a comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains abstract as an alternative to domain discretization methods the boundary element method bem provides a powerful tool for the calculation of dynamic structural response in frequency and time domain field equations of motion and boundary conditions are cast into boundary integral equations bie which are discretized only on the boundary fundamental solutions are used as weighting functions in the bie which fulfil the sommerfeld radiation condition i e the energy radiation into a surrounding medium is modelled correctly therefore infinite and semi infinite domains can be effectively treated by the method the soil represents such a semi infinite domain in soil structure interaction problems the response to vibratory loads superimposed to static pre loads can often be calculated by linear viscoelastic constitutive equations conventional viscoelastic constitutive equations can be generalized by taking fractional order time derivatives into account in the present paper two time domain bem approaches including generalized viscoelastic behaviour are compared with the laplace domain bem approach and subsequent numerical inverse transformation one of the presented time domain approaches uses an analytical integration of the elastodynamic bie in a time step viscoelastic constitutive properties are introduced after laplace transformation by means of an elastic viscoelastic correspondence principle the transient response is obtained by inverse transformation in each time step the other time domain approach is based on the so called convolution quadrature method in this formulation the convolution integral in the bie is numerically approximated by a quadrature formula whose weights are determined by the same laplace transformed fundamental solutions used in the first method and a linear multistep method a numerical study of wave propagation problems in 3 d viscoelastic continuum is performed for comparing the three bem formulations

elastodynamics by bem a new direct formulation a new direct be formulation is proposed for the solution of elastodynamic problems an analytical regularization procedure is devised via an integration by parts technique without introducing any hypothesis about either the discretization of the boundary geometry or the space time interpolation of the elastic elds involved the only requirement is for continuity in the displacement eld the regularization of the integral equations for static elasticity using the same approach already available in the literature is presented as a particular case of the general procedure introduced herein the numerical implementation of this technique is discussed and two dimensional examples are presented copyright 1999 john wiley sons ltd

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

generalized domino shuffling the problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting perfect matchings of some subgraph of an aztec diamond graph an or more generally calculating the sum of the weights of all the matchings where the weight of a matching is equal to the product of the pre assigned weights of the constituent edges assumed to be non negative this article presents efficient algorithms that work in this context to solve three problems finding the sum of the weights of the matchings of a weighted aztec diamond graph an computing the probability that a randomly chosen matching of an will include a particular edge where the probability of a matching is proportional to its weight and generating a matching of an at random the first of these algorithms is equivalent to a special case of mihai ciucu s cellular complementation algorithm j combin theory ser a 81 1998 34 and can be used to solve many of the same problems the second of the three algorithms is a generalization of not yet published work of alexandru ionescu and can be employed to prove an identity governing a three variable generating function whose coefficients are all the edge inclusion probabilities this formula has been used duke math j 85 1996 117 as the basis for asymptotic formulas for these probabilities but a proof of the generating function identity has not hitherto been published the third of the three algorithms is a generalization of the domino shuffling algorithm presented in j algebraic combin 1 1992 111 it enables one to generate random diabolo tilings of fortresses and thereby to make intriguing inferences about their asymptotic behavior

a variational boundary integral equation method for an elastodynamic antiplane crack this paper investigates the transient wave scattering by a crack the author has developed a new formulation to solve the bie for the crack opening displacement the solution is represented by means of a retarded double layer potential and the resulting bie with the cod as unknown has a hypersingular kernel the corresponding difficulty is overcome by using a variational method

a new regularization method for mathematical programs with complementarity constraints with strong convergence properties mathematical programs with equilibrium or complementarity constraints mpecs form a difficult class of optimization problems the feasible set has a very special structure and violates most of the standard constraint qualifications therefore one typically applies specialized algorithms in order to solve mpecs one very prominent class of specialized algorithms are the regularization or relaxation methods the first regularization method for mpecs is due to scholtes siam j optim 11 2001 pp 918 936 but in the meantime there exist a number of different regularization schemes which try to relax the difficult constraints in different ways however almost all regularization methods converge to c stationary points only which is a very weak stationarity concept an exception is a recent method by kadrani dussault and benchakroun siam j optim 20 2009 pp 78 103 whose limit points are shown to be m stationary here we provide a new regularization method which also converges to m sta

