a uniformly convergent difference scheme for a semilinear singular perturbation problem we present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders it is shown that a solution of the scheme converges uniformly in a perturbation parameter to that of the continuous problem

symmetry and phaselocking in chains of weakly coupled oscillators weakly coupled chains of oscillators with nearest neighbor interactions are analyzed for phaselocked solutions it is shown that the symmetry properties of the coupling affect the qualitative form of the phaselocked solutions and the scaling behavior of the system as the number of oscillators grows without bound it is also shown that qualitative behavior of these solutions depends on whether the coupling is diffusive or i synaptic terms defined in the paper the methods include the demonstration that the equations for phaselocked solutions can be approximated by a singularly perturbed two point continuum boundary value problem that is easier to analyze the issue of convergence of the phaselocked solutions to solutions of the continuum equation is closely related to questions involving numerical entropy in computation schemes for a conservation law an application to the neurophysiology of motor behavior is discussed briefly

an algebraic approximation for the matrix exponential in singularly perturbed boundary value problems a symmetric difference scheme for linear stiff or singularly perturbed boundary value problems of first order with constant coefficients is constructed being based on a stability function containing a matrix square root its essential feature is the unconditional stability in the absence of purely imaginary eigenvalues of the coefficient matrix local damping of errors uniform stability and uniform second order convergence are proved the computation of the specific matrix square root by a well known stable variant of newton s method is discussed a numerical example confirming the results is given

a priori error estimates for numerical methods for scalar conservation laws part ii flux splitting monotone schemes on irregular cartesian grids this paper is the second of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed in this paper we focus on how the lack of consistency introduced by the nonuniformity of the grids influences the convergence of flux splitting monotone schemes to the entropy solution we obtain the optimal rate of convergence of x 1 2 in l l 1 for consistent schemes in arbitrary grids without the use of any regularity property of the approximate solution we then extend this result to less consistent schemes called p consistent schemes and prove that they converge to the entropy solution with the rate of x min 1 2 p in l l 1 again no regularity property of the approximate solution is used finally we propose a new explanation of the fact that even inconsistent schemes converge with the rate of x 1 2 in l l 1 we show that this well known supraconvergence phenomenon takes place because the consistency of the numerical flux and the fact that the scheme is written in conservation form allows the regularity properties of its approximate solution total variation boundedness to compensate for its lack of consistency the nonlinear nature of the problem does not play any role in this mechanism all the above results hold in the multidimensional case provided the grids are cartesian products of one dimensional nonuniform grids

the anisotropic total variation flow we prove existence and uniqueness of solutions of the anisotropic total variation flow when the initial data is an l2 function and we give a characterization of such solutions that allows us to find explicit evolutions of sets in the presence of an anisotropy

a uniform scheme for the singularly perturbed riccati equation we consider the singularly perturbed riccati equation varepsilon u x a x u 2 x b x u x c x 0 u 0 a and present a new finite difference scheme which is exact when the coeffcientsa b andc are constant we show that under certain restrictions the solution u i h of this difference scheme converges uniformly in e tou xi the solution of the differential equation on the uniform meshxi ih numerical results are presented

a local estimate for vectorial total variation minimization in one dimension abstract let u be the minimizer of vectorial total variation v t v with l 2 data fidelity term on an interval i we show that the total variation of u over any subinterval of i is bounded by that of the datum over the same subinterval we deduce analogous statement for the vectorial total variation flow on i

decay rate for perturbations of stationary discrete shocks for convex scalar conservation laws this paper is to study the decay rate for perturbations of stationary discrete shocks for the lax friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method if the summation of the initial perturbation over j is small and decays at the algebraic rate as j then the solution approaches the stationary discrete shock profiles at the corresponding rate as n this rate seems to be almost optimal compared with the rate in the continuous counterpart proofs are given by applying the weighted energy integration method to the integrated scheme of the original one the selection of the time dependent discrete weight function plays a crucial role in this procedure

