eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

hodge integrals and degenerate contributions hodge integral techniques are used to compute the degree 1 degenerate contributions of curves of arbitrary genus in the gromov witten theory of 3 folds in the calabi yau case the contributions are compared to related m theoretic calculations in the fano case the contributions suggest new integrality conditions

tracing the equilibrium path beyond compound critical points a unified presentation of some popular continuation procedures used in the non linear finite element analysis of structural mechanics is introduced an extension of the elliptical constraint equation proposed by crisfield is given it is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur for bifurcation points a modification of rheinboldt s branching procedure is presented post critical response after limit and bifurcation points is determined in some numerical examples

gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

real gromov witten theory in all genera and real enumerative geometry construction the first part of this work constructs positive genus real gromov witten invariants of realorientable symplectic manifolds of odd complex dimensions the second part studies the orientations on the moduli spaces of real maps used in constructing these invariants the present paper applies the results of the latter to obtain quantitative and qualitative conclusions about the invariants defined in the former after describing large collections of real orientable symplectic manifolds we show that the genus 1 real gromov witten invariants of sufficiently positive almost kahler threefolds are signed counts of real genus 1 curves only and thus provide direct lower bounds for the counts of these curves in such targets we specify real orientations on the real orientable complete intersections in projective spaces the real gromov witten invariants they determine are in a sense canonically determined by the complete intersection itself at least in most cases we also obtain equivariant localization data that computes the real invariants of projective spaces and determines the contributions from many torus fixed loci for other complete intersections our results confirm walcher s predictions for the vanishing of these invariants in certain cases and for the localization data in other cases

numerical treatment of complete load deflection curves a method for direct computation of complete load deflection curves including both primary and secondary branches as well as exact calculation of singular points is presented the method used for path following is the cylindrical arc length method in accordance with crisfield to calculate singular points an extended system as proposed by keener and keller has been adopted the numerical problems arising from ill conditioned stiffness matrices near the singular points are circumvented using a deflation technique by a modification of the constraint equation used in the arc length method a reliable method for branch switching has been obtained this leads to a unified approach to complete path following of structures with limit and bifurcation points the use of this approach is demonstrated both on a simple two bar truss as well as on a star shaped shallow truss dome which exhibits complex stability characteristics comparisons are made with calculations found in the literature 1998 john wiley sons ltd

geometrically nonlinear analysis of functionally graded plates using the element free kp ritz method abstract the nonlinear response of functionally graded ceramic metal plates fgps under mechanical and thermal loads is investigated using the mesh free kp ritz method the nonlinear formulation is based on the first order shear deformation plate theory and the von karman strains which deal with small strains and moderate rotations the material properties of fgps are assumed to be graded through the thickness direction according to a power law distribution of the volume fraction of the constituents the approximation of the displacement field is expressed in terms of a set of mesh free kernel particle functions the bending stiffness of the plates is evaluated using a stabilized conforming nodal integration method and the membrane and shear stiffnesses are computed using direct nodal integration to eliminate shear locking the nonlinear behavior of the deflection and axial stress is studied for fgps under thermal and mechanical loading and the influences of the volume fraction exponent boundary condition and material properties on the nonlinear response of fgps are examined

gauss manin connection in disguise calabi yau threefolds we describe a lie algebra on the moduli space of non rigid compact calabi yau threefolds enhanced with differential forms and its relation to the bershadsky cecotti ooguri vafa holomorphic anomaly equation in particular we describe algebraic topological string partition functions bf f g rm alg g geq 1 which encode the polynomial structure of holomorphic and non holomorphic topological string partition functions our approach is based on grothendieck s algebraic de rham cohomology and on the algebraic gauss manin connection in this way we recover a result of yamaguchi yau and alim lange in an algebraic context our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of calabi yau threefolds correspond to coordinates on such a moduli space we discuss the mirror quintic as an example

invariant measure of scalar first order conservation laws with stochastic forcing under an hypothesis of non degeneracy of the flux we study the long time behaviour of periodic scalar first order conservation laws with stochastic forcing in any space dimension for sub cubic fluxes we show the existence of an invariant measure moreover for sub quadratic fluxes we show uniqueness and ergodicity of the invariant measure also since this invariant measure is supported by l p for some p small we are led to generalize to the stochastic case the theory of l 1 solutions developed by chen and perthame ann inst h poincare anal non lineaire 20 4 645 668 2003