monomer dimer problem on random planar honeycomb lattice we consider the monomer dimer md problem on a random planar honeycomb lattice model namely the random multiple chain this is a lattice system with non periodic boundary condition whose generating process is inspired by the growth of single walled zigzag carbon nanotubes by applying algebraic and combinatorial techniques we establish a calculating expression of the md partition function for bipartite graphs which corresponds to the permanent of a matrix further by using the transfer matrix argument we show that the computing problem of the permanent of high order matrix can be converted into some lower order matrices for this family of lattices based on which we derive an explicit recurrence formula for evaluating the md partition function of multiple chains and random multiple chains finally we analyze the expectation of the number of monomer dimer arrangements on a random multiple chain and the asymptotic behavior of the annealed md entropy when the multiple chain becomes infinite in width and length respectively

a quadratic identity for the number of perfect matchings of plane graphs we present a quadratic identity on the number of perfect matchings of plane graphs by the method of graphical condensation which generalizes the results found by propp j propp generalized domino shuffling theoret comput sci 303 2003 267 301 kuo e h kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yan yeh and zhang w g yan y n yeh f j zhang graphical condensation of plane graphs a combinatorial approach theoret comput sci 349 2005 452 461

computing the numbers of independent sets and matchings of all sizes for graphs with bounded treewidth abstract in the theory and applications of graphs it is a basic problem to compute the numbers of independent sets and matchings of given sizes since the problem of computing the total number of independent sets and that of matchings of graphs is p complete it is unlikely to give efficient algorithms to find the numbers of independent sets and matchings of given sizes in this paper for graphs with order n and treewidth at most p we present two dynamic algorithms to compute the numbers of independent sets of all sizes with runtime o 2p pn3 and the numbers of matchings of all sizes with runtime o 22p pn3 respectively by the algorithms presented in this paper for graphs with small treewidths the numbers of independent sets and matchings of all possible sizes can be computed efficiently

graphical condensation of plane graphs a combinatorial approach the method of graphical vertex condensation for enumerating perfect matchings of plane bipartite graph was found by propp generalized domino shuffling theoret comput sci 303 2003 267 301 and was generalized by kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yah and zhang graphical condensation for enumerating perfect matchings j combin theory ser a 110 2005 113 125 in this paper by a purely combinatorial method some explicit identities on graphical vertex condensation for enumerating perfect matchings of plane graphs which do not need to be bipartite are obtained as applications of our results some results on graphical edge condensation for enumerating perfect matchings are proved and we count the sum of weights of perfect matchings of weighted aztec diamond

dimers belonging to three orientations on plane honeycomb lattices it is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice and in each type all dimers are mutually parallel based on a previous result we can compute the partition function of the dimer problem of the plane free boundary honeycomb lattices with three different activities by using the number of its pure dimer coverings perfect matchings the explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way for a shape of plane honeycomb lattices the procedure that the size goes to infinite corresponds to a way that the honeycomb lattice goes to infinite from these results an interesting phenomena is observed in the case of the regions of the plane honeycomb lattice has zero entropy per dimer when its size goes to infinite though in the thermodynamic limit there is no freedom in placing a dimer at all but if we distinguish three types of dimers with nonzero activities then its free energy per dimer is nonzero furthermore a sufficient condition for the plane honeycomb lattice with zero entropy per dimer when the three activities are equal to 1 is obtained finally the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed

numerical treatment of acoustic problems with boundary singularities by the singular boundary method abstract the singular boundary method sbm is a novel boundary type meshless method based on the fundamental solution of the given governing equation the sbm employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions in this paper we investigate the acoustic problems with boundary singularities using the sbm this is achieved by combining the sbm with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution the singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities then the regular solution is obtained by the sbm numerical examples show the excellent performance of the proposed technique

