moduli of fibered surface pairs from twisted stable maps in this paper we use the theory of twisted stable maps to construct compactifications of the moduli space of pairs x rightarrow c s f where x rightarrow c is a fibered surface s is a sum of sections f is a sum of marked fibers and x s f is a stable pair in the sense of the minimal model program this generalizes the work of abramovich vistoli who compactified the moduli space of fibered surfaces with no marked fibers furthermore we compare our compactification to alexeev s space of stable maps and the ksba compactification as an application we describe the boundary of a compactification of the moduli space of elliptic surfaces

growth and decay of shock and acceleration waves in a traffic flow model with relaxation abstract the usual ficken based constitutive relation for traffic flux is replaced with one based on the maxwell cattaneo model the resulting flux law which now takes into account the reaction time of driver and vehicle results in a second order hyperbolic generalization of burgers equation as the pde governing the traffic density an analytical study of this equation is presented with an emphasis on shock and related kinematic wave phenomena specifically the exact traveling wave solution tws is derived and it is shown that shock formation is possible only if the diffusivity is non vanishing using singular surface theory exact amplitude expressions for both shock and acceleration waves are obtained and their temporal evolution determined the exact upper bound of the reaction time parameter is established and connections between singular surface and tws results are noted

a quintic b spline finite elements scheme for the kdvb equation abstract an algorithm for solving the korteweg de vries burgers kdvb equation based on the collocation method with quintic b spline finite elements is set up to simulate the solutions of the kdv burgers and the kdvb equations the migration of solitary waves and temporal evolution of a maxwellian initial pulse are studied for the kdv equation burgers equation is solved for different values of reynolds number the time evaluation of the solutions of the kdvb equation with different values for the diffusion and dispersion coefficients is studied invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm a linear stability analysis shows the scheme to be unconditionally stable

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

stable maps in higher dimensions we formulate a notion of stability for maps between polarised varieties which generalises kontsevich s definition when the domain is a curve and tian donaldson s definition of k stability when the target is a point we give some examples such as kodaira embeddings and fibrations we prove the existence of a projective moduli space of canonically polarised stable maps generalising the kontsevich alexeev moduli space of stable maps in dimensions one and two we also state an analogue of the yau tian donaldson conjecture in this setting relating stability of maps to the existence of certain canonical kahler metrics

exponential methods for singularly perturbed ordinary differential difference equations abstract a variety of exponential methods based on piecewise analytical solutions of advection reaction diffusion operators is proposed for the numerical solution of linear ordinary differential difference equations with small delay these methods are shown to be exact in exact arithmetic for linear ordinary differential equations with constant coefficients and right hand side are non standard and include three point non local approximations for the coefficients right hand side and dependent variable also a variety of exponential methods based on the piecewise analytical solution of advection diffusion operators with non local approximations is presented it is shown that exponential methods based on the advection diffusion reaction operator provide more accurate results than those based on the analytical solution of the advection diffusion operator it is also shown that at least for the problems considered here non local approximations for either the coefficients or the right hand side of the differential equations do not result in an increase of accuracy over those based on local approximations

singular perturbation analysis of boundary value problems for differential difference equations vi small shifts with rapid oscillations this paper continues the authors study of boundary value problems for singularly perturbed linear second order differential difference equations with small shifts this study was initiated in the companion paper siam j appl math 54 1994 pp 249 272 in this paper the study is extended to problems that have solutions that exhibit rapid oscillations restrictions on the sizes of the shifts in terms of the small parameter are found such that generally the shifted terms cannot be replaced with truncated taylor series in particular it is shown that even when the shifts are small relative to the width of an oscillation they can affect the solution to leading order the conclusion is that oscillatory solutions are more sensitive to small delays than are layer solutions it is shown that a suitably modified version of the standard wkb method can be used to obtain leading order oscillatory solutions of these differential difference equations these preliminary studies of differential difference eq

