g and those such that g t 2 g even if restricted to be planar and with maximum degree at most 4 and we provide forbidden induced subgraph characterisations for the graphs hereditarily satisfying either of these two equalities

algorithm and hardness results on neighborhood total domination in graphs abstract a set d v of a graph g v e is called a neighborhood total dominating set of g if d is a dominating set and the subgraph of g induced by the open neighborhood of d has no isolated vertex given a graph g min ntds is the problem of finding a neighborhood total dominating set of g of minimum cardinality the decision version of min ntds is known to be np complete for bipartite graphs and chordal graphs in this paper we extend this np completeness result to undirected path graphs chordal bipartite graphs and planar graphs we also present a linear time algorithm for computing a minimum neighborhood total dominating set in proper interval graphs we show that for a given graph g v e min ntds cannot be approximated within a factor of 1 e log v unless np dtime v o log log v and can be approximated within a factor of o log where is the maximum degree of the graph g finally we show that min ntds is apx complete for graphs of degree at most 3

representations of the q deformed algebras uq so2 1 and uq so3 1 representations of the algebra uq so2 1 are studied this algebra is a q deformation of the universal enveloping algebra u so2 1 of the lie algebra of the group so0 2 1 and differs from the quantum algebra uq su1 1 classifications of irreducible representations and of infinitesimally unitary irreducible representations of uq so2 1 with simple and discrete spectrum of one of generators are derived the set of infinitesimally unitary representations of uq so2 1 does not coincide with that for the algebra uq su1 1 the sets of irreducible representations and of infinitesimally unitary irreducible representations of the algebra uq so3 1 are given we also consider representations of uq son 1 which are of class 1 with respect to the subalgebra uq son

a staggered grid finite difference method with perfectly matched layers for poroelastic wave equations a particle velocity strain finite difference fd method with a perfectly matched layer pml absorbing boundary condition is developed for the simulation of elastic wave propagation in multidimensional heterogeneous poroelastic media instead of the widely used second order differential equations a first order hyperbolic leap frog system is obtained from biot s equations to achieve a high accuracy the first order hyperbolic system is discretized on a staggered grid both in time and space the perfectly matched layer is used at the computational edge to absorb the outgoing waves the performance of the pml is investigated by calculating the reflection from the boundary the numerical method is validated by analytical solutions this fd algorithm is used to study the interaction of elastic waves with a buried land mine three cases are simulated for a mine like object buried in sand in purely dry sand and in mud the results show that the wave responses are significantly different in these cases the target can be detected by using acoustic measurements after processing

approximation hardness of dominating set problems in bounded degree graphs we study approximation hardness of the minimum dominating set problem and its variants in undirected and directed graphs using a similar result obtained by trevisan for minimum set cover we prove the first explicit approximation lower bounds for various kinds of domination problems connected total independent in bounded degree graphs asymptotically for degree bound approaching infinity these bounds almost match the known upper bounds the results are applied to improve the lower bounds for other related problems such as maximum induced matching and maximum leaf spanning tree

absorbing boundary condition for the elastic wave equation velocity stress formulation this paper describes an absorbing boundary condition for finite difference modeling of elastic wave propagation in two and three dimensions the boundary condition is particularly effective for obliquely incident waves typically quite troublesome for absorbing boundaries analytical predictions of the boundary reflection coefficients of a few percent or less for angles of incidence up to 89 are verified in example finite difference applications the algorithm is appropriate for use in a velocity stress finite difference vs fd formulation it is computationally simpler than a similar absorbing boundary given previously for the standard displacement formulation a second algorithm is presented which may be advantageous when the boundary of interest is exposed to strong evanescent waves both algorithms require that the adjacent elastic medium be locally homogeneous

conformal pml fdtd schemes for electromagnetic field simulations a dynamic stability study we present a study on the dynamic stability of the perfectly matched layer pml absorbing boundary condition for finite difference time domain fdtd simulations of electromagnetic radiation and scattering problems in body conformal orthogonal grids this work extends a previous dynamic stability analysis of cartesian cylindrical and spherical pmls to the case of a conformal pml it is shown that the conformal pml defined over surface terminations with positive local radii of curvature concave surfaces as viewed from inside the computational domain is dynamically stable while the conformal pml defined over surface terminations with a negative local radius convex surfaces as viewed from inside the computational domain is dynamically unstable numerical results illustrate the analysis