graphs determined by polynomial invariants many polynomials have been defined associated to graphs like the characteristic matchings chromatic and tutte polynomials besides their intrinsic interest they encode useful combinatorial information about the given graph it is natural then to ask to what extent any of these polynomials determines a graph and in particular whether one can find graphs that can be uniquely determined by a given polynomial in this paper we survey known results in this area and at the same time we present some new results

numerical integration of functions with boundary singularities abstract in this paper we deal with the problem of constructing efficient rules for the numerical evaluation of integrals of functions which are very smooth everywhere in the domain of integration except at the boundaries where they possess mild singularities in particular we consider integrals defined on bounded intervals or on triangles integrals of this type appear for example in the numerical solution of singular and weakly singular integral equations by boundary element methods

maximum matchings and minimum dominating sets in apollonian networks and extended tower of hanoi graphs abstract the apollonian networks display the remarkable power law and small world properties as observed in most realistic networked systems their dual graphs are extended tower of hanoi graphs which are obtained from the tower of hanoi graphs by adding a special vertex linked to all its three extreme vertices in this paper we study analytically maximum matchings and minimum dominating sets in apollonian networks and their dual graphs both of which have found vast applications in various fields e g structural controllability of complex networks for both networks we determine their matching number domination number the number of maximum matchings as well as the number of minimum dominating sets

pfaffian orientations and perfect matchings of scale free networks counting perfect matchings is of great interest in theoretical computer science mathematics among other disciplines however explicitly determining the number of perfect matchings of general graphs is a challenge in this paper we present a first analytical study of the enumeration problem of perfect matchings on scale free networks which are ubiquitous in real life systems we focus on two iteratively growing scale free networks one is fractal while the other is non fractal for each network we construct an orientation and prove that it is pfaffian then based on the connection between the number of perfect matchings and determinant of the skew adjacency matrix corresponding to a pfaffian orientation we derive the recursive expressions for the number of perfect matchings of the networks at two successive iterations furthermore using the recursive relations we show that for both scale free networks their entropy is zero which is in sharp contrast to the previously obtained results for other networks without scale free behavior but having the same average degree as the studied networks such as square lattice and honeycomb lattice whose entropies are larger than zero our results indicate from another angle that scale free networks have a distinct architecture in comparison with those lattices lacking the power law property

grassmannian representation of the two dimensional monomer dimer model we present an application of the grassmann algebra to the problem of the monomer dimer statistics on a two dimensional square lattice the exact partition function or total number of possible configurations of a system of dimers with a finite set of n monomers at fixed positions can be expressed via a quadratic fermionic theory we give an answer in terms of a product of two pfaffians and the solution is closely related to the kasteleyn result of the pure dimer problem correlation functions are in agreement with previous results both for monomers on the boundary where a simple exact expression is available in the discrete and continuous case and in the bulk where the expression is evaluated numerically

on the construction of graphs with a planar bipartite double cover from boolean formulas and its application to counting satisfying solutions abstract we address the problem to construct a graph g with binary edge weights from the incidence graph of a boolean formula in a way that g has a planar bipartite double cover g this allows one to use the identity between the permanent of g s adjacency matrix a g and the number of perfect matchings of g i e perm a g pm g due to the algorithm of fisher kasteleyn and temperlay fkt the right hand side of the equation can be counted in polynomial time if g is planar we prove a theorem that describes necessary conditions for the gadgets i e small subgraphs with certain properties of g to allow a planar bipartite double cover g for arbitrary 3cnf formulas and the known approaches to build g our theorem shows that gadgets which enable a planar bipartite double cover do not exist however we show that for certain classes of boolean formulas e g 5 pl rtw 2cnf 7 pl rtw 2cnf and 3 forest 3cnf such gadgets exist hence these counting problems are in p the results probably extended to other moduli p and perhaps further counting classes

