a fast algorithm for simulating vesicle flows in three dimensions vesicles are locally inextensible fluid membranes that can sustain bending in this paper we extend the study of veerapaneni et al s k veerapaneni d gueyffier g biros d zorin a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows journal of computational physics 228 19 2009 7233 7249 to general non axisymmetric vesicle flows in three dimensions although the main components of the algorithm are similar in spirit to the axisymmetric case spectral approximation in space semi implicit time stepping scheme important new elements need to be introduced for a full 3d method in particular spatial quantities are discretized using spherical harmonics and quadrature rules for singular surface integrals need to be adapted to this case an algorithm for surface reparameterization is needed to ensure stability of the time stepping scheme and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs to characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi implicit time stepping scheme we perform a spectral analysis of the evolution operator on the unit sphere by introducing these algorithmic components we obtain a time stepping scheme that circumvents the stability constraint on the time step and achieves spectral accuracy in space we present results to analyze the cost and convergence rates of the overall scheme to illustrate the applicability of the new method we consider a few vesicle flow interaction problems a single vesicle in relaxation sedimentation shear flows and many vesicle flows

a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d we present a new method for the evolution of inextensible vesicles immersed in a stokesian fluid we use a boundary integral formulation for the fluid that results in a set of nonlinear integro differential equations for the vesicle dynamics the motion of the vesicles is determined by balancing the non local hydrodynamic forces with the elastic forces due to bending and tension numerical simulations of such vesicle motions are quite challenging on one hand explicit time stepping schemes suffer from a severe stability constraint due to the stiffness related to high order spatial derivatives and a milder constraint due to a transport like stability condition on the other hand an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step we present two semi implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme we discretize the equations by using a spectral method in space and a multistep third order accurate scheme in time we use the fast multipole method fmm to efficiently compute vesicle vesicle interaction forces in a suspension with a large number of vesicles we report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

convergence of parallel multisplitting iterative methods for m matrices abstract despite the major recent activity in parallel processing few effective new algorithms designed exclusively for multiprocessors have been put forth one such is the multisplitting iterative algorithm suggested by o leary and white although they have given some sufficient conditions for convergence a general convergence theory has not been developed even for the classical situation where the coefficient matrix a is an m matrix or is symmetric positive definite in this paper we study the m matrix case in detail the multisplitting process for a rn n is recast as an ordinary iterative process for a certain block matrix a r kn kn where k is the number of processors and standard convergence results are used to develop a convergence theory for multisplitting iterative methods where a is an m matrix comparison results between multisplitting methods are established in terms of monotonic norms and for the case where a is irreducible in terms of the asymptotic convergence rate a key observation here is that in certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of a and is independent of the manner in which the work is distributed among the processors thus in general one can distribute the work for load balancing purposes without affecting the convergence rate

block ilu factorization preconditioners for a block tridiagonal h matrix abstract we propose new parallelizable block ilu incomplete lu factorization preconditioners for a nonsymmetric block tridiagonal h matrix theoretical properties of these block ilu preconditioners are compared with those of block ilu preconditioners for the corresponding comparison matrix numerical results of the bicgstab using these block preconditioners are compared with those of the bicgstab using a standard ilu factorization preconditioner to see the effectiveness of the block ilu preconditioners lastly parallel computations of the block ilu preconditioners are carried out and evaluated on the cray c90

incomplete blockwise factorizations of block h matrices the use of incomplete blockwise factorizations as preconditioners in conjugate gradient like methods has become more and more popular in recent years most of the theory concerning existence and applicability of these factorizations has been limited to m matrices so far here we introduce a more general definition of block h matrices robert 8 and we extend the theory to this class of matrices

