coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method we propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate eulerian and lagrangian subdomains that is the equations are written in eulerian form in one subdomain and in lagrangian form in the other subdomain this is of interest for example when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target on the one hand high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible euler equations to avoid problems associated with tangling of a lagrangian mesh on the other hand solid dynamics calculations are traditionally carried out using lagrangian numerical methods to avoid problems associated with numerical smearing in eulerian calculations we use the ghost fluid method to create accurate discretizations across the eulerian lagrangian interface the numerical method is presented in both one and two spatial dimensions three dimensional extensions to the interface coupling method are straightforward

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

a remark on computing distance functions we propose a new method for the reconstruction of the signed distance function in the context of level set methods the new method is a modification of the algorithm which makes use of the pde equation for the distance function introduced by m sussman p smereka and s osher 1994 j comput phys 119 146 it is based mainly on the use of a truly upwind discretization near the interface comparison with the previous algorithm shows a definite improvement when used with a first order upwind scheme the method provides first order accuracy for the signed distance function in the whole computational domain and second order accuracy in the location of the interface a second order version of the method is also presented

embeddings of submanifolds and normal bundles this paper studies the embeddings of a complex submanifold s inside a complex manifold m in particular we are interested in comparing the embedding of s in m with the embedding of s as the zero section in the total space of the normal bundle ns of s in m we explicitly describe some cohomological classes allowing to measure the difference between the two embeddings in the spirit of the work by grauert griffiths and camacho movasati and sad we are also able to explain the geometrical meaning of the separate vanishing of these classes our results hold for any codimension but even for curves in a surface we generalize previous results due to laufert and camacho movasati and sad

language preorder as a precongruence groote and vaandrager introduced the tyft format which is a congruence format for strong bisimulation equivalence this article proposes additional syntactic requirements on the tyft format extended with predicates to obtain a precongruence format for language preorder

residual indices of holomorphic maps relative to singular curves of fixed points on surfaces let m be a two dimensional complex manifold and let f m to m be a holomorphic map that fixes pointwise a possibly singular compact reduced and globally irreducible curve c subset m we give a notion of degeneracy of f at a point of c it turns out that f is non degenerate at one point if and only if it is non degenerate at every point of c when f is non degenerate on c we define a residual index for f at each point of c then we prove that the sum of the indices is equal to the self intersection number of c

structural operational semantics for weak bisimulations in this study we present rule formats for four main notions of bisimulation with silent moves weak bisimulation is a congruence for any process algebra defined by wb cool rules we have similar results for rooted weak bisimulation milner s observational equivalence branching bisimulation and rooted branching bisimulation the theorems stating that say observational equivalence is an appropriate notion of equality for ccs are corollaries of the results of this paper we also give sufficient conditions under which equational axiom systems can be generated from operational rules indeed many equational axiom systems appearing in the literature are instances of this general theory

topological invariants and equidesingularization for holomorphic vector fields on etudie l invariance du nombre de milnor et ses applications on demontre un theoreme d equidesingularisation

germs of holomorphic vector fields in c3 without a separatrix oblatum 28 xii 1988 26 iii 1990 10 x 1990 13 vi 1991 30 ix 1991 supported by universite de toulouse conacyt cnrs and caicyt 87 336 fulltext preview

darboux integrating factors inverse problems abstract we discuss planar polynomial vector fields with prescribed darboux integrating factors in a nondegenerate affine geometric setting we establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems and show that the space of vector fields with a given integrating factor modulo a subspace of explicitly known standard vector fields has finite dimension for several classes of examples we determine this space explicitly

extendable cohomologies for complex analytic varieties we introduce a cohomology called extendable cohomology for abstract complex singular varieties based on suitable differential forms beside a study of the general properties of such a cohomology we show that given a complex vector bundle one can compute its topological chern classes using the extendable chern classes defined via a chern weil type theory we also prove that the localizations of the extendable chern classes represent the localizations of the respective topological chern classes thus obtaining an abstract residue theorem for compact singular complex analytic varieties as an application of our theory we prove a camacho sad type index theorem for holomorphic foliations of singular complex varieties

