the characteristic class and ramification of an l adic etale sheaf we introduce the characteristic class of an l adic etale sheaf using a cohomological pairing due to verdier sga5 as a consequence of the lefschetz verdier trace formula its trace computes the euler poincare characteristic of the sheaf we compare the characteristic class to two other invariants arising from ramification theory one is the swan class of kato saito 17 and the other is the 0 cycle class defined by kato for rank 1 sheaves in 16

ramification of local fields with imperfect residue fields we define two decreasing filtrations by ramification groups on the absolute galois group of a complete discrete valuation field whose residue field may not be perfect in the classical case where the residue field is perfect we recover the classical upper numbering filtration the definition uses rigid geometry and log structures we also establish some of their properties

duality and nearby cycles over general bases this paper studies the sliced nearby cycle functor and its commutation with duality over a henselian discrete valuation ring we show that this commutation holds confirming a prediction of deligne as an application we give a new proof of beilinson s theorem that the vanishing cycle functor commutes with duality up to twist over an excellent base scheme we show that the sliced nearby cycle functor commutes with duality up to modification of the base we deduce that duality preserves universal local acyclicity over an excellent regular base we also present gabber s theorem that local acyclicity implies universal local acyclicity over a noetherian base

a godunov type method in lagrangian coordinates for computing linearly perturbed planar symmetric flows of gas dynamics linear stability studies of complex flows require that efficient numerical methods be devised for predicting growth rates of multi dimensional perturbations for one dimensional 1d basic flow i e of planar cylindrical or spherical symmetry a general numerical approach is viable which consists in solving simultaneously the one dimensional equations of gas dynamics and their linearized forms for three dimensional perturbations extensions of artificial viscosity methods have thus been used in the past more recently equations aux derivees partielles et applications articles dedies a j l lions 1998 godunov type schemes for single fluid flows of gas dynamics and magnetohydrodynamics have been proposed pursuing this effort we introduce within the lagrangian perturbation approach a class of godunov type schemes which is well suited for solving multi material problems of gas dynamics these schemes tire developed here for the planar symmetric case and comprise two second order extensions the numerical capabilities of these methods are illustrated by computations of richtmyer meshkov instabilities occurring at a single material interface a systematic comparison of numerically computed growth rates with results of the linear theory for the richtmyer meshkov instability is provided

lagrangian gas dynamics in two dimensions and lagrangian systems we propose a new and canonical way of writing the equations of gas dynamics in lagrangian coordinates in two dimensions as a weakly hyperbolic system of conservation laws one part of the system is called the physical part and contains physical variables the other part is the geometrical part we show that the physical part is symmetrizable we show that the weak hyperbolicity is due to shear contact discontinuities free divergence constraints play an important role in the system we prove the l2 stability of the physical part of the system based on this formulation we derive a new conservative and entropy consistent finite volume numerical scheme we prove the stability of the numerical scheme numerical results show the potential interest of this approach various examples born infeld mhd 3d lagrangian gas dynamics can be written using the same abstract formalism

are points in tennis independent and identically distributed evidence from a dynamic binary panel data model this article tests whether points in tennis are independent and identically distributed iid we model the probability of winning a point on service and show that points are neither independent nor identically distributed winning the previous point has a positive effect on winning the current point and at important points it is more difficult for the server to win the point than at less important points furthermore the weaker a player the stronger are these effects deviations from iid are small however and hence the iid hypothesis will still provide a good approximation in many cases the results are based on a large panel of matches played at wimbledon 1992 1995 in total almost 90 000 points our panel data model takes into account the binary character of the dependent variable uses random effects to capture the unobserved part of a player s quality and includes dynamic explanatory variables

navier stokes equations with several independent pressure laws and explicit predictor corrector schemes this work is concerned with the numerical capture of stiff viscous shock solutions of navier stokes equations for complex compressible materials in the regime of large reynolds numbers after 2 and 6 a relevant numerical capture is known to require the satisfaction of an extended set of non classical rankine hugoniot conditions due to the non conservation form of the governing pde model here we show how to enforce their validity at the discrete level without the need for solving local non linear algebraic problems non linearities are bypassed when introducing new averaging techniques which are proved to satisfy all the desirable stability properties when invoking suitable approximate riemann solutions a relaxation procedure is proposed to that purpose with the benefit of a fairly simple overall numerical method

the characteristic cycle and the singular support of a constructible sheaf we define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by beilinson we prove a formula a la milnor for the total dimension of the space of vanishing cycles and an index formula computing the euler poincare characteristic generalizing the grothendieck ogg shafarevich formula to higher dimension an essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi continuity of the swan conductor due to deligne laumon we prove the index formula by establishing certain functorial properties of characteristic cycles