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

l algebre de hopf et le groupe de galois motiviques d un corps de caracteristique nulle ii this is the second article of a series of two aiming at constructing and studying motivic galois groups in the context of triangulated motives these motivic galois groups were constructed in the first article and their algebras of regular functions were described concretely in terms of differential forms or algebraic cycles in the present article we gather important complements to the first one in the first part of this article we describe the link between the motivic galois group and the usual galois group of a subfield of in the second part we develop the basis of a theory of ramification for the motivic galois groups by constructing motivic versions of the decomposition and inertia groups associated to a geometric valuation we also introduce the relative motivic galois group of an extension k k which measures the difference between the motivic galois groups of k and k the latter is more accessible than its absolute counterpart in effect we show that it is a quotient of the pro algebraic completion of the topological fundamental pro group of a the pro variety homk k at least when the extension k k is of finite type

motivic periods and grothendieck arithmetic invariants abstract we construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers for the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective showing that a suitable betti de rham realization of 1 motives is fully faithful we can verify this period conjecture in several cases the divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical grothendieck period conjecture for algebraic cycles on smooth and proper schemes these divisibility properties are treated in an appendix by b kahn extending previous work of bloch and colliot thelene raskind

the universal regular quotient of the chow group of points on projective varieties let x be a projective variety of dimension n de ned over an algebraically closed eld k for x irreducible and non singular matsusaka ma constructed an abelian variety alb x and a morphism a x alb x called the albanese variety and mapping respectively depending on the choice of a base point on x which is universal among the morphisms to abelian varieties see lang la serre se for other constructions over the eld of complex numbers the existence of alb x and a was known before and has a purely hodge theoretic description see igusa i for the hodge theoretic construction incidentally the terminology albanese variety was introduced by a weil for reasons explained in his commentary on the article 1950a of volume i of his collected works see w one of which is that the paper alb of albanese de nes it for a surface as a quotient of the group of 0 cycles of degree 0 modulo an equivalence relation let chn x deg 0 denote the chow group of 0 cycles of degree 0 on x modulo rational equivalence when x is irreducible and non singular a remarkable feature of the albanese morphism a is that it factors through a regular homomorphism u chn x deg 0 alb x that is a homomorphism which when composed with the cycle map c x chn x deg 0 gives an algebraic morphism this follows immediately from the fact that an abelian variety does not contain any rational curve thus one can reformulate matsusaka s theorem as the invent math 135 595 664 1999 doi 10 1007 s002229900890

convergence of two stage and multisplitting methods using various types of splittings we first study the convergence of both two stage iterative method and multisplitting methods using various types of splittings for solving a linear system whose coefficient matrix is an m matrix or an h matrix we next study a parallel implementation of two stage multisplitting method associated with a special multisplitting and an application of the two stage multisplitting method to parallel preconditioner of krylov subspace methods lastly we provide parallel performance results of both two stage multisplitting method and krylov subspace method with a parallel preconditioner which is derived from two stage multisplitting method on the ibm p690 supercomputer

mixed hodge complexes on algebraic varieties using the theory of mixed hodge modules we introduce the notion of mixed hodge complex on an algebraic variety and establish the relation between the filtered complex of du bois and the corresponding complex of mixed hodge modules some application to the du bois singularity is given

convergence behaviors of multisplitting methods with k 1 relaxed parameters in this paper two multisplitting methods with k 1 relaxed parameters are established for solving a linear system whose coefficient matrix is a large sparse m matrix or h matrix and the corresponding convergence behaviors are studied then the implementation of these two methods with ilu factorizations as inner splittings is investigated finally some numerical experiments are presented to illustrate the effectiveness of the preconditioners obtained from our methods when combined with bicgstab

on the stability of the incomplete lu factorizations and characterizations of h matrices meijerink and van der vorst 8 have shown that the incomplete lu factorizations are numerically stable for m matrices varga saff and mehrmann 16 gave some characterizations of the h matrices by using the incomplete lu factorizations of them the purpose of this paper is to show that the incomplete lu factorizations of an h matrix are at least as stable as the complete lu factorizations of its comparison matrix we give also some new characterizations of the h matrices in connection with their incomplete lu factorizations

the filtered ogus realisation of motives abstract we construct the filtered ogus realisation of voevodsky motives over a number field k this realisation extends the functor defined on 1 motives by andreatta barbieri viale and bertapelle as an illustration we note that the analogue of the tate conjecture holds for k3 surfaces

iterative solution methods for certain sparse linear systems with a non symmetric matrix arising from pde problems abstract in this paper methods are described for the solution of certain sparse linear systems with a non symmetric matrix the power of these methods is demonstrated by extensive numerical experiments application of the methods is limited to problems where the matrix has only eigenvalues with positive real part an important class of this type of matrix arises from discretisation of second order partial differential equations with first order derivative terms