nonstandard finite difference equations for odes and 1 d pdes based on piecewise linearization a method for the solution of initial and boundary value problems in nonlinear ordinary differential equations and for one dimensional partial differential equations which provides c 1 solutions is presented the method is based on the linearization of the differential equation in intervals which contain only two grid points and provides three point nonstandard finite difference equations for the nodal amplitudes the method is applied to steady reaction diffusion equations two point singularly perturbed boundary value problems and the steady burgers equation and compared with standard finite difference and finite element formulations for one dimensional partial differential equations the temporal derivatives are first discretized and the resulting ordinary differential equation accounts for both the temporal and spatial stiffnesses and is solved by means of piecewise linearization since the linearization includes a jacobian matrix it may be easily employed to refine the mesh where steep gradients occur

log canonical singularities are du bois a recurring difficulty in the minimal model program mmp is that while log terminal singularities are quite well behaved for instance they are rational log canonical singularities are much more complicated they need not even be cohenmacaulay the aim of this paper is to prove that as conjectured in kol92 1 13 log canonical singularities are du bois the concept of du bois singularities abbreviated as db was introduced by steenbrink in ste83 as a weakening of rationality it is not clear how to define du bois singularities in positive characteristic so we work over a field of characteristic 0 throughout the paper the precise definition is rather involved see 1 10 but our main applications rely only on the following consequence

spatio temporal chaos and intermittency in a 1 dimensional energy conserving coupled map lattice abstract the klein gordon equation with cubic nonlinearity the 4 equation is considered and an energy conserving difference scheme is proposed for its solution the scheme extended to finite time increments and spacing is then used to define a coupled map lattice for which an energy like functional is conserved the case of linear instability of the vacuum state is considered when this energy is not positive definite and found to lead under certain additional conditions to spatio temporal chaos the statistical properties of this type of solution such as probability densities and correlation functions are calculated strong intermittency whereby the process wanders between two sub manifolds is found and studied in detail

an analytic study of fisher s equation by using adomian decomposition method in this paper we develop a framework to obtain exact solutions to fisher s equation and to a nonlinear diffusion equation of the fisher type by employing adomian decomposition method the proposed scheme is supported by examining nonlinear diffusion equations of the fisher type

an infinite ramsey theorem and some banach space dichotomies a problem of banach asks whether every infinite dimensional banach space which is isomorphic to all its infinite dimensional subspaces must be isomorphic to a separable hilbert space in this paper we prove a result of a ramsey theoretic nature which implies an interesting dichotomy for subspaces of banach spaces combined with a result of komorowski and tomczakjaegermann this gives a positive answer to banachxs problem we then generalize the ramsey theoretic result and deduce a further dichotomy for banach spaces with an unconditional basis

a numerical solution of the generalized burger s huxley equation by pseudospectral method and darvishi s preconditioning abstract in this paper we present a new method for solving of the generalized burger s huxley equation by using the collocation formula for calculating spectral differentiation matrix for chebyshev gauss lobatto point to reduce round off error in spectral collocation method we use darvishi s precondotioning firstly theory of application of spectral collocation method on burger s huxley equation presented this method yields burger s huxley equation to a system of ordinary differential equations odes secondly we use forth order runge kutta formula for the numerical integration of the system of ode the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method

hyperbolic partial differential difference equation in the mathematical modeling of neuronal firing and its numerical solution abstract first we assume a simple neuronal model based on stein s model richard b stein a theoretical analysis of neuronal variability biophys j 5 1965 173 194 in which after a refractory period excitatory and inhibitory exponentially decaying inputs of constant size occur at random intervals and sum until a threshold is reached we briefly discuss the distribution of time intervals between successive neuronal firings the firing rate as a function of input frequency the strength duration curve and the role of inhibition then a first order partial differential difference equation for the distribution of neuronal firing intervals is derived and a numerical scheme based on finite difference is constructed for solving such type of initial and boundary value problems the proposed method is analyzed for stability and convergence finally some test examples are given to validate convergence and the computational efficiency of the present scheme

