cored hypergraphs power hypergraphs and their laplacian h eigenvalues abstract in this paper we introduce the class of cored hypergraphs and power hypergraphs and investigate the properties of their laplacian h eigenvalues from an ordinary graph one may generate a k uniform hypergraph called the kth power hypergraph of that graph power hypergraphs are cored hypergraphs but not vice versa sunflowers loose paths and loose cycles are power hypergraphs while squids generalized loose s paths and loose s cycles for 2 s k 2 are cored hypergraphs but not power graphs in general we show that the largest laplacian h eigenvalue of an even uniform cored hypergraph is equal to its largest signless laplacian h eigenvalue especially we find out these largest h eigenvalues for even uniform squids moreover we show that the largest laplacian h eigenvalue of an odd uniform squid loose path and loose cycle is equal to the maximum degree i e 2 we also compute the laplacian h spectra of the class of sunflowers when k is odd the laplacian h spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well

on the spectral radius of trees with fixed diameter let t n d be the set of trees on n vertices with diameter d in this paper the first d2 1 spectral radii of trees in the set t n d 3 d n 4 are characterized

the first few unicyclic and bicyclic hypergraphs with largest spectral radii abstract a connected k uniform hypergraph with n vertices and m edges is called r cyclic if n m k 1 r 1 for r 1 or 2 the hypergraph is simply called unicyclic or bicyclic in this paper we investigate hypergraphs that attain largest spectral radii among all simple connected k uniform unicyclic and bicyclic hypergraphs specifically by using some edge operations the formula on power hypergraph eigenvalues the weighted incidence matrix and a result on linear unicyclic hypergraphs we determined the first five hypergraphs with largest spectral radius among all unicyclic hypergraphs and the first three over all bicyclic hypergraphs

polynomially bounded error estimates for trapezoidal rule convolution quadrature abstract we clarify the dependence with respect to the time variable of some estimates about the convergence of the trapezoidal rule based convolution quadrature method applied to hyperbolic problems this requires a careful investigation of the article of lehel banjai where the first convergence estimates were introduced and of some technical results from a classical paper of christian lubich

on some properties of graph irregularity indices with a particular regard to the σ index abstract some well known graph irregularity indices of a connected graph g are investigated our study is focused mainly on the comparison of the bell s degree variance var g and the collatz sinogowitz irregularity index cs g with the recently introduced g irregularity index it is a degree based topological invariant calculated as g f g 2 m 2 g where m2 g is the second zagreb index f g d 3 v and d v is the degree of the vertex v in g by introducing the notion of the complete split like graphs representing a broad subclass of bidegreed connected graphs it is shown that for these graphs the equality g n 2 v a r g holds

on the spectral radius of uniform hypertrees abstract we determine the unique hypertrees with maximum spectral radius among k uniform non hyper caterpillars with m edges and diameter d for 4 d m 2 among k uniform non hyper caterpillars with m edges for m 6 among k uniform hypertrees with m edges and independence number for m k 1 1 k m among k uniform hypertrees with m edges and matching number for 1 m k 1 1 k and among k uniform hypertrees with m edges and s branch vertices for 0 s m 1 2 respectively

ordering of some uniform supertrees with larger spectral radii abstract a supertree is a connected and acyclic hypergraph we study some uniform supertrees with larger spectral radii we first define a new type of edge moving operation on hypergraphs and study its applications on the comparison of the spectral radii of hypergraphs by using this new operation on some supertrees together with the general edge moving operation introduced by li shao and qi in 2015 and using a result by zhou et al in 2014 about the relation between the spectral radii of an ordinary graph and its power hypergraph we are able to determine the first eight k uniform supertrees on n vertices with the largest spectral radii

statistics of epicenters in the olami feder christensen model in two and three dimensions abstract recently abe and suzuki pointed out that epicenters of earthquakes could be connected in order to generate a graph with properties of a scale free network we have shown that the olami feder christensen ofc model for the dynamics of earthquakes defined both in square and cubic lattices is able to reproduce this new behavior the distribution of distances between successive earthquakes is also presented our results indicate the robustness of the ofc model to describe earthquake dynamics surprisingly we found that only the non conservative version of the ofc model generates a network with scale free properties the conservative version instead behaves like a random graph the distribution of distances in 3 d and the distribution of connectivities in a 2 d lattice confirm the differences observed between the conservative and non conservative regime