boundary integral method for the flow of vesicles with viscosity contrast in three dimensions we propose numerical algorithms for the simulation of the dynamics of three dimensional vesicles suspended in viscous stokesian fluid our method is an extension of our previous work s k veerapaneni et al 2011 37 to flows with viscosity contrast this generalization requires a change in the boundary integral formulation of the solution in which a double layer stokes integral is introduced and leads to changes in the fluid dynamics due to the viscosity contrast of the vesicles which can no longer be efficiently resolved with existing algorithms in this paper we describe the algorithms needed to handle flows with viscosity contrast accurately and efficiently we show that a globally semi implicit method does not have any time step stability constraint for flows with single and multiple vesicles with moderate viscosity contrast and the computational cost per simulation unit time is comparable to or less than that of an explicit scheme automatic oversampling adaptation enables us to achieve high accuracy with very low spectral resolution we conduct numerical experiments to investigate the stability accuracy and the computational cost of the algorithms overall our method achieves several orders of magnitude speed up compared to the standard explicit schemes

deligne s conjecture on 1 motives we reformulate a conjecture of deligne on 1 motives by using the integral weight filtration of gillet and soule on cohomology and prove it this implies the original conjecture up to isogeny if the degree of cohomology is at most two we can prove the conjecture for the hodge realization without isogeny and even for 1 motives with torsion

the neron severi group of a proper seminormal complex variety we prove a lefschetz 1 1 theorem for proper seminormal varieties over the complex numbers

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

on generalizations of the albanese variety in this note the relation between two generalizations of the classical albanese variety namely the one for smooth non complete varieties by faltings and wustholz and the one for singular varieties by esnault srinivas and viehweg is investigated over the field of complex numbers

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

a note on comparison theorems for splittings and multisplittings of hermitian positive definite matrices abstract we discuss iterative methods for the solution of the linear system ax b which are based on a single splitting or a multisplitting of a in order to compare different methods it is common to compare the spectral radius of the iterative matrix for m matrices a and weak regular splittings there exist well known comparison theorems here we give a comparison theorem for splittings of hermitian positive definite matrices furthermore we establish a comparison theorem for multisplittings of a hermitian positive definite matrix

variation of mixed hodge structure i around 1970 griffiths introduced the notion of a variation of hodge structure on a complex manifold s see 17 w 2 it constitutes the axiomatization of the features possessed by the local systems of cohomology associated to a family of compact k ihler manifolds esp smooth projective varieties parametrized by s these are for a variation of hodge structure u of weight m 0 a locally constant sheaf u of q vector spaces or u of real vector spaces 1 hodge filtration horizontality a decreasing filtration o r of gs by holomorphic subbundles such that the evident connection v on takes o p into q 2 hodge decompositions if gs denotes the sheaf of functions on s and if

une version relative de la conjecture des periodes de kontsevich zagier we start with a series f p r1 fr r with indeterminate and where the coecients fr fr z1 zn are holomorphic functions dened on an open neighborhood of the closed polydisc d n f z1 zn jzij 1g integrating the coecients of this series on the n dimensional real cube 0 1 n yields a laurent series r 0 1 n f when f is algebraic we say that r 0 1 n f is a series of periods in this article our goal is to determine the algebraic series f such that r 0 1 n f is zero in principle this gives informations on the transcendence properties of series of periods our main result is reminiscent to the kontsevich zagier conjecture on periods in a modied form

interfacial dynamics in stokes flow via a three dimensional fully implicit interfacial spectral boundary element algorithm since the pioneering work of youngren and acrivos g k youngren a acrivos on the shape of a gas bubble in a viscous extensional flow j fluid mech 76 1976 433 442 30 years ago interfacial dynamics in stokes flow has been implemented through explicit time integration of boundary integral schemes which require that the time step is sufficiently small to ensure numerical stability to avoid this difficulty we have developed an efficient fully implicit time integration algorithm based on a mathematically rigorous combination of implicit formulas with a jacobian free three dimensional newton method the resulting algorithm preserves the stability of the employed implicit formula and thus it has strong stability properties e g it is not affected by the courant condition or by physical stiffness such as that associated with the critical conditions of interfacial deformation in our work the numerical solution of our implicit algorithm is achieved through our spectral boundary element method our numerical results for free suspended droplets are in excellent agreement with experimental findings analytical predictions and earlier computational results at both subcritical and supercritical conditions and establish the properties of our fully implicit spectral boundary element algorithm