innovated higher criticism for detecting sparse signals in correlated noise higher criticism is a method for detecting signals that are both sparse and weak although first proposed in cases where the noise variables are independent higher criticism also has reasonable performance in settings where those variables are correlated in this paper we show that by exploiting the nature of the correlation performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer indeed it turns out that the case of independent noise is the most difficult of all from a statistical viewpoint and that more accurate signal detection for a given level of signal sparsity and strength can be obtained when correlation is present we characterize the advantages of correlation by showing how to incorporate them into the definition of an optimal detection boundary the boundary has particularly attractive properties when correlation decays at a polynomial rate or the correlation matrix is toeplitz

a partial upwind difference scheme for nonlinear parabolic equations abstract in this paper we present an explicit partial upwind difference scheme for the problem u t du xx f u x g x u 0 d 0 0 x 1 t 0 with u x 0 u 0 t and u 1 t all prescribed formulas for the upwind factors are provided we use the method of lower and upper solutions and the theory of m matrices the present method is more accurate and allows larger time steps than the corresponding one sided method we obtain the order of convergence for our scheme we also prove the convergence of the time evolving solutions to the unique steady state solution as the time approaches infinity the method can be generalized to multi dimensional analogues to support the theory numerical results are given

an engquist osher type scheme for conservation laws with discontinuous flux adapted to flux connections we consider scalar conservation laws with the spatially varying flux h x f u 1 h x g u where h x is the heaviside function and f and g are smooth nonlinear functions adimurthi mishra and veerappa gowda j hyperbolic differ equ 2 2005 pp 783 837 pointed out that such a conservation law admits many l 1 contraction semigroups one for each so called connection a b here we define entropy solutions of type a b involving kruzkov type entropy inequalities that can be adapted to any fixed connection a b it is proved that these entropy inequalities imply the l 1 contraction property for l infty solutions in contrast to the piecewise smooth setting of adimurthi mishra and veerappa gowda for a fixed connection these entropy inequalities include a single adapted entropy of the type used by audusse and perthame proc roy soc edinburgh sect a 135 2005 pp 253 265 we prove convergence of a new difference scheme that approximates entropy solutions of type a b for any connection a b if a few parameters are varied the scheme relies on a modification of the standard engquist osher flux is simple as no 2 times2 riemann solver is involved and is designed such that the steady state solution connecting a to b is preserved in contrast to most analyses of similar problems our convergence proof is not based on the singular mapping or compensated compactness methods but on standard spatial variation estimates away from the flux discontinuity some numerical examples are presented

total variation flow and sign fast diffusion in one dimension abstract we consider the dynamics of the total variation flow tvf u t div d u d u and of the sign fast diffusion equation sfde u t sign u in one spatial dimension we find the explicit dynamic and sharp asymptotic behaviour for the tvf and we deduce the one for the sfde by an explicit correspondence between the two equations

a new multiple testing method in the dependent case the most popular multiple testing procedures are stepwise procedures based on p values for individual test statistics included among these are the false discovery rate fdr controlling procedures of benjamini hochberg j roy statist soc ser b 57 1995 289 300 and their offsprings even for models that entail dependent data p values based on marginal distributions are used unlike such methods the new method takes dependency into account at all stages furthermore the p value procedures often lack an intuitive convexity property which is needed for admissibility still further the new methodology is computationally feasible if the number of tests is large and the proportion of true alternatives is less than say 25 percent simulations demonstrate a clear preference for the new methodology applications are detailed for models such as testing treatments against control or any intra class correlation model testing for change points and testing means when correlation is successive