cohomology and base change for algebraic stacks we prove that cohomology and base change holds for algebraic stacks generalizing work of brochard in the tame case we also show that hom spaces on algebraic stacks are represented by abelian cones generalizing results of grothendieck brochard olsson lieblich and roth starr to accomplish all of this we prove that a wide class of relative ext functors in algebraic geometry are coherent in the sense of m auslander

e uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general ddes we consider some problems arising from singularly perturbed general differential difference equations first we construct in a new way and analyze a fitted operator finite difference method fofdm which is first order e uniformly convergent with the aim of having just one function evaluation at each step attempts have been made to derive a higher order method via shishkin mesh to which we refer as the fitted mesh finite difference method fmfdm this fmfdm is a direct method and e uniformly convergent with the nodal error as o n 2ln 2n which is an improvement over the existing direct methods i e those which do not use any acceleration of convergence techniques e g richardson s extrapolation or defect correction etc for such problems on a mesh of shishkin type that lead the error as o n 1lnn where n denotes the total number of sub intervals of 0 1 comparative numerical results are presented in support of the theory

comparative study of singularly perturbed two point bvps via fitted mesh finite difference method b spline collocation method and finite element method abstract the objective of this paper is to present a comparative study of fitted mesh finite difference method b spline collocation method and finite element method for general singularly perturbed two point boundary value problems due to the small parameter the boundary layer arises we have taken a piecewise uniform fitted mesh to resolve the boundary layer and we have shown that fitted mesh finite difference method has uniform first order convergence b spline collocation method has almost second order uniform convergence and ritz galerkin method also has almost second order uniform convergence two test examples have been solved to compare the maximum absolute error and rate of convergence of the methods

operators whose dual has non separable range let x and y be separable banach spaces and t x y be a bounded linear operator we characterize the non separability of t y by means of fixing properties of the operator t

adomian decomposition method for burger s huxley and burger s fisher equations the approximate solutions for the burger s huxley and burger s fisher equations are obtained by using the adomian decomposition method solving frontier problems of physics the decomposition method kluwer boston 1994 the algorithm is illustrated by studying an initial value problem the obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient

maximum norm a posteriori error estimates for a singularly perturbed differential difference equation with small delay we consider an adaptive grid approach to solve a singularly perturbed differential difference equation with small delay the mesh is constructed adaptively by equidistributing a arc length monitor function we derive a first order maximum norm a posteriori estimate for the full discretization scheme a first order rate of convergence independent of the perturbation parameter and the small delay parameter is established a singularly perturbed differential difference equation with small delay is discretized on an adaptive grid which is formed by equidistributing arc length monitor function we first derive first order maximum norm a posteriori estimates for the full discretization scheme of these problems then a first order rate of convergence independent of the perturbation parameter and the small delay parameter is established numerical results are provided that support our theoretical estimates

fibred surfaces varieties isogenous to a product and related moduli spaces a fibration of an algebraic surface s over a curve b with fibres of genus at least 2 has constant moduli iff it is birational to the quotient of a product of curves by the action of a finite group g a variety isogenous to a higher product is the quotient of a product of curves of genus at least 2 by the free action of a finite group theorem b gives a characterization of surfaces isogenous to a higher product in terms of the fundamental group and of the euler number theorem c classifies the groups thus occurring and shows that after fixing the group and the euler number one obtains an irreducible moduli space the result of theorem b is extended to higher dimension in theorem g thus generalizing cf also theorem h results of jost yau and mok concerning varieties whose universal cover is a polydisk theorem a shows that fibrations where the fibre genus and the genus of the base b are at least 2 are invariants of the oriented differentiable structure the main theorems d and e characterize surfaces carrying constant moduli fibrations as surfaces having a zariski open set satisfying certain topological conditions e g having the right euler number the right fundamental group and the right fundamental group at infinity 0 introduction the study of fibrations of a smooth algebraic surface s over a smooth algebraic curve b lies at the heart of the classification theory and of the geometry of algebraic surfaces our main results in this paper theo rems d e concern a topological characterization of surfaces admitting a constant moduli fibration these results are intimately related to a series of variations on the same theme also in higher dimension and to a circle of allied techniques which we present in the course of the paper the first new result we have in this direction and which is presented in section 2 after we recall several known results some classical some quite recent is the following theorem on the dif ferentiable invariance of the genus of fibres cf theorem 2 9 for a more precise statement theorem a let f s b be a fibration of the surface s over a curve b of genus b 2 and with fibre f of genus g 1 assume that s is another smooth compact kahler surface which is orientedly diffeomorphic to s then the subspace of h 1 s corresponding to f h 1 b determines a fibration f s b with

