a reconstruction based chebyshev collocation method for the poisson equation an accurate treatment of the gibbs wilbraham phenomenon on irregular interfaces abstract an accurate numerical solution of the laplace equation and poisson equation is desirable in physical problems related to fluid flows and spectral methods are well suited towards this goal however in the presence of an interface the solution is discontinuous owing to the interface jump conditions and thus the numerical approximation is susceptible to the gibbs wilbraham phenomenon leading to a reduced solution accuracy in order to resolve the discontinuity at the interface we propose a reconstruction technique wherein the approximate solution is expressed as the sum of an infinitely differentiable smooth function and a modified heaviside function the smooth function is composed of chebyshev polynomials while the modified heaviside function is expressed in a weak form using the jump conditions across the interface the reconstruction framework allows us to impose the interfacial conditions exactly to motivate further application of the technique we first present the underlying rationale by revisiting the work of wilbraham 1848 13 followed by the numerical implementation we present numerical solution of four equations to illustrate the application of the proposed technique i an ordinary differential equation ode ii the euler bernoulli equation iii the laplace equation and iv the poisson equation the laplace and poisson equation are solved on a square domain embedded with complex interfacial geometries in two dimensions and on a cube with a spherical interface in three dimensions the method achieves error in the maximum norm o 10 14 using approximately 30 modes in each direction and requires a computational time of less than a second for all the problems we also conduct a sensitivity analysis to demonstrate the robustness of the algorithm under sub grid scale perturbations to interface location an alternate derivation for the modified heaviside function is proposed that is distinct from the taylor series expansion used to treat interface conditions in difference methods the pointwise error plots are subsequently presented to demonstrate that the gibbs wilbraham phenomenon is accurately resolved finally we present concluding thoughts on the potential applications of the reconstruction technique

exact closed form solution for the vibration modes of the euler bernoulli beam with multiple open cracks abstract in this study exact closed form expressions for the vibration modes of the euler bernoulli beam in the presence of multiple concentrated cracks are presented the proposed expressions are provided explicitly as functions of four integration constants only to be determined by the standard boundary conditions the enforcement of the boundary conditions leads to explicit expressions of the natural frequency equations besides the evaluation of the natural frequencies neither computational work nor recurrence expressions for the vibration modes are required the cracks that are not subjected to the closing phenomenon are modelled as a sequence of dirac s delta generalised functions in the flexural stiffness the eigen mode governing equation is formulated over the entire domain of the beam without enforcement of any continuity conditions which are already accounted for in the adopted flexural stiffness model the vibration modes of beams with different numbers of cracks under different boundary conditions have been analysed by means of the proposed closed form expressions in order to show their efficiency

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

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

penetration through slots in conducting cylinders part 2 tm case three methods for determining the penetration through small apertures in closed conducting surfaces are outlined and their salient features discussed these methods are designated 1 the scatterer method 2 the short circuit current method and 3 the equivalent current method they are implemented by integral equation techniques but are amenable to differential equation or hybrid methods procedures for applying each method are outlined as are schemes for repairing singular equations rendered invalid by the presence of false resonances reasons for inaccuracies in the three methods are also delineated data determined for a given structure by all three methods are presented and numerical examples that illustrate important features of the methods and their relative accuracies are described it is pointed out that some methods yield incorrect penetration data an outline is given of the integral equation formulations and numerical schemes needed to accurately determine the field that penetrates through a slot in a conducting cylinder excited by an axially independent te source