a comparison theorem for gromov witten invariants in the symplectic category abstract we exploit the geometric approach to the virtual fundamental class due to fukaya ono and li tian to compare gromov witten invariants of a symplectic manifold and a symplectic submanifold whenever all constrained stable maps to the former are contained in the latter to first order various special cases of the comparison theorem in this paper have long been used in the algebraic category some of them have also appeared in the symplectic setting combined with the inherent flexibility of the symplectic category the main theorem leads to a confirmation of pandharipande s gopakumar vafa prediction for gw invariants of fano classes in 6 dimensional symplectic manifolds the proof of the main theorem uses deformations of the cauchy riemann equation that respect the submanifold and carleman similarity principle for solutions of perturbed cauchy riemann equations in a forthcoming paper we apply a similar approach to relative gromov witten invariants and the absolute relative correspondence in genus 0

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

an orthogonal residual procedure for non linear finite element equations a general and robust solution procedure for non linear finite element equations with limit points is developed at each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state the method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector the orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters passage of load and displacement limit points is discussed as well as the relation to line search minimum residual and arc length methods the method is illustrated by two examples

a hybrid method for efficient solution of geometrically nonlinear structures abstract we propose a novel hybrid method for calculating accurate responses of geometrically nonlinear structures exhibiting complex snap through and snap back behaviours the proposed method employs a hybrid evolutionary algebraic method to obtain each point of the equilibrium path where the equilibrium is formulated generally as a minimisation problem genetic algorithm and nelder mead simplex methods are used together as the hybrid optimiser to obtain any arbitrary point of the equilibrium path we only need a series of sparse matrix to vector multiplications and do not require information about previous equilibrium states the assembly of tangent stiffness matrix the solution of a set of system of linear equations or factorisation processes both primary and secondary paths can be followed in addition utilising the tangent stiffness matrix this method can effectively find both the limit and bifurcation points directly the state of non proportional loading can also be considered successfully additionally we show how to generate the solution of a structure whose geometrical and mechanical properties vary slightly starting from the original solution finally to demonstrate the efficiency and capabilities of the present approach three examples that are well known for their complex snap through snap back load deflection curves are comprehensively studied and the results obtained are compared with those reported in the literature

mirror symmetry for closed open and unoriented gromov witten invariants abstract in the first part of this paper we obtain mirror formulas for twisted genus 0 two point gromov witten gw invariants of projective spaces and for the genus 0 two point gw invariants of fano and calabi yau complete intersections this extends previous results for projective hypersurfaces following the same approach but we also completely describe the structure coefficients in both cases and obtain relations between these coefficients that are vital to the applications to mirror symmetry in the rest of this paper in the second and third parts of this paper we confirm walcher s mirror symmetry conjectures for the annulus and klein bottle gw invariants of calabi yau complete intersection threefolds these applications are the main results of this paper in a separate paper the genus 0 two point formulas are used to obtain mirror formulas for the genus 1 gw invariants of all calabi yau complete intersections

boundary element free method befm for two dimensional elastodynamic analysis using laplace transform in this paper we present a direct meshless method of boundary integral equation bie known as the boundary element free method befm for two dimensional 2d elastodynamic problems that combines the bie method for 2d elastodynamics in the laplace transformed domain and the improved moving least squares imls approximation the formulae for the befm for 2d elastodynamic problems are given and the numerical procedures are also shown the befm is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables and the boundary conditions can be implemented directly and easily that leads to a greater computational precision for the purpose of demonstration some selected numerical examples are solved using the befm copyright 2005 john wiley sons ltd

landau ginzburg calabi yau correspondence for quintic three folds via symplectic transformations we compute the recently introduced fan jarvis ruan witten theory of w curves in genus zero for quintic polynomials in five variables and we show that it matches the gromov witten genus zero theory of the quintic three fold via a symplectic transformation more specifically we show that the j function encoding the fan jarvis ruan witten theory on the a side equals via a mirror map the i function embodying the period integrals at the gepner point on the b side this identification inscribes the physical landau ginzburg calabi yau correspondence within the enumerative geometry of moduli of curves matches the genus zero invariants computed by the physicists huang klemm and quackenbush at the gepner point and yields via givental s quantization a prediction on the relation between the full higher genus potential of the quintic three fold and that of fan jarvis ruan witten theory

