unique real variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3d bem a general efficient and robust boundary element method bem formulation for the numerical solution of three dimensional linear elastic problems in transversely isotropic solids is developed in the present work the bem formulation is based on the closed form real variable expressions of the fundamental solution in displacements uik and in tractions tik originated by a unit point force valid for any combination of material properties and for any orientation of the radius vector between the source and field points a compact expression of this kind for uik was introduced by ting and lee q j mech appl math 1997 50 407 426 in terms of the stroh eigenvalues on the oblique plane normal to the radius vector working from this expression of uik and after a revision of their final formula a new approach based on the application of the rotational symmetry of the material for deducing the derivative kernel uik j and the corresponding stress kernel ijk and traction kernel tik has been developed in the present work these expressions of uik uik j ijk and tik 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 uik uik j ijk and tik 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 analytical solutions for different classes of transversely isotropic materials copyright 2007 john wiley sons ltd

examples of attractors in scalar reaction diffusion equations on considere l equation de reaction diffusion scalaire avec des conditions aux limites de neumann u t e 2 u xx f x u 0 x 1 u x 0 t u x 1 t 0 pour une non linearite f x u u 1 u u a x ou a 0 1 0 1 est une fonction echelon on etudie la caracterisation de l attracteur quand e est petit

jacobi matrices and transversality the paper deals with smooth nonlinear ode systems in n f x such that the derivative f x has a matrix representation of jacobi type not necessarily symmetric with positive off diagonal entries a discrete functional is introduced and is discovered to be nonincreasing along the solutions of the associated linear variational system f x t y two families of transversal cones invariant under the flow of that linear system allow us to prove transversality between the stable and unstable manifolds of any two hyperbolic critical points of the given nonlinear system it is also proved that the nonwandering points are critical points a new class of morse smale systems in n is then explicitly constructed

the singular limit dynamics of semilinear damped wave equations on considere la dynamique qualitative d une equation d onde amortie semi lineaire a une dimension dans la limite singuliere correspondant a l annulation du coefficient de la derivee d ordre 2 en temps

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

boundary element method for thermoelastic analysis of three dimensional transversely isotropic solids abstract thermal effects are well known to manifest themselves as additional volume integral terms in the direct formulation of the boundary integral equation bie for linear elastic solids when using the boundary element method bem this domain integral has been successfully transformed in an exact manner to surface ones only in isotropy and in 2d anisotropy thereby restoring the bem as a truly boundary solution technique the difficulties with extending it to 3d general anisotropic solids lie in the mathematical complexity of the green s function and its derivatives for such materials these quantities are required items in the bem formulation in this paper the exact analytical transformation of the volume integral associated with thermal effects to surface ones is achieved for a transversely isotropic material using a similar approach which the authors have previously employed for the same task in bem for 2d general anisotropy a numerical scheme however needs to be employed to evaluate some of the new terms introduced in the surface integrals that arise from this process here the mathematical soundness of the formulation is demonstrated by a few examples the numerical results obtained are checked by alternative means including those obtained from the commercial fem code ansys

structural stability for time periodic one dimensional parabolic equations denote q w x 0 l x r the nonlinear term f is assumed to satisfy the following conditions f l f q r is of class c f 2 f t l x u f t x u for all te w xe o l and uer define a self adjoint operator a in x l2 0 l by a t bxx for e d a h2 0 l a ha o l for each c1 e r let a be the fractional power of a and x d a be the fractional power space equipped with the graph norm ii 11 xn 1111 11x iia i ii x throughout this section we fix a c1 1 by the above assumptions f l f 2 for any u0 e x there exists a unique local in time classical solution u t x u t x of

on the bottleneck tree alignment problems given a set w of k sequences and a tree t with k leaves labeled with a unique sequence in w a label tree is used to assign a sequence label to each internal node of the tree t the cost of a tree edge is defined as the distance such as the hamming distance or the levenshtein edit distance between the sequence labels of a pair of nodes in the edge the bottleneck edge of a label tree is the edge with the maximum cost in the label tree the bottleneck tree alignment problem is concerned with the determination of a label tree with minimum cost of the bottleneck edge a lifted label tree is a label tree in which the sequence label of each internal node is equal to the sequence label of some child of the node the bottleneck lifted tree alignment problem involves the minimization of cost of the bottleneck edge among all possible lifted label trees of the tree t this paper shows that when the distance function is a metric the bottleneck tree alignment problem is np complete even when the tree structure resembles a binary tree for special cases an exact algorithm is used to solve the bottleneck lifted tree alignment problem in polynomial time a 2 h 1 approximation algorithm is used to solve the bottleneck tree alignment problem where h is the height of the tree t it is observed that the bound is existentially tight finally this paper shows that any lifted label tree is an optimal solution to the bottleneck tree alignment problem if the distance function is an ultrametric

