topological bf theories in 3 and 4 dimensions in this paper we discuss topological bf theories in 3 and 4 dimensions observables are associated to ordinary knots and links in 3 dimensions and to 2 knots in 4 dimensions the vacuum expectation values of such observables give a wide range of invariants here we consider mainly the 3 dimensional case where these invariants include alexander polynomials homfly polynomials and kontsevich integrals

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

remarks on chern simons invariants the perturbative chern simons theory is studied in a finite dimensional version or assuming that the propagator satisfies certain properties as is the case e g with the propagator defined by axelrod and singer it turns out that the effective bv action is a function on cohomology with shifted degrees that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely out of it one obtains invariants

wilson surfaces and higher dimensional knot invariants an observable for nonabelian higher dimensional forms is introduced its properties are discussed and its expectation value in bf theory is described this is shown to produce potential and genuine invariants of higher dimensional knots

on generalised free products of conjugacy separable groups abstract in this paper we prove that a free product of conjugacy separable groupsaandb amalgamating a cyclic subgroup is conjugacy separable ifaandbare subgroup separable cyclic conjugacy separable 2 free and residuallyp finite for all prime numbersp the following result is an example of the applications we obtain as consequences of our main theorem letaandbeach be a free product of surface groups amalgamating a maximal cyclic subgroup then a free product ofaandb amalgamating a cyclic subgroup is conjugacy separable

the wilson loop observables of chern simons theory on ℝ3 in axial gauge we define the wilson loop observables wlos for pure chern simons models with base manifold m 3 rigorously as infinite dimensional oscillatory integrals by exploiting an axial gauge fixing and applying certain regularization techniques like loop smearing and framing the values of the wlos can be computed explicitly if the structure group g of the model considered is abelian one obtains well known linking number expressions for the wlos if g is non abelian one obtains expressions which are similar but not identical to the state sum representations for the homfly and kauffman polynomials by jones and turaev

finite volume flows and morse theory in this paper we present a new approach to morse theory based on the de rham federer theory of currents the full classical theory is derived in a transparent way the methods carry over uniformly to the equivariant and the holomorphic settings moreover the methods are substantially stronger than the classical ones and have interesting applications to geometry they lead for example to formulas relating characteristic forms and singularities of bundle maps

automatic classification of protein structure by using gauss integrals we introduce a method of looking at analyzing and comparing protein structures the topology of a protein is captured by 30 numbers inspired by vassiliev knot invariants to illustrate the simplicity and power of this topological approach we construct a measure scaled gauss metric sgm of similarity of protein shapes under this metric protein chains naturally separate into fold clusters we use sgm to construct an automatic classification procedure for the cath2 4 database the method is very fast because it requires neither alignment of the chains nor any chain chain comparison it also has only one adjustable parameter we assign 95 51 of the chains into the proper c class a architecture t topology and h homologous superfamily fold find all new folds and detect no false geometric positives using the sgm we display a map of the space of folds projected onto two dimensions show the relative locations of the major structural classes and zoom into the space of proteins to show architecture topology and fold clusters the existence of a simple measure of a protein fold computed from the chain path will have a major impact on automatic fold classification

fast numerical solution of weakly singular volterra integral equations abstract we give a fortran program for the numerical solution of abel volterra convolution equations of the second and first kind we use a fractional linear multistep method bdf4 1 2 and use fast fourier transform techniques to exploit the convolution structure a detailed description of the computation of the quadrature weights using fft is given numerical examples are included

inequalities involving bessel and modified bessel functions abstract some inequalities for the ratios j v 1 x j v x and i v 1 x i v x of bessel and modified bessel functions of the first kind and order v 1 are given the inequalities are found easily from a different definition of the ratios and improve many results obtained recently by several authors

remarks on legendrian self linking the thurston bennequin invariant provides one notion of self linking for any homologically trivial legendrian curve in a contact three manifold here we discuss related analytic notions of self linking for legendrian knots in r3 our definition is based upon reformulation of the elementary gauss linking integral and is motivated by ideas from supersymmetric gauge theory we recover the thurston bennequin invariant as a special case the thurston bennequin invariant provides one notion of self linking for any homologically trivial legendrian curve in a contact three manifold here we discuss related analytic notions of self linking for legendrian knots in r3 our definition is based upon reformulation of the elementary gauss linking integral and is motivated by ideas from supersymmetric gauge theory we recover the thurston bennequin invariant as a special case