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

a difference scheme for conservation laws with a discontinuous flux the nonconvex case in a previous work by the author convergence was established for a simple difference scheme approximating a scalar conservation law where the flux was concave and had a discontinuous spatially varying coefficient j d towers siam j numer anal 38 2000 pp 681 698 the main result of this paper is an extension of that convergence theorem to the situation where the flux may have any finite number of critical points additionally spatially varying source terms are allowed the spatially varying numerical flux is also shown to satisfy maximum and minimum principles and to be total variation decreasing tvd in time

a rigorous derivation of the coupling of a kinetic equation and burgers equation in this article we investigate the kinetic fluid coupling on a toy model which we obtain rigorously from a hydrodynamical limit the idea is that at the level of the full kinetic model the coupling is obvious we then investigate the coupling obtained when passing into the limit we show that especially in presence of a shock stuck on the interface the coupling involves a kinetic layer known as the milne problem due to this layer the limit process is quite delicate and some blow up techniques are needed to ensure its strong convergence

the 1 harmonic flow with values into a smooth planar curve abstract we introduce a notion of solution to the 1 harmonic flow i e the formal gradient flow of the total variation with respect to the l 2 distance from a domain of r m into a connected subset of the image of a smooth jordan curve for such notion we establish existence and uniqueness of solutions to the homogeneous neumann problem we also discuss a consistent notion of solution when the target space is a smooth n 1 dimensional manifold whose geodesics are unique presenting conjectures and open questions related to it

asymptotic and numerical analysis of singular perturbation problems a survey this paper is intended to be a brief survey of the asymptotic and numerical analysis of singular perturbation problems the purpose is to find out what problems are treated and what numerical asymptotic methods are employed with an eye toward the goal of developing general methods to solve such problems a summary of the results of some recent methods is presented and this leads to conclusions and recommendations about what methods to use on singular perturbation problems finally some areas of current research are indicated a bibliography of about 130 items is provided

second order conservative schemes and the entropy condition we consider numerical approximations to solutions of systems of hyperbolic conservation laws of the form au at af u ax 0 u e r andf r r smooth we show that conservative three point second order accurate methods cannot satisfy a local entropy inequality

a conservative uniformly accurate difference method for a singular perturbation problem in conservation form a conservative three point finite difference method is presented for the numerical solution of the singular perturbation problem varepsilon u xx b x u x f x 0 x 1 u 0 and u 1 given b x ne 0 certain a priori estimates are established for this problem and are then used to obtain uniform error estimates for the difference scheme some illustrative numerical results are also given

a global uniformly convergent finite element method for a quasi linear singularly perturbed elliptic problem abstract in this paper we construct a bilinear finite element method based on a special piecewise uniform mesh for solving a quasi linear singularly perturbed elliptic problem in two space dimensions a quasi optimal global uniform convergence rate o n 2x ln2 nx n 2y ln2 ny was obtained which is independent of the perturbation parameter here nx and ny are the number of elements in the x and y directions respectively

uniform high order difference schemes for a singularly perturbed two point boundary value problem on construit une famille de schemas aux differences finies uniformement precis pour le probleme du type eu a x u b x u f x on donne une analyse complete de l erreur de discretisation basee sur les resultats de stabilite on presente des essais numeriques

nonlinear stability of discrete shocks for systems of conservation laws in this paper we study the asymptotic nonlinear stability of discrete shocks for the lax friedrichs scheme for approximating general m systems of nonlinear hyperbolic conservation laws it is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the lp norm for all p 1 provided that the sums of the initial perturbations equal zero these results should shed light on the convergence of the numerical solution constructed by the lax friedrichs scheme for the single shock solution of system of hyperbolic conservation laws if the riemann solution corresponding to the given far field states is a superposition of m single shocks from each characteristic family we show that the corresponding multiple discrete shocks are nonlinearly stable in l p p 2 these results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the lax friedrichs scheme

convergence of upwind schemes for a stationary shock a nonlinear first order boundary value problem with discontinuous solutions is considered it arises in the study of gasflow through a duct and allows in general for multiple solutions new convergence results for three difference schemes are presented and the sharpness of numerical layers is established for the eo scheme stability of a physically correct solution with respect to time evolution is shown

monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem in this paper we consider monotone explicit iterations of the finite element schemes for the nonlinear equations associated with the boundary value problem u bu 2 based on piecewise linear polynomials and the lumping operator these iterations construct the monotonically decreasing and increasing sequences and convergence proofs are given finally we present some numerical examples verifying the effectiveness of the theory