theoretical aspects of the application of convolution quadrature to scattering of acoustic waves in this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non homogeneous obstacles using convolution quadrature cq techniques for the time variable and coupled boundary element method finite element method for the space variable the applicability of cq to waves requires polynomial type bounds for operators related to the operator s 2 in the right half complex plane we propose a new systematic way of dealing with this problem both at the continuous and semidiscrete in space cases we apply the technique to three different situations scattering by a group of sound soft and hard obstacles by homogeneous and non homogeneous obstacles

a finite difference delay modeling approach to the discretization of the time domain integral equations of electromagnetics a new method for solving the time domain integral equations of electromagnetic scattering from conductors is introduced this method called finite difference delay modeling appears to be completely stable and accurate when applied to arbitrary structures the temporal discretization used is based on finite differences specifically based on a mapping from the laplace domain to the z transform domain first and second order unconditionally stable methods are derived spatial convergence is achieved using the higher order divergence conforming vector bases of graglia et al low frequency instability problems are avoided with the loop tree decomposition approach numerical results will illustrate the accuracy and stability of the technique

the largest laplacian and signless laplacian h eigenvalues of a uniform hypergraph a b s t r a c t in this paper we show that the largest laplacian h eigen value of a k uniform nontrivial hypergraph is strictly larger than the maximum degree when k is even a tight lower bound for this eigenvalue is given for a connected even uniform hypergraph this lower bound is achieved if and only if it is a hyperstar however when k is odd in certain cases the largest laplacian h eigenvalue is equal to the maximum degree which is a tight lower bound on the other hand tight upper and lower bounds for the largest signless laplacian h eigenvalue of a k uniform connected hypergraph are given for connected k uniform hypergraphs of fixed number of vertices respectively fixed maximum degree the upper respectively lower bound of their largest signless laplacian h eigenvalues is achieved exactly for the complete hypergraph respectively the hyperstar the largest laplacian h eigenvalue is always less than or equal to the

the maximum spectral radii of uniform supertrees with given degree sequences abstract this paper generalizes the breadth first search ordering on trees to k uniform supertrees by using 2 switch operation and edge moving operation on supertrees we determine the unique k uniform supertree with the maximum spectral radius among all k uniform supertrees with a given degree sequence moreover we generalize the majorization theorem on trees to k uniform supertrees

upper bounds for h and z spectral radii of uniform hypergraphs abstract the h spectral radius and z spectral radius of a uniform hypergraph are the h spectral radius and the z spectral radius of its adjacency tensor respectively we give upper bounds for the h spectral radius and z spectral radius of uniform hypergraphs in terms of parameters such as number of vertices number of edges maximum degree and minimum degree and characterize the extremal hypergraphs some classical results on the spectral radius of an ordinary graph are generalized

rapid solution of the wave equation in unbounded domains in this paper we propose and analyze a new fast method for the numerical solution of time domain boundary integral formulations of the wave equation we employ lubich s convolution quadrature method for the time discretization and a galerkin boundary element method for the spatial discretization the coefficient matrix of the arising system of linear equations is a triangular block toeplitz matrix possible choices for solving the linear system arising from the above discretization include the use of fast fourier transform fft techniques and the use of data sparse approximations by using fft techniques the computational complexity can be reduced substantially while the storage cost remains unchanged and is typically high using data sparse approximations the gain is reversed i e the computational cost is approximately unchanged while the storage cost is substantially reduced the method proposed in this paper combines the advantages of these two approaches first the discrete convolution related to the block toeplitz system is transformed into the discrete fourier image thereby arriving at a decoupled system of discretized helmholtz equations with complex wave numbers a fast data sparse e g fast multipole or panel clustering method can then be applied to the transformed system additionally significant savings can be achieved if the boundary data are smooth and time limited in this case the right hand sides of many of the helmholtz problems are almost zero and hence can be disregarded finally the proposed method is inherently parallel we analyze the stability and convergence of these methods thereby deriving the choice of parameters that preserves the convergence rates of the unperturbed convolution quadrature we also present numerical results which illustrate the predicted convergence behavior

on the principal eigenvectors of uniform hypergraphs abstract let a h be the adjacency tensor of r uniform hypergraph h if h is connected the unique positive eigenvector x x 1 x 2 x n t with x r 1 corresponding to spectral radius h is called the principal eigenvector of h the maximum and minimum entries of x are denoted by x max and x min respectively in this paper we investigate the bounds of x max and x min in the principal eigenvector of h meanwhile we also obtain some bounds of the ratio x i x j for i j n as well as the principal ratio h x max x min of h as an application of these results we finally give an estimate of the gap of spectral radii between h and its proper sub hypergraph h