a new proof of the density hales jewett theorem the hales jewett theorem asserts that for every r and every k there exists n such that every r colouring of the n dimensional grid 1 k contains a monochromatic combinatorial line this result is a generalization of van der waerden s theorem and it is one of the fundamental results of ramsey theory the theorem of van der waerden has a famous density version conjectured by erd s and turan in 1936 proved by szemeredi in 1975 and given a different proof by furstenberg in 1977 the hales jewett theorem has a density version as well proved by furstenberg and katznelson in 1991 by means of a significant extension of the ergodic techniques that had been pioneered by furstenberg in his proof of szemeredi s theorem in this paper we give the first elementary proof of the theorem of furstenberg and katznelson and the first to provide a quantitative bound on how large n needs to be in particular we show that a subset of 1 2 3 of density contains a combinatorial line if n is at least as big as a tower of 2s of height o 1 our proof is surprisingly simple indeed it gives arguably the simplest known proof of szemeredi s theorem

the local discontinuous galerkin method for burger s huxley and burger s fisher equations abstract in this paper a numerical solution for the generalized burger s huxley equation and the generalized burger s fisher equation are presented by using the local discontinuous galerkin method firstly we rewrite the two kinds of equations into first order systems then apply the discontinuous galerkin method to the systems secondly the systems for ordinary differential equations yielded are solved by the third order runge kutta time integration method the numerical results obtained by this way are compared with exact solution to demonstrate accuracy and capability of the method

ramsey theory in noncommutative semigroups by utilizing ultrafilters we give a general version of the central sets theorem 6 proposition 8 21 this enables us to derive noncommutative versions of van der waerden s theorem and several of its generalizations we also derive some standards results including the hales jewett theorem

spectral collocation method for the solution of the generalized burger fisher equation abstract in this paper we present a new method for solving the generalized burger fisher equation by using the collocation formula for calculating spectral differentiation matrix for chebyshev gauss lobatto point firstly theory of application of pseudospectral method on burger fisher equations is presented this method yields burger fisher equation to a system of ordinary differential equations odes secondly we use forth order runge kutta formula for the numerical integration of the system of ode the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method

a quasi interpolation method for solving stiff ordinary differential equations based on the idea of quasi interpolation and radial basis functions approximation a numerical method is developed to quasi interpolate the forcing term of differential equations by using radial basis functions a highly accurate approximation for the solution can then be obtained by solving the corresponding fundamental equation and a small size system of equations related to the initial or boundary conditions this overcomes the ill conditioning problem resulting from using the radial basis functions as a global interpolant error estimation is given for a particular second order stiff differential equation with boundary layer the result of computations indicates that the method can be applied to solve very stiff problems with the use of multiquadric a special class of radial basis functions it has been shown that a reasonable choice for the optimal shape parameter is obtained by taking the same value of the shape parameter as the perturbed parameter contained in the stiff equation copyright 2000 john wiley sons ltd