tensor products of uq sl 2 modules and the big q2 jacobi function transform four tensor products of evaluation modules of the quantum affine algebra uq sl 2 obtained from the negative and positive series the complementary and the strange series representations are investigated linear operators r z satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums r t r t z 0 and r t r t z 0 involving big q2 jacobi functions or related nonterminating basic hypergeometric series inhomogeneous recurrence relations can be derived for both sets evaluations of the simplest sums provide the corresponding initial conditions for the first set of sums the relations entail a big q2 jacobi function transform pair an integral decomposition is obtained for the sum r t a partial description of the relation between the decompositions of the tensor products with respect to uqsl 2 or with respect to its complement in uq sl 2 can be formulated in terms of askey wilson

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

high order finite difference methods for the helmholtz equation high order finite difference methods for solving the helmholtz equation are developed and analyzed in one and two dimensions on uniform grids the standard pointwise representation has a second order accurate local truncation error we also study two schemes which have a fourth order accurate local truncation error one of the high order schemes is based on generalizations of the pade approximation the second scheme is based on high order approximation to the derivative calculated from the helmholtz equation itself a symmetric high order representation is developed for a neumann boundary condition numerical results are presented on model problems approximated with the developed schemes

an optimal absorbing boundary condition for finite difference modeling of acoustic and elastic wave propagation this paper presents an optimal absorbing boundary condition designed to model acoustic and elastic wave propagation in two dimensional and three dimensional media using the finite difference method in this condition extrapolation on the artificial boundaries of a finite difference domain is expressed as a linear combination of wave fields at previous time steps and or interior grids the acoustic and elastic reflection coefficients from the artificial boundaries are derived they are found to be identical to the transfer functions of two cascaded systems the inverse of a causal system and an anticausal system the method makes use of the zeros and poles of reflection coefficients in a complex plane the optimal absorbing boundary condition described in this paper yields on the average reflection coefficients about 10 db smaller than higdon s absorbing boundary condition and about 20 db smaller than reynolds absorbing boundary condition

higher order finite and infinite elements for the solution of helmholtz problems abstract in recent years the focus in the field of acoustic finite element computations has shifted to the mid frequency regime at higher frequencies however the conventional finite elements with linear shape functions fail to provide reliable results due to so called pollution effects this motivates the use of higher order shape functions and related p fem concepts the solution of large systems of equations arising from engineering problems often involves the use of iterative solution procedures mostly by means of krylov subspace methods the performance of these methods strongly depends on the spectrum of the resulting system matrices which is affected by the polynomial approximation within the finite element formulation the current work shows that finite elements based on bernstein polynomials yield a favorable spectrum of the system matrix and particularly good performance in combination with commonly employed krylov solvers this is shown for interior as well as exterior helmholtz problems where an infinite element formulation is employed to account for the sound radiation

harmonics on the quantum euclidean space we study harmonic polynomials on the quantum euclidean space enq generated by quantum coordinates xi i 1 2 n on which the quantum group soq n acts they are defined as solutions of the equation qp 0 where q is the q laplace operator on enq we construct a q analogue of the classical zonal polynomials and associated spherical polynomials with respect to the quantum subgroup soq n 2 the associated spherical polynomials constitute an orthogonal basis of the spaces of homogeneous harmonic polynomials they are represented as products of polynomials depending on q radii and xj xj j n j 1 this representation is in fact a q analogue of the classical separation of variables

perfectly matched layers for time harmonic elastodynamics of unbounded domains theory and finite element implementation abstract one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies this paper develops the pml concept for time harmonic elastodynamics in cartesian coordinates utilising insights obtained with electromagnetics pmls and presents a novel displacement based symmetric finite element implementation of the pml for time harmonic plane strain or three dimensional motion the pml concept is illustrated through the example of a one dimensional rod on elastic foundation and through the anti plane motion of a two dimensional continuum the concept is explored in detail through analytical and numerical results from a pml model of the semi infinite rod on elastic foundation and through numerical results for the anti plane motion of a semi infinite layer on a rigid base numerical results are presented for the classical soil structure interaction problems of a rigid strip footing on a i half plane ii layer on a half plane and iii layer on a rigid base the analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by pml models even with small bounded domains

