a priori l 2 error estimates for finite element methods for nonlinear diffusion equations with memory this paper studies finite element approximations to the solutions of the nonlinear diffusion equations with memory an elliptic projection with memory associated with our equations is defined and then used in the derivations of optimal error estimates for semidiscrete and crank nicolson finite element approximations

time discretization of an integro differential equation of parabolic type the stability and convergence properties of two time discretizations of an integro differential equation of parabolic type are studied the methods reduce to the backward euler and crank nicolson methods if the integral term is absent the integral term is approximated in each case by a quadrature rule with relatively high order truncation error so that a relatively large time step can be used for the quadrature in order to reduce the memory and computational requirements of the method

a counterexample to the isomorphism problem for integral group rings let x be a finite group and denote its integral group ring by zx a group basis of zx is a subgroup y of the group of units of zx of augmentation 1 such that zx zy and ixi yi an example of a finite group x is given such that zx has a group basis which is not isomorphic to x a main ingredient is the existence of a subgroup g of x which possesses a non inner automorphism which becomes inner in the integral group ring zg the question whether a finite group x is determined by its integral group ring zx is known as the isomorphism problem for integral group rings it was

sharp l 2 error estimates and superconvergence of mixed finite element methods for non fickian flows in porous media a sharper l2 error estimate is obtained for the non fickian flow of fluid in porous media by means of a mixed ritz volterra projection instead of the mixed ritz projection used in r e ewing y lin and j wang acta math univ comenian n s 70 2001 pp 75 84 moreover local l2 superconvergence for the velocity along the gauss lines and for the pressure at the gauss points is derived for the mixed finite element method via the ritz volterra projection and global l2 superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique on the basis of the superconvergence estimates some useful a posteriori error estimators are presented for this mixed finite element method

metric lie algebras with maximal isotropic centre a metric lie algebra is a lie algebra equipped with an invariant non degenerate symmetric bilinear form it is called indecomposable if it is not the direct sum of two metric lie algebras we are interested in describing the isomorphism classes of indecomposable metric lie algebras in the present paper we restrict ourselves to a certain class of solvable metric lie algebras which includes all indecomposable metric lie algebras with maximal isotropic centre we will see that each metric lie algebra belonging to this class is a twofold extension associated with an orthogonal representation of an abelian lie algebra we will describe equivalence classes of such extensions by a certain cohomology set in particular we obtain a classification scheme for indecomposable metric lie algebras with maximal isotropic centre and the classification of metric lie algebras of index 2

n ary algebras a review with applications this paper reviews the properties and applications of certain n ary generalizations of lie algebras in a self contained and unified way these generalizations are algebraic structures in which the two entries lie bracket has been replaced by a bracket with n entries each type of n ary bracket satisfies a specific characteristic identity which plays the role of the jacobi identity for lie algebras particular attention will be paid to generalized lie algebras which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized jacobi identity and to filippov or n lie algebras which are defined by fully antisymmetric n brackets that satisfy the filippov identity three lie algebras have surfaced recently in multi brane theory in the context of the bagger lambert gustavsson model because of this filippov algebras will be discussed at length including the cohomology complexes that govern their central extensions and their deformations it turns out that whitehead s lemma extends to all semisimple n lie algebras when the skewsymmetry of the lie or n lie algebra bracket is relaxed one is led to a more general type of n algebras the n leibniz algebras these will be discussed as well since they underlie the cohomological properties of n lie algebras the standard poisson structure may also be extended to the n ary case we shall review here the even generalized poisson structures whose generalized jacobi identity reproduces the pattern of the generalized lie algebras and the nambu poisson structures which satisfy the filippov identity and determine filippov algebras finally the recent work of bagger lambert and gustavsson on superconformal chern simons theory will be briefly discussed emphasis will be made on the appearance of the 3 lie algebra structure and on why the a4 model may be formulated in terms of an ordinary lie algebra and on its nambu bracket generalization