qualitatively stable finite difference schemes for advection reaction equations a systematic procedure is proposed and implemented for the design of nonstandard finite difference methods as reliable numerical simulations that preserve significant properties inherent to the solutions of advection reaction equations in the case of hyperbolic fixed points a renormalization of the denominators of the discrete derivatives is performed for the numerical solutions to display the linear stability properties of the exact solutions non hyperbolic fixed points are described with the help of two new monotonic properties the construction of schemes which preserve these properties being done by nonlocal approximation of nonlinear terms in the reaction terms

a density version of the halpern lauchli theorem abstract we prove a density version of the halpern lauchli theorem this settles in the affirmative a conjecture of r laver specifically let us say that a tree t is homogeneous if t has a unique root and there exists an integer b 2 such that every t t has exactly b immediate successors we show that for every d 1 and every tuple t 1 t d of homogeneous trees if d is a subset of the level product of t 1 t d satisfying lim sup n d t 1 n t d n t 1 n t d n 0 then there exist strong subtrees s 1 s d of t 1 t d having a common level set such that the level product of s 1 s d is a subset of d

ramsey families of subtrees of the dyadic tree we show that for every rooted finitely branching pruned tree t of height w there exists a family f which consists of order isomorphic to t subtrees of the dyadic tree c 0 1 n with the following properties i the family f is a g subset of 2 c ii every perfect subtree of c contains a member of f iii if k is an analytic subset of f then for every perfect subtree s of c there exists a perfect subtree s of s such that the set a f a c s either is contained in or is disjoint from k

a numerical solution of the generalized burger s huxley equation by spectral collocation method abstract in this paper we present a new method for solving of the generalized burger s huxley equation by using the collocation formula for calculating spectral differentiation matrix for chebyshev gauss lobatto points firstly theory of application of pseudospectral method on burger s huxley equations presented this method yields burger s huxley equation to a system of ordinary differential equations odes secondly we use fourth order runge kutta formula for the numerical integration of the system of ode the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method

a dual form of ramsey s theorem abstract let k where is the set of all natural numbers ramsey s theorem deals with colorings of the k element subsets of our dual form deals with colorings of the k element partitions of let k respectively be the set of all partitions of having exactly k respectively infinitely many blocks given x let x k be the set of all y k such that y is coarser than x dual ramsey theorem if k c 0 c t 1 where each c i is borel then there exists x such that x k c i for some i l dual galvin prikry theorem same as before with k replaced by we also obtain dual forms of theorems of ellentuck and mathias our results also provide an infinitary generalization of the graham rothschild parameter set theorem trans amer math soc 159 1971 257 292 and a new proof of the halpern lauchli theorem trans amer math soc 124 1966 360 367

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

a non standard numerical scheme for a generalized gause type predator prey model abstract a non standard finite difference scheme is constructed to simulate a predator prey model of gause type with a functional response using fixed point analysis it is shown that the scheme preserves the physical properties of the model and gives results that are qualitatively equivalent to the real dynamics of the model it is also shown that the scheme undergoes a supercritical hopf bifurcation for a specific value of the bifurcation parameter k0 this leads to the existence of a stable limit cycle created by the scheme when the bifurcation parameter passes through k0 as predicted by the continuous model the scheme is used to simulate the model with the functional responses of holling types ii and iii the simulation results generated by the non standard finite difference scheme are compared with those obtained from the standard methods such as forward euler and runge kutta methods these comparisons show that the standard methods give erroneous results that disagree with the theoretical predictions of the model however it is proved that the proposed non standard finite difference scheme is consistent with the asymptotic dynamics of the model numerical simulations are presented to support these facts

comparison of some recent numerical methods for initial value problems for stiff ordinary differential equations we consider the combustion equation as one of the candidates from the class of stiff ordinary differential equations a solution over a length of time that is inversely proportional to d 0 where d 0 is a small disturbance of the pre ignition state is sought this problem has a transient at the midpoint of the integration interval the solution changes from being non stiff to stiff and afterwards becomes non stiff again we provide its asymptotic and numerical solution obtained via a variety of methods comparisons are made for the numerical results which we obtain with the matlab ode solvers ode45 ode15s and ode23s and some nonstandard finite difference methods results corresponding to standard finite difference method are also presented furthermore the discussion on these approaches along with the others provides several open problems for new and young researchers

