lower bounds for the perron root of a nonnegative matrix abstract new lower bounds frequently better than previous bounds and readily computable for the perron root r a of a nonnegative matrix a are obtained the theoretical comparison of new bounds with the known ones is supplemented with two numerical examples

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

dynamics of a predator prey model we describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator prey model proposed by r m may stability and complexity in model ecosystems princeton university press princeton nj 1974 in particular we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear moreover we show that locally asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator prey models

two direct methods in linear programming abstract in this paper we introduce two direct methods for solving some classes of linear programming problems the first method produces the extreme vertex or a neighboring vertex with respect to the extreme point the second method is based on the game theory both these methods can be used in the preparation of the starting point for the simplex method the efficiency of the improved simplex method whose starting point is constructed by these introduced methods is compared with the original simplex method and the interior point methods and illustrated by examples also we investigate the elimination of excessive constraints

some lower bounds for the spectral radius of matrices using traces abstract let a be an n n matrix with eigenvalues 1 2 n and let m be an integer satisfying rank a m n if a is real the best possible lower bound for its spectral radius in terms of m tr a and tr a 2 is obtained if a is any complex matrix two lower bounds for j 1 n j 2 are compared and furthermore a new lower bound for the spectral radius is given only in terms of tr a tr a 2 a a a aa n and m

a sequence of lower bounds for the spectral radius of nonnegatfve matrices abstract we present a sequence of progressively better lower bounds for the s pectral radius of a nonnegative matrix each element of the sequence is a function of the spectral radius of the geometric symmetrization of a power of the matrix as defined by schwenk each element provides a better approximation to the spectral radius than the elements in the sequences provided by other authors

spatial activity allocation modelling the dominant eigenvalue and its corresponding eigenvector for the garin lowry model criteria are derived for convergence and it is shown how the forecasts are affected by changes in the parameters of the model and by fluctuations in the exogenous variables convergence occurs if and only if the dominant eigenvalue is smaller than one expressing the upper and lower bounds for the dominant eigenvalue in terms of the parameters of the model yields interpretable convergence conditions for the sensitivity analysis the model is rewritten as an eigensystem in which the endogenous variables appear as the elements of the eigenvector corresponding with the dominant eigenvalue that is the perron vector the sensitivity of the forecasts is analyzed by examining the effects of perturbations in a matrix on the perron vector

lower bounds for the spectral radius of a matrix abstract we develop lower bounds for the spectral radius of symmetric skew symmetric and arbitrary real matrices our approach utilizes the well known leverrier faddeev algorithm for calculating the coefficients of the characteristic polynomial of a matrix in conjunction with a theorem by lucas which states that the critical points of a polynomial lie within the convex hull of its roots our results generalize and simplify a proof recently published by tarazaga for a lower bound on the spectral radius of a symmetric positive definite matrix in addition we provide new lower bounds for the spectral radius of skew symmetric matrices we apply these results to a problem involving the stability of fixed points in recurrent neural networks

sharp bounds for the largest eigenvalue of the signless laplacian of a graph let g be a simple connected graph with n vertices and m edges denote the degree of vertex vi by d vi the matrix q g d g a g is called the signless laplacian of g where d g diag d v1 d v2 d vn and a g denote the diagonal matrix of vertex degrees and the adjacency matrix of g respectively let q1 g be the largest eigenvalue of q g in this paper we first present two sharp upper bounds for q1 g involving the maximum degree and the minimum degree of the vertices of g and give a new proving method on another sharp upper bound for q1 g then we present three sharp lower bounds for q1 g involving the maximum degree and the minimum degree of the vertices of g moreover we determine all extremal graphs which attain these sharp bounds

improved enhanced strain four node element with taylor expansion of the shape functions a class of enhanced strain four node elements with taylor expansion of the shape function derivatives is presented a new concept of enhancement using besides the standard enhanced strain fields also two other enhanced fields is developed on the basis of the hu washizu principle for first order taylor expansion enhanced modes become uncoupled thus only a negligible amount of computing effort for the static condensation of enhanced modes is needed furthermore the formulation permits a symbolic integration which leads to a closed form solution for the element tangent matrix several numerical examples show that the element is stable invariant passes the patch test and yields good results especially in the highly distorted regime 1997 by john wiley sons ltd