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

sharp bounds for ordinary and signless laplacian spectral radii of uniform hypergraphs we give sharp upper bounds for the ordinary spectral radius and signless laplacian spectral radius of a uniform hypergraph in terms of the average 2 degrees or degrees of vertices respectively and we also give a lower bound for the ordinary spectral radius we also compare these bounds with known ones

hypocenter interval statistics between successive earthquakes in the two dimensional burridge knopoff model abstract we study statistical properties of spatial distances between successive earthquakes the so called hypocenter intervals produced by a two dimensional 2d burridge knopoff model involving stick slip behavior it is found that cumulative distributions of hypocenter intervals can be described by the q exponential distributions with q 1 which is also observed in nature the statistics depend on a friction and stiffness parameters characterizing the model and a threshold of magnitude the conjecture which states that q t q r 2 where q t and q r are an entropy index of time intervals and spatial intervals respectively can be reproduced semi quantitatively it is concluded that we provide a new perspective on the burridge knopoff model which addresses that the model can be recognized as a realistic one in view of the reproduction of the spatio temporal interval statistics of earthquakes on the basis of nonextensive statistical mechanics

a general product of tensors with applications abstract we study a general product of two n dimensional tensors a and b with orders m 2 and k 1 this product satisfies the associative law and is a generalization of the usual matrix product using this product many concepts and known results of tensors can be simply expressed and or proved and a number of applications of it will be given using the associative law of this tensor product and some properties on the resultant of a system of homogeneous equations on n variables we define the similarity and congruence of tensors which are also the generalizations of the corresponding relations for matrices and prove that similar tensors have the same characteristic polynomials thus the same spectra we study two special kinds of similarity permutational similarity and diagonal similarity and their applications in the study of the spectra of hypergraphs and nonnegative irreducible tensors we also define the direct product of tensors in matrix case it is also called the kronecker product and give its applications in the study of the spectra of two kinds of the products of hypergraphs we also give applications of this general product in the study of nonnegative tensors including a characterization of primitive tensors the upper bounds of primitive degrees and the cyclic indices of some nonnegative irreducible tensors

p tensors p0 tensors and their applications abstract p and p0 matrix classes have wide applications in mathematical analysis linear and nonlinear complementarity problems etc since they contain many important special matrices such as positive semi definite matrices m matrices diagonally dominant matrices etc by modifying the existing definitions of p and p0 tensors that work only for even order tensors in this paper we propose a homogeneous formula for the definition of p and p0 tensors the proposed p and p0 tensor classes coincide the existing ones of even orders and include many important structured tensors of odd orders we show that many checkable classes of structured tensors such as the nonsingular m tensors the nonsingular h tensors with positive diagonal entries the strictly diagonally dominant tensors with positive diagonal entries are p tensors under the new definition regardless of whether the order is even or odd in the odd order case our definition of p0 tensors to some extent can be regarded as an extension of positive semi definite psd tensors the theoretical applications of p and p0 tensors under the new definition to tensor complementarity problems and spectral hypergraph theory are also studied

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

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

on the spectral radius of a class of non odd bipartite even uniform hypergraphs abstract in order to investigate the non odd bipartiteness of even uniform hypergraphs starting from a simple graph g we construct a generalized power of g denoted by g k s which is obtained from g by blowing up each vertex into a s set and each edge into a k 2 s set where s k 2 when s k 2 g k s is always odd bipartite we show that g k k 2 is non odd bipartite if and only if g is non bipartite and find that g k k 2 has the same adjacency respectively signless laplacian spectral radius as g so the results involving the adjacency or signless laplacian spectral radius of a simple graph g hold for g k k 2 in particular we characterize the unique graph with minimum adjacency or signless laplacian spectral radius among all non odd bipartite hypergraphs g k k 2 of fixed order and prove that 2 5 is the smallest limit point of the non odd bipartite hypergraphs g k k 2 in addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors

principal eigenvectors and spectral radii of uniform hypergraphs abstract in this paper some inequalities among the principal eigenvector spectral radius and vertex degrees of a connected uniform hypergraph are established necessary and sufficient conditions of equalities holding are presented which are related to the regularity of a hypergraph furthermore we present some bounds on the spectral radius for a connected irregular uniform hypergraph in terms of some parameters such as principal ratio maximum degree diameter and the number of vertices and edges

the first two largest spectral radii of uniform supertrees with given diameter abstract a supertree is a connected and acyclic hypergraph let s m d k be the set of k uniform supertrees with m edges and diameter d in this paper we determine the supertrees with the first two largest spectral radii among all supertrees in s m d k for 3 d m 1

runge kutta convolution quadrature for operators arising in wave propagation an error analysis of runge kutta convolution quadrature is presented for a class of non sectorial operators whose laplace transform satisfies besides the standard assumptions of analyticity in a half plane re s 0 and a polynomial bound operatorname o s mu 1 there the stronger polynomial bound operatorname o s mu 2 in convex sectors of the form operatorname arg s leq pi 2 theta for 0 the order of convergence of the runge kutta convolution quadrature is determined by 2 and the underlying runge kutta method but is independent of 1 time domain boundary integral operators for wave propagation problems have laplace transforms that satisfy bounds of the above type numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour of runge kutta convolution quadrature for this class of applications our results show in particular that the full classical order of the runge kutta method is attained away from the scattering boundary

network of epicenters of the olami feder christensen model of earthquakes we study the dynamics of the olami feder christensen ofc model of earthquakes focusing on the behavior of sequences of epicenters regarded as a growing complex network besides making a detailed and quantitative study of the effects of the borders the occurrence of epicenters is dominated by a strong border effect which does not scale with system size we examine the degree distribution and the degree correlation of the graph we detect sharp differences between the conservative and nonconservative regimes of the model removing border effects the conservative regime exhibits a poisson like degree statistics and is uncorrelated while the nonconservative has a broad power law like distribution of degrees if the smallest events are ignored which reproduces the observed behavior of real earthquakes in this regime the graph has also an unusually strong degree correlation among the vertices with higher degree which is the result of the existence of temporary attractors for the dynamics as the system evolves the epicenters concentrate increasingly on fewer sites exhibiting strong synchronization but eventually spread again over the lattice after a series of sufficiently large earthquakes we propose an analytical description of the dynamics of this growing network considering a markov process network with hidden variables which is able to account for the mentioned properties

spectral properties of general hypergraphs abstract in this paper we investigate spectral properties of the adjacency tensor laplacian tensor and signless laplacian tensor of general hypergraphs including uniform and non uniform hypergraphs we give some properties for the spectral radius of hypergraphs and obtain spectral upper bounds for the chromatic number of hypergraphs the odd bipartiteness of hypergraphs can be recognized from the spectrum we give a relation between the analytic connectivity and edge connectivity of a hypergraph and show that a hypergraph with even rank is connected if and only if its analytic connectivity is larger than 0 we also give some relations between the analytic bipartiteness and odd bipartiteness of hypergraphs

self organized criticality and universality in a nonconservative earthquake model we make an extensive numerical study of a two dimensional nonconservative model proposed by olami feder and christensen to describe earthquake behavior phys rev lett 68 1244 1992 by analyzing the distribution of earthquake sizes using a multiscaling method we find evidence that the model is critical with no characteristic length scale other than the system size in agreement with previous results however in contrast to previous claims we find a convergence to universal behavior as the system size increases over a range of values of the dissipation parameter alpha we also find that both free and open boundary conditions tend to the same result our analysis indicates that as l increases the behavior slowly converges toward a power law distribution of earthquake sizes p s approximately equal s tau with an exponent tau approximately equal 1 8 the universal value of tau we find numerically agrees quantitatively with the empirical value tau b 1 associated with the gutenberg richter law

local modularity measure for network clusterizations many complex networks have an underlying modular structure i e structural subunits communities or clusters characterized by highly interconnected nodes the modularity q has been introduced as a measure to assess the quality of clusterizations q has a global view while in many real world networks clusters are linked mainly locally among each other local cluster connectivity here we introduce a measure of localized modularity lq which reflects local cluster structure optimization of q and lq on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters yielding a complementary view of higher granularity