more on uq su 1 1 with q a root of unity highest weight representations of uq su 1 1 with q exp i n are investigated the structures of the irreducible highest weight modules are discussed in detail the clebsch gordan decomposition for the tensor product of two irreducible representations is discussed by using the results a representation of sl 2 r uq su 2 is also presented in terms of holomorphic sections which also have uq su 2 index furthermore zn graded supersymmetry is realized in terms of the representation an explicit realization of osp 1 2 via the highest weight representation of uq su 1 1 with q2 1 is given

three dimensional perfectly matched layer for the absorption of electromagnetic waves the perfectly matched layer is a technique of free space simulation developed for solving unbounded electromagnetic problems with the finite difference time domain method referred to as pml this technique has been described in a previous paper for two dimensional problems the present paper is devoted to the three dimensional case the theory of the perfectly matched layer is generalized to three dimensions and some numerical experiments are shown to illustrate the efficiency of this new method of free space simulation

a perfectly matched layer for the helmholtz equation in a semi infinite strip the perfectly matched layer pml has become a widespread technique for preventing reflections from far field boundaries for wave propagation problems in both the time dependent and frequency domains we develop a discretization to solve the helmholtz equation in an infinite two dimensional strip we solve the interior equation using high order finite differences schemes the combined helmholtz pml problem is then analyzed for the parameters that give the best performance we show that the use of local high order methods in the physical domain coupled with a specific second order approximation in the pml yields global high order accuracy in the physical domain we discuss the impact of the parameters on the effectiveness of the pml numerical results are presented to support the analysis

a laplace operator and harmonics on the quantum complex vector space the aim of this article is to study the q laplace operator and q harmonic polynomials on the quantum complex vector space generated by elements zi wi i 1 2 n on which the quantum group glq n or uq n acts the q harmonic polynomials are defined as solutions of the equation qp 0 where p is a polynomial in zi wi i 1 2 n and the q laplace operator q is determined in terms of q derivatives the q laplace operator q commutes with the action of glq n the projector hm m am m hm m is constructed where am m and hm m are the spaces of homogeneous of degree m in zi and of degree m in wi polynomials and homogeneous q harmonic polynomials respectively by using these projectors a q analog of the classical zonal spherical and associated spherical harmonics are constructed they constitute an orthogonal basis of hm m a q analog of separation of variables is given the quantum algebra uq gln acting on hm m determines an irreducible representation of uq gln this action is explicitly con

generalized threshold processes on graphs we consider an iterative irreversible process on graphs starting with some initial set s of vertices of a given graph g this process iteratively adds to s all vertices u of g outside of s for which the intersection of the current set s with the neighborhood ng u of u in g belongs to a collection u of subsets of ng u given for each vertex u inspired by discrete convexity notions we study the corresponding interval number where only one iteration is executed and the hull number where the number of iterations is unbounded special choices of the function allow to include several well studied graph processes and parameters within this framework our contributions comprise hardness results for very restricted cases linear time algorithms for trees and a probabilistic upper bound

a q analogue of bargmann space and its scalar product a q analogue of bargmann space is defined using the properties of coherent states associated with a pair of q deformed bosons the space consists of a class of entire functions of a complex variable z and has a reproducing kernel on this space the q boson creation and annihilation operators are represented as multiplication by z and q differentiation with respect to z respectively a q integral analogue of bargmann s scalar product is defined involving the q exponential as a weight function associated with this is a completeness relation for the q coherent states

perfectly matched layers for elastic waves in cylindrical and spherical coordinates the perfectly matched layer pml for elastic waves in cylindrical and spherical coordinates is developed using an improved scheme of complex coordinates as is known for electromagnetic waves berenger s original pml scheme does not apply to cylindrical and spherical coordinates the straightforward extension of the complex coordinates for elastic waves to cylindrical and spherical coordinates requires extra unknowns for time domain solutions wasting computer memory and computation time the main idea of the improved scheme in this work is the use of integrated complex variables it is shown that for three dimensional cylindrical and spherical coordinates this improved pml scheme requires no more unknowns than in cartesian coordinates the number of unknowns can be further reduced through the use of symmetry in the partial differential equations the pml scheme allows an arbitrary inhomogeneity in the medium and is suitable for numerical solutions of wave equations by finite difference finite element