symmetric multisplitting of a symmetric positive definite matrix abstract a parallel symmetric multisplitting method for solving a symmetric positive system ax b is presented here the s p d symmetric positive definite matrix a need not be assumed in a special form e g the dissection form r e white siam j matrix anal appl 11 1990 69 82 the main tool for deriving our method is the diagonally compensated reduction cf o axelsson l kolotilina numer linear algebra appl 1 1994 155 177 the convergence of the presented parallel symmetric multisplitting method is also discussed by using this tool

convergence of non stationary parallel multisplitting methods for hermitian positive definite matrices non stationary multisplitting algorithms for the solution of linear systems are studied convergence of these algorithms is analyzed when the coefficient matrix of the linear system is hermitian positive definite asynchronous versions of these algorithms are considered and their convergence investigated

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

performance of ilu factorization preconditioners based on multisplittings in this paper we study the convergence of multisplitting methods associated with a multisplitting which is obtained from the ilu factorizations of a general h matrix and then we propose parallelizable ilu factorization preconditioners based on multisplittings for a block tridiagonal h matrix we also describe a parallelization of preconditioned krylov subspace methods with the ilu preconditioners based on multisplittings on distributed memory computers such as the cray t3e lastly parallel performance results of the preconditioned bicgstab are provided to evaluate the efficiency of the ilu preconditioners based on multisplittings on the cray t3e

pic is a contracted functor we show that there is a natural decomposition pic a t t 1 cong pic a oplus npic a oplus npic a oplus h 1 a for any commutative ringa where pic a is the picard group of invertiblea modules andh1 a is the etale cohomology grouph1 spec a a similar decomposition of pic x t t 1 holds for any schemex this makes pic a contracted functor in the sense of bass h1 a is always a torsionfree group and is zero ifa is normal for pseudo geometric rings h1 a is an effectively computable finitely generated free abelian group we also show thath1 a t t 1 h1 a i e nh1 lh1 0 this yields the formula for group rings pic a t 1 t 1 1 t m t m 1 cong pic a oplus coprod limits i 1 m h 1 a oplus coprod limits k 1 m coprod limits i 1 2 k left k m right n k pic a

nori 1 motives let mathsf ehm be nori s category of effective homological mixed motives in this paper we consider the thick abelian subcategory mathsf ehm 1 subset mathsf ehm generated by the i th relative homology of pairs of varieties for i in 0 1 we show that mathsf ehm 1 is naturally equivalent to the abelian category t mathcal m 1 of 1 motives with torsion this is our main theorem along the way we obtain several interesting results firstly we realize t mathcal m 1 as the universal abelian category obtained using nori s formalism from the betti representation of an explicit diagram of curves secondly we obtain a conceptual proof of a theorem of vologodsky on realizations of 1 motives thirdly we verify a conjecture of deligne on extensions of 1 motives in the category of mixed realizations for those extensions that are effective in nori s sense

generalized 1 motivic sheaves abstract let k be a field of characteristic 0 we extend the definition of the category of 1 motivic sheaves introduced by barbieri viale and kahn allowing quotients of connected algebraic k groups by formal k groups we show that its bounded derived category is equivalent to the bounded derived category of the category of generalized 1 motives with torsion

parallel relaxed multisplitting methods for a symmetric positive definite matrix we first study convergence of both the relaxed multisplitting method and the relaxed nonstationary two stage multisplitting method using incomplete factorizations for solving a linear system whose coefficient matrix is a large sparse symmetric positive definite matrix we next study a parallel implementation of the relaxed two stage multisplitting method using incomplete factorizations as inner splittings and an application of the relaxed two stage multisplitting method to parallel preconditioner of the cg conjugate gradient method lastly we provide parallel performance results of both the relaxed two stage multisplitting method and the cg method with a parallel preconditioner which is derived from the relaxed two stage multisplitting method on the ibm p690 supercomputer