the perron frobenius theorem for homogeneous monotone functions if a is a nonnegative matrix whose associated directed graph is strongly connected the perron frobenius theorem asserts that a has an eigenvector in the positive cone r n we associate a directed graph to any homogeneous monotone function f r n r n and show that if the graph is strongly connected then f has a nonlinear eigenvector in r n several results in the literature emerge as corollaries our methods show that the perron frobenius theorem is really about the boundedness of invariant subsets in the hilbert projective metric they lead to further existence results and open problems

a galerkin method for retarded boundary integral equations with smooth and compactly supported temporal basis functions we consider retarded boundary integral formulations of the three dimensional wave equation in unbounded domains our goal is to apply a galerkin method in space and time in order to solve these problems numerically in this approach the computation of the system matrix entries is the major bottleneck we will propose new types of finite dimensional spaces for the time discretization they allow variable time stepping variable order of approximation and simplify the quadrature problem arising in the generation of the system matrix substantially the reason is that the basis functions of these spaces are globally smooth and compactly supported in order to perform numerical tests concerning our new basis functions we consider the special case that the boundary of the scattering problem is the unit sphere in this case explicit solutions of the problem are available which will serve as reference solutions for the numerical experiments

time domain boundary integral equation modeling of heat transmission problems this paper investigates the numerical modeling of a time dependent heat transmission problem by the convolution quadrature boundary element method it introduces the latest theoretical development into the error analysis of the numerical scheme semigroup theory is applied to obtain stability in the spatially semidiscrete scheme functional calculus is employed to yield convergence in the fully discrete scheme we compare the results to a more traditional laplace domain approach

on the spectral radius of trees with n vertices and diameter d eigenvalues of bipartite graphs have significance in quantum chemistry therefore it is of great practical value to study the eigenvalues of bipartite graphs denote by pd 1 d 2 2 n d 1 and pd 1 d 4 2 n d 1 the trees obtained respectively from the path pd 1 by joining n d 1 pendant edges to the d 2 2 st and d 4 2 st vertices of pd 1 in this paper we prove that the spectral radius of the tree pd 1 d 2 2 n d 1 is the largest among all the trees with n vertices and diameter d and that the spectral radius of the tree pd 1 d 4 4 n d 1 is the second largest

brauer type eigenvalue inclusion sets and the spectral radius of tensors abstract in this paper we give two brauer type eigenvalue inclusion sets and some bounds on the spectral radius for tensors as applications some bounds on the spectral radius of uniform hypergraphs are presented

connected hypergraphs with small spectral radius abstract in 1970 smith classified all connected graphs with spectral radius at most 2 here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix recently the definition of spectral radius has been extended to r uniform hypergraphs in this paper we generalize smith s theorem to r uniform hypergraphs we show that the smallest limit point of the spectral radii of connected r uniform hypergraphs is r 4 r we discovered a novel method for computing the spectral radius of hypergraphs and classified all connected r uniform hypergraphs with spectral radius at most r

runge kutta methods for parabolic equations and convolution quadrature we study the approximation properties of runge kutta time discretizations of linear and semilinear parabolic equations including incompressible navier stokes equations we derive asymptotically sharp error bounds and relate the temporal order of convergence which is generally noninteger to spatial regularity and the type of boundary conditions the analysis relies on an interpretation of runge kutta methods as convolution quadratures in a different context these can be used as efficient computational methods for the approximation of convolution integrals and integral equations they use the laplace transform of the confolution kernal via a discrete operational calculus 23 refs 2 tabs

self organized criticality in the olami feder christensen model a system is in a self organized critical state if the distribution of some measured events obeys a power law the finite size scaling of this distribution with the lattice size is usually enough to assume that the system displays self organized criticality this approach however can be misleading in this paper we analyze the behavior of the branching rate ensuremath sigma of the events to establish whether a system is in a critical state we apply this method to the olami feder christensen model to obtain evidence that in contrast to previous results the model is critical in the conservative regime only

energy estimates for galerkin semidiscretizations of time domain boundary integral equations in this paper we present a battery of results related to how galerkin semidiscretization in space affects some formulations of wave scattering and propagation problems when retarded boundary integral equations are used