on the multistep time discretization of linear initial boundary value problems and their boundary integral equations convergence estimates in terms of the data are shown for multistep methods applied to non homogeneous linear initial boundary value problems similar error bounds are derived for a new class of time discrete and fully discrete approximation schemes for boundary integral equations of such problems e g for the single layer potential equation of the wave equation in both cases the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions these estimates which are also proved here depend on bounds of the laplace transform of the distributional convolution kernel outside the stability region scaled by the time stepsize and on the smoothness of the data

mathematical programs with complementarity constraints we study mathematical programs with complementarity constraints several stationarity concepts based on a piecewise smooth formulation are presented and compared the concepts are related to stat

a new space time energetic formulation for wave propagation analysis in layered media by bems in this paper considering a dirichlet neumann problem for 1d wave propagation analysis in layered media reformulated in terms of boundary integral equations we compare two classical weak formulations for the boundary element method with a new space time energetic formulation continuity and coerciveness of the bilinear form corresponding to this last formulation are proved several numerical results will be presented pointing out the numerical properties of the derived linear systems instability phenomena arising using one of the classical techniques can be prevented choosing suitable time steps in the discretization phase of course with a higher computational cost with respect to the new procedure which appears to be unconditionally stable copyright 2008 john wiley sons ltd

on the hosoya index of a family of deterministic recursive trees abstract in this paper we calculate the hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule we then obtain a recursive solution of the hosoya index based on the operations of a determinant the computational complexity of our proposed algorithm is o log 2 n with n being the network size which is lower than that of the existing numerical methods finally we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the hosoya index

stationarity conditions and constraint qualifications for mathematical programs with switching constraints in optimal control switching structures demanding at most one control to be active at any time instance appear frequently discretizing such problems a so called mathematical program with switching constraints is obtained although these problems are related to other types of disjunctive programs like optimization problems with complementarity or vanishing constraints their inherent structure makes a separate consideration necessary since standard constraint qualifications are likely to fail at the feasible points of switching constrained optimization problems stationarity notions which are weaker than the associated karush kuhn tucker conditions need to be investigated in order to find applicable necessary optimality conditions furthermore appropriately tailored constraint qualifications need to be formulated in this paper we introduce suitable notions of weak mordukhovich and strong stationarity for mathematical programs with switching constraints and present some associated constraint qualifications our findings are exploited to state necessary optimality conditions for discretized optimal control problems with switching constraints furthermore we apply our results to optimization problems with either or constraints first a novel reformulation of such problems using switching constraints is presented second the derived surrogate problem is exploited to obtain necessary optimality conditions for the original program

applications of graphical condensation for enumerating matchings and tilings a technique called graphical condensation is used to prove various combinatorial identities among numbers of perfect matchings of planar bipartite graphs and tilings of regions graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph and then re partitioning the united matching actually a multigraph into matchings of two other subgraphs in one of two possible ways this technique can be used to enumerate perfect matchings of a wide variety of planar bipartite graphs applications include domino tilings of aztec diamonds and rectangles diabolo tilings of fortresses plane partitions and transpose complement plane partitions

mathematical programs with cardinality constraints reformulation by complementarity type conditions and a regularization method optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization here we introduce a mixed integer formulation whose standard relaxation still has the same solutions in the sense of global minima as the underlying cardinality constrained problem the relation between the local minima is also discussed in detail since our reformulation is a minimization problem in continuous variables it allows us to apply ideas from that field to cardinality constrained problems here in particular we therefore also derive suitable stationarity conditions and suggest an appropriate regularization method for the solution of optimization problems with cardinality constraints this regularization method is shown to be globally convergent to a mordukhovich stationary point extensive numerical results are given to illustrate the behavior of this method

a study of the difference of convex approach for solving linear programs with complementarity constraints this paper studies the difference of convex dc penalty formulations and the associated difference of convex algorithm dca for computing stationary solutions of linear programs with complementarity constraints lpccs we focus on three such formulations and establish connections between their stationary solutions and those of the lpcc improvements of the dca are proposed to remedy some drawbacks in a straightforward adaptation of the dca to these formulations extensive numerical results including comparisons with an existing nonlinear programming solver and the mixed integer formulation are presented to elucidate the effectiveness of the overall dc approach