a stable method for the incomplete factorization of h matrices abstract ahac and olesky have shown that by using the most diagonal dominat column as a pivot element for m matrices was numerically stable the purpose of this paper is to show that this method of selecting a pivoting is stable when finding the incomplete factorization of an h matrix

comparisons of weak regular splittings and multisplitting methods comparison results for weak regular splittings of monotone matrices are derived as an application we get upper and lower bounds for the convergence rate of iterative procedures based on multisplittings this yields a very simple proof of results of neumann plemmons on upper bounds and establishes lower bounds which has in special cases been conjectured by these authors

ogus realization of 1 motives abstract after introducing the ogus realization of 1 motives we prove that it is a fully faithful functor more precisely following a framework introduced by ogus considering an enriched structure on the de rham realization of 1 motives over a number field we show that it yields a full functor by making use of an algebraicity theorem of bost

convergence of two stage iterative methods using incomplete factorization we first study the convergence of two stage iterative methods using the incomplete factorization for solving a linear system whose coefficient matrix is an h matrix and then we study the convergence of two stage iterative methods using the incomplete factorization for solving a linear system whose coefficient matrix is a symmetric positive definite matrix lastly numerical experiments are provided to analyze theoretical results

a multipole accelerated algorithm for close interaction of slightly deformable drops an efficient multipole accelerated boundary integral algorithm is developed to study close contact three dimensional interaction of two drops at zero reynolds numbers and very small but non zero capillary numbers ca when the drops are nearly spherical the numerical difficulties compared to the case of larger deformations include severe stability limitations on the time step and a singular perturbation for ca 1 requiring very high surface resolution both in the small gap and in the outer region the mesh triangle vertices are grouped into a large number of non overlapping patches with economical rotation based multipole reexpansions to handle patch to patch interactions and limit the use of expensive direct summations a novel concept of a dynamical projective mesh is developed to maintain fixed topology gap adaptive surface triangulations for o 10 5 boundary elements per drop in close contact the algorithm has at least an order of magnitude advantage over the standard boundary integral method making such dynamical calculations feasible in gravity induced and shear induced motion exact results are obtained for the dynamics of the surface clearance h m i n which attains values less than 0 001 of the drop radii and for the separation angle b s e p determining the configuration when two drops in apparent contact start to separate the shear flow problem is studied in the wide range of drop to medium viscosity ratios 0 25 0

convergence of nonstationary multisplitting methods using ilu factorizations in this paper we first study convergence of nonstationary multisplitting methods associated with a multisplitting which is obtained from the ilu factorizations for solving a linear system whose coefficient matrix is a large sparse h matrix we next study a parallel implementation of the relaxed nonstationary two stage multisplitting method called algorithm 2 in this paper using ilu factorizations as inner splittings and an application of algorithm 2 to parallel preconditioner of krylov subspace methods lastly we provide parallel performance results of both algorithm 2 using ilu factorizations as inner splittings and the bicgstab with a parallel preconditioner which is derived from algorithm 2 on the ibm p690 supercomputer

crystalline realizations of 1 motives we consider the crystalline realization of deligne s 1 motives in positive characteristics and prove a comparison theorem with the de rham realization of formal liftings to zero characteristic we then show that one dimensional crystalline cohomology of an algebraic variety defined by forcing universal cohomological descent via de jong s alterations coincides with the crystalline realization of the picard 1 motive over perfect fields of characteristic 2

guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems abstract this paper presents incomplete decompositions for various types of matrices as they occur in the implicit discretisation of practical problems a review is given of methods for the usual five point discretisation of a self adjoint elliptic second order partial differential equation in two dimensions on a square the matrices which occur in this type of problem are symmetric m matrices of very regular structure the convergence behaviour of the different decompositions for this case is demonstrated by numerical experiments the paper also gives decompositions for the following type of matrices i symmetric m matrices of a different structure ii symmetric positive definite matrices iii non symmetric matrices

stable lu factorization of h matrices abstract results are given concerning the lu factorization of h matrices and gaussian elimination with column diagonal dominant pivoting is shown to be applicable to h matrices this algorithm which uses a symmetric permutation to exchange the most diagonally dominant column of the unreduced submatrix into the pivotal position is shown to be numerically stable by deriving an upper bound on the growth factor associated with the backward error analysis for gaussian elimination