an algorithm to construct candidates to counterexamples to the zassenhaus conjecture abstract let g be a finite group n a nilpotent normal subgroup of g and let v z g n denote the group formed by the units of the integral group ring z g of g which map to the identity under the natural homomorphism z g z g n sehgal asked whether any torsion element of v z g n is conjugate in the rational group algebra of g to an element of g this is a special case of the zassenhaus conjecture by results of cliff and weiss and hertweck sehgal s problem has a positive solution if n has at most one non cyclic sylow subgroup we present some algorithms to study sehgal s problem when n has at most one non abelian sylow subgroup they are based on the cliff weiss inequalities introduced by the authors in a previous paper with the help of these algorithms we obtain some positive answers to sehgal s problem and use them to show that for units in v z g n our method is strictly stronger than the well known help method we then present a method to use the output of one of the algorithms to construct explicit metabelian groups which are candidates to a negative solution to sehgal s problem recently eisele and margolis showed that some of the examples proposed in this paper are indeed counterexamples to the zassenhaus conjecture these are the first known counterexamples moreover we prove that every metabelian negative solution of sehgal s problem satisfying some minimal conditions is given by our construction

finite groups of matrices over group rings we investigate certain finite subgroups r of gln zf where ii is a finite nilpotent group such a group r gives rise to a z r x fl7 module we study the characters of these modules to limit the structure of r we also exhibit some exotic subgroups r

on a type of commutative algebras abstract we introduce some basic concepts for jacobi jordan algebras such as representations crossed products or frobenius metabelian co flag objects a new family of solutions for the quantum yang baxter equation is constructed arising from any 3 step nilpotent jacobi jordan algebra crossed products are used to construct the classifying object for the extension problem in its global form for a given jacobi jordan algebra a and a given vector space v of dimension c a global non abelian cohomological object g h 2 a v is constructed it classifies from the view point of the extension problem all jacobi jordan algebras that have a surjective algebra map on a with kernel of dimension c the object g h 2 a k responsible for the classification of co flag algebras is computed all 1 dim a dimensional jacobi jordan algebras that have an algebra surjective map on a are classified and the automorphism groups of these algebras is determined several examples involving special sets of matrices and symmetric bilinear forms as well as equivalence relations between them generalizing the isometry relation are provided

nonlocal reactive transport with physical and chemical heterogeneity localization errors the origin of nonlocality in macroscale models for subsurface chemical transport is illustrated it is argued that media that are either nonperiodic e g media with evolving heterogeneity or periodic viewed on a scale wherein a unit cell is discernible must display some nonlocality in the mean a metaphysical argument suggests that owing to the scarcity of information on natural scales of heterogeneity and on scales of observation associated with an instrument window constitutive theories for the mean concentration should at the outset of any modeling effort always be considered nonlocal the intuitive appeal to nonlocality is reinforced with an analytical derivation of the constitutive theory for a conservative tracer without appeal to any mathematical approximations deng et al 1993 present a first order nonlocal eulerian theory for transport of a conservative solute in an infinite nondeforming domain under steady flow conditions hu et al this issue extended these results to account for nonequilibrium linear sorption with random partition coefficient kd but deterministic constant reaction rate kr these theories are localized herein and comparisons are made between the fully nonlocal fnl nonlocal in time nlt and fully localized fl theories for conservative transport there is little difference between the first order fl and fnl models for spatial moments up to and including the third however for conservative transport the first order nlt model differs significantly from the fnl model in the third spatial moments for reactive transport all spatial moments differ between the fnl and fl models the second transverse horizontal and third longitudinal horizontal moments for the nlt model differ from the fnl model these results suggest that localized first order transport models for conservative tracers are reasonable if only lower order moments are desired however when the chemical reacts with its environment the localization approximation can lead to significant error in all moments and a fnl model will in general be required for accurate simulation