the burgers equation with poisson random forcing we consider the burgers equation on the real line with forcing given by poissonian noise with no periodicity assumption under a weak concentration condition on the driving random force we prove existence and uniqueness of a global solution in a certain class we describe its basin of attraction that can also be viewed as the main ergodic component for the model we establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics we also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case

geometric non linear analysis of folded plate structures by the spline strip kernel particle method this paper investigates the geometric non linear behaviour of stiffened and un stiffened folded plate structures using the spline strip kernel particle method sskpm the first order shear deformable plate theory and large deflection theory of von karman are employed the folded plate structures are considered as assemblies of individual stiffened and un stiffened flat plates that lie on different planes we regard these stiffened and un stiffened plate structures as superelements and superpose their stiffness matrices to derive the final global stiffness matrices several numerical example problems are examined and comparison studies are carried out with other available results the effect of the size of the support the order of the polynomial basis functions and the spacing of the spline nodes on the convergence of the proposed method is examined

stability boundaries of two parameter non linear elastic structures abstract the load bearing capacity of structures can be influenced by variations in parameters such as initial geometric defects multi parameter loadings material specifications and temperature this paper aims to introduce a new formulation to trace the stability boundaries of two parameter elastic structures the proposed procedure can find a set of critical points both limit and bifurcation ones via a modified newton s method in the authors formulation the residual force is set to zero and a critically constraint is satisfied simultaneously numerical examples presented in this paper demonstrate the efficiency of the suggested method

on the calculation of limit and bifurcation points in stability problems of elastic shells abstract numerical methods for the computation of singular points of nonlinear equations g u 0 are discussed where and are real parameters simple and double limit points are treated in some detail and numerical algorithms are presented and applied to elastic shell stability problems the case of simple symmetry breaking bifurcation points is also treated with applications to nonsymmetric bifurcation from axisymmetric states of deformation of shells of revolution

localization computation of one point disk invariants of projective calabi yau complete intersections we define one point disk invariants of a smooth projective calabi yau complete intersection in the presence of an anti holomorphic involution via localization we show that these invariants are rational numbers and obtain a formula for them which confirms in particular a conjecture by jinzenji shimizu int j geom method m 11 1 1456005 2014 conjecture 1

numerical simulation of thermomechanical behaviours of shape memory alloys via a non linear mesh free galerkin formulation a new computational approach is developed based on the mesh free method for the numerical simulation of shape memory alloys a thermomechanical constitutive model is used to describe the complex material response the incremental displacement based mesh free formulation is constructed in a total lagrangian description by employing the moving least square shape function and rate form of the shape memory alloy constitutive model in the variational equations this mesh free formulation is not only applicable to large deformation problems but also accounts for both stress and thermally induced phase transformation moreover the newly developed mesh free codes can deal with complex loading paths and multiple temperature cycles in numerical simulation the performance of the proposed mesh free scheme for the simulation of shape memory alloys is demonstrated in several numerical examples copyright 2005 john wiley sons ltd

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a general procedure for the direct computation of turning and bifurcation points we address the formulation and numerical implementation of general purpose algorithme suitable for the direct computation of stability points in non linear solid mechanics the effectiveness of the resulting algorithm is illustrated by numerical simulation that include bifurcation and loss of stability in elastoplasticity non linear rods and non linear three dimensional shells

enumeration of genus two curves with a fixed complex structure in ℙ 2 and ℙ 3 the main concrete result of this paper is enumeration of genus two curves with complex structure fixed in p and p along the way rational curves with certain simple singularities are counted as well while the methods described can be used to count positive genus curves in some other cases the most powerful direct applications of the machinery developed are to enumeration of rational curves with a very large class of singularities in projective spaces

the reduced genus 1 gromov witten invariants of calabi yau hypersurfaces 0 introduction 691 0 1 mirror symmetry predictions for a quintic threefold 691 0 2 computing gw invariants of hypersurfaces 693 0 3 mirror symmetry formulas for projective cy hypersurfaces 695 1 equivariant cohomology and stable maps 698 1 1 definitions and notation 698 1 2 setup for localization computation on m1 1 p d 701 1 3 contributions from fixed loci i 704 1 4 contributions from fixed loci ii 708 2 localization computations 712 2 1 regularizable power series in rational functions 712 2 2 regularizability of gw generating functions 714 2 3 proofs of propositions 1 1 and 1 2 717 3 algebraic computations 721 3 1 linear independence in symmetric rational functions 722 3 2 the genus 0 generating functions 723 3 3 proof of theorem 3 725 appendix a some combinatorics 730 appendix b comparison of mirror symmetry formulations 733 acknowledgments 736 references 736