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

a sequential algorithm for solving nonlinear optimization problems with chance constraints an algorithm is presented for solving nonlinear optimization problems with chance constraints i e those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability in particular the algorithm is designed to solve cardinality constrained nonlinear optimization problems that arise in sample average approximations of chance constrained problems as well as in other applications in which it is only desired to enforce a minimum number of constraints the algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved the effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear ca

the complexity of counting in sparse regular and planar graphs we show that a number of graph theoretic counting problems remain cal np hard indeed cal p complete in very restricted classes of graphs in particular we prove that the problems of counting matchings vertex covers independent sets and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree we obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2 cnf formulae to achieve these results a new interpolation based reduction technique which preserves properties such as constant degree is introduced

a simple proof of an identity concerning pfaffians of skew symmetric matrices abstract in the present paper we prove an identity concerning pfaffians similar to the well known grassmann plucker relations for determinants using tools from multilinear algebra more precisely we shall derive the identity as a corollary to an equation concerning skew symmetric bilinear forms and operators acting on the exterior algebra m of an r module m over some fixed commutative ring r with 1 r

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

computational study of a family of mixed integer quadratic programming problems we present computational experience with a branch and cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables such problems arise in financial applications the algorithm solves the largest real life problems in a few minutes of run time

maximum matchings in scale free networks with identical degree distribution the size and number of maximum matchings in a network have found a large variety of applications in many fields as a ubiquitous property of diverse real systems power law degree distribution was shown to have a profound influence on size of maximum matchings in scale free networks where the size of maximum matchings is small and a perfect matching often does not exist in this paper we study analytically the maximum matchings in two scale free networks with identical degree sequence and show that the first network has no perfect matchings while the second one has many for the first network we determine explicitly the size of maximum matchings and provide an exact recursive solution for the number of maximum matchings for the second one we design an orientation and prove that it is pfaffian based on which we derive a closed form expression for the number of perfect matchings moreover we demonstrate that the entropy for perfect matchings is equal to that corresponding to the extended sierpiski graph with the same average degree as both studied scale free networks our results indicate that power law degree distribution alone is not sufficient to characterize the size and number of maximum matchings in scale free networks

two dimensional monomer dimer systems are computationally intractable the classic problem of counting monomer dimer arrangements on a two dimensional lattice is analyzed using techniques from theoretical computer science under a certain assumption made precise in the text it can be shown that the general problem is computationally intractable this negative result contrasts with the special case of a system with monomer density zero for which efficient solutions have been known for some time a second much easier result obtained under the same assumption is that the partition function of a three dimensional ising system is computationally intractable again the negative result contrasts with known efficient techniques for evaluating the partition function of a two dimensional system

logarithmic corrections in the free energy of monomer dimer model on plane lattices with free boundaries using exact computations we study the classical hard core monomer dimer models on m x n plane lattice strips with free boundaries for an arbitrary number v of monomers or vacancies we found a logarithmic correction term in the finite size correction of the free energy per lattice site the coefficient of the logarithmic correction term depends on the number of monomers present v and the parity of the width n of the lattice strip the coefficient equals to v when n is odd and v 2 when n is even the results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers we also study the finite size correction in the low dimer density limit where the number of dimers d is fixed in this case the coefficient of the logarithmic correction term equals to d for both odd and even n

a galerkin bem for transient acoustic scattering by an absorbing obstacle this paper deals with the numerical resolution of the so called time domain boundary integral equations the scattering problem by an absorbing obstacle serves as the model for this discussion a new system of retarded potential boundary integral equations rpbie is set up to solve the problem using an energy identity we are able to prove the unconditional stability for standard conforming galerkin approximation of the rpbie the actual space time boundary elements are described in some detail and their implementation has confirmed that stability in a wide range of situations and for large run times never reached before