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

studies of fe pml for exterior problems of time harmonic elastic waves the equation of an absorbing layer for time harmonic elastic waves based on the perfectly matched layer pml concept is formulated in a manner that is easily implemented in finite element software in the proposed approach the layer is viewed as an anisotropic material with continuously varying complex material properties the effect of the pml parameters on its discrete representation is investigated through dispersion analysis guidelines for proper selection of the pml parameters are presented the formulation with the parameters selected according to the guidelines proposed performs well in computation

representations of the quantum algebra uq su1 1 all irreducible representations of the quantum group uq su1 1 are given they are determined by two complex numbers infinitesimally unitary representations are separated from the set of irreducible representations it is shown that the symmetric operators of irreducible infinitesimally unitary representations corresponding to generators of the lie algebra su1 1 admit self adjoint extensions

algorithmic aspects of semitotal domination in graphs abstract for a graph g v e a set d v is called a semitotal dominating set of g if d is a dominating set of g and every vertex in d is within distance 2 of another vertex of d the minimum semitotal domination problem is to find a semitotal dominating set of minimum cardinality given a graph g and a positive integer k the semitotal domination decision problem is to decide whether g has a semitotal dominating set of cardinality at most k the semitotal domination decision problem is known to be np complete for general graphs in this paper we show that the semitotal domination decision problem remains np complete for planar graphs split graphs and chordal bipartite graphs we give a polynomial time algorithm to solve the minimum semitotal domination problem in interval graphs we show that the minimum semitotal domination problem in a graph with maximum degree admits an approximation algorithm that achieves the approximation ratio of 2 3 ln 1 showing that the problem is in the class log apx we also show that the minimum semitotal domination problem cannot be approximated within 1 ln v for any 0 unless np dtime v o log log v finally we prove that the minimum semitotal domination problem is apx complete for bipartite graphs with maximum degree 4

an efficient time domain perfectly matched layers formulation for elastodynamics on spherical domains summary many practical applications require the analysis of elastic wave propagation in a homogeneous isotropic media in an unbounded domain one widely used approach for truncating the infinite domain is the so called method of perfectly matched layers pmls most existing pml formulations are developed for finite difference methods based on the first order velocity stress form of the elasticity equations and they are not straight forward to implement using standard finite element methods fems on unstructured meshes some of the problems with these formulations include the application of boundary conditions in half space problems and in the treatment of edges and or corners for time domain problems several pml formulations which do work with fems have been proposed although most of them still have some of these problems and or they require a large number of auxiliary nodal history memory variables in this work we develop a new pml formulation for time domain elastodynamics on a spherical domain which reduces to a two dimensional formulation under the assumption of axisymmetry our formulation is well suited for implementation using fems where it requires lower memory than existing formulations and it allows for natural application of boundary conditions we solve example problems on two dimensional and three dimensional domains using a high order discontinuous galerkin dg discretization on unstructured meshes and explicit time stepping we also study an approach for stabilization of the discrete equations and we show several practical applications for quality factor predictions of micromechanical resonators along with verifying the accuracy and versatility of our formulation copyright 2014 john wiley sons ltd

approximation for the minimum cost doubly resolving set problem locating source of diffusion in networks is crucial for controlling and preventing epidemic risks it has been studied under various probabilistic models in this paper we study source location from a deterministic point of view by modeling it as the minimum cost doubly resolving set drs problem which is a strengthening of the well known metric dimension problem let g be an undirected graph on n vertices where each vertex has a nonnegative cost a vertex subset s of g is a doubly resolving set drs of g if for every pair of vertices u v in g there exist x ys such that the difference of distances in terms of number of edges between u and x y is not equal to the difference of distances between v and x y the minimum cost drs problem consists of finding a drs in g with minimum total cost we establish lnn approximability of the minimum drs problem on general graphs for both weighted and unweighted versions this provides the first explicit lower and upper bounds on approximation for the minimum cost drs which are nearly tight moreover we design the first known strongly polynomial time exact algorithms for the minimum cost drs problem on general wheels and trees with additional constant k0 edges