properties of a bursting model with two slow inhibitory variables models for certain excitable cells such as the pancreatic beta cell must reproduce bursting oscillations of the membrane potential this has previously been done using one slow variable to drive bursts the dynamics of such models have been analyzed however new models for the beta cell often include additional slow variables and therefore the previous analysis is extended to two slow variables using a simplified version of a beta cell model some unusual time courses of this model motivated a geometric singular perturbation analysis and the application of averaging to reduce the dynamics to the slow variable phase plane a geometric understanding of the solutionstructure and of transitions between various modes of behavior was then developed a novel use of the bifurcation code auto finds nullclines for the slow variables when the fast variables are periodic by averaging over the fast oscillations in contrast with the parabolic neuronal burster this model requires bistability in th

on matrices whose numerical ranges have circular or weak circular symmetry in 18 among other equivalent conditions it is proved that a square complex matrix a is permutationally similar to a block shift matrix if and only if for any complex matrix b with the same zero pattern as a w b the numerical range of b is a circular disk centered at the origin in this paper we add a long list of further new equivalent conditions the corresponding result for the numerical range of a square complex matrix to be invariant under a rotation about the origin through an angle of 2 m where m 2 is a given positive integer is also proved many interesting by products are obtained in particular on the numerical range of a square nonnegative matrix a the following unexpected results are established i when the undirected graph of a is connected if w a is a circular disk centered at the origin then so is w b for any complex matrix b with the same zero pattern as a ii when a is irreducible if is an eigenvalue in the peripheral spectrum of a that lies on the boundary of w a then is a sharp point of w a we also obtain results on the numerical range of an irreducible square nonnegative matrix which strengthen or clarify the work of issos 9 and nylen and tam 14 on this topic open questions are posed at the end

influence of solitons in the initial state on chaos in the driven damped sine gordon system abstract the appearance of chaos in the a c driven damped sine gordon equation is studied numerically several transitions from periodic to chaotic behaviour are investigated in detail for flat initial conditions spatial structures breather kink in the initial conditions smooth out many of these transitions and give rise to an interesting symbiosis of time and spatial intermittency this symbiosis appears to be due to the competition between the background tendency towards chaos and the system s preference to maintain a spatial pattern the way that this competition is relieved is also found to depend very strongly on symmetry in the initial conditions

nested bounds for the perron root of a nonnegative matrix abstract it is well known that for a nonnegative matrix a the smallest row sum r a and the largest row sum r a provide lower and upper bounds respectively for the perron root of a these bounds are generalized for a partitioned nonnegative matrix a the new bounds are better than r a and r a and they can be further improved by a refinement of the partition known monotonicity and convergence properties of r a and r a are generalized for the new bounds

travelling solitons in the externally driven nonlinear schrodinger equation we consider the undamped nonlinear schr dinger equation driven by a periodic external force in the absence of damping solitons do not have undulations on their tails yet we show that they can bind into stationary multisoliton complexes using two previously known stationary solitons and two newly found stationary complexes as starting points we obtain classes of localized travelling waves by the numerical continuation in the parameter space two families of stable solitons are identified one family is stable for sufficiently low velocities while solitons from the second family stabilize when travelling faster than a certain critical speed the stable solitons of the former family can also form stably travelling bound states

order bound for a family of parallel runge kutta nystrom methods through computer algebra abstract we prove a bound on the obtainable order of consistency for a family of parallel runge kutta nystrom methods using computer algebra

the use of regularization methods in computing radon nikodým derivatives application to grain size distributions let a probability law nu on a b be absolutely continuous with respect to another probability law mu specified equivalent to the lebesgue measure lambda on a b we seek to approximate the density frac d nu d mu assumed to be in l mu 2 a b in the least square sense given the values of the distribution function nu a t at fixed points t j 1 leq j leq p we obtain a convenient solution of this ill posed problem via a hilbert space embedding and the associated discretized problem is solved by using regularization methods this problem is connected with sedimentological topics such as sediment transport and changes of scale as an example a weight frequency cumulative curve is processed