index theorems for holomorphic self maps let m be a complex manifold and s subset m a possibly singular subvariety of m let f colon m to m be a holomorphic map such that f restricted to s is the identity we show that one can associate to f a holomorphic section x f of a sheaf related to the embedding of s in m and that such a section reads the dynamical behavior of f along s in particular we prove that under generic hypotheses the canonical section x f induces a holomorphic action in the sense of bott on the normal bundle of the regular part of s in m and this allows to obtain for holomorphic self maps with non isolated fixed points index theorems similar to camacho sad baum bott and variation index theorems for holomorphic foliations finally we apply our index theorems to obtain information about topology and dynamics of holomorphic self maps of surfaces with a compact curve of fixed points

towards perfectly absorbing boundary conditions for euler equations in this paper we examine the effectiveness of absorbing layers as non reflecting computational boundaries for the euler equations the absorbing layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation this methodology is similar to that used by berenger for the numerical solutions of maxwell s equations specifically we apply this methodology to three physical problems shock vortex interactions a plane free shear flow and an axisymmetric jet with emphasis on acoustic wave propagation our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered

glimm s method applied to underwater explosions abstract the random choice method conceived by glimm and developed by chorin for solving hyperbolic partial differential equations is applied to calculate the disturbance produced by a spherical underwater explosion results are compared with earlier calculations under similar conditions using the method of characteristics good qualitative agreement with earlier results is observed

meromorphic vector fields with single valued solutions on complex surfaces abstract we study ordinary differential equations in the complex domain given by meromorphic vector fields on compact complex kahler surfaces we prove that if such an equation has a maximal single valued solution in particular an entire one whose image is not contained in a proper analytic subset then up to a bimeromorphic transformation either the vector field is holomorphic or it preserves a fibration

complete algebraic vector fields on affine surfaces part ii in this work we study the singularities at infinity of algebraic vector fields in dimension 2 these singularities will be classified under a mild assumption the general problem is also reduced to the study of the combinatorics of certain resolutions which will be developed in part ii our main results are local and therefore can be carried over more general surfaces whereas we deal with complete vector fields the results also apply to complete ones thanks to a theorem of forstneric 7

ntyft ntyxt rules reduce to ntree rules groote and vaandrager introduced thetyft tyxt formatfor transition system specifications tsss and established that for each tss in this format that iswell founded the bisimulation equivalence it induces is a congruence in this paper we construct for each tss in tyft tyxt format an equivalent tss that consists oftree rulesonly as a corollary we can give an affirmative answer to an open question namely whether the well foundedness condition in the congruence theorem for tyft tyxt can be dropped these results extend to tyft tyxt with negative premises and predicates

three dimensional perfectly matched layer for the absorption of electromagnetic waves the perfectly matched layer is a technique of free space simulation developed for solving unbounded electromagnetic problems with the finite difference time domain method referred to as pml this technique has been described in a previous paper for two dimensional problems the present paper is devoted to the three dimensional case the theory of the perfectly matched layer is generalized to three dimensions and some numerical experiments are shown to illustrate the efficiency of this new method of free space simulation

the meaning of negative premises in transition system specifications we present a general theory for the use of negative premises in the rules of transition system specifications tsss we formulate a criterion that should be satisfied by a tss in order to be meaningful that is to unequivocally define a transition relation we also provide powerful techniques for proving that a tss satisfies this criterion meanwhile constructing this transition relation both the criterion and the techniques originate from logic programming van gelder et al 1988 gelfond and lifschitz 1988 to which tsss are close in an appendix we provide an extensive comparison between them as in groote 1993 we show that the bisimulation relation induced by a tss is a congruence provided that it is in ntyft ntyxt format and can be proved meaningful using our techniques we also considerably extend the conservativity theorems of groote 1993 and groote and vaandrager 1992 as a running example we study the combined addition of priorities and abstraction to basic process algebra bpa under some reasonable conditions we show that this tss is indeed meaningful which could not be shown by other methods bloom et al 1995 groote 1993 finally we provide a sound and complete axiomatization for this example