a residual a posteriori error estimate for the time domain boundary element method this article investigates residual a posteriori error estimates and adaptive mesh refinements for time dependent boundary element methods for the wave equation we obtain reliable estimates for dirichlet and acoustic boundary conditions which hold for a large class of discretizations efficiency of the error estimate is shown for a natural discretization of low order numerical examples confirm the theoretical results the resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems

wavelets and convolution quadrature for the efficient solution of a 2d space time bie for the wave equation abstract we consider a wave propagation problem in 2d reformulated in terms of a boundary integral equation bie in the space time domain for its solution we propose a numerical scheme based on a convolution quadrature formula by lubich for the discretization in time and on a galerkin method in space it is known that the main advantage of lubich s formulas is the use of the fft algorithm to retrieve discrete time integral operators with a computational complexity of order r log r r being twice the total number of time steps performed since the discretization in space leads in general to a quadratic complexity the global computational complexity is of order m 2 r log r and the working storage required is m 2 r 2 where m is the number of grid points on the domain boundary to reduce the complexity in space we consider here approximant functions of wavelet type by virtue of the properties of wavelet bases the discrete integral operators have a rapid decay to zero with respect to time and the overwhelming majority of the associated matrix entries assume negligible values based on an a priori estimate of the decaying behaviour in time of the matrix entries we devise a time downsampling strategy that allows to compute only those elements which are significant with respect to a prescribed tolerance such an approach allows to retrieve the temporal history of each entry e corresponding to a fixed couple of wavelet basis functions via a fast fourier transform with computational complexity of order r e log r e the parameter r e depends on the two basis functions and it satisfies r e r for a relevant percentage of matrix entries percentage which increases significantly as time and or space discretization are refined globally the numerical tests show that the computational complexity and memory storage of the overall procedure are linear in space and time for small velocities of the wave propagation and even sub linear for high velocities

holographic algorithms the power of dimensionality resolved valiant s theory of holographic algorithms is a novel methodology to achieve exponential speed ups in computation a fundamental parameter in holographic algorithms is the dimension of the linear basis vectors we completely resolve the problem of the power of higher dimensional bases we prove that 2 dimensional bases are universal for holographic algorithms

an energy approach to space time galerkin bem for wave propagation problems in this paper we consider dirichlet or neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential starting from a natural energy identity a space time weak formulation for 1d integral problems is briefly introduced and continuity and coerciveness properties of the related bilinear form are proved then a theoretical analysis of an extension of the introduced formulation for 2d problems is proposed pointing out the novelty with respect to existing literature results at last various numerical simulations will be presented and discussed showing unconditional stability of the space time galerkin boundary element method applied to the energetic weak problem copyright 2009 john wiley sons ltd

fast convolution quadrature for the wave equation in three dimensions this work addresses the numerical solution of time domain boundary integral equations arising from acoustic and electromagnetic scattering in three dimensions the semidiscretization of the time domain boundary integral equations by runge kutta convolution quadrature leads to a lower triangular toeplitz system of size n this system can be solved recursively in an almost linear time o n log 2 n but requires the construction of o n dense spatial discretizations of the single layer boundary operator for the helmholtz equation this work introduces an improvement of this algorithm that allows to solve the scattering problem in an almost linear time the new approach is based on two main ingredients the near field reuse and the application of data sparse techniques exponential decay of runge kutta convolution weights w n h d outside of a neighborhood of d n h where h is a time step allows to avoid constructing the near field i e singular and near singular integrals for most of the discretizations of the single layer boundary operators near field reuse the far field of these matrices is compressed with the help of data sparse techniques namely h matrices and the high frequency fast multipole method numerical experiments indicate the efficiency of the proposed approach compared to the conventional runge kutta convolution quadrature algorithm

a wave problem in a half space with a unilateral constraint at the boundary in this paper we study the following problem let omega be a half space of mathbb r n defined by omega x x x n in mathbb r x n where x x ldots x n 1 is the usual notation and let there be given functions u 0 in h 1 omega and u 1 in l 2 omega we assume that u 0 x n 0 is nonnegative and similarly partial u 0 partial x n x n 0 which is a priori an element of h 1 2 mathbb r n 1 is nonnegative