a criterion for the conjugacy separability of amalgamated free products of conjugacy separable groups abstract we first prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a cyclic subgroup applying this result we show that tree products of a finite number of conjugacy separable residually finitely generated torsion free nilpotent groups amalgamating cyclic subgroups are conjugacy separable from this we derive that tree products of finitely generated torsion free nilpotent groups free groups or surface groups amalgamating cyclic subgroups are conjugacy separable

statistics of nonlinear stochastic dynamical systems under levy noises by a convolution quadrature approach this paper describes a novel numerical approach to find the statistics of the non stationary response of scalar nonlinear systems excited by levy white noises the proposed numerical procedure relies on the introduction of an integral transform of the wiener hopf type into the equation governing the characteristic function once this equation is rewritten as partial integro differential equation it is then solved by applying the method of convolution quadrature originally proposed by lubich here extended to deal with this particular integral transform the proposed approach is relevant for two reasons 1 statistics of systems with several different drift terms can be handled in an efficient way independently from the kind of white noise 2 the particular form of wiener hopf integral transform and its numerical evaluation both introduced in this study are generalizations of fractional integro differential operators of potential type and grunwald letnikov fractional derivatives respectively

higher dimensional bf theories in the batalin vilkovisky formalism the bv action and generalized wilson loops this paper analyzes in detail the batalin vilkovisky quantization procedure for bf theories on an n dimensional manifold and describes a suitable superformalism to deal with the master equation and the search of observables in particular generalized wilson loops for bf theories with additional polynomial b interactions are discussed in any dimensions the paper also contains the explicit proofs to the theorems stated in 16

integration of singular braid invariants and graph cohomology we prove necessary and sufficient conditions for an arbitrary in variant of braids with m double points to be the mth derivative of a braid invariant we show that the primary obstruction to integration i5 the only obstruction this gives a slight generalization of the existence theorem for vassiliev invariants of braids we give a direct proof by induction on m which works for invariants with values in any abelian group we snd that to prove our theorem we must show that every relation among four term relations satisses a certain geometric condition to snd the relations among relations we show that h1 of a variant of kontsevich s graph complex vanishes we discuss related open questions for invariants of links and other things

integral geometry of plane curves and knot invariants we study the integral expression of a knot invariant obtained as the second coefficient in the perturbative expansion of witten s chern simons path integral associated with a knot one of the integrals involved turns out to be a generalization of the classical crofton integral on convex plane curves and it is related with the invariants of generic plane curves recently defined by arnold with deep motivations in symplectic and contact geometry quadratic bounds on these plane curve invariants are derived using their relationship with the knot invariant

tree products of conjugacy separable groups abstract a group g is said to be conjugacy separable if for each pair of elements x y g such that x and y are not conjugate in g there exists a finite homomorphic image of g such that the images of x y are not conjugate in in this note we show that the tree products of finitely many conjugacy separable and subgroup separable groups amalgamating central subgroups with trivial intersections are conjugacy separable we then apply our results to polycyclic by finite groups and free by finite groups

a numerical method for a partial integro differential equation a method is considered for the integration in time of a partial integro differential equation the discretization technique employed is patterned after an idea of ch lubich error bounds are derived for both smooth and nonsmooth initial data

runge kutta convolution quadrature methods for well posed equations with memory runge kutta based convolution quadrature methods for abstract well posed linear and homogeneous volterra equations non necessarily of sectorial type are developed a general representation of the numerical solution in terms of the continuous one is given the error and stability analysis is based on this representation which for the particular case of the backward euler method also shows that the numerical solution inherits some interesting qualitative properties such as positivity of the exact solution numerical illustrations are provided

on the quadrature error in operational quadrature methods for convolutions we analyze the quadrature error associated with operational quadrature methods for convolution equations the assumptions are that the convolution kernel is inl 1 and that its laplace transform is analytic and bounded in an obtuse sector of the complex plane under these circumstances the laplace transform has a slow variation property which admits a fourier analysis of the quadrature error we provide generall p error estimates assuming suitable smoothness conditions on the function under convolution

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

feynman integrals and motives of configuration spaces we formulate the problem of renormalization of feynman integrals and its relation to periods of motives in configuration space instead of momentum space the algebro geometric setting is provided by the wonderful compactifications overline conf gamma x of arrangements of subvarieties associated to the subgraphs of a feynman graph with x a quasi projective variety the motive and the class in the grothendieck ring are computed explicitly for these wonderful compactifications in terms of the motive of x and the combinatorics of the feynman graph using recent results of li li the pullback to the wonderful compactification of the form defined by the unrenormalized feynman amplitude has singularities along a hypersurface whose real locus is contained in the exceptional divisors of the iterated blowup that gives the wonderful compactification a regularization of the feynman integrals can be obtained by modifying the cycle of integration by replacing the divergent locus with a leray coboundary the ambiguities are then defined by poincare residues while these residues give periods associated to the cohomology of the exceptional divisors and their intersections the regularized integrals give rise to periods of the hypersurface complement in the wonderful compactification