monte carlo tennis the probability of winning a game set match or single elimination tournament in tennis is computed using monte carlo simulations based on each player s probability of winning a point on serve which can be held constant or varied from point to point game to game or match to match the theory described in newton and keller stud appl math 114 2005 pp 241 269 is based on the assumption that points in tennis are independent identically distributed i i d random variables this is used as a baseline to compare with the simulations which under similar circumstances are shown to converge quickly to the analytical curves in accordance with the weak law of large numbers the concept of the importance of a point game and set to winning a match is described based on conditional probabilities and is used as a starting point to model non i i d effects allowing each player to vary from point to point his or her probability of winning on serve several non i i d models are investigated including the hot hand effect in which we increase each player s probability of winning a point on serve on the next point after a point is won the back to the wall effect is modeled by increasing each player s probability of winning a point on serve on the next point after a point is lost in all cases we find that the results provided by the theoretical curves based on the i i d assumption are remarkably robust and accurate even when relatively strong non i i d effects are introduced we end by showing examples of tournament predictions from the 2002 men s and women s u s open draws based on the monte carlo simulations we also describe arrow s impossibility theorem and discuss its relevance with regard to sports ranking systems and we argue for the development of probability based ranking systems as a way to soften its consequences

lagrangian systems of conservation laws we study the mathematical structure of 1d systems of conservation laws written in the lagrange variable modifying the symmetrization proof of systems of conservation laws with three hypothesis we prove that these models have a canonical formalism these hypothesis are i the entropy flux is zero ii galilean invariance iii reversibility for smooth solutions then we study a family of numerical schemes for the solution of these systems we prove that they are entropy consistent we also prove from general considerations the symmetry of the spectrum of the jacobian matrix

ramification theory for varieties over a perfect field for an l adic sheaf on a variety of arbitrary dimension over a perfect field we define the swan class measuring the wild ramification as a 0 cycle class supported on the ramification locus we prove a lefschetz trace formula for open varieties and a generalization of the grothendieck ogg shararevich formula using the swan class

the perron frobenius theorem and the ranking of football teams the author describes four different methods to rank teams in uneven paired competition and shows how each of these methods depends in some fundamental way on the perron frobenius theorem

entropy satisfying flux vector splittings and kinetic bgk models we establish forward and backward relations between entropy satisfying bgk relaxation models such as those introduced previously by the author and the first order flux vector splitting numerical methods for general systems of conservation laws classically to a kinetic bgk model that is compatible with some family of entropies we can associate an entropy flux vector splitting we prove that the converse is true any entropy flux vector splitting can be interpreted by a kinetic model and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes we deduce a new proof of discrete entropy inequalities under a sharp cfl condition that generalizes the monotonicity criterion in the scalar case in particular this gives a stability condition for numerical kinetic methods with noncompact velocity support a new interpretation of general kinetic schemes is also provided via approximate riemann solvers we deduce the construction of finite velocity relaxation systems for gas dynamics and obtain a hllc scheme for which we are able to prove positiveness of density and internal energy and discrete entropy inequalities

characteristic varieties and vanishing cycles on presente une etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres ce sont des sous varietes lagrangiennes coniques dans le fibre cotangent t x

wild ramification and k pi 1 spaces we prove that every connected affine scheme of positive characteristic is a k pi 1 space for the etale topology the main ingredient is the special case of the affine space mathbf a k n over a field k this is dealt with by induction on n using a key bertini type statement regarding the wild ramification of ell adic local systems on affine spaces which might be of independent interest its proof uses in an essential way recent advances in higher ramification theory due to t saito we also give rigid analytic and mixed characteristic versions of the main result

a two dimensional nodal riemann solver based on one dimensional riemann solver for a cell centered lagrangian scheme we develop a new and more general formula for the construction of two dimensional nodal riemann solver for a cell centered lagrangian scheme developed by maire and his co workers which allows us to use general one dimensional riemann solvers that have intermediate velocity and pressure in the construction the old formula for the scheme used in the papers of maire et al is only a special case of our new formula we present an entropy discussion which indicates that the schemes with nodal solvers constructed following the old formula which can only use the 1d riemann solvers satisfying our strong entropy condition are usually numerically very dissipative to develop numerically less dissipative schemes we introduce a so called weak entropy condition and present a one dimensional riemann solver that satisfies the weak entropy condition but not the strong entropy condition analysis shows that the scheme using this 1d solver is numerically less dissipative than the schemes using solvers satisfying the strong condition finally several numerical examples are presented to show that our new formula works well and the scheme using the one dimensional solver satisfying the weak entropy condition improves the accuracy in smooth region resolution around rarefaction waves and two dimensional symmetry however it sometimes produces small velocity oscillations and mesh distortions

coupling of general lagrangian systems this work is devoted to the coupling of two fluid models such a s two euler systems in lagrangian coordinates at a fixed interface we define coupling conditi ons which can be expressed in terms of continuity of some well chosen variables and then solve the coupled riemann problem in the present setting where the interface is characteristic a particula r choice of dependent variables which are transmitted ensures the overall conservativity