non approximability of weighted multiple sequence alignment we consider a weighted generalization of multiple sequence alignment msa with sum of pair score msa without weights is known to be np complete and can be approximated within a constant factor but it is unknown whether it has a polynomial time approximation scheme weighted multiple sequence alignment wmsa can be approximated within a factor of o log2n where n is the number of sequences we prove that wmsa alignment is max jnp hard and establish a numerical lower bound on its approximability namely 324 323 e this lower bound is obtained already for the simple binary weighted case where the weights are restricted to 0 and 1 furthermore we show that wmsa and its restriction to binary weights can be approximated to the same degree

boundary integral equation solution of three dimensional elastostatic problems in transversely isotropic solids using closed form displacement fundamental solutions the boundary integral equation method is used for the solution of three dimensional elastostatic problems in transversely isotropic solids using closed form fundamental solutions the previously published point force solutions for such solids were modified and are presented in a convenient form especially suitable for use in the boundary integral equation method the new presentations are used as a basis for accurate numerical computations of all green s functions necessary in the bem process without inaccuracy and redundant computations the validity of the new presentation is shown through three numerical examples copyright 2000 john wiley sons ltd

a computational model for rna multiple structural alignment this paper addresses the problem of aligning multiple sequences of noncoding rna ncrna genes we approach this problem with the biologically motivated paradigm that scoring of ncrna alignments should be based primarily on secondary structure rather than nucleotide conservation we introduce a novel graph theoretic model nlg for analyzing algorithms based on this approach prove that the rna multiple alignment problem is np complete in this model and present a polynomial time algorithm that approximates the optimal structure of size s within a factor of o log 2s

a sequence of order relations encoding heteroclinic connections in scalar parabolic pde abstract we address the problem of heteroclinic connections in the attractor of dissipative scalar semilinear parabolic equations type display u t u xx f x u u x 0 on a bounded interval with neumann conditions introducing a sequence of order relations we prove a new and simple criterion for the existence of heteroclinic connections using only information about nodal properties of solutions to the stationary ode problem this result also allows for a complete classification of possible attractors in terms of the permutation of the equilibria given by their order at the two boundaries of the interval

sturm attractors for quasilinear parabolic equations abstract the goal of this paper is to construct explicitly the global attractors of quasilinear parabolic equations as it was done for the semilinear case by brunovsk and fiedler 1986 8 and generalized by fiedler and rocha 1996 13 in particular we construct heteroclinic connections between hyperbolic equilibria stating necessary and sufficient conditions for heteroclinics to occur such conditions can be computed through a permutation of the equilibria lastly an example is computed yielding the well known chafee infante attractor

self similar blow up in higher order semilinear parabolic equations we study the cauchy problem in re times re for one dimensional 2mth order m 1 semilinear parabolic pdes of the form d x partial partial x u t dx u u p 1 u mbox where p 1 quad mbox and quad u t dx u e u with bounded initial data u0 x specifically we are interested in those solutions that blow up at the origin in a finite time t we show that in contrast to the solutions of the classical second order parabolic equations ut uxx up and ut uxx eu from combustion theory the blow up in their higher order counterparts is asymptotically self similar in particular there exist exact nontrivial self similar blow up solutions u x t t t 1 p 1 f y in the case of the polynomial nonlinearity and u x t ln t t f y for the exponential nonlinearity where y x t t 1 2m is the backward higher order heat kernel variable the profiles f y satisfy related semilinear odes that share the same non self adjoint higher order linear dif

3d bem for general anisotropic elasticity abstract a new method for computing the system matrices g and h of the three dimensional boundary element method is presented for the elastostatic problems of general anisotropy green s functions expressed by the line integrals over a semi circle have a simple structure that allows analytical integration over the boundary elements the computation for the system matrices g and h is reduced to numerical integration of regular line integrals over the unit semi circle the proposed method has been implemented and tested with numerical examples

the complexity of multiple sequence alignment with sp score that is a metric this paper analyzes the computational complexity of computing the optimal alignment of a set of sequences under the sum of all pairs sp score scheme we solve an open question by showing that the problem is np complete in the very restricted case in which the sequences are over a binary alphabet and the score is a metric this result establishes the intractability of multiple sequence alignment under a score function of mathematical interest which has indeed received much attention in biological sequence comparison