boundary conditions for simulations of oscillating bubbles using the non linear acoustic approximation we have developed a new boundary condition for finite volume simulations of oscillating bubbles our method uses an approximation to the motion outside the domain based on the solution at the domain boundary we then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary our boundary condition is applicable in regions where the motion is close to spherically symmetric we have tested our method on a range of one and two dimensional test cases results show good agreement with previous studies the method allows simulations of oscillating bubbles for long run times 5 10 5 time steps with a cfl number of 0 8 on highly truncated domains in which the boundary condition may be applied within 0 1 of the maximum bubble radius conservation errors due to the boundary conditions are found to be of the order of 0 1 after 105 time steps the method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles two dimensional results demonstrate that highly asymmetric bubble features such as surface instabilities and the formation of jets may be captured on a small domain using this boundary condition

liouvillian integration and bernoulli foliations analytic foliations in the 2 dimensional complex projective space with algebraic invariant curves are studied when the holonomy groups of these curves are solvable it is shown that such a condition leads to the existence of a liouville type first integral and under generic extra conditions it is proven that these foliations can be defined by bernoulli equations

centennial history of hilbert s 16th problem the second part of hilbert s 16th problem deals with polynomial differential equations in the plane it remains unsolved even for quadratic polynomials there were several attempts to solve it that failed yet the problem inspired significant progress in the geometric theory of planar differential equations as well as bifurcation theory normal forms foliations and some topics in algebraic geometry the dramatic history of the problem as well as related developments are presented below 1 the problem and its counterparts what may be said about the number and location of limit cycles of a planar polynomial vector field of degree n the limit cycle is an isolated closed orbit of a vector field this second part of hilbert s 16th problem appears to be one of the most persistent in the famous hilbert list h second only to the riemann function conjecture traditionally hilbert s question is split into three each one requiring a stronger answer problem 1 is it true that a planar polynomial vector field has but a finite number of limit cycles problem 2 is it true that the number of limit cycles of a planar polynomial vector field is bounded by a constant depending on the degree of the polynomials only the bound on the number of limit cycles in problem 2 is denoted by h n and known as the hilbert number linear vector fields have no limit cycles hence h 1 0 it is still unknown whether or not h 2 exists problem 3 give an upper bound for h n a solution to any of these problems implies a solution for the previous ones only the first problem is solved now the positive answer was established in e92 i91 there are analytic counterparts of problems 1 and 2 received by the editors december 2001 2000 mathematics subject classification primary 34cxx 34mxx 37f75

on invariance of plurigenera for foliations on surfaces let x be a smooth algebraic surface a foliation f on x is roughly speaking a subline bundle t f of the tangent bundle of x the dual of t f is called the canonical bundle of the foliation k f in the last few years birational methods have been successfully used in order to study foliations more precisely geometric properties of the foliation are translated into properties of the canonical bundle of the foliation one of the most important invariants describing the properties of a line bundle l is its kodaira dimension kappa l which measures the growth of the global sections of l and its tensor powers the kodaira dimension of a foliation f is defined as the kodaira dimension of its canonical bundle kappa k f in their fundamental works brunella and mcquillan give a classfication of foliations on surfaces on the model of enriques kodaira classification of surfaces the next step is the study of the behaviour of families of foliations brunella proves that for a family of foliations x t f t of dimension one on surfaces satisfying certain hypotheses of regularity the kodaira dimension of the foliation does not depend on t by analogy with siu s invariance of plurigenera it is natural to ask whether for a family of foliations x t f t the dimensions of global sections of the canonical bundle and its powers depend on t in this talk we will discuss to which extent an invariance of plurigenera for foliations is true and under which hypotheses on the family of foliations it holds