associahedra cyclohedra and a topological solution to the a deligne conjecture abstract we give a topological solution to the a deligne conjecture using associahedra and cyclohedra to this end we construct three cw complexes whose cells are indexed by products of polytopes giving new explicit realizations of the polytopes in terms of different types of trees we are able to show that the cw complexes are cell models for the little discs the cellular chains of one complex in particular which is built out of associahedra and cyclohedra naturally act on the hochschild cochains of an a algebra yielding an explicit topological and minimal solution to the a deligne conjecture along the way we obtain new results about the cyclohedra such as new decompositions into products of cubes and simplices which can be used to realize them via a new iterated blow up construction

on conjugacy separability of fundamental groups of graphs of groups a complete determination of when the elements of a fundamental group of a countable graph of profinite groups are conjugacy distinguished is given by embedding an arbitrary fundamental group g into one with profinite vertex groups and making use of the above result questions on conjugacy separability of g can be reduced to the solution of equations in the vertex groups of g

from simplicial chern simons theory to the shadow invariant ii this is the second of a series of papers in which we introduce and study a rigorous simplicial realization of the non abelian chern simons path integral for manifolds m of the form m s1 and arbitrary simply connected compact structure groups g more precisely we introduce for general links l in m a rigorous simplicial version wlorig l of the corresponding wilson loop observable wlo l in the so called torus gauge by blau and thompson nucl phys b 408 2 345 390 1993 for a simple class of links l we then evaluate wlorig l explicitly in a non perturbative way finding agreement with turaev s shadow invariant l

knot theory and the heuristics of functional integration abstract this paper is an exposition of the relationship between the heuristics of witten s functional integral and the theory of knots and links in three dimensional space

an algorithm for approximate solutions to weakly filtered synchronous control systems and nonlinear renewal processes a multi time perturbation algorithm is derived to study certain synchronous control systems and nonlinear renewal processes the new methods presented here study singular perturbation problems for nonlinear volterra integro differential equations whose kernels are close to the dirac delta function the algorithm provides useful approximate solutions to weakly filtered phase locked loop circuits and to nonlinear renewal equations describing certain population dynamics

implicit runge kutta methods for the discretization of time domain integral equations implicit runge kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory the proposed technique maps a laplace domain equation to a domain equation using the butcher tableau of the implicit runge kutta scheme a discrete time domain system is recovered by computing the inverse transform numerically the resulting technique is capable of third or fifth order accuracy in time and is stable independent of time step numerical results illustrate the accuracy and stability of the technique

diffraction of waves on square lattice by semi infinite crack in this paper a discrete analogue of sommerfeld half plane diffraction is investigated the two dimensional problem of diffraction on a square lattice of a plane transverse wave by a semi infinite crack is solved the discrete wiener hopf method has been used to obtain the exact solution of the discrete helmholtz equation with input data prescribed on the crack boundary sites due to a time harmonic incident wave it is established that there exists a unique saddle point for the diffraction integral and its properties are characterized an asymptotic approximation of the solution in the far field is provided and for some values of the frequency it is compared with the numerical solution of the diffraction problem using a finite grid a low frequency approximation of the solution in integral form recovers the classical continuum solution at sufficiently large frequency in the pass band the effects due to discreteness and anisotropy appear the analysis is relevant to a 5 point discretization bas

the topology of spaces of knots cosimplicial models we present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial these models build on the calculus of isotopy functors and are weakly homotopy equivalent to knot spaces when the ambient dimension is greater than three the mapping space model and the evaluation map on which it builds is suitable for analysis through differential topology the cosimplicial model gives rise to spectral sequences which converge to ohomology and homotopy groups of spaces of knots when they are connected we explicitly identify and establish vanishing lines in these spectral sequences

one relator groups with torsion are conjugacy separable we prove that one relator groups with torsion are hereditarily conjugacy separable our argument is based on a combination of recent results of dani wise and the first author as a corollary we obtain that any quasiconvex subgroup of a one relator group with torsion is also conjugacy separable

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

functional estimates for derivatives of the modified bessel function k0 and related exponential functions abstract let k 0 denote the modified bessel function of second kind and zeroth order in this paper we will study the function n x x n k 0 n x n for positive argument the function n plays an important role for the formulation of the wave equation in two spatial dimensions as a retarded potential integral equation we will prove that the growth of the derivatives n m with respect to n can be bounded by o n 1 m 2 while for small and large arguments x the growth even becomes independent of n these estimates are based on an integral representation of k 0 which involves the function g n t t n n exp t and its derivatives the estimates then rely on a subtle analysis of g n and its derivatives which we will also present in this paper