implicit conservative schemes for the euler equations a new approach to a characteristic modeling scheme is presented that does not require the governing equations to be written in characteristi c variables or the flux terms to be split into positive and negative parts the method is based on the observation that for certain finite volume schemes the upwind influence can be accounted for through the conditions applied at the boundaries of individual cells instead of flux differencing the method is developed and applied to the one dimensional nozzle flow equations for subsonic transonic and supersonic flows and is then extended to two dimensions using an approximate factorization for the problem of a shock wave reflecting from a flat plate the present solution algorithm reduces the computational work per time step by 40 of that required by standard central difference implicit calculations i introduction n umerical methods that attempt to model the physics of the differential equations being approximated by properly accounting for the directions in which signals are propagated can be called characteristic modeling schemes the standard approach to characteristic modeling schemes is through the implementation of upwind schemes see refs 1 7 to devise an upwind scheme the primative fluxes are split into contributions whose jacobians have eigenvalues that are either 0 or 0 respectively at every point on the numerical mesh these fluxes are then differenced either upwind or downwind of that point

a higher order method for stationary shock problems an equidistant finite difference method is proposed for quasilinear singularly perturbed boundary value problems the method uses a combination of one sided schemes and a third order three point scheme it is easy to implement and produces third order accuracy away from shocks

a weighted difference scheme and monotone iterative methods for quasilinear boundary value problems abstract we consider the boundary value problem y xx f x y y x g x y 0 0 x y 0 b 0 y 1 b 1 we present a weighted two sided difference scheme to approximate the differential equation monotone iterative methods are proposed to solve the resulting nonlinear system the scheme applies equally well to multidimensional analogues numerical results are included

on a difference scheme of exponential type for a nonlinear singular perturbation problem a difference scheme of exponential type for solving a nonlinear singular perturbation problem is analysed although this scheme is not of monotone type al 1 convergence result is obtained relations between this scheme and engquist osher scheme are also discussed

finite difference schemes for quasilinear singular perturbation problems finite difference schemes for singularly perturbed quasilinear boundary value problems are considered the schemes have fitting factors which guarantee their uniform stability with respect to the perturbation parameter besides the usual stability in the discrete l1 norm we consider the maximum norm stability as well various schemes are compared numerically

some results on false discovery rate in stepwise multiple testing procedures the concept of false discovery rate fdr has been receiving increasing attention by researchers in multiple hypotheses testing this paper produces some theoretical results on the fdr in the context of stepwise multiple testing procedures with dependent test statistics it was recently shown by benjamini and yekutieli that the benjamini hochberg step up procedure controls the fdr when the test statistics are positively dependent in a certain sense this paper strengthens their work by showing that the critical values of that procedure can be used in a much more general stepwise procedure under similar positive dependency it is also shown that the fdr controlling benjamini liu step down procedure originally developed for independent test statistics works even when the test statistics are positively dependent in some sense an explicit expression for the fdr of a generalized stepwise procedure and an upper bound to the fdr of a step down procedure are obtained in terms of probability distributions of ordered components of dependent random variables before establishing the main results 1 introduction the main purpose of this paper is to present some formulas and inequalities providing theoretical insight into when and what stepwise procedures control the false discovery rate fdr at a prespecified level in multiple hypotheses testing the fdr first introduced in multiple testing by benjamini and hochberg 1995 is the expected proportion of erroneously rejected null hypotheses with v and r representing respectively the number of true null hypotheses rejected and the total number of null hypotheses rejected in a multiple testing procedure let q v r if r 0a nd 0i fr 0 then e q is the fdr of that procedure as they have argued it is an appropriate error rate to control in many practical situations particularly where a large number of null hypotheses are involved they also put forward an fdr controlling stepup procedure that is more powerful than comparable procedures controlling the traditional familywise error fwe rate when the underlying test statistics are independent benjamini and liu 1999 recently introduced a step down procedure with the same property the concept of fdr is now being used in a wide variety of applications abramovich and benjamini 1996 basford and tukey 1997 drigalenko