determination of interior point stresses in two dimensional bem thermoelastic analysis of anisotropic bodies abstract in conventional boundary element method bem analysis the displacements and stresses at an interior point of an elastic body are obtained using the respective somigliana s identities after the boundary solutions for the displacements and tractions have been solved for this paper presents the derivation of somigliana s identity for the strains at any interior point of an anisotropic domain subjected to thermal effects from these strains the corresponding stresses at the interior point may be calculated directly using the duhamel neumann relation this identity is obtained in terms of integrals over the boundary of the solution domain only difficulties arising from the exact transformation of the volume integral term associated with thermal loading in bem analysis into surface integrals in the anisotropic case are discussed and the procedures to overcome them are described three numerical examples are presented to demonstrate the veracity of the formulations developed

generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle in this paper we show that for scalar reaction diffusion equations on the circle s 1 the property of hyperbolicity of all equilibria and periodic orbits is generic with respect to the non linearity in other words we prove that in an appropriate functional space of non linear terms in the equation the set of functions for which all equilibria and periodic orbits are hyperbolic is a countable intersection of open dense sets the main tools in the proof are the property of the lap number and the sard smale theorem

approximation algorithms for multiple sequence alignment we consider the problem of aligning of k sequences of length n the cost function is sum of pairs and satisfies triangle inequality earlier results on finding approximation algorithms for this problem are due to gusfield 1991 who achieved an approximation ratio of 2 2 k and pevzner 1992 who improved it to 2 3 k we generalize this approach to assemble an alignment of k sequences from optimally aligned subsets of l k sequences to obtain an improved performance guarantee for arbitrary l k we devise deterministic and randomized algorithms yielding performance guarantees of 2 l k for fixed l the running times of these algorithms are polynomial in n and k

a permutation characterization of sturm global attractors of hamiltonian type abstract we consider neumann boundary value problems of the form u t u x x f on the interval 0 x for dissipative nonlinearities f f u a permutation characterization for the global attractors of the semiflows generated by these equations is well known even in the much more general case f f x u u x we present a permutation characterization for the global attractors in the restrictive class of nonlinearities f f u in this class the stationary solutions of the parabolic equation satisfy the second order ode v f v 0 and we obtain the permutation characterization from a characterization of the set of 2 periodic orbits of this planar hamiltonian system our results are based on a diligent discussion of this mere pendulum equation

a poincare bendixson theorem for scalar reaction diffusion equations for scalar equations u t u xx f x u u x with x e s 1 and f e c 2 we show that the classical theorem of poincare and bendixson holds the limit set of any bounded solution satisfies exactly one of the following alternatives this is surprising because the system is genuinely infinite dimensional

the morse smale property for a semi linear parabolic equation on etudie la dynamique d equations aux derivees partielles paraboliques semi lineaires du type suivant u t u xx f x u 0 0 u 0 t u 1 t 0 t 0 u x 0 x

realization of meander permutations by boundary value problems abstract we consider neumann boundary value problems of the form uxx f x u ux 0 on the unit interval 0 x 1 for a certain class of dissipative nonlinearities f associated to these problems we have i meanders in the phase space u ux r 2 which are connected oriented simple curves on the plane intersecting a fixed oriented line the u axis in n points corresponding to the solutions and ii meander permutations f s n obtained by ordering the intersection points first along the u axis and then along the meander the meander permutation f is the permutation defined by the braid of solutions in the space x u ux it was recently shown by fiedler and rocha that f determines the global attractor of the dynamical system generated by the semilinear parabolic differential equation ut uxx f x u ux up to c0 orbit equivalence therefore these permutations are of considerable importance in the classification problem of the morse smale attractors for these dynamical systems in this paper we present a purely combinatorial characterization of the set of meander permutations that are realizable by the above boundary value problems

on a spectrum of blow up patterns for a higher order semilinear parabolic equation we describe a spectrum of blow up patterns for the 2 m th order semilinear parabolic equation u t m u u p x r n t 0 m 1 p 1 this problem is well understood in the second order case m 1 the semilinear heat equation where for p p s n 2 n 2 the inner space time structure of blow up patterns is locally governed by separable hermite polynomials of arbitrary finite order as eigenfunctions of a linear self adjoint differential operator we consider m 1 and describe a principle idea of constructing of a spectrum of blow up patterns which in the inner self similar region are composed of a countable subset of separable kummer9s polynomials which are eigenfunctions of a non self adjoint linear differential operator a matching procedure extends such linearized structures to the nonlinear intermediate region where the asymptotic blow up behaviour is described by a unique self similar solution of the first order hamilton jacobi equation