mesh free radial point interpolation method for the buckling analysis of mindlin plates subjected to in plane point loads in this paper a mesh free approach is employed for buckling analysis of mindlin plates that are subjected to in plane point loads the radial point interpolation method rpim is used to approximate displacements based on nodes variational forms of the system equations are established two step solution procedures are implemented the non uniform pre stress distribution of plate is first obtained using the rpim based on a two dimensional 2d elastic plane stress problem this predetermined non uniform pre stress distribution is then used to compute buckling loads of plate using the rpim based on mindlin s plate assumption the rpim can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads numerical examples considered here include circular and rectangular mindlin plates that are subjected to in plane uniform and point loads with different aspect ratios and boundary conditions the present results are validated against the available analytical and numerical solutions copyright 2004 john wiley sons ltd

lower bounds for enumerative counts of positive genus real curves abstract we transform the positive genus real gromov witten invariants of many real orientable symplectic threefolds into signed counts of curves these integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints we conclude with some implications and related conjectures for hodge integrals

reduced genus one gromov witten invariants in a previous paper we described a natural closed subset m 0 1 k x a j of the moduli space m1 k x a j of stable genus one j holomorphic maps into a symplectic manifold x in this paper we generalize the definition of the main component to moduli spaces of perturbed in a restricted way j holomorphic maps this generalization implies that m 0 1 k x a j just like m1 k x a j carries a virtual fundamental class and can be used to define symplectic invariants these truly genus one invariants constitute part of the standard genus one gromovwitten invariants which arise from the entire moduli space m1 k x a j the new invariants are more geometric and can be used to compute the genus one gw invariants of complete intersections as shown in a separate paper

flip a method for adaptively zoned particle in cell calculations of fluid flows in two dimensions a method is presented for calculating fluid flow in two dimensions using a full particle in cell representation on an adaptively zoned grid the method has many interesting properties among them an almost total absence of numerical dissipation and the ability to represent large variations in the data the method is described using a standard formalism and its properties are illustrated by supersonic flow over a step and the interaction of a shock with a thin foil

direct computation of critical equilibrium states for spatial beams and frames summary in this paper explicit formulas for second order derivatives of the residual vector with respect to the state variables for a geometrically exact 3d beam element based on the reissner s model are presented these derivatives are required when a direct non linear stability eigenvalue problem is solved by the newton s method if the external load is parametrized by a single parameter such an eigenvalue problem consists of solving the critical state variables the eigenmode and the critical load parameter from the equation system consisting of the equilibrium equations the criticality condition and some auxiliary conditions depending on the type of a critical point copyright 2011 john wiley sons ltd

ergodicity of 2d navier stokes equations with random forcing and large viscosity the stochastically forced two dimensional incompressable navier stokes equations are shown to possess an unique invariant measure if the viscosity is taken large enough this result follows from a stronger result showing that at high viscosity there is a unique stationary solution which attracts solutions started from arbitrary initial conditions that is to say the system has a trivial random attractor along the way results controling the expectation and averaging time of the energy and enstrophy are given

transversality in elliptic morse theory for the symplectic action our goal in this paper is to settle some transversality question for the perturbed nonlinear cauchy riemann equations on the cylinder these results play a central role in the denition of symplectic floer homology and hence in the proof of the arnold conjecture there is currently no other reference to these transversality results in the open literature our approach does not require aronszajn s theorem instead we derive the unique continuation theorem from a generalization of the carleman similarity principle

buckling and free vibration analyses of stiffened plates using the fsdt mesh free method this paper presents a mesh free galerkin method for the free vibration and stability analyses of stiffened plates via the first order shear deformable theory fsdt the model of a stiffened plate is formed by 1 regarding the plate and the stiffener separately 2 imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the mid surface displacement of the plate and 3 superimposing the strain energy of plate and stiffener because there are no meshes used in this method the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines several numerical examples are computed by this method to show its accuracy and convergence the present results demonstrate good agreement with the existing solutions given by other researchers and the ansys influences of support size and order of the complete basis functions on the numerical accuracy are also investigated