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

integral invariants of 3 manifolds ii this note is a sequel to our earlier paper of the same title 4 and describes invariants of rational homology 3 spheres associated to acyclic orthogonal local systems our work is in the spirit of the axelrod singer papers 1 generalizes some of their results and furnishes a new setting for the purely topological implications of their work

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

new perspectives on self linking abstract we initiate the study of classical knots through the homotopy class of the nth evaluation map of the knot which is the induced map on the compactified n point configuration space sending a knot to its nth evaluation map realizes the space of knots as a subspace of what we call the nth mapping space model for knots we compute the homotopy types of the first three mapping space models showing that the third model gives rise to an integer valued invariant we realize this invariant in two ways in terms of collinearities of three or four points on the knot and give some explicit computations we show this invariant coincides with the second coefficient of the conway polynomial thus giving a new geometric definition of the simplest finite type invariant finally using this geometric definition we give some new applications of this invariant relating to quadrisecants in the knot and to complexity of polygonal and polynomial realizations of a knot

permutahedra and generalized associahedra given a finite coxeter system w s w s and a coxeter element c or equivalently an orientation of the coxeter graph of w we construct a simple polytope whose outer normal fan is n reading s cambrian fan fc settling a conjecture of reading that this is possible we call this polytope the c generalized associahedron our approach generalizes loday s realization of the associahedron a type a c generalized associahedron whose outer normal fan is not the cluster fan but a coarsening of the coxeter fan arising from the tamari lattice to any finite coxeter group a crucial role in the construction is played by the c singleton cones the cones in the c cambrian fan which consist of a single maximal cone from the coxeter fan moreover if w is a weyl group and the vertices of the permutahedron are chosen in a lattice associated to w then we show that our realizations have integer coordinates in this lattice

vassiliev knot invariants and chern simons perturbation theory to all orders at any order the perturbative expansion of the expectation values of wilson lines in chern simons theory gives certain integral expressions we show that they all lead to knot invariants moreover these are finite type invariants whose order coincides with the order in the perturbative expansion together they combine to give a universal vassiliev invariant

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

the cyclic bar construction on a h spaces abstract we set up a general framework for enriching a category a over a symmetric monoidal category c using a non operad p in c to do this we require a to come with a functor u a to the category of noncommutative sets by viewing the simplicial indexing category as a category over in two different ways we obtain two generalizations of simplicial objects for the operad given by the stasheff associahedra we obtain a model for the 2 sided bar construction in the first case and the cyclic bar and cobar construction in the second case using either the associahedra or the cyclohedra in place of the geometric simplices we can define the geometric realization of these objects

surface holonomy for non abelian 2 bundles via double groupoids in the context of non abelian gerbes we define a cubical version of categorical group 2 bundles with connection over a smooth manifold we address their two dimensional parallel transport study its properties and construct non abelian wilson surface functionals

coxeter submodular functions and deformations of coxeter permutahedra abstract we describe the cone of deformations of a coxeter permutahedron or equivalently the nef cone of the toric variety associated to a coxeter complex this class of polytopes contains important families such as weight polytopes signed graphic zonotopes coxeter matroids root cones and coxeter associahedra our description extends the known correspondence between generalized permutahedra polymatroids and submodular functions to any finite reflection group

conjugacy separability of certain 1 relator groups with torsion abstract a group a is said to be conjugacy separable c s if for each pair of elements x y a such that x y are not conjugate in a there exists a finite homomorphic image a of a such that the images of x y in a are not conjugate in a we show that certain special polyhedral groups and 1 relator groups with torsion of the form b t t 1bltbm s s 1 are c s the latter partly answers a question raised by anshel in math rev 81f review 20038

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

solutions to the discrete airy equation application to parabolic equation calculations in the case of the equidistant discretization of the airy differential equation discrete airy equation the exact solution can be found explicitly this fact is used to derive a discrete transparent boundary condition tbc for a schrodinger type equation with linear varying potential which can be used in parabolic equation simulations in underwater acoustics and for radar propagation in the troposphere we propose different strategies for the discrete tbc and show an efficient implementation finally a stability proof for the resulting scheme is given a numerical example in the application to underwater acoustics shows the superiority of the new discrete tbc

uniform error estimates of galerkin methods for monotone abel volterra integral equations on the half line we consider galerkin methods for monotone abel volterra integral equations of the second kind on the half line the l2 theory follows from kolodner s theory of monotone hammerstein equations we derive the loo theory from the l2 theory by relating the l2and loo spectra of operators of the form x b ax to one another here denotes convolution and b e l1 and a e loo as an extra condition we need b t o t a 1 with a 0 we also prove the discrete analogue in particular we verify that the galerkin matrix satisfies the discrete conditions