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

physically based dirac s delta functions in the static analysis of multi cracked euler bernoulli and timoshenko beams abstract dirac s delta functions enable simple and effective representations of point loads and singularities in a variety of structural problems leading very often to elegant and otherwise unworkable closed form solutions this is the case of cracked beams under static loads whose theoretical and practical significance has attracted in recent years the interest of many researchers nevertheless analytical formulations currently available for this problem are not completely satisfactory either in terms of computational efficiency when the continuity conditions must be enforced with auxiliary equations or in terms of physical consistency when the singularities in the beam s flexural rigidity are represented with dirac s delta functions having a questionable negative sign these considerations motivate the present study which offers a novel and physically based modelling of slender euler bernoulli beams and short timoshenko beams with any number and severity of cracks conducing in both cases to exact closed form solutions for validation purposes a standard finite element code is used along with two nascent deltas uniform and gaussian density functions to describe a smeared increase in the bending flexibility around the abscissa of the crack

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

on applications of generalized functions to beam bending problems using a mathematical approach this paper seeks an eacient solution to the problem of beams bending under singular loading conditions and having various jump discontinuities for two instances the boundary value problem that describes beam bending cannot be written in the space of classical functions in the first instance the beam is under singular loading conditions such as point forces and moments and in the second instance the dependent variable s and its derivatives have jump discontinuities in the most general case we consider both instances first we study singular loading conditions and present a theorem by which the equivalent distributed force of a general class of singular loading conditions can be found as a consequence of obtaining the equivalent distributed force of a distributed moment we find a mathematical explanation for the corner condition in classical plate theory while plate theory is not the focus of this paper this explanation is interesting then beams with various jump discontinuities are considered when beams have jump discontinuities the form of the governing diaerential equations changes we find the governing diaerential equations in the space of generalized functions it is shown that for euler bernoulli beams with jump discontinuities the operator of the diaerential equation remains unchanged only the force term changes so that delta function and its distributional derivatives appear within it but for timoshenko beams with jump discontinuities in addition to changes in the force terms the operator of one of the governing diaerential equations changes we then propose a new method for solving these equations this method which we term the auxiliary beam method is to solve the governing diaerential equations not in the space of generalized functions but rather to solve them by means of solving equivalent boundary value problems in the space of classical functions the auxiliary beam method reduces the number of diaerential equations and at the same time obviates the need to solve these diaerential equations in the space of generalized functions which can be more diacult 7 2000 elsevier science ltd all rights reserved

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

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

multi cracked euler bernoulli beams mathematical modeling and exact solutions localized flexibility models of cracks enable one for simple and effective representation of the behavior of damaged beams and frames important applications such as the determination of closed form solutions and the development of diagnostic methods of analysis have attracted the interest of many researchers in recent years nevertheless certain fundamental questions have not been completely clarified yet one of these issues concerns with the mechanical justification of the macroscopic model of rotational elastic spring commonly used to describe the presence of an open crack in a beam under bending deformation two main analytical formulations have been recently proposed to take into account the singularity generated by the crack the crack is represented by suitable dirac s delta functions either in the beam s flexural rigidity or in the beam s flexural flexibility both approaches require some caution due to mathematical subtleties of the analysis motivated by these considerations in this paper we propose a justification of the rotational elastic spring model of an open crack in a beam in bending deformation we show that this localized flexibility model of a crack is the variational limit of a family of one dimensional beams when the flexural stiffness of these beams tends to zero in an interval centered at the cracked cross section and simultaneously the length of the interval vanishes in a suitable way we also show that the static and dynamic problem for the flexibility model of cracked beam can be formulated within the classical context of the theory of distributions avoiding the hindrances encountered in previous approaches to the problem in addition the proposed treatment leads to a simple and efficient determination of exact closed form solutions of both static and dynamic problems for beams with multiple cracks

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

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

closed form solutions of euler bernoulli beams with singularities abstract the problem of the integration of the static governing equations of the uniform euler bernoulli beam with discontinuities is studied in particular two types of discontinuities have been considered flexural stiffness and slope discontinuities both the above mentioned discontinuities have been modeled as singularities of the flexural stiffness by means of superimposition of suitable distributions generalized functions to a uniform one dimensional field closed form solutions of governing differential equation requiring the knowledge of the boundary conditions only are proposed and no continuity conditions are enforced at intermediate cross sections where discontinuities are shown the continuity conditions are in fact embedded in the flexural stiffness model and are automatically accounted for by the proposed integration procedure finally the proposed closed form solution for the cases of slope discontinuity is compared with the solution of a beam having an internal hinge with rotational spring reproducing the slope discontinuity