boundary element free method befm and its application to two dimensional elasticity problems in this study we first discuss the moving least square approximation mls method in some cases the mls may form an ill conditioned system of equations so that the solution cannot be correctly obtained hence in this paper we propose an improved moving least square approximation imls method in the imls method the orthogonal function system with a weight function is used as the basis function the imls has higher computational efficiency and precision than the mls and will not lead to an ill conditioned system of equations combining the boundary integral equation bie method and the imls approximation method a direct meshless bie method the boundary element free method befm for two dimensional elasticity is presented compared to other meshless bie methods befm is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables and the boundary conditions can be applied easily hence it has higher computational precision for demonstration purpose selected numerical examples are given

on nonlinear stochastic balance laws we are concerned with multidimensional stochastic balance laws we identify a class of nonlinear balance laws for which uniform spatial bv bound for vanishing viscosity approximations can be achieved moreover we establish temporal equicontinuity in l1 of the approximations uniformly in the viscosity coefficient using these estimates we supply a multidimensional existence theory of stochastic entropy solutions in addition we establish an error estimate for the stochastic viscosity method as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions various further generalizations of the results are discussed

averaging lemmas without time fourier transform and application to discretized kinetic equations we prove classical averaging lemmas in the l2 framework with the help of the fourier transform in variables x and v but not t this method is then used to study discretized problems arising out of the numerical analysis of kinetic equations

analytic torsion for calabi yau threefolds after bershadsky cecotti ooguri vafa we introduce an invariant of calabi yau threefolds which we call the bcov invariant and which we obtain using analytic torsion we give an explicit formula for the bcov invariant as a function on the compactified moduli space when it is isomorphic to a projective line as a corollary we prove the formula for the bcov invariant of quintic mirror threefolds conjectured by bershadsky cecotti ooguri vafa

stochastic scalar conservation laws we introduce a notion of stochastic entropic solution a la kruzkov but with ito s calculus replacing deterministic calculus this results in a rich family of stochastic inequalities defining what we mean by a solution a uniqueness theory is then developed following a stochastic generalization of l1 contraction estimate an existence theory is also developed by adapting compensated compactness arguments to stochastic setting we use approximating models of vanishing viscosity solution type for the construction while the uniqueness result applies to any spatial dimensions the existence result in the absence of special structural assumptions is restricted to one spatial dimension only

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

complex variable boundary element free method for two dimensional elastodynamic problems abstract we proposed a new direct meshless boundary integral equation technique the complex variable boundary element free method cvbefm based on the complex variable moving least squares cvmls approximation and the boundary element free method befm to study the two dimensional elastodynamic problems with the cvmls approximation the trial function of a two dimensional problem is formed with a one dimensional basis function the number of unknown coefficients in the trial function of the cvmls approximation is less than that in the trial function of the moving least squares mls approximation therefore it requires fewer nodes in the meshless method which formed from the cvmls approximation than that formed from the mls approximation with no lose of precision the laplace transform is used to formulate the boundary integral equations of the two dimensional elastodynamics and then the formulae of the cvbefm for two dimensional elastodynamic problems are derived the cvbefm is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables moreover in the cvbefm the boundary conditions can be applied directly and easily that leads to a greater computational precision in this paper we selected a few numerical examples to illustrate the applicability of the cvbefm

gopakumar vafa bps invariants hilbert schemes and quasimodular forms i we prove a closed formula for leading gopakumar vafa bps invariants of local calabi yau geometries given by the canonical line bundles of toric fano surfaces it shares some sim ilar features with gottsche yau zaslow formula connection with hilbert schemes connection with quasimodular forms and qua dratic property after suitable transformation in part i of this paper we will present the case of projective plane more general cases will be presented in part ii the problem of counting curves in algebraic varieties dates back to the nineteenth century classical examples include the famous 27 lines on a cubic surface and the 2875 lines on a quintic 3 fold through the interaction with string theory spectacular progresses in this classi cal branch of algebraic geometry have been made over the years since 1990 s first of all gromov witten theory and its various variants have laid the foundation for the modern treatment of many classical enumerative problems and greatly expanded the range of enumerative problems being considered see pt for an introduction to some of the exciting developments the study of the problems of counting curves in surfaces and calabi yau 3 folds have served both as motivations and applications of gromov witten theory we will recall some results in these directions in 2 and 3 to serve as motivations for this work we emphasize on the following three salient features for the curving counting problems for algebraic surfaces connection with hilbert schemes connection with quasimod ular forms and quadratic properties of the node polynomials after suit able transformation our main results will show that these features are also shared in the curve counting problems of some noncompact calabi yau 3 folds arising as the the total space of the canonical line bundles of toric fano surfaces 1