new techniques for approximating optimal substructure problems in power law graphs the remarkable discovery of many large scale real networks is the power law distribution in degree sequence the number of vertices with degree i is proportional to i b for some constant b 1 a lot of researchers believe that it may be easier to solve some optimization problems in power law graphs unfortunately many problems have been proved np hard even in power law graphs intuitively a theoretical question is raised are these problems on power law graphs still as hard as on general graphs in this paper we show that many optimal substructure problems such as minimum dominating set minimum vertex cover and maximum independent set are easier to solve in power law graphs by illustrating better inapproximability factors an optimization problem has the property of optimal substructure if its optimal solution on some given graph is essentially the union of the optimal sub solutions on all maximal connected components in particular we prove the above problems and a more general problem r minimum dominating set remain apx hard and their constant inapproximability factors on general power law graphs by using the cycle based embedding technique to embed any d bounded graphs into a power law graph in addition in simple power law graphs we further prove the corresponding inapproximability factors of these problems based on the graphic embedding technique as well as that of maximum clique and minimum coloring using the embedding technique in 1 as a result of these inapproximability factors the belief that there exists some 1 o 1 approximation algorithm for these problems on power law graphs is proven to be not always true at last we do in depth investigations in the relationship between the exponential factor b and constant greedy approximation algorithms

an efficient finite element time domain formulation for the elastic second order wave equation a non split complex frequency shifted convolutional pml the perfectly matched layer pml technique has demonstrated very high efficiency as absorbing boundary condition for the elastic wave equation recast as a first order system in velocity and stress in attenuating non grazing bulk and surface waves this paper develops a novel convolutional pml formulation based on the second order wave equation with displacements as the only unknowns to annihilate spurious reflections from near grazing waves the derived variational form allows for the use of e g finite element and the spectral element methods as spatial discretization schemes a recursive convolution update scheme of second order accuracy is employed such that highly stable effective time integration with the newmark beta implicit and explicit with mass lumping method is achieved the implementation requires minor modifications of existing displacement based finite element software and the stability and efficiency of the proposed formulation is verified by relevant two dimensional benchmarks that accommodate bulk and surface waves copyright 2011 john wiley sons ltd

on non reflecting boundary conditions in unbounded elastic solids problems in unbounded domains can be solved using domain based computation by introducing an artificial boundary and then selecting appropriate boundary conditions the dtn method which specifies such boundary conditions is investigated in this work for wave problems in elastic solids the dtn method defines an exact relation between the displacement field and its normal and tangential tractions on an artificial boundary this relation is expressed in terms of an infinite series the dtn boundary conditions are shown to be non reflective thus uniqueness of the solution is guaranteed for practical purposes the full dtn operator is truncated the truncated dtn operator fails to completely inhibit reflections of higher modes resulting in loss of uniqueness at characteristic wave numbers of higher harmonics guidelines for determining a sufficient number of terms in the truncated operator to retain uniqueness of the solution at any given wave number are derived the validity of these guidelines is examined and verified by numerical examples local dtn boundary conditions are also investigated and it is shown that local boundary conditions guarantee uniqueness of the solution for all wave numbers regardless of the number of terms in the operator this property is used here to modify the truncated dtn operator and to enhance its capability to retain uniqueness of solutions a modified dtn operator combining the truncated operator with the local one is introduced the modified dtn operator is shown to retain uniqueness of solutions regardless of the number of terms and regardless of the wave number

time harmonic elasticity with controllability and higher order discretization methods the time harmonic solution of the linear elastic wave equation is needed for a variety of applications the typical procedure for solving the time harmonic elastic wave equation leads to difficulties solving large scale indefinite linear systems to avoid these difficulties we consider the original time dependent equation with a method based on an exact controllability formulation the main idea of this approach is to find initial conditions such that after one time period the solution and its time derivative coincide with the initial conditions the wave equation is discretized in the space domain with spectral elements the degrees of freedom associated with the basis functions are situated at the gauss lobatto quadrature points of the elements and the gauss lobatto quadrature rule is used so that the mass matrix becomes diagonal this method is combined with the second order central finite difference or the fourth order runge kutta time discretization as a consequence of these choices only matrix vector products are needed in time dependent simulation this makes the controllability method computationally efficient