torsion units in integral group rings of some metabelian groups let g be an extension of an elementary abelian p group a by an abelian group x with faithful and irreducible action then any torsion unit of the integral group ring zg is rationally conjugate to a trivial unit this confirms a conjecture of zassenhaus for these groups g

lattices and cohomological mackey functors for finite cyclic p groups abstract for a finite cyclic p group g and a discrete valuation domain r of characteristic 0 with maximal ideal p r the r g permutation modules are characterized in terms of the vanishing of first degree cohomology on all subgroups cf theorem a as a consequence any r g lattice can be presented by r g permutation modules cf theorem c the proof of these results is based on a detailed analysis of the category of cohomological g mackey functors with values in the category of r modules it is shown that this category has global dimension 3 cf theorem e a crucial step in the proof of theorem e is the fact that a gentle r order category with parameter p has global dimension less than or equal to 2 cf theorem d

on the structure of symmetric self dual lie algebras a finite dimensional lie algebra is called symmetric self dual if it possesses an invariant nondegenerate symmetric bilinear form symmetric self dual lie algebras have been studied by medina and revoy who have proven a very useful theorem about their structure in this paper we prove a refinement of their theorem that has wide applicability in conformal field theory where symmetric self dual lie algebras start to play an important role due to the fact that they are precisely the lie algebras that admit a sugawara construction we also prove a few corollaries that are important in conformal field theory

observations on the behavior of radial basis function approximations near boundaries abstract rbf approximations would appear to be very attractive for approximating spatial derivatives in numerical simulations of pdes rbfs allow arbitrarily scattered data generalize easily to several space dimensions and can be spectrally accurate however accuracy degradations near boundaries in many cases severely limit the utility of this approach with that as motivation this study aims at gaining a better understanding of the properties of rbf approximations near the ends of an interval in 1 d and towards edges in 2 d

autour de la conjecture de l markus sur les varietes affines for any subgroupg of n we introduce some integer discg n called thediscompacity ofg this number measures to what extent the closure ofg is not compact the markus conjecture says that a compact affinely flat unimodular manifold is complete our main result called the discompact theorem is that this conjecture is true under the assumption that the linear holonomy i e the parallel transport has discompacity 1 because discso n 1 1 1 this ensures that a compact flat lorentz manifoldm is geodesically complete hence by a previous result of w goldman and y kamishima gk such am is up to finite covering a solvmanifold this achieves the proof of a bieberbach s theorem for compact lorentz flat manifolds

the identity component of the isometry group of a compact lorentz manifold this result may be compared with a theorem of e ghys ghy see also bel asserting a similar conclusion but assuming that m has dimension 3 and that the action is just volume preserving and locally free the statement there is that the action of ag may be extended to an action of a finite cover of psl 2 r or to an action of the solvable 3 dimensional lie group sol here we have another motivation we want to understand the structure of lie groups acting isometrically on compact lorentz manifold the first results in the subject are due to zim and gro a final result is due to a s and zeg1 independently necessary and sufficient conditions were given in order that a lie group acts isometrically and locally faithfully on a compact lorentz manifold note however that if a group acts in such a fashion then its subgroups also act in the same way for instance all known examples of isometric actions of ag are obtained by viewing it as a subgroup of sl 2 r so a natural question is what are the maximal connected lie groups acting isometrically on a compact lorentz manifold equivalently

canonical complex structures associated to connections and complexifications of lie groups the notion of adapted complex structure is extended from riemannian manifolds to general koszul connections the case of the canonical connection of a lie group and the levi civita connection of a pseudo riemannian manifold is studied

solving high order ordinary differential equations with radial basis function networks this paper is concerned with the application of radial basis function networks rbfns for numerical solution of high order ordinary differential equations odes two unsymmetric rbf collocation schemes namely the usual direct approach based on a differentiation process and the proposed indirect approach based on an integration process are developed to solve high order odes directly and the latter is found to be considerably superior to the former good accuracy and high rate of convergence are obtained with the proposed indirect method