on the boltzmann equation with stochastic kinetic transport global existence of renormalized martingale solutions this article studies the cauchy problem for the boltzmann equation with stochastic kinetic transport under a cut off assumption on the collision kernel and a coloring hypothesis for the noise coefficients we prove the global existence of renormalized in the sense of diperna lions martingale solutions to the boltzmann equation for large initial data with finite mass energy and entropy our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations this study includes a criterion for renormalization the weak closedness of the solution set and tightness of velocity averages in l 1

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

the dirichlet problem for a conservation law with a multiplicative stochastic perturbation abstract in this paper we are interested in the dirichlet boundary value problem for a multi dimensional nonlinear conservation law with a multiplicative stochastic perturbation using the concept of measure valued solutions and kruzhkov s semi entropy formulations a result of existence and uniqueness of the entropy solution is proved

on the genus one gromov witten invariants of complete intersections we state and prove a long elusive relation between genus one gromov witten of a complete intersection and twisted gromov witten invariants of the ambient projective space as shown in a previous paper certain naturally arising cones of holomorphic vector bundle sections over the main component m 0 1 k p d of the moduli space of stable genus one holomorphic maps into p have a well defined euler class in this paper we extend this result to moduli spaces of perturbed in a restricted way j holomorphic maps this extension is used to show that these cones are the correct genus one analogues of the vector bundles relating genus zero gromov witten invariants of a complete intersection to those of the ambient projective space a relationship for highergenus invariants is conjectured as well

a priori estimates for rough pdes with application to rough conservation laws we introduce a general framework to study pdes driven by rough paths we develop new a priori estimates based on a rough gronwall lemma argument for weak solutions to rough pdes this will allow us to follow standard pde strategies to obtain existence and uniqueness results in particular our approach does not rely on any sort of transformation formula flow transformation feynman kac representation formula etc and is therefore rather flexible as an application we study conservation laws driven by rough paths establishing well posedness for the corresponding kinetic formulation

burgers turbulence and random lagrangian systems we consider a spatially periodic inviscid random forced burgers equation in arbitrary dimension and the random time dependent lagrangian system related to it we construct a unique stationary distribution for viscosity solutions of the burgers equation we also show that with probability 1 there exists a unique minimizing trajectory for the random lagrangian system which generates a non trivial ergodic invariant measure for the non random skew product extension of the lagrangian system

absolute and relative gromov witten invariants of very ample hypersurfaces for any smooth complex projective variety x and any smooth very ample hypersurface y subset x we develop the technique of genus zero relative gromov witten invariants of y in x in algebro geometric terms we prove an equality of cycles in the chow groups of the moduli spaces of relative stable maps which relates these relative invariants to the gromov witten invariants of x and y given the gromov witten invariants of x we show that these relations are sufficient to compute all relative invariants as well as all genus zero gromov witten invariants of y whose homology and cohomology classes are induced by x

path dependent convex conservation laws abstract for convex scalar conservation laws in 1 d driven by a rough path z t in the sense of lions perthame and souganidis in 32 we show that it is possible to replace z t by a piecewise linear path and still obtain the same solution at a given time this result is connected to the spatial regularity of solutions we show that solutions are spatially lipschitz continuous for an a priori set of times depending on the path and the initial data fine properties of the map z u for a prescribed time are studied we provide a detailed description of the properties of the rough path z t that influence the solution this description is extracted by a factorization of the solution operator at time in a companion paper 24 we make use of the observations herein to construct computationally efficient numerical methods

enumerative geometry of calabi yau 4 folds gromov witten theory is used to define an enumerative geometry of curves in calabi yau 4 folds the main technique is to find exact solutions to moving multiple cover integrals the resulting invariants are analogous to the bps counts of gopakumar and vafa for calabi yau 3 folds we conjecture the 4 fold invariants to be integers and expect a sheaf theoretic explanation