models of q algebra representations tensor products of special unitary and oscillator algebras this paper begins a study of one and two variable function space models of irreducible representations of q analogs of lie enveloping algebras motivated by recurrence relations satisfied by q hypergeometric functions the algebras considered are the quantum algebra uq su2 and a q analog of the oscillator algebra not a quantum algebra in each case a simple one variable model of the positive discrete series of finite and infinite dimensional irreducible representations is used to compute the clebsch gordan coefficients it is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a lie algebra to its lie group and the corresponding matrix elements of the group operators on these representation spaces are computed it is shown that the matrix elements are polynomials satisfying orthogonality relations analogous to those holding for true irreducible group representations it is also demonstrated that general q hypergeometric functions can occur as

a classification of unitary highest weight modules of the quantum analogue of the symmetric pair an an 1 abstract we study the irreducibility and unitarity of highest weight modules of the quantized enveloping algebra associated to s u n 1 we obtain a classification of these modules analogous to that of ehw in the classical context we also compute all commutation relations between root vectors in u q s u n 1

spectra eigenvectors and overlap functions for representation operators of q deformed algebras operators of representations corresponding to symmetric elements of theq deformed algebrasuq su1 1 uq so2 1 uq so3 1 uq son and representable by jacobi matrices are studied closures of unbounded symmetric operators of representations of the algebrasuq su1 1 anduq so2 1 are not selfadjoint operators for representations of the discrete series their deficiency indices are 1 1 bounded symmetric operators of these representations are trace class operators or have continuous simple spectra eigenvectors of some operators of representations are evaluated explicitly coefficients of transition to eigenvectors overlap coefficients are given in terms ofq orthogonal polynomials it is shown how results on eigenvectors and overlap coefficients can be used for obtaining new results in representation theory ofq deformed algebras

a staggered upwind embedded boundary sueb method to eliminate the fdtd staircasing error in spite of its flexibility and second order accuracy in a homogeneous medium yee s finite difference time domain fdtd method suffers from serious degradation when treating material interfaces greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors indeed such so called staircasing approximation may lead to local zeroth order and global first order errors in this work an embedded fdtd scheme the staggered upwind embedded boundary sueb method is developed for the solution of oneand two dimensional maxwell s equations this simple embedded technique uses upwind conditions in the fdtd method to correctly represent the location and physical conditions of material and metallic boundaries hence eliminating problems caused by the staircasing approximation accuracy analysis has been made to show that the sueb method maintains a second order accuracy globally since the entire problem has been embedded into the simple staggered grid similar to that employed by the yee s scheme extra effort is only needed when treating the grid points close to the interfaces therefore little additional computational cost is needed over yee s scheme the sueb method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the tm wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder

big q laguerre and q meixner polynomials and representations of the quantum algebra uq su1 1 diagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra uq su1 1 is studied spectrum and eigenfunctions of this operator are explicitly found these eigenfunctions when normalized constitute an orthonormal basis in the representation space the initial uq su1 1 basis and the basis of these eigenfunctions are interconnected by a matrix with entries expressed in terms of big q laguerre polynomials the unitarity of this connection matrix leads to an orthogonal system of functions which are dual with respect to big q laguerre polynomials this system of functions consists of two separate sets of functions which can be expressed in terms of q meixner polynomials mn x b c q either with positive or negative values of the parameter b the orthogonality property of these two sets of functions follows directly from the unitarity of the connection matrix as a consequence one obtains an orthogonality relation for the q meixner polynomials mn x b c q with b 0 a biorthogonal system of functions with respect to the scalar product in the representation space is also derived

hardness results approximation and exact algorithms for liar s domination problem in graphs a subset l v of a graph g v e is called a liar s dominating set of g if i n g u l 2 for every vertex u v and ii n g u n g v l 3 for every pair of distinct vertices u v v the min liar dom set problem is to find a liar s dominating set of minimum cardinality of a given graph g and the decide liar dom set problem is the decision version of the min liar dom set problem the decide liar dom set problem is known to be np complete for general graphs in this paper we first present approximation algorithms and hardness of approximation results of the min liar dom set problem in general graphs bounded degree graphs and p claw free graphs we then show that the decide liar dom set problem is np complete for doubly chordal graphs and propose a linear time algorithm for computing a minimum liar s dominating set in block graphs