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

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

a symmetric system of mixed painleve iii v equations and its integrable origin a mixed symmetric painleve iii v model which describes a hybrid of both equations is defined and obtained by successive self similarity and dirac lagrange multiplier reductions from an integrable 4 boson hierarchy

generalized solutions to a linear discontinuous differential equation in this paper we construct generalized solutions weak solutions to a linear discontinuous differential equation which appears as mathematical model in mechanics and for which usual methods are not quite adequate the result is applied to the equation of an elastic beam on a winkler type of foundation

an accurate boundary value problem solver applied to scattering from cylinders with corners in this paper we consider the classic problem of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries the scattering problems are formulated as integral equations and solved using a nystrom scheme where the corners of the cylinders are efficiently handled by a method referred to as recursively compressed inverse preconditioning rcip this method has been very successful in treating static problems in nonsmooth domains and the present paper shows that it works equally well for the helmholtz equation in the numerical examples we focus on scattering of e and h waves from a cylinder with one corner even at a size kd 1000 where k is the wavenumber and d the diameter the scheme produces at least 13 digits of accuracy in the electric and magnetic fields everywhere outside the cylinder

one generalization of the second painleve hierarchy new integrable hierarchy of ordinary differential equations is presented this hierarchy is shown to generalize the p2 hierarchy while on the other hand this hierarchy gives a special case of the third painleve equation the isomonodromic linear problem is used to find this new hierarchy the painleve approach to investigate the fourth order ordinary differential equation of this hierarchy is applied

the application of chebyshev polynomials to the solution of the nonprismatic timoshenko beam vibration problem abstract chebyshev series approximation is applied to solve the problem of vibration of the nonprismatic timoshenko beam resting on a two parameter elastic foundation as a result a system of equations whose coefficients have a closed form for calculating the coefficients of the sought solution is obtained the method is used to solve the free vibration problem for simple supported and clamped free nonprismatic beams the results are compared with the results obtained by other authors also the nonprismatic beam stability problem is solved and the results are compared with those obtained for euler beams to demonstrate the method s applicability to more complex systems the problem of stability of a frame system is solved

exact solution of the multi cracked euler bernoulli column abstract the use of distributions generalized functions is a powerful tool to treat singularities in structural mechanics and besides providing a mathematical modelling their capability of leading to closed form exact solutions is shown in this paper in particular the problem of stability of the uniform euler bernoulli column in presence of multiple concentrated cracks subjected to an axial compression load under general boundary conditions is tackled concentrated cracks are modelled by means of dirac s delta distributions an integration procedure of the fourth order differential governing equation which is not allowed by the classical distribution theory is proposed the exact buckling mode solution of the column as functions of four integration constants and the corresponding exact buckling load equation for any number position and intensity of the cracks are presented as an example a parametric study of the multi cracked simply supported and clamped clamped euler bernoulli columns is presented

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

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

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

on euler bernoulli discontinuous beam solutions via uniform beam green s functions abstract the bending problem of euler bernoulli discontinuous beams is dealt with the purpose is to show that uniform beam green s functions can be used to build efficient solutions for beams with internal discontinuities due to along axis constraints and flexural stiffness jumps specifically upon deriving the equilibrium equation in the space of generalized functions first it is seen that the original bending problem may be recast as linear superposition of a principal and an auxiliary bending problem both involving a uniform reference beam and homogeneous boundary conditions then based on the green s functions of the reference beam closed form solutions are developed for the principal beam response while the auxiliary beam response is obtained by solving in general r 2 s algebraic equations written at the discontinuity locations being r the number of discontinuities due to along axis constraints and s the number of flexural stiffness jumps in this manner an appreciable reduction of computational effort is achieved as compared to alternative analytical solutions in the literature