growing 1d and quasi 2d unstable manifolds of maps we present a new 1d algorithm for computing the global one dimensional unstable manifold of a saddle point of a map our method can be generalized to compute two dimensional unstable manifolds of maps with three dimensional state spaces this is shown here with a quasi 2d q2d algorithm for the special case of a quasiperiodically forced map which allows for a substantial simplification of the general case described in krauskopf and osinga 1998 the key idea is to grow the manifold in steps which consist of finding a new point on the manifold at a prescribed distance from the last point the speed of growth is determined only by the curvature of the manifold and not by the dynamics the performance of the 1d algorithm is demonstrated with a constructed test example and it is then used to compute one dimensional manifolds of a map modeling mixing in a stirring tank with the q2d algorithm we compute two dimensional unstable manifolds in the quasiperiodically forced henon map

frequency and phase locking of spatially periodic perturbed sine gordon breather trains this paper considers the damped driven sine gordon equation with even periodic boundary conditions on a finite length nearly integrable perturbation methods are applied to infer approximate solution branches of space and time periodic breather trains of order one amplitude these approximate solutions consist of coherent spatial structures either homogeneous or with one breather per period which lock in frequency and phase to the small time periodic perturbation in the presence of uniform weak damping the predicted resonant breather trains are then verified by overman via direct simulation of the perturbed sine gordon pde and shown to be accurate within the order of the perturbation theory

a quasi periodic route to chaos in a near integrable pde abstract pattern formation and transitions to chaos are described for the damped ac driven one dimensional periodic sine gordon equation in a nonlinear schrodinger regime a generic quasi periodic route to intermittent chaos is exhibited in detail using a range of dynamical systems diagnostics in addition a nonlinear spectral transform is exploited i to identify and quantify coordinates of space time attractors in terms of a small number of soliton modes of the underlying integrable system ii to use these analytic coordinates to identify homoclinic orbits as possible sources of chaos and iii to demonstrate the significance of energy transfer between coherent and extended states in this chaotic system

asymptotic approximations for second order linear difference equations in banach algebras ii abstract a liouville green wkb asymptotic approximation theory is developed for some classes of linear second order difference equations in banach algebras the special case of linear matrix difference equations or equivalently of second order systems is emphasized rigorous and explicitly computable bounds for the error terms are obtained and this when both the sequence index and some parameter that may enter the coefficients go to infinity a simple application is made to orthogonal matrix polynomials in the nevai class

nystrom solution to oblique scattering of arbitrarily polarized waves by dielectric filled slotted cylinders we investigate oblique diffraction of arbitrarily polarized waves by axially slotted dielectric filled perfectly conducting circular cylinders with infinitesimally thin walls the relevant 2 2 system of coupled singular integral integrodifferential equations is solved by a highly accurate nystrom method for enhanced efficiency several asymptotic terms are extracted from the kernels this helps isolate the inherent singularities and thus transform the initial slowly converging green function expansions into rapidly converging series as a consequence all elements of the resulting nystrom matrix take exact expressions in the form of very rapidly converging series of elementary terms numerical examples and case studies are presented that validate the algorithm illustrate its rapid convergence and bring to light the effect of changing several physical and geometrical parameters on the reflection transmission and absorption characteristics of the structure

a lower bound for the perron root of a nonnegative matrix ii abstract this paper is a continuation of an earlier one by the author we obtain a new lower bound for the perron root r a of a nonnegative n n matrix a we show that for a with at least one principal submatrix of order two with different diagonal entries and with at least one positive off diagonal entry the bound is at least as good as the one from 7 and we determine a class of nonnegative matrices for which it is essentially better we also show that not every nonnegative square matrix is similar to a nonnegative square matrix with identical diagonal entries

the best possible lower bound for the perron root using traces abstract let a be an n n matrix with real eigenvalues wolkowicz and styan presented bounds for the eigenvalues using only n tr a and tr a 2 we show that their lower bound for the largest eigenvalue works also as a lower bound for the perron root of a if a is nonnegative and its eigenvalues are not necessarily real we also show that this bound is optimal under certain conditions finally we solve completely the problem to find the optimal lower bound for the perron root using only n tr a and tr a 2