multistep and multistage convolution quadrature for the wave equation algorithms and experiments we describe how a time discretized wave equation in a homogeneous medium can be solved by boundary integral methods the time discretization can be a multistep runge kutta or a more general multistep multistage method the resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of lubich the aim of this work is twofold it describes an efficient robust and easily parallelizable method for solving the semidiscretized system the resulting algorithm has the main advantages of time stepping methods and of fourier synthesis at each time step a system of linear equations with the same system matrix needs to be solved yet computations can easily be done in parallel the computational cost is almost linear in the number of time steps and only the laplace transform of the time domain fundamental solution is needed the new aspect of the algorithm is that all this is possible without ever explicitly constructing the weights of the convolution quadrature this approach also readily allows the use of modern data sparse techniques to efficiently perform computation in space we investigate theoretically and numerically to which extent hierarchical matrix mathcal h matrix techniques can be used to speed up the space computation the second aim of this article is to perform a series of large scale 3d experiments with a range of multistep and multistage time discretization methods the backward difference formula of order 2 bdf2 the trapezoid rule and the 3 stage radau iia methods are investigated in detail one of the conclusions of the experiments is that the radau iia method often performs overwhelmingly better than the linear multistep methods especially for problems with many reflections yet in connection with hyperbolic problems bdfs have so far been predominant in the literature on convolution quadrature

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

potential evaluation in space time bie formulations of 2d wave equation problems in this paper we examine the computation of the potential generated by space time bie representations associated with dirichlet and neumann problems for the 2d wave equation in particular we consider the efficient evaluation of the convolution time integral that appears in the potential representation for this we propose two simple quadrature rules which appear more efficient than the currently used ones both are of gaussian type the classical gauss jacobi quadrature rule in the case of a dirichlet problem and the classical gauss radau quadrature rule in the case of a neumann problem both of them give very accurate results by using a few quadrature nodes as long as the potential is evaluated at a point not very close to the boundary of the pde problem domain to deal with this latter case we propose an alternative rule which is defined by a proper combination of a gauss legendre formula with one of product type the latter having only 5 nodes the proposed quadrature formulas are compared with the second order bdf lubich convolution quadrature formula and with two higher order lubich formulas of runge kutta type an extensive numerical testing is presented this shows that the new proposed approach is very competitive from both the accuracy and efficiency points of view

generalized convolution quadrature based on runge kutta methods in this paper we develop the runge kutta generalized convolution quadrature with variable time stepping for the numerical solution of convolution equations for time and space time problems and present the corresponding stability and convergence analysis for this purpose some new theoretical tools such as tensorial divided differences summation by parts with runge kutta differences and a calculus for runge kutta discretizations of generalized convolution operators such as an associativity property will be developed in this paper numerical examples will illustrate the stable and efficient behavior of the resulting discretization

signed k uniform hypergraphs and tensors abstract a signed k graph is a k graph with an incidence function on each vertex and its incident edge in this paper we extend some concepts of the adjacency and laplacian tensor from k graphs to signed k graphs based on the spectral properties of the real symmetric tensor we investigate the h spectrum of adjacency and laplacian tensors for signed k graphs finally the inverse perron value of any vertex is present some bounds for the inverse perron value are established in terms of some invariants including the number of vertices edges the degree sequence

transient elastic wave analysis of 3 d large scale cavities by fast multipole bem using implicit runge kutta convolution quadrature abstract existing boundary element methods bems have been proven to be efficient numerical techniques particularly in modeling wave propagation problems but still remain limitations in solving large scale problems the main disadvantages may be caused by several problems including high cost and large amount of computer memory for the computation a time domain bem in which a collocation method is used for the time discretization also shows numerical instability for small cfl courant friedrichs lewy number in this work we propose a new three dimensional 3 d approach for solving transient elastic wave propagation problems of large scale spherical and spheroidal cavities by the convolution quadrature bem accelerated by fast multipole method fmm using an implicit runge kutta scheme in abbreviation we name it as irk based cq fmbem two special techniques pertaining to the fmm including the scaling of modified spherical bessel functions and the truncation method are used to enhance the efficiency and stability of our proposed method this approach is found to be particularly suitable for 3 d large scale problems as its high accuracy stability of time marching process and computational efficiency these properties are subsequently illustrated through numerical examples dealing with large scale wave problems of 3 d single spherical and spheroidal cavities and multiple equally and irregularly spherical cavities the accuracy of the present formulation is verified by comparing the obtained results with available reference solutions in the literature some numerical aspects of time increments sizes and topological shapes of cavities and their influences on the deformations and the waveforms are investigated also detailed investigation of the computational efficiency of our proposed method such as cpu time required memory etc is presented all the implementation tasks are carried out using the tokyo tech supercomputer which is called tsubame 2 5 42