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

exponentially converging nystro spl uml m s methods for systems of singular integral equations with applications to open closed strip or slot loaded 2 d structures this paper concerns the fast highly accurate and exponentially convergent solution of three sets of integral equations pertaining to two dimensional generalized microstrip or microslot structures the analysis relies on nystroumlm s method with due regard to all singular integrals and slowly converging series that appear in the kernels the sophisticated treatment and efficient computation of such series and integrals is of paramount importance entailing the use of advanced techniques as a result of our specialized treatment the discretization procedures developed herein a fully account for both the singular nature of the kernels and the singularities of the solution at the edges b obviate the need for taking inner products with testing functions c appear to converge exponentially versus matrix size and d enable expressing all matrix elements via single finite sums detailed numerical examples and case studies illustrate the simplicity flexibility and remarkable efficiency of the algorithms

exponentially converging nystrom methods in scattering from infinite curved smooth strips part 1 tm case low order subdomain basis methods of moments provide little help when highly accurate electromagnetic computations are required high order modeling on the other hand can fill the need for enhanced accuracy but at the expense of greater implementation cost to supplement such methods this paper presents nystrom techniques both easily implemented and highly accurate relevant to te scattering by arbitrarily shaped smooth infinite curved strips the analysis takes full account of both the singular nature of the kernels and the singularities of the solution at the edges as a result the proposed solutions are exponentially converging in addition by eliminating inner product integrals closed form analytical expressions are obtained for all matrix elements thus our algorithms have very low implementation and computational cost detailed numerical examples and case studies amply demonstrate the efficiency stability and extremely high accuracy of the algorithms these algorithms apply uniformly from electrically small to electrically large conducting screens with only slight modifications the present analysis can be also used to obtain exponentially converging galerkin solutions

special polynomials associated with rational solutions of the fifth painleve equation in this paper special polynomials associated with rational and algebraic solutions of the fifth painleve equation pv are studied these special polynomials defined by second order bilinear differential difference equations which are equivalent to toda equations the structure of the zeroes of these special polynomials which involve a parameter is investigated and it is shown that these have an intriguing symmetric and regular structure for large negative values of the parameter the zeroes have an approximate triangular structure as the parameter increases the zeroes coalesce for certain values and eventually for large positive values of the parameter the zeroes also have an approximate triangular structure though with the orientation reversed in fact the interaction of the zeroes is solitonic in nature since the same pattern reappears with its orientation reversed

on nonuniform euler bernoulli and timoshenko beams with jump discontinuities application of distribution theory in this article bending of nonuniform euler bernoulli and timoshenko beams with jump discontinuities in the slope deflection and mechanical properties are studied the governing equations are obtained in the space of generalized functions and the expression of its governing differential equations in terms of a single displacement function and a single rotation function is shown always to be possible in contrast for a nonuniform euler bernoulli beam with jump discontinuities in slope and deflection and abrupt changes in flexural stiffness the governing equation can be written in terms of a single displacement function only under certain conditions it is observed that for most discontinuous nonuniform euler bernoulli beams we cannot write the governing differential equation in terms of a single displacement function usually if there are n discontinuity points on a nonuniform euler bernoulli beam n 1 displacement functions appear in the governing equilibrium equation

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

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

analysis of non homogeneous timoshenko beams with generalized damping distributions abstract this paper presents a study on the effects of generalized damping distributions on non homogeneous timoshenko beams on the basis of some fundamentals of modal analysis for damped continuous systems applied to the particular case of the timoshenko beam model the eigenproblem is solved by applying a method combining a state space representation with a transfer matrix technique yielding closed form expressions for the eigenfunctions after validation by means of numerical examples using the finite element method response functions in both the time and the frequency domain are discussed and compared according to different damping distributions