bayesian d optimal designs on a fixed number of design points for heteroscedastic polynomial models summary we consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially however this dependence is not known precisely and additional parameters are required in the model our design criteria permit various subsets of the parameters to be estimated with different emphasis bayesian d optimal designs on a compact interval with the number of support points restricted to be one more than the degree of the polynomial are found analytically for a large class of priors these designs may or may not be optimal within the class of all designs depending on the prior distribution

transient sloshing in half full horizontal elliptical tanks under lateral excitation a semi analytical mathematical model is developed to study the transient liquid sloshing characteristics in half full horizontal cylindrical containers of elliptical cross section subjected to arbitrary lateral external acceleration the problem solution is achieved by employing the linear potential theory in conjunction with conformal mapping resulting in linear systems of ordinary differential equations which are truncated and then solved numerically by implementing laplace transform technique followed by durbin s numerical inversion scheme a ramp step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver the effects of tank aspect ratio excitation input time and baffle configuration on the resultant sloshing characteristics are examined limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained

fourth order differential equations satisfied by the generalized co recursive of all classical orthogonal polynomials a study of their distribution of zeros the unique fourth order differential equation satisfied by the generalized co recursive of all classical orthogonal polynomials is given for any but fixed level of recursivity up to now these differential equations were known only for each classical family separately and also for a specific recursivity level moreover we use this unique fourth order differential equation in order to study the distribution of zeros of these polynomials via their newton sum rules i e the sums of powers of their zeros which are closely related with the moments of such distribution both results are obtained with the help of two programs built in mathematica symbolic language

analytical stiffness matrices with green lagrange strain measure separating the dependence on material and stress strain state from the dependence on initial geometry we obtain analytical secant and tangent stiffness matrices for the case of a linear displacement triangle with uniform thickness and uniform constitutive behaviour closed form results are listed directly suited for coding in a finite element program the nodal positions of an element and the displacement assumption give three basic matrices of order three these matrices do not depend on material and stress strain state and thus are unchanged during the necessary iterations for obtaining a solution based on green lagrange strain measure the approach is especially useful in design optimization because analytical sensitivity analysis then can be performed the case of a three node triangular ring element for axisymmetric analysis involves small modifications and extension to four node tetrahedron elements should be straight forward copyright 2004 john wiley sons ltd

the center manifold and bifurcations of damped and driven sine gordon breathers abstract the generic bifurcations of breathers in the damped and driven sine gordon equation are investigated both numerically and analytically the linear stability analysis and information from periodic spectral theory suggest that three modes are relevant for the system they correspond to frequency and temporal phase changes and to the flat pendulum using these modes nonautonomous amplitude equations are derived and compared with numerical simulations of the perturbed sine gordon equation

quadrature formulas based on rational interpolation we consider quadrature formulas based on interpolation using the ba sis functions 1 1 tkx k 1 2 3 on 1 1 where tk are parameters on the interval 1 1 we investigate two types of quadratures quadrature formulas of maximum accuracy which correctly integrate as many basis functions as possible gaussian quadrature and quadrature formulas whose nodes are the zeros of the orthogonal functions obtained by orthogonalizing the system of basis functions or thogonal quadrature we show that both approaches involve orthogonal polynomials with modified or varying weights which depend on the number of quadrature nodes the asymptotic distribution of the nodes is obtained as well as various interlacing properties and monotonicity results for the nodes

tight bounds on the spectral radius of asymmetric nonnegative matrices abstract for an arbitrary asymmetric nonnegative n n matrix a we identify a pair of symmetric matrices whose largest eigenvalues bound the spectral radius of a furthermore we show that these bounding matrices are best possible by characterizing matrices a which attain equality with either the upper or the lower bounding matrix the lower bound may be extended to some matrices with negative entries provided they have no negative cycles