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

counting alternating knots by genus it is shown that the number of alternating knots of given genus g 1 grows as a polynomial of degree 6g 4 in the crossing number the leading coefficient of the polynomial which depends on the parity of the crossing number is related to planar trivalent graphs with a bieulerian path the rate of growth of the number of such graphs is estimated

an analysis of the modified l1 scheme for time fractional partial differential equations with nonsmooth data we introduce a modified l1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous c

nonsmooth data error estimates for approximations of an evolution equation with a positive type memory term we study the numerical approximation of an integro differential equation which is intermediate between the heat and wave equations the proposed discretization uses convolution quadrature based on the first and second order backward difference methods in time and piecewise linear finite elements in space optimal order error bounds in terms of the initial data and the inhomogeneity are shown for positive times without assumptions of spatial regularity of the data

strong order of convergence of a fully discrete approximation of a linear stochastic volterra type evolution equation in this paper we investigate a discrete approximation in time and in space of a hilbert space valued stochastic process u t t 0 t satisfying a stochastic linear evolution equation with a positive type memory term driven by an additive gaussian noise the equation can be written in an abstract form as du t 0 b t s au s ds dt dw t 0 t u 0 u0 h where w is a q wiener process on h l d and where the main example of b we consider is given by b t t 1 0 0 such that a has finite trace and that q is bounded from h into d a for some real with 1 1 the discretization is achieved via an implicit euler scheme and a laplace transform convolution quadrature in time parameter t t n and a standard continuous finite element method in space parameter h let un h be the discrete solution at t n t we show that e un h u t 1 2 o h t for any 1 1 2 and 1 1 m kovacs department of mathematics and statistics university of otago po box 56 dunedin 9054 new zealand e mail mkovacs maths otago ac nz j printems laboratoire d analyse et de mathematiques appliquees cnrs umr 8050 61 avenue du general de gaulle universite paris est 94010 creteil france e mail printems u pec fr 2 mihaly kovacs jacques printems

kontsevich integral for vassiliev invariants from chern simons perturbation theory in the light cone gauge we analyze the structure of the perturbative series expansion of chern simons gauge theory in the light cone gauge after introducing a regularization prescription that entails the consideration of framed knots we present the general form of the vacuum expectation value of a wilson loop the resulting expression turns out to give the same framing dependence as the one obtained using nonperturbative methods and perturbative methods in covariant gauges it also contains the kontsevich integral for vassiliev invariants of framed knots

systems based decomposition schemes for the approximate solution of multi term fractional differential equations we give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi term fractional differential equations using the caputo form of the fractional derivative the schemes we compare are based on conversion of the original problem into a system of equations we review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation

abelian bf theories and knot invariants in the context of the batalin vilkovisky formalism a new observable for the abelian bf theory is proposed whose vacuum expectation value is related to the alexander conway polynomial the three dimensional case is analyzed explicitly and it is proved to be anomaly free moreover at the second order in perturbation theory a new formula for the second coefficient of the alexander conway polynomial is obtained an account on the higher dimensional generalizations is also given

on the self linking of knots this note describes a subcomplex f of the de rham complex of parametrized knot space which is combinatorial over a number of universal anomaly integrals the self linking integrals of guadaguini martellini and mintchev perturbative aspects of chern simons field theory phys lett b 227 111 1989 and bar natan perturbative aspects of the chern simons topological quantum field theory ph d thesis princeton university 1991 also on the vassiliev knot invariants to appear in topology are seen to represent the first nontrivial element in h0 f occurring at level 4 and are anomaly free however already at the next level an anomalous term is possible

boundary integral solvers for an evolutionary exterior stokes problem this paper proposes and analyzes a full discretization of the exterior transient stokes problem with dirichlet boundary conditions the method is based on a single layer boundary integral representation using galerkin semidiscretization in the space variables and multistep convolution quadrature in time convergence estimates are based on a laplace domain analysis which translates into a detailed study of the exterior brinkman problem some numerical experiments are provided

fractional linear multistep methods for abel volterra integral equations of the second kind fractional powers of linear multistep methods are suggested for the numerical solution of weakly singular volterra integral equations the proposed methods are convergent of the order of the underlying multistep method also in the generic case of solutions which are not smooth at the origin the stability properties stability region a stability a a stability are closely related to those of the underlying linear multistep method