genus one stable maps local equations and vakil zinger s desingularization we describe an algebro geometric approach to vakil zinger s desingularization of the main component of the moduli of genus one stable maps to mathbb p n vakil and zinger in res announc am math soc 13 53 59 2007 geom topol 12 1 1 95 2008 our approach is based on understanding the local structure of this moduli space it also gives a partial desingularization of the entire moduli space the results proved should extend to higher genera

virtual moduli cycles and gromov witten invariants of noncompact symplectic manifolds this paper constructs and studies the gromov witten invariants and their properties for noncompact geometrically bounded symplectic manifolds two localization formulas for gw invariants are also proposed and proved as applications we get solutions of the generalized string equation and dilation equation and their variants the more solutions of wdvv equation and quantum products on cohomology groups are also obtained for the symplectic manifolds with finitely dimensional cohomology groups to realize these purposes we further develop the language introduced by liu tian to describe the virtual moduli cycle defined by liu tian fukaya ono li tian ruan and siebert

a spline strip kernel particle method and its application to two dimensional elasticity problems in this paper we present a novel spline strip kernel particle method sskpm that has been developed for solving a class of two dimensional 2d elasticity problems this new approach combines the concepts of the mesh free methods and the spline strip method for the interpolation of the assumed displacement field we employed the kernel particle shape functions in the transverse direction and the b3 spline function in the longitudinal direction the formulation is validated on several beam and semi infinite plate problems the numerical results of these test problems are then compared with the existing solutions obtained by the exact or numerical methods from this study we conclude that the sskpm is a potential alternative to the classical finite strip method fsm copyright 2003 john wiley sons ltd

buckling of folded plate structures subjected to partial in plane edge loads by the fsdt meshfree galerkin method this paper presents a meshfree galerkin method that is based on the first order shear deformation theory fsdt to study the elastic buckling behaviour of stiffened and un stiffened folded plates under partial in plane edge loads the un stiffened folded plates are modelled as assemblies of flat plates the stiffness and initial stress matrices of the flat plates are derived by the meshfree galerkin method a treatment is implemented to modify the stiffness and initial stress matrices and the matrices are then superposed to obtain the stiffness and initial stress matrix of the entire folded plate the analytical process for stiffened folded plates is similar except that the effects of the stiffeners must be taken into account because no mesh is required the proposed method is superior for studying problems that would involve remeshing in the finite element method several examples are employed to show the convergence and accuracy of the proposed method the results obtained show good agreement with the results computed from the finite element analysis software ansys copyright 2005 john wiley sons ltd

analysis of post buckling branches at multiple symmetric bifurcations a method to analyse and solve symmetric bifurcations by establishing the bifurcation equations using an asymptotic expansion method is presented the bifurcation equations are obtained using a decomposition of the spaces by means of the theory of lyapunov schmidt to solve the bifurcation equations an asymptotic expansion method along the lines of koiter is applied the expansion is presented in a form suited for implementation in a finite element context the present paper is focused on the treatment of symmetric multiple bifurcations where new forms of the bifurcation equations are established the accuracy of the method is verified with three examples copyright 2001 john wiley sons ltd

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

a meshfree hermite type radial point interpolation method for kirchhoff plate problems a meshfree computational method is proposed in this paper to solve kirchhoff plate problems of various geometries the deflection of the thin plate is approximated by using a hermite type radial basis function approximation technique the standard galerkin method is adopted to discretize the governing partial differential equations which were derived from using the kirchhoff s plate theory the degrees of freedom for the slopes are included in the approximation to make the proposed method effective in enforcing essential boundary conditions numerical examples with different geometric shapes and various boundary conditions are given to verify the efficiency accuracy and robustness of the method copyright 2005 john wiley sons ltd

analysis of 3d solids using the natural neighbour radial point interpolation method abstract in this work an improved meshless method is proposed based on the combination of the natural neighbour finite element method with the radial point interpolation method the natural neighbour radial point interpolation method nnrpim the nodal connectivity and the node dependent integration background mesh are constructed resorting to the voronoi tessellation and to the delaunay triangulation within nnrpim the obtained shape functions pass through all nodes inside the influence cell providing shape functions with the delta kronecker property optimization tests and examples of well known 2d and 3d problems are solved in order to prove the high accuracy and convergence rate of the proposed method