isotropy of semisimple group actions on manifolds with geometric structure we prove results concerning isotropy of noncompact semisimple lie group actions that preserve pseudo riemannian or affine structures on compact or finite volume manifolds for example if a lie group g acts locally faithfully on a connected compact complete affine manifold m and preserves the affine structure then the connected component of the identity of each isotropy subgroup is a compact extension of a solvable group this is a consequence of the result that nontrivial affine actions of connected groups locally isomorphic to sl 2 inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i on such manifolds cannot have fixed points we also prove that if g is connected semisimple without compact factors and acts isometrically and topologically transitively on a connected finite volume pseudo riemannian m then the action must be everywhere locally free this answers affirmatively a special case of a conjecture by g d ambra and m gromov with only the assumption that no factor of g acts trivially local freeness is also assured when m is compact and complete

a counterexample to the first zassenhaus conjecture abstract hans j zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group g there exists a unit a in the rational group algebra of g such that a 1 u a g for some g g we disprove this conjecture by first proving general results that help identify counterexamples and then providing an infinite number of examples where these results apply our smallest example is a metabelian group of order 2 7 3 2 5 7 2 19 2 whose integral group ring contains a unit of order 7 19 which in the rational group algebra is not conjugate to any element of the form g

on principal blocks of p constrained groups a theorem of k w roggenkamp and l l scott shows that for a finite group g with a normal p subgroup containing its own centralizer any two group bases of the integral group ring mathbb z g are conjugate in the units of mathbb z p g though the theorem presents itself in the work of others and appears to be needed there is no published account there seems to be a flaw in the proof because a theorem appearing in the survey k w roggenkamp the isomorphism problem for integral group rings of finite groups progress in mathematics 95 birkhauser basel 1991 pp 193 220 where the main ingredients of a proof are given is false in this paper it is shown how to close this gap at least if one is only interested in the conclusion mentioned above therefore some consequences of the results of a weiss on permutation modules are stated the basic steps of which any proof should consist are discussed in some detail in doing so a complete yet short proof of the theorem is given in the case that g has a normal sylow p subgroup 2000 mathematical subject classification primary 16u60 secondary 20c05

on picard groups of blocks of finite groups we show that the subgroup of the picard group of ap block ofa finite group given by bimodules with endopermutation sources modulo theautomorphism group of a source algebra is determined locally in terms of thefusion system on a defect group we show that the picard group of a block overa complete discrete valuation ringoof characteristic zero with an algebraicclosurekoffpas residue field is a colimit of finite picard groups of blocks overp adic subrings ofo we apply the results to blocks with an abelian defectgroup and frobenius inertial quotient and specialise this further to blockswith cyclic or klein four defect groups

on lorentz dynamics from group actions to warped products via homogeneous spaces we show a geometric rigidity of isometric actions of non compact semisimple lie groups on lorentz manifolds namely we show that the manifold has a warped product structure of a lorentz manifold with constant curvature by a riemannian manifold

structure of lorentzian tori with a killing vector field all lorentzian tori with a non discrete group of isometries are characterized and explicitly obtained they can lie into three cases a flat b conformally flat but non flat and c geodesically incomplete a detailed study of many of their properties including results on the logical dependence of the three kinds of causal completeness on geodesic connectedness and on prescribed curvature is carried out the incomplete case is specially analyzed and several known examples and results in the literature are generalized from a unified point of view

numerical solution of the nonlinear fredholm integral equations by positive definite functions a numerical method for solving the nonlinear fredholom integral equations is presented the method is based on interpolation by radial basis functions rbf to approximate the solution of the fredholm nonlinear integral equations several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method

embedding problems over large fields in this paper we study galois theoretic properties of a large class of fields a class which includes all fields satisfying a universal local global principle for the existence of rational points on varieties as applications we give a positive answer to a long standing conjecture which originates in an unpublished note of roquette and asserts that the absolute galois group of a countable hilbertian pac field is profinite free see f j problem 24 41 secondly we give new evidence for the conjecture of shafarevich which asserts that the absolute galois group of qab is profinite free finally one of the most interesting applications of the theory we develop here is the insight in the galois structure of the totally eg adic numbers

a sylow theorem for the integral group ring of psl 2 q abstract for g psl 2 p f denote by z g the integral group ring over g and by v z g the group of units of augmentation 1 in z g let r be a prime different from p using the so called help method we prove that units of r power order in v z g are rationally conjugate to elements of g as a consequence we prove that subgroups of prime power order in v z g are rationally conjugate to subgroups of g if p 2 or f 1

a comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential equations abstract in this article we present a thorough numerical comparison between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of boundary value problems for partial differential equations a series of test examples was solved with these two schemes different problems with different type of governing equations and boundary conditions particular emphasis was paid to the ability of these schemes to solve the steady state convection diffusion equation at high values of the peclet number from the examples tested in this work it was observed that the system of algebraic equations obtained with the symmetric method was in general simpler to solve than the one obtained with the unsymmetric method and that the resulting algorithm performs better however the unsymmetric method has the advantage of being simpler to implement two main features about the results obtained in this work are worthy of special attention first with the symmetric method it was possible to solve convection diffusion problems at a very high peclet number without the need of any artificial damping term and second with these two approaches symmetric and unsymmetric it is possible to impose free boundary conditions for problems in unbounded domains

on morita and derived equivalences for cohomological mackey algebras by results of the second author a source algebra equivalence between two p blocks of finite groups induces an equivalence between the categories of cohomological mackey functors associated with these blocks and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological mackey functors the main result of this paper proves a partial converse an equivalence resp rickard equivalence between the categories of cohomological mackey functors of two blocks of finite groups induces a permeable morita resp derived equivalence between the two block algebras

a meshfree method for the numerical solution of the rlw equation in this paper we present a meshfree technique for the numerical solution of the regularized long wave rlw equation this approach is based on a global collocation method using the radial basis functions rbfs different kinds of rbfs are used for this purpose accuracy of the new method is tested in terms of l 2 and l error norms in case of non availability of the exact solution performance of the new method is compared with existing methods stability analysis of the method is established propagation of single and double solitary waves wave undulation and conservation properties of mass energy and momentum of the rlw equation are discussed

a numerical solution of the nonlinear controlled duffing oscillator by radial basis functions in this research a new numerical method is applied to investigate the nonlinear controlled duffing oscillator this method is based on the radial basis functions rbfs to approximate the solution of the optimal control problem by using the collocation method we apply legendre gauss lobatto points for rbfs center nodes in order to use the numerical integration method more easily then the method of lagrange multipliers is used to obtain the optimum of the problems for this purpose different applications of rbfs are used the differential and integral expressions which arise in the dynamic systems the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients illustrative examples are included to demonstrate the validity and applicability of the technique

a quasi linear theory of non fickian and fickian subsurface dispersion 1 theoretical analysis with application to isotropic media a theory is presented which accounts for nonlinearity caused by the deviation of plume particles from their mean trajectory in three dimensional statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities existing linear theories predict that in the absence of local dispersion transverse dispersivities tend asymptotically to zero as fickian conditions are reached according to our new quasi linear theory these dispersivities ascend to peak values and then diminish gradually toward nonzero fickian asymptotes which are proportional to y4 when the log hydraulic conductivity variance y2 is much less than 1 all existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to y2 when y2 1 and all are nominally restricted to mildly heterogeneous media in which this inequality is satisfied however the quasi linear theory appears to be less prone to error than linear theories when extended to strongly heterogeneous media because it deals with the above nonlinearity without formally limiting y2 it predicts that when y 1 in isotropic media both the longitudinal and transverse