discrete kinetic schemes for multidimensional systems of conservation laws we present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations which includes the relaxation schemes by s jin and z xin these schemes have a simple formulation even in the multidimensional case and do not need the solution of the local riemann problems for these approximations we give a suitable multidimensional generalization of the whitham s stability subcharacteristic condition in the scalar multidimensional case we establish the rigorous convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

singular perturbation analysis of boundary value problems for differential difference equations v small shifts with layer behavior in this paper an investigation is initiated of boundary value problems for singularly perturbed linear second order differential difference equations with small shifts i e where the second order derivative is multiplied by a small parameter and the shift depends on the small parameter similar boundary value problems are associated with expected first exit times of the membrane potential in models for neurons in particular this paper focuses on problems with solutions that exhibit layer behavior at one or both of the boundaries the analyses of the layer equations using laplace transforms lead to novel results it is shown that the layer behavior can change its character and even be destroyed as the shifts increase but remain small in the companion paper siam j appi math 54 1994 pp 273283 similar boundary value problems with solutions that exhibit rapid oscillations are studied

a disjoint unions theorem for trees abstract we prove an infinitary disjoint unions theorem for level products of trees to implement the proof we develop a hales jewett type result for words indexed by a level product of trees

projectivity of the moduli space of stable log varieties and subadditivity of log kodaira dimension reference epfl article 231100doi 10 1090 jams 871 url http dx doi org 10 1090 jams 871 record created on 2017 09 19 modified on 2017 10 02

stable numerical methods for conservation laws with discontinuous flux function abstract we develop numerical methods for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients using a relaxation approximation the nonlinear equation is transformed to a semilinear diagonalizable problem with linear characteristic variables eulerian and lagrangian methods are used for the advection stage while an implicit explicit scheme solves the relaxation stage the main advantages of this approach are neither riemann problem solvers nor linear iterations are required during the solution process moreover the characteristic based relaxation method is unconditionally stable such that no cfl conditions are imposed on the selection of time steps numerical results are shown for models on traffic flows and two phase flows

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

fibered stable varieties reference epfl article 231103doi 10 1090 tran 6386 url http dx doi org 10 1090 tran 6386 record created on 2017 09 19 modified on 2017 10 02

e uniformly convergent non standard finite difference methods for singularly perturbed differential difference equations with small delay abstract non standard finite difference methods nsfdms now a days are playing an important role in solving the real life problems governed by odes and or by pdes many differential models of sciences and engineerings for which the existing methodologies do not give reliable results these nsfdms are solving them competitively to this end in this paper we consider second order linear singularly perturbed differential difference equations using the second of the five non standard modeling rules of mickens r e mickens nonstandard finite difference models of differential equations world scientific singapore 1994 the new finite difference methods are obtained for the particular cases of these problems this rule suggests us to replace the denominator function of the classical second order derivative with a positive function derived systematically in such a way that it captures most of the significant properties of the governing differential equation s both theoretically and numerically we show that these nsfdms are e uniformly convergent