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

some upper bounds on the eigenvalues of uniform hypergraphs abstract let h be a uniform hypergraph let a h and q h be the adjacency tensor and the signless laplacian tensor of h respectively in this note we prove several bounds for the spectral radius of a h and q h in terms of the degrees of vertices of h

runge kutta convolution quadrature for the boundary element method abstract time domain boundary element formulations can be established either directly in time domain or via laplace or fourier domain somewhere in between are the convolution quadrature based boundary element formulations which utilize the laplace domain fundamental solution but establish a time stepping procedure up to now in applications mostly backward differential formulas of second order are used as the underlying multistep method however in recent mathematical literature also runge kutta methods have been applied here the use of runge kutta methods is explained in detail and some numerical studies are given in these studies the backward difference based procedures are compared to runge kutta methods for a non smooth problem an l 2 norm of the error is used as the basis of comparison the convergence of which is investigated theoretically as well the results confirm that the usage of the new techniques is preferable with regard to less numerical oscillations in the solution and better representation of wave fronts

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

a fully discrete bem fem scheme for transient acoustic waves abstract we study a symmetric bem fem coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field an incident wave in free space interacts with the obstacles and produces a combination of transmission and scattering the transmitted part of the wave is discretized in space by finite elements while the scattered wave is reduced to two fields defined on the boundary of the obstacles and is discretized in space with boundary elements we choose a coupling formulation that leads to a symmetric system of integro differential equations the retarded boundary integral equations are discretized in time by convolution quadrature and the interior field is discretized in time with the trapezoidal rule we show that the scattering problem generates a c 0 group of isometries in a hilbert space and use associated estimates to derive stability and convergence results we provide numerical experiments and simulations to validate our results and demonstrate the flexibility of the method

adaptive time discretization for retarded potentials in this paper we will present advanced discretization methods for solving retarded potential integral equations we employ a c infty c partition of unity method in time and a conventional boundary element method for the spatial discretization one essential point for the algorithmic realization is the development of an efficient method for approximation the elements of the arising system matrix we present here an approach which is based on quadrature for non analytic c infty c functions in combination with certain chebyshev expansions furthermore we introduce an a posteriori error estimator for the time discretization which is employed also as an error indicator for adaptive refinement numerical experiments show the fast convergence of the proposed quadrature method and the efficiency of the adaptive solution process

symmetric nonnegative tensors and copositive tensors abstract we first prove two new spectral properties for symmetric nonnegative tensors we prove a maximum property for the largest h eigenvalue of a symmetric nonnegative tensor and establish some bounds for this eigenvalue via row sums of that tensor we show that if an eigenvalue of a symmetric nonnegative tensor has a positive h eigenvector then this eigenvalue is the largest h eigenvalue of that tensor we also give a necessary and sufficient condition for this we then introduce copositive tensors this concept extends the concept of copositive matrices symmetric nonnegative tensors and positive semi definite tensors are examples of copositive tensors the diagonal elements of a copositive tensor must be nonnegative we show that if each sum of a diagonal element and all the negative off diagonal elements in the same row of a real symmetric tensor is nonnegative then that tensor is a copositive tensor some further properties of copositive tensors are discussed

convexity and log convexity for the spectral radius abstract the starting point of this paper is a theorem by j f c kingman which asserts that if the entries of a nonnegative matrix are log convex functions of a variable then so is the spectral radius of the matrix a related result of j cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements the first section of this paper gives a new unified proof of these results and also analyzes exactly when one has strict convexity the second section gives some very simple proofs of results of friedland and karlin concerning min max characterizations of the spectral radius of nonnegative matrices these arguments also yield as will be shown in another paper min max characterizations of the principal eigenvalue of second order elliptic boundary value problems on bounded domains the third section considers the cone k of nonnegative vectors in r n and continuous maps f k k which are homogeneous of degree one and preserve the partial order induced by k the cone spectral radius of such maps is defined and a direct generalization of kingman s theorem to a subclass of such nonlinear maps is given the final section of this paper treats a problem that arises in population biology if k 0 denotes the interior of k and f is as above when can one say that f has a unique eigenvector to within normalization in k 0 a subtle point to be noted is that f may have other eigenvectors in the boundary of k if u k 0 is an eigenvector of f u 1 and g x f x f x when can one say that for any x k 0 g p x the p th iterate of g acting on x converges geometrically to u the fourth section provides answers to these questions that are adequate for many of the population biology problems