mel nikov analysis of numerically induced chaos in the nonlinear schro dinger equation abstract certain hamiltonian discretizations of the periodic focusing nonlinear schrodinger equation nls have been shown to be responsible for the generation of numerical instabilities and chaos in this paper we undertake a dynamical systems type of approach to modeling the observed irregular behavior of a conservative discretization of the nls using heuristic mel nikov methods the existence of a pair of isolated homoclinic orbits is indicated for the perturbed system the structure of the persistent homoclinic orbits that are predicted by the mel nikov theory possesses the same features as the wave form observed numerically in the perturbed system after the onset of chaotic behavior and appears to be the main structurally stable feature of this type of chaos the mel nikov analysis implemented in the pde context appears to provide relevant qualitative information about the behavior of the pde in agreement with the numerical experiments in a neighborhood of the persistent homoclinic orbits the existence of a horseshoe is investigated and related with the onset of chaos in the numerical study

half explicit runge kutta methods for differential algebraic systems of index 2 half explicit runge kutta methods for differential algebraic problems of index 2 are investigated it is shown how the arising order conditions can be solved and a particular method of order 4 is constructed in addition this paper simplifies the known convergence theory for such methods and demonstrates by numerical experiments their excellent properties when applied to constrained multibody systems

plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading free plane wave propagation in infinitely long periodic elastic structures with and without heavy fluid loading is considered the structures comprise continuous elements of two different types connected in an alternating sequence in the absence of fluid loading an exact solution which describes wave motion in each unboundedly extended element is obtained analytically as a superposition of all propagating and evanescent waves continuity conditions at the interfaces between elements are formulated and standard floquet theory is applied to set up a characteristic determinant an efficient algorithm to compute bloch parameters propagation constants as a function of the excitation frequency is suggested and the location of band gaps is studied as a function of non dimensional parameters of the structure s composition in the case of heavy fluid loading an infinitely large number of propagating or evanescent waves exist in each unboundedly extended elasto acoustic element of a periodic structure wave motion in each element is then presented in the form of a modal decomposition with a finite number of terms retained in these expansions and the accuracy of such an approximation is assessed a generalized algorithm is used to compute bloch parameters for a periodic structure with heavy fluid loading as a function of the excitation frequency and similarly to the previous case the location of band gaps is studied

a higher accuracy finite difference method for an elliptic equation of order four the elliptic equation 1 with boundary value conditions either 2 or 3 is solved by an o h4 convergent finite difference method combined with an implicit iterative method the method is tested by examples of boundary value problems with use of the enclosed mathematica module solve bhpeq the module solve bhpeq gives options either it implements the o h4 convergent nine mesh points scheme or the o h2 convergent standard five points scheme when the finite difference approximation of eq 1 is considered

existence threshold for the ac driven damped nonlinear schrodinger solitons abstractithasbeenknownforsometimethatsolitonsoftheexternallydriven dampednonlinearschrodingerequationcanonlyexistif the driver s strength h exceeds approximately 2 where is the dissipation coef cient although this perturbativeresultwasexpectedtobecorrectonlytotheleadingorderin recentstudieshavedemonstratedthattheformulah thr d 2 gives a remarkably accurate description of the soliton s existence threshold prompting suggestions that it is in fact exact in this note we evaluate the next order in the expansion of h thr showing that the actual reason for this phenomenon issimply that the next ordercoef cient is anomalously small h thr d 2 c0 002 3 our approach is based on a singularperturbation expansion of the soliton near the turning point it allows to evaluate h thr to all orders in and can be easilyreformulated for other perturbed soliton equations 1999 elsevier science b v all rights reserved pacs 03 40 kf 42 65 tg 42 81 dp 1 introductiontheexternallydriven dampednonlinearschrodinger nls equation i9

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

bounds for the spectral radius and the largest singular value abstract we derive an increasing sequence of lower bounds for the spectral radius of a matrix with real spectrum and progressively improved bounds for the largest singular value of a complex matrix we also find estimates for the rank of normal matrices with real spectrum and for the rank of normal nonnegative matrices including some sufficient condition for such matrices to be invertible

perron root bounding for nonnegative persymmetric matrices the eigenvalue problem for a symmetric persymmetric matrix can be reduced to two symmetric eigenvalue problems of lower order in this paper we find in which of these problems the perron root of a nonnegative symmetric persymmetric matrix lies this is applied to bound the perron root of such class of matrices