explicit construction of an inertial manifold for a reaction diffusion equation abstract an inertial manifold is constructed for the scalar reaction diffusion equation u t vu xx u with a cubic nonlinearity uniform bounds are obtained for the number of zeros along solutions to the variational equations satisfied by the difference of two elements on the unstable manifolds of equilibria this uniformity leads to the global parameterization of the attractor as a function defined in the linear unstable manifold of the least stable equilibrium by the introduction of local techniques near each equilibrium we succeed in constructing an inertial manifold of lowest possible dimension

on the two dimensional muskat problem with monotone large initial data we consider the evolution of two incompressible immiscible fluids with different densities in porous media known as the muskat problem 21 which in two dimensions is analogous to the hele shaw cell 24 we establish for a class of large and monotone initial data the global existence of weak solutions the proof is based on a local well posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function 2016 wiley periodicals inc

transversality in scalar reaction diffusion equations on a circle abstract we prove that stable and unstable manifolds of hyperbolic periodic orbits for general scalar reaction diffusion equations on a circle always intersect transversally the argument also shows that for a periodic orbit there are no homoclinic connections the main tool used in the proofs is matano s zero number theory dealing with the sturm nodal properties of the solutions

transversality of stable and unstable manifolds for parabolic problems arising in composite materials abstract in this paper we study one dimensional parabolic problems that arise from composite materials we show that the eigenvalues and eigenfunctions of the associated linear unbounded operator have the sturm liouville property and the nonincrease of the lap number along the solutions these results are used to show that the stable and unstable manifolds of equilibrium points are transversal

curve shortening and the topology of closed geodesics on surfaces we study flat knot types of geodesics on compact surfaces m2 for every flat knot type and any riemannian metric g we introduce a conley index associated with the curve shortening flow on the space of immersed curves on m2 we conclude existence of closed geodesics with prescribed flat knot types provided the associated conley index is nontrivial

the dynamics of rotating waves in scalar reaction diffusion equations on etudie l attracteur compact maximal pour l equation u t u xx f u u x avec des conditions aux limites periodiques on montre qu un ensemble limite contient une onde de rotation

complicated dynamics in scalar semilinear parabolic equations in higher space dimension abstract we study the dynamics of the boundary value problem ut lu g x u u x 1 u 0 2 where l is a second order uniformly elliptic operator and r n is diffeomorphic to the ball in r n n 2 the main result asserts that given any ck vector field v on r n 1 with v 0 0 one can adjust coefficients of l and the function g such that the corresponding problem 1 2 has an n 1 dimensional invariant manifold through the equilibrium u 0 and the taylor expansion at u 0 of the vector field representing the flow on this manifold coincides in appropriate coordinates with the taylor expansion of v up to k th order terms this result implies that a hyperbolic invariant n torus can be found in 1 2 if l and g are appropriately chosen this result also indicates that chaotic dynamics is likely to occur for some choices of l and g

solutions to the nonautonomous bistable equation with specified morse index part i existence we investigate the existence of unstable solutions of specified morse index for the equation e 2 u xx f x u 0 on a finite interval and neumann boundary conditions

generic hyperbolicity for the equilibria of the one dimensional parabolic equation ut a x ux x f u abstract we show for some classes of diffusion coefficients that generically in f all equilibria of the reaction diffusion equation u t a x u x x f u 0 with homogeneous neumann boundary conditions are hyperbolic

floquet bundles for scalar parabolic equations for linear scalar parabolic equations such as u t u xx a t x u x b t x u on a finite interval 0 x with various boundary conditions we obtain canonical floquet solutions u n t x these solutions are characterized by the property that z u n t x n for all te where z denotes the zero crossing lap number of matano the coefficients a t x and b t x are not assumed to be periodic in t but if they are the solutions u n t x reduce to the standard floquet solutions our results may naturally be expressed in the language of linear skew product flows in this context we obtain for each n 1 an exponential dichotomy between the bundles span u n 1 and overline span u n cdot cdot n n 1 infty

stable patterns for fourth order parabolic equations we consider fourth order parabolic equations of gradient type for the sake of simplicity the analysis is carried out for the specific equation u

heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle abstract we investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction advection diffusion equations with periodic boundary conditions using zero number properties of the solutions and the phase shift equivariance of the equation we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves

derivatives of the three dimensional green s functions for anisotropic materials abstract a concise formulation is presented for the derivatives of green s functions of three dimensional generally anisotropic elastic materials direct calculation for derivatives of the green s function on the cartesian coordinate system is a common practice which however usually leads to a complicated course in this paper the green s function derived by ting and lee ting t c t lee v g 1997 the three dimensional elastostatic green s function for general anisotropic linear elastic solids the quarterly journal of mechanics and applied mathematics 50 3 407 426 is extended to obtain the derivatives using a spherical coordinate system the green s function can be shown as the composition of two independent functions one depends only on the radial distance of the field point to the origin and the other is in spherical angles the method of derivation is based on the total differential scheme and then takes its partial differentiation accordingly with the application of cauchy residue theorem the contour integral can be evaluated in terms of the stroh eigenvalues of a sextic equation for the degenerate case evaluation of residues at multiple poles is also given applications of the present result are made to examine the green s functions and stress components for isotropic and transversely isotropic materials the results are in exact agreement with existing solutions

connectivity and design of planar global attractors of sturm type ii connection graphs abstract based on a morse smale structure we study planar global attractors a f of the scalar reaction advection diffusion equation u t u x x f x u u x in one space dimension we assume neumann boundary conditions on the unit interval dissipativeness of f and hyperbolicity of equilibria we call a f sturm attractor because our results strongly rely on nonlinear nodal properties of sturm type the planar sturm attractor consists of equilibria of morse index 0 1 or 2 and their heteroclinic connecting orbits the unique heteroclinic orbits between adjacent morse levels define a plane graph c f which we call the connection graph its 1 skeleton c f 1 consists of the unstable manifolds separatrices of the index 1 morse saddles we present two results which completely characterize the connection graphs c f and their 1 skeletons c f 1 in purely graph theoretical terms connection graphs are characterized by the existence of pairs of hamiltonian paths with certain chiral restrictions on face passages their 1 skeletons are characterized by the existence of cycle free orientations with certain restrictions on their criticality such orientations are called bipolar in h de fraysseix p o de mendez p rosenstiehl bipolar orientations revisited discrete appl math 56 1995 157 179 in b fiedler c rocha connectivity and design of planar global attractors of sturm type i orientations and hamiltonian paths crelle j reine angew math 2007 in press we have shown the equivalence of the two characterizations moreover we have established that connection graphs of sturm attractors indeed satisfy the required properties in the present paper we show conversely how to design a planar sturm attractor with prescribed plane connection graph or 1 skeleton of the required properties in b fiedler c rocha connectivity and design of planar global attractors of sturm type iii small and platonic examples 2007 submitted for publication we describe all planar sturm attractors with up to 11 equilibria we also design planar sturm attractors with prescribed platonic 1 skeletons

analytical transformation of the volume integral in the boundary integral equation for 3d anisotropic elastostatics involving body force abstract in the boundary element method bem it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations to restore the bem s distinctive notion of boundary discretization the present work analytically transforms the volume integral to surface ones for the body force effect in the 3d anisotropic elasticity on applying green s theorem new fundamental solutions with explicit forms of fourier series are introduced to facilitate the volume to surface transformation the coefficients of the fourier series representations are determined by solving a banded matrix formulated from integrations of the constrained equation of no doubt such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3d anisotropic elasticity involving body force at the end numerical verifications of the volume to surface integral transformation are presented also such an approach has been implemented in an existing bem code for demonstrating the implementation numerical examples are presented with comparisons with ansys analysis to the author s knowledge this is the first work in the open literature that reports the successful transformation for 3d anisotropic elasticity

reaction diffusion systems coupled at the boundary and the morse smale property abstract we study an one dimensional nonlinear reaction diffusion system coupled on the boundary such system comes from modeling problems of temperature distribution on two bars of same length jointed together with different diffusion coefficients we prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic to this end we write the system as an equation with noncontinuous diffusion coefficient we then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the sturm liouville properties of the solutions of a linear elliptic problem

order structures and the heat equation abstract in this paper we shall introduce the notion of order structure and use it to study properties of a solution u x t of a scalar linear parabolic equation it is well known that in one space dimension the number of zeros of u t is nonincreasing with t this zero number is an example of an order structure and the zero number property is very useful in unfolding the structure of the global attractor of the semiflow generated by a scalar parabolic equation we shall prove that in one space dimension the zero number is the only order structure preserved by linear parabolic equations in two dimensions the only order structure preserved by linear parabolic equations is the order structure induced by the comparison principle for second order equations consequently in two dimensions there does not exist a fine decomposition into equivalence classes as in the one dimensional case