on some numerical schemes for transonic flow problems new second order accurate finite difference approximations for a class of nonlinear pdes of mixed type which includes the two dimensional low frequency transonic small disturbance equation tsd and full potential equation fp are presented for the tsd equation the scheme is implemented via a time splitting algorithm the inclusion of flux limiters keeps the total variation nonincreasing and eliminates spurious oscillations near shocks global linear stability tvd and entropy stability results are proved numerical results for the flow over a thin airfoil are presented current techniques used to solve the tsd equation may easily be extended to second order accuracy by this method for the fp equation the new scheme requires no subsonic supersonic switching and no numerical flux biasing global linear stability for all values of the mach number is proved

accuracy bounds for semidiscretizations of hyperbolic problems bounds are given for the error constant of stable finite difference methods for first order hyperbolic equations in one space dimension which use r downwind and s upwind points in the discretization of the space derivatives and which are of optimal order p min r s 2 r 2 2 s it is known that this order can be obtained by interpolatory methods examples show however that their error constants can be improved

analysis of difference schemes for a stationary shock problem we consider the limit function u of the solutions u varepsilon of a singularly perturbed boundary value problem in general u will be discontinuous two difference approximations of the boundary value problem are studied and the discrete values for varepsilon 0 h to 0 are compared with u error estimates of order o h and o h 2 are proved and the sharpness of numerical layers is established

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

nonlinear singular perturbation problems and one sided difference schemes we consider the boundary value problem varepsilon y a y y b x y f x 1 leqq x leqq 1 for y 1 and y 1 given and b x 0 equiv 0 b y x y geqq 0 we construct a simple difference scheme approximating varepsilon u xx a u u x b x u f x u t for t geqq 0 1 leqq x leqq 1 with the same boundary conditions and an arbitrary initial guess as the numerical artificial time approaches infinity we prove convergence to a unique steady state solution as the mesh size delta x and the parameter varepsilon approach zero in any order we prove convergence to the solution of the corresponding o d e we use one sided differences to approximate the transport term the method applies equally well to multidimensional analogues we present numerical results verifying the theory

stability and accuracy for implicit semidiscretizations of hyperbolic problems in this paper we give bounds for the error constants of certain classes of stable implicit finite difference methods for first order hyperbolic equations in one space dimension we consider classes of methods that user downwind ands upwind points in the explicit part andr downwind ands upwind points in the implicit part respectively and that are of optimal orderp min r r s s 2 r r 1 2 s s

well posedness in bv t and convergence of a difference scheme for continuous sedimentation in ideal clarifier thickener units we consider a scalar conservation law modeling the settling of particles in an ideal clarifier thickener unit the conservation law has a nonconvex flux which is spatially dependent on two discontinuous parameters we suggest to use a kru kov type notion of entropy solution for this conservation law and prove uniqueness l1 stability of the entropy solution in the bvt class functions w x t with tw being a finite measure the existence of a bvt entropy solution is established by proving convergence of a simple upwind finite difference scheme of the engquist osher type a few numerical examples are also presented

numerical approximations to nonlinear conservation laws with locally varying time and space grids an explicit time differencing technique is introduced to approximate nonlinear conservation laws this differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments previous stability requirements i e the cfl condition placed a global bound on the size of the time increments for scalar monotone approximations in one space dimension using this variable step time differencing convergence to the correct physical solution is proven given only a local cfl condition

l 1 stability of stationary discrete shocks the nonlinear stability in the l sup p norm p ge 1 of stationary weak discrete shocks for the lax friedrichs scheme approximating general m times m systems of nonlinear hyperbolic conservation laws is proved provided that the summations of the initial perturbations equal zero the result is proved by using a both weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the lax friedrichs scheme 13 refs