consequences of double allee effect on the number of limit cycles in a predator prey model the main goal of this work is to show a comparative analysis of simple continuous time predator prey models considering the allee effect affecting the prey population also known as depensation in fisheries sciences this phenomenon may be expressed by different mathematical forms yielding a distinct number of limit cycles surrounding a positive equilibrium point when two of these different formalizations are considered in the same system it is known that the volterra predation model using the most usual form to express the allee effect has a unique limit cycle in this work considering a more complex mathematical expression the existence of two limit cycles is proved by means of the lyapunov quantities we argue that the second equation explains the existence of two allee effects affecting the same population which could justify the difference observed between the models these results imply that the election of mathematical formulation can have consequences on the fit of the observed data thus leading to mistakes for ecologists we conclude that the oscillatory behaviors and overall dynamics depend strongly on the algebraic expression of the allee effect making difficult the proposition of general results nevertheless the techniques reviewed in this paper emerge as key tools to analyze the existence of limit cycles in the presence of multiple allee effects

stability and bifurcation of spatially coherent solutions of the damped driven nls equation an analytical study is conducted of the structure stability and bifurcation of the spatially dependent time periodic solutions of the damped driven sine gordon equation in the nonlinear schrodinger approximation locked states are found for which the spatial structure consists of coherent excitations localized about x 0 or l 2 a bifurcation analysis reveals the relationship of these spatially localized solutions to the spatially independent ones and provides a cutoff wavenumber above which there are no spatially dependent solutions this establishes an upper bound on the number of local excitations comprising the spatial pattern a linear stability analysis shows that the spatially localized solutions undergo a hopf bifurcation to temporal quasi periodicity as the driver amplitude gamma is increased for sufficiently high driver frequencies the temporally periodic solution regains its stability via another hopf bifurcation in a gamma window of finite width before undergoing a third hop

vsvo formulation of the taylor method for the numerical solution of odes this paper presents an analysis of the taylor method for the numerical solution of odes when a very high precision of the solution is required some theoretical properties of the taylor method are considered from the practical point of view a variable stepsize variable order vsvo scheme is presented and its utility is discussed with several examples to reach the goal of high precision the use of multiprecision libraries is considered finally some numerical tests based on the test problems given in 1 and on a set of important problems in dynamical systems and astrodynamics are presented showing the benefits of the vsvo formulation especially for high precision demands compared with a well established runge kutta code

unique real variable expressions of the integral kernels in the somigliana stress identity covering all transversely isotropic elastic materials for 3d bem abstract a formulation and computational implementation of the hypersingular stress boundary integral equation for the numerical solution of three dimensional linear elastic problems in transversely isotropic solids is developed the formulation is based on a new closed form real variable expression of the integral kernel s ijk giving tractions originated by an infinitesimal dislocation loop the source of singularity work conjugated to stress tensor this expression is valid for any combination of material properties and for any orientation of the radius vector between the source and field points the expression is based on compact expressions of u ik in terms of the stroh eigenvalues on the plane normal to the radius vector performing double differentiation of u ik for deducing the second derivative kernel u ik jl the stress influence function of an infinitesimal dislocation loop ijkl loop are first obtained obtaining then the integral kernel s ijk the expressions of s ijk and of the related kernels ijkl loop and u ik jl do not suffer from the difficulties of some previous expressions obtained by other authors in different ways with complex valued functions appearing for some combinations of material parameters and or with division by zero for the radius vector at the rotational symmetry axis the expressions of the above mentioned kernels have been presented in a form suitable for an efficient computational implementation the correctness of these expressions and of their implementation in a three dimensional collocational bem code has been tested numerically by solving problems with known analytic solutions for different classes of transversely isotropic materials the obtained expressions will be useful in the development of bem codes applied to composite materials geomechanics and biomechanics in particular an application to biomechanics of the bem code developed is shown additionally these expressions can be employed in the distributed dislocation technique to solve crack problems