a variational approach to boundary element elastodynamic analysis and extension to multidomain problems abstract time dependent discontinuities of both tractions and displacements are considered on the boundary of a homogeneous linear elastic solid conceived as embedded in the elastic space the analysis of the dynamic response of the solid to external actions is formulated in the time domain by means of suitable integral representations of boundary displacements and of boundary tractions using time dependent fundamental solutions the integral operator generated is proven to be symmetric in both space and time with respect to a time convolutive bilinear form as a consequence the history of boundary tractions and displacements along any assigned time interval 0 is shown to be characterized by a variational theorem the variational formulation developed is generalized to zonewise homogeneous systems and to elastically constrained bodies the linear algebraic equations generated by boundary element modelling in space and time turn out to exhibit symmetry of the coefficient matrix

approximating the permanent via importance sampling with application to the dimer covering problem we estimate the asymptotic growth rate of the number of dimer covers of a cubic lattice our estimate 3 0 4466 0 0006 is consistent with the lower bounds obtained by hammersley and later schrijver and the more recent improved upper bound obtained by ciucu obtaining this estimate is an important step toward approximating the partition function of the cubic monomer dimer system from the partition function all of the standard thermodynamic quantities can be evaluated it is well known that computing 3 is equivalent to computing the permanent of a certain 0 1 matrix we describe an extremely efficient monte carlo algorithm for approximating the permanent previous work on monte carlo approaches includes the pioneering results of jerrum and sinclair who use a rapidly mixing random walk our method is inspired by results of soules on convergence of sinkhorn balancing to obtain a maximum entropy doubly stochastic matrix we use the sinkhorn balanced matrix to generate an importance function that allows us to do direct random sampling rather than a random walk that converges to a limiting distribution

structural properties of affine sparsity constraints we introduce a new constraint system for sparse variable selection in statistical learning such a system arises when there are logical conditions on the sparsity of certain unknown model parameters that need to be incorporated into their selection process formally extending a cardinality constraint an affine sparsity constraint asc is defined by a linear inequality with two sets of variables one set of continuous variables and the other set represented by their nonzero patterns this paper aims to study an asc system consisting of finitely many affine sparsity constraints we investigate a number of fundamental structural properties of the solution set of such a non standard system of inequalities including its closedness and the description of its closure continuous approximations and their set convergence and characterizations of its tangent cones for use in optimization based on the obtained structural properties of an asc system we investigate the convergence of b ouligand stationary solutions when the asc is approximated by surrogates of the step ell 0 function commonly employed in sparsity representation our study lays a solid mathematical foundation for solving optimization problems involving these affine sparsity constraints through their continuous approximations

on the energetic galerkin boundary element method applied to interior wave propagation problems we consider two dimensional interior wave propagation problems with vanishing initial and mixed boundary conditions reformulated as a system of two boundary integral equations with retarded potential these latter are then set in a weak form based on a natural energy identity satisfied by the solution of the differential problem and discretized by the related energetic galerkin boundary element method numerical results are presented and discussed

permanents pfaffian orientations and even directed circuits given a 0 1 square matrix a when can some of the 1 s be changed toi1 s in such a way that the permanent of a equals the determinant of the modifled matrix when does a real square matrix have the property that every real matrix with the same sign pattern that is the corresponding entries either have the same sign or are both zero is nonsingular when is a hypergraph with n vertices and n hyperedges minimally nonbipartite when does a bipartite graph have a pfa an orientation given a digraph does it have no directed circuit of even length given a digraph does it have a subdivision with no even directed circuit it is known that all of the above problems are equivalent we prove a structural characterization of the feasible instances which implies a polynomial time algorithm to solve all of the above problems the structural characterization says roughly speaking that a bipartite graph has a pfa an orientation if and only if it can be obtained by piecing together in a specifled way planar bipartite graphs and one sporadic nonplanar bipartite graph