composite scheme using localized relaxation with non standard finite difference method for hyperbolic conservation laws non standard finite difference methods nsfdm introduced by mickens non standard finite difference models of differential equations world scientific singapore 1994 are interesting alternatives to the traditional finite difference and finite volume methods when applied to linear hyperbolic conservation laws these methods reproduce exact solutions in this paper the nsfdm is first extended to hyperbolic systems of conservation laws by a novel utilization of the decoupled equations using characteristic variables in the second part of this paper the nsfdm is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws the original nsfdms introduced by mickens 1994 were not in conservation form which is an important feature in capturing discontinuities at the right locations mickens construction and analysis of a non standard finite difference scheme for the burgers fisher equations journal of sound and vibration 257 4 2002 791 797 recently introduced a nsfdm in conservative form this method captures the shock waves exactly without any numerical dissipation in this paper this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks as a remedy to this defect we use the strategy of composite schemes r liska b wendroff composite schemes for conservation laws siam journal of numerical analysis 35 6 1998 2250 2271 in which the accurate nsfdm is used as the basic scheme and localized relaxation nsfdm is used as the supporting scheme which acts like a filter relaxation schemes introduced by jin and xin the relaxation schemes for systems of conservation laws in arbitrary space dimensions communications in pure and applied mathematics 48 1995 235 276 are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi linear system with a stiff relaxation term the relaxation parameter is chosen locally on the three point stencil of grid which makes the proposed method more efficient this composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme as demonstrated by the test cases together with comparisons with popular numerical methods like roe scheme and eno schemes

compact subsets of the first baire class perhaps the earliest results about pointwise compact sets of baire class 1 functions are the two selection theorems of e helly found in most of the standard texts on real variable see e g lo n these two theorems are really theorems about a particular example of a compact set of baire class 1 functions known today as helly space the space of all nondecreasing functions from the unit interval i 0 1 into itself more recently the notion of baire class 1 function turned out to also be important in some areas of functional analysis see r3 for example odell and rosenthal or showed that the double dual of a separable banach space e with the weak topology consists only of baire class 1 functions defined on the unit ball of e if and only if the space e contains no subspace isomorphic to 1 this resulted in a renewed interest in this class of spaces for example building on the work of rosenthal r2 bourgain fyemlin and talagrand bft proved analogues of the two theorems of helly for the whole first baire class using their results godefroy go showed that this class of spaces enjoys some interesting permanence properties for example if a compact space k is representable as a compact set of baire class 1 functions then so is p k the space of all radon probability measures on k with the weak topology some further permanence properties of this class of spaces were obtained by marciszewski ml m2 and an excellent survey of the early results is given by r pol po2 our paper is an attempt towards a fine structure theory of compact subsets of first baire class the first result that we give is a positive answer to a natural question one usually asks in such a context

arakelov parshin rigidity of towers of curve fibrations arakelov parshin rigidity is concerned with varieties mapping rigidly to the moduli stack mathfrak m h of canonically polarized manifolds affirmative answer for any class of maps implies finiteness of the given class this article studies arakelov parshin rigidity on an open subspace of mathfrak m h on the locus mathfrak k mathfrak f h of iterated kodaira fibrations first we prove rigidity for all complete curves mapping finitely onto mathfrak k mathfrak f h then for generic affine curves mapping into mathfrak k mathfrak f h rigidity is shown when deg h 2 the method used in the latter part is showing that the iterated kodaira spencer map is injective

an infinite self dual ramsey theorem abstract in a recent paper 5 s solecki proved a finite self dual ramsey theorem that extends simultaneously the classical finite ramsey theorem 4 and the graham rothschild theorem 2 in this paper we prove the corresponding infinite dimensional version of the self dual theorem as a consequence we extend the classical infinite ramsey theorem 4 and the carlson simpson theorem 1

singular perturbation analysis of boundary value problems for differential difference equations a study is made of a class of boundary value problems for linear second order differential difference equations in which the highest order derivative is multiplied by a small parameter consideration of the exact solution of simple model equations provides insight into the appropriate use of singular perturbation techniques for more general problems the resulting analysis leads to several novel features which are not present in problems without differences

a restrictive pade approximation for the solution of the generalized fisher and burger fisher equations solving generalized fisher and burger fisher equations by the finite difference technique yields difficult nonlinear system of equations in this paper linearization and restrictive pade approximation is considered it yields more accurate and faster results also the stability analysis is discussed numerical results are treated