scalar conservation laws with stochastic forcing we show that the cauchy problem for a randomly forced periodic multi dimensional scalar first order conservation law with additive or multiplicative noise is well posed it admits a unique solution characterized by a kinetic formulation of the problem which is the limit of the solution of the stochastic parabolic approximation

multidimensional potential burgers turbulence we consider the multidimensional generalised stochastic burgers equation in the space periodic setting frac partial mathbf u partial t nabla f mathbf u cdot nabla mathbf u nu delta mathbf u nabla eta quad t geq 0 mathbf x in mathbb t d mathbb r mathbb z d under the assumption that u is a gradient here f is strongly convex and satisfies a growth condition is small and positive while is a random forcing term smooth in space and white in time for solutions u of this equation we study sobolev norms of u averaged in time and in ensemble each of these norms behaves as a given negative power of these results yield sharp upper and lower bounds for natural analogues of quantities characterising the hydrodynamical turbulence namely the averages of the increments and of the energy spectrum these quantities behave as a power of the norm of the relevant parameter which is respectively the separation l in the physical space and the wavenumber k in the fourier space our bounds do not depend on the initial condition and hold uniformly in nu we generalise the results obtained for the one dimensional case in 10 confirming the physical predictions in 4 30 note that the form of the estimates does not depend on the dimension the powers of nu mathbf k ell are the same in the one and the multi dimensional setting

generalized deflated block elimination a stable algorithm is presented to solve a nonsingular bordered system of the form left begin array 20 c a b c t d end array right left begin array 20 c x y end array right left begin array 20 c f g end array right where b and c are n by m matrices and the n by n matrix a could be nearly singular with at most mu small singular values the algorithm needs only a solver for a and the solution to an m mu by m mu dense linear system it is thus well suited for problems for which a has easily exploitable structures and m mu ll n such as in continuation methods bifurcation problems and constrained optimization

an improved moving least squares ritz method for two dimensional elasticity problems we propose an improved moving least squares ritz imls ritz method with its element free framework developed for studying two dimensional elasticity problems using the imls approximation for the field variables the discretized governing equations of the problem are derived via the ritz procedure in the imls an orthogonal function system with a weight function is employed as the basis for construction of its displacement field by using the element free imls ritz method solutions of the two dimensional elasticity problems are obtained the applicability of the element free imls ritz method is illustrated through three selected example problems the convergence characteristics of the method are examined by varying the number of nodes and geometric parameters of these examples the accuracy of the method is validated by comparing the computed results with the efg and exact solutions

on the structure of certain natural cones over moduli spaces of genus one holomorphic maps we show that certain naturally arising cones over the main component of a moduli space of j0 holomorphic maps into pn have a well defined euler class we also prove that this is the case if the standard complex structure j0 on pn is replaced by a nearby almost complex structure j the genus zero analogue of the cone considered in this paper is a vector bundle the genus zero gromov witten invariant of a projective complete intersection can be viewed as the euler class of such a vector bundle as shown in a separate paper this is also the case for the genus one part of the genus one gw invariant the remaining part is a multiple of the genus zero gw invariant

quantum lefschetz hyperplane theorem the mirror theorem is generalized to any smooth projective variety x that is a fundamental relation between the gromov witten invariants of x and gromov witten invariants of complete intersections y in x is established

path by path regularization by noise for scalar conservation laws abstract we prove a path by path regularization by noise result for scalar conservation laws in particular this proves regularizing properties for scalar conservation laws driven by fractional brownian motion and generalizes the respective results obtained in 8 we introduce a new path by path scaling property which is shown to be sufficient to imply regularizing effects

moving least squares differential quadrature method and its application to the analysis of shear deformable plates a moving least squares differential quadrature mlsdq method is developed and employed for the analysis of moderately thick plates based on the first order shear deformation theory fsdt to carry out the analysis the governing equations in terms of the generalized displacements transverse deflection and two rotations of the plate are formulated by employing the moving least squares approximation the weighting coefficients used in the mlsdq approximation are computed through a fast computation of shape functions and their derivatives numerical examples illustrating the accuracy stability and convergence of the mlsdq method are presented effects of support size order of completeness and node irregularity on the numerical accuracy are investigated copyright 2003 john wiley sons ltd