characterization of bayes procedures for multiple endpoint problems and inadmissibility of the step up procedure the problem of multiple endpoint testing for k endpoints is treated as a 2 k finite action problem the loss function chosen is a vector loss function consisting of two components the two components lead to a vector risk one component of the vector risk is the false rejection rate frr that is the expected number of false rejections the other component is the false acceptance rate far that is the expected number of acceptances for which the corresponding null hypothesis is false this loss function is more stringent than the positive linear combination loss function of lehmann ann math statist 28 1957 1 25 and cohen and sackrowitz ann statist 2005 33 126 144 in the sense that the class of admissible rules is larger for this vector risk formulation than for the linear combination risk function in other words fewer procedures are inadmissible for the vector risk formulation the statistical model assumed is that the vector of variables z is multivariate normal with mean vector and known intraclass covariance matrix e the endpoint hypotheses are h i i 0 vs k i i 0 1 k a characterization of all symmetric bayes procedures and their limits is obtained the characterization leads to a complete class theorem the complete class theorem is used to provide a useful necessary condition for admissibility of a procedure the main result is that the step up multiple endpoint procedure is shown to be inadmissible

explicit time marching methods for the time dependent euler computations four explicit type time marching methods including one proposed by the authors are examined the tvd conditions of this method are analyzed with the linear conservation law as the model equation performance of these methods when applied to the euler equations are numerically tested seven examples are tested the main concern is the performance of the methods when discontinuities with different strengths are encountered when the discontinuity is getting stronger spurious oscillation shows up for three existing methods while the method proposed by the authors always gives the results with satisfaction the effect of the limiter is also investigated to put these methods in the same basis for the comparison the same spatial discretization is used roe s solver is used to evaluate the fluxes at the cell interface spatially second order accuracy is achieved by the muscl reconstruction

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

a modified crank nicolson scheme with incremental unknowns for convection dominated diffusion equations a modified crank nicolson scheme based on one sided difference approximations is proposed for solving time dependent convection dominated diffusion equations in two dimensional space the modified scheme is consistent and unconditionally stable a priori l 2 error estimate for the fully discrete modified scheme is derived with the use of the incremental unknowns preconditioner at each time step a comparison among several classical numerical schemes has been made and numerical results confirm stability and efficiency of the modified crank nicolson scheme

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

the large time behavior of the scalar genuinely nonlinear lax friedrichs scheme the lax friedrichs scheme approximating the scalar genuinely nonlinear conservation law u sub t f sub x u 0 where f u is say strictly convex double dot f dot a sub asterisk 0 is studied the divided differences of the numerical solution at time t do not exceed 2 t dot a sub asterisk to the 1 this one sided lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case in particular it is independent of the initial amplitude in sharp contrast to liner problems it guarantees the entropy compactness of the scheme in this case as well as providing a quantitive insight into the large time behavior of the numerical computation

on some difference schemes for singular singularly perturbed boundary value problems singularly perturbed boundary value ordinary differential problems are considered where the problem defining the reduced solution is singular for numerical approximation families of symmetric difference schemes which are equivalent to certain collocation schemes based on gauss and lobatto points are used convergence results previously obtained for the regular singularly perturbed case are extended while gauss schemes are extended with no change lobatto schemes require a small modification in the mesh selection procedure with meshes as prescribed in the text highly accurate solutions can be obtained with these schemes for singular singularly perturbed problems at a very reasonable cost this is demonstrated by examples

application of the petrov galerkin method to chemical flooding reservoir simulation in one dimension abstract a one dimensional chemical flooding simulator is described this program models the effect that polymers surfactants and salts have on the enhanced recovery of oil the flow equations are convection dominated and often shock like profiles develop which traverse the domain the simulator incorporates with a few modifications most of the physical and chemical package which is set forth by pope and nelson the spacial discretization is performed via the petrov galerkin finite element method this technique is mainly derived from the work of hughes and brooks and is modified for the case of chemical flooding we compare this finite element method to the upstream finite difference method and to galerkin s method generally speaking the petrov galerkin results are significantly less sensitive to the number of grid points than are those of the upstream method its stability properties are nearly the same as those of the upstream techniques which in turn are superior to those of galerkin s method