local discontinuous galerkin methods for nonlinear dispersive equations we develop local discontinuous galerkin dg methods for solving nonlinear dispersive partial differential equations that have compactly supported traveling waves solutions the so called compactons the schemes we present extend the previous works of yan and shu on approximating solutions for linear dispersive equations and for certain kdv type equations we present two classes of dg methods for approximating solutions of such pdes first we generate nonlinearly stable numerical schemes with a stability condition that is induced from a conservation law of the pde an alternative approach is based on constructing linearly stable schemes i e schemes that are linearly stable to small perturbations the numerical simulations we present verify the desired properties of the methods including their expected order of accuracy in particular we demonstrate the potential advantages of using dg methods over pseudospectral methods in situations where discontinuous fronts and rapid oscillations co exist in a solution

a fitted numerical method for a system of partial delay differential equations we consider a system of two coupled partial delay differential equations pddes describing the dynamics of two cooperative species the original system is reduced to a system of ordinary delay differential equations ddes obtained by applying the method of lines then we construct a fitted operator finite difference method fofdm to solve this resulting system the model considered in this paper is very sensitive to small changes in the parameters associated in with the model depending on the values of these parameters the solution can be stable periodic and or aperiodic such behavior of the solution is exploited via the proposed fofdm this fofdm is analyzed for convergence and it is seen that this method is unconditionally stable and has the accuracy of o k h 2 where k and h denote time and space step sizes respectively some numerical results confirming theoretical observations are also presented these results are comparable with those obtained in the literature

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

finiteness theorems for the picard objects of an algebraic stack abstract we prove some finiteness theorems for the picard functor of an algebraic stack in the spirit of sga 6 exp xii and xiii in particular we give a stacky version of raynaud s relative representability theorem we give sufficient conditions for the existence of the torsion component of the picard functor and for the finite generation of the neron severi groups or of the picard group itself we give some examples and applications in appendix a we prove the semicontinuity theorem for a non necessarily tame algebraic stack

local discontinuous galerkin methods for nonlinear schrodinger equations in this paper we develop a local discontinuous galerkin method to solve the generalized nonlinear schrodinger equation and the coupled nonlinear schrodinger equation l 2 stability of the schemes are obtained for both of these nonlinear equations numerical examples are shown to demonstrate the accuracy and capability of these methods

the westervelt equation with viscous attenuation versus a causal propagation operator a numerical comparison abstract the numerical solution of acoustic pulse propagation through dispersive media requires the inclusion of attenuation and its causal companion phase velocity for the case of propagation in a linear medium szabo time domain wave equations for lossy media obeying a frequency power law journal of the acoustic society of america 96 1994 491 500 introduced the concept of a causal convolutional propagation operator that plays the role of a causal propagation factor in the time domain the convolutional operator has been successfully employed in the linear wave equation for both isotropic and non isotropic dispersive media this operator was originally proposed by szabo to replace the loss term responsible for attenuation due to thermal conduction and viscosity of the fluid in the westervelt equation the westervelt equation with a traditional loss term fails to incorporate the full dispersive characteristics of the medium a deficiency which can be removed at least in principle by replacing the traditional loss term with the causal convolutional propagation factor previously no comparison has been made between the westervelt equation with the traditional loss term and with szabo s causal convolutional propagation operator in this paper we show numerically that by employing the convolutional propagation operator the full dispersive characteristics of the media are properly incorporated into the solution and that the results can differ significantly from the westervelt equation with the traditional loss term the equations will be solved via the method of finite differences

unconditional families in banach spaces it is shown that for every separable banach space x with non separable dual the space x contains an unconditional family of size x the proof is based on ramsey theory for trees and finite products of perfect sets of reals among its consequences it is proved that every dual banach space has a separable quotient

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal

solving partial differential equation by using multiquadric quasi interpolation abstract in this paper we use a kind of univariate multiquadric mq quasi interpolation to solve partial differential equation pde we obtain the numerical scheme by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement our numerical experiment includes two examples one is solving viscid burgers equation for initial trapezoidal conditions another is simulating the interaction of two waves travelling in opposite direction from the numerical experiment we can see that the present scheme is valid