a composite polynomial zerofinding matrix algorithm abstract a globally convergent matrix algorithm is presented for finding the real and complex zeros of a complex polynomial p x a combination of schmeisser s and fiedler s matrices is used in the algorithm first the greatest common divisor g x of p x and its derivative p x is obtained and used to reduce p x to a polynomial q x p x q x with simple zeros second the zeros of q x are computed either by finding the eigenvalues of the first block of schmeisser s matrix or by applying fiedler s algorithm recursively in either case the eigenvalues are obtained by the qr algorithm third the multiplicity of each zero of p x is calculated by means of lagouanelle s modified limiting formula sample numerical results are given to demonstrate the effectiveness of the algorithm

calculation of manin s invariant for del pezzo surfaces for r 7 and 8 we consider an action of the weyl group of type e r on a unimodular lattice of rank r 1 we give the tables of the first cohomology groups for all cyclic subgroups of the weyl group with respect to this action these are important in the arithmetic theory of del pezzo surfaces

inequalities for the perron root related to levinger s theorem abstract for the perron roots of square nonnegative matrices a b and a d 1btd where d is a diagonal matrix with positive diagonal entries the inequality a d 1btd a b is proved under the assumption that a and b have a common unordered pair of nonorthogonal right and left perron vectors the case of equality is analyzed the above inequality generalizes the inequality a 1 bt a 1 b proved under stronger assumptions by bapat and implies a generalization of levinger s theorem on the monotonicity of the perron root of a weighted arithmetic mean of a nonnegative matrix and its transpose also for the perron root a c d 1atd c c 1 0 c of a weighted entrywise geometric mean of a and d 1atd where a ij and o denotes the hadamard product the monotonicity property dual to that asserted by generalized levinger s theorem is established

on the spectral radius of positive operators on banach sequence spaces abstract let k 1 k n be infinite non negative matrices that define operators on a banach sequence space given a function f 0 0 0 of n variables we define a non negative matrix f k 1 k n and consider the inequality r f k 1 k n 1 n r k 1 r k n where r denotes the spectral radius we find the largest function f for which this inequality holds for all k 1 k n we also obtain an infinite dimensional extension of the result of cohen asserting that the spectral radius is a convex function of the diagonal entries of a non negative matrix

some monotonicity properties of schur powers of matrices and related inequalities abstract a series of inequalities are developed relating the spectral radius a b of the schur product a b of two nonnegative matrices a and b with those of a a and b b yielding a b a a b b 1 2 as a corollary it is proved that the spectral radius of the schur powers r a r a r a a a r factors satisfies 1 r log r is decreasing while 1 r 1 log r is increasing the latter provided a is a stochastic matrix the entropy of a finite stationary markov chain is identified with d r dr r 1 a number of majorization comparisons for the spectral radius of schur powers is given

a poincare birkhoff witt theorem for generalized lie color algebras a proof of the poincare birkhoff witt theorem is given for a class of generalized lie algebras closely related to the gurevich s lie algebras as concrete examples we construct the positive negative parts of the quantized universal enveloping algebras of type an and mp q e n k which is a nonstandard quantum deformation of gl n in particular we get for both algebras a unified proof of the poincare birkhoff witt theorem and we show that they are genuine universal enveloping algebras of certain generalized lie algebras

inequalities of rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices abstract given a square nonnegative symmetric matrix a the rayleigh quotient of a nonnegative vector u under a is given by q a u u t au u t u we show that qa u au is not less than qa u where denotes coordinatewise square roots and is the hadamard product but that qa au may be smaller than qa u further we examine issues of convergence

a lower bound for the spectral radius of a digraph abstract we show that the spectral radius d of a digraph d with n vertices and c 2 closed walks of length 2 satisfies d c 2 n moreover equality occurs if and only if d is the symmetric digraph associated to a c 2 n regular graph plus some arcs that do not belong to cycles as an application of this result we construct new sharp upper bounds for the low energy of a digraph which extends koolen and moulton bounds of the energy to digraphs

an integral with three parameters in this paper we give an exact expression for the integral begin eqnarray i a b r int 0 infty left frac x 2 x 4 2a x 2 1 right r cdot frac x 2 1 x b 1 cdot frac dx x 2 nonumber end eqnarray in terms of euler s beta function several classical integrals are deduced from it the expression for i a b r provides a method for unifying a large class of integrals