on incomplete block factorization methods of generalized ssor type for h matrices abstract two types of modified incomplete block factorization methods are considered and the existence and convergence of the related splittings are established for h matrices this is done by studying in parallel the similar preconditioner for an m matrix a which satisfies a m a we show also for the m matrix case somewhat more general results for the type of preconditioners considered than previously found in the literature

sharp de rham realization we introduce the sharp universal extension of a 1 motive with additive factors and torsion over a field of characteristic zero we define the sharp de rham realization t by passing to the lie algebra over the complex numbers we then show a sharp de rham comparison theorem in the category of formal hodge structures for a free 1 motive along with its cartier dual we get a canonical connection on their sharp extensions yielding a perfect pairing on sharp realizations thus we show how to provide one dimensional sharp de rham cohomology h dr1 of algebraic varieties

a boundary integral model for drop deformation between two parallel plates with non unit viscosity ratio drops a boundary integral method is presented for drop deformation between two parallel walls for non unit viscosity ratio systems to account for the effect of the walls the green s functions are modified and all terms for the double layer potential are derived the full three dimensional implementation is validated and the model is shown to be accurate and consistent the method is applied to study drop deformation in shear flow an excellent match with small deformation theory is found at low capillary numbers and our results match with other bim simulations for pressure driven flows for shear flow with moderate capillary numbers we see that the behavior of a low viscosity drop is similar to that of drop with a viscosity ratio of unity high viscosity drops on the other hand are prevented from rotating in shear flow which results in a larger deformation but less overshoot in the drop axes is observed in contrast with unconfined flow high viscosity drops can be broken in shear flow between parallel plates for low viscosity drops the critical capillary number is higher in confined situations

nonstationary parallel relaxed multisplitting methods abstract relaxed nonstationary multisplitting methods are studied for the parallel solution of nonsingular linear systems convergence results of the synchronous and asynchronous versions for systems with h matrices are presented computational results of these methods on a shared memory multiprocessor vector computer are reported these results show that nonstationary methods synchronous and asynchronous are better than the standard ones especially when the matrix of the linear system has a relatively small bandwidth moreover asynchronous versions always behave better than the synchronous ones

interfacial dynamics for stokes flow theoretical and computational aspects of the method of interfacial dynamics for flow at vanishing reynolds number are considered the mathematical formulation relies on the boundary integral representation that expresses the flow in terms of distributions of stokes flow singularities over the interfaces the densities of the distributions are identified with the jump in the hydrodynamic traction due to interfacial in plane and transverse tensions the interfacial velocity or the strength of a hydrodynamic potential the numerical procedure involves describing the interfaces in terms of interfacial marker points that reproduce the evolving shapes of the interfaces by global or local interpolation solving integral equations of the second kind for the interfacial velocity or for the density of a hydrodynamic potential and computing the motion of the marker points while simultaneously updating interfacial fields relevant to the dynamics including the concentration of a surfactant and the position of interfacial point particles at an equilibrium configuration interfaces exhibiting isotropic tension elastic tensions viscous and incompressible behavior are considered the mathematical modeling of the tensions and bending moments developing over interfaces with a membrane like constitution is discussed in the context of the theory of thin shells to facilitate the numerical implementation the coupling of the interfacial mechanics to the hydrodynamics by means of interface force and torque balances is formulated in global cartesian coordinates recent progress in the implementation of boundary element methods is reviewed and areas for further research are identified

some remarks concerning the grothendieck period conjecture we discuss various results and questions around the grothendieck period conjecture which is a counterpart concerning the de rham betti realization of algebraic vari eties over number fields of the classical conjectures of hodge and tate these results give new evidence towards the conjectures of grothendieck and kontsevich zagier concerning transcen dence properties of the torsors of periods of varieties over number fields let q be the algebraic closure of q in c let x be a smooth projective variety over q and let x an c denote the compact complex analytic manifold that it defines the grothendieck period conjecture in codimension k on x denoted gpc k x asserts that any class in the

convergence of relaxed parallel multisplitting methods abstract multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation is used we investigate two different variants of relaxed multisplitting methods if a is an h matrix these methods converge if the relaxation parameter is from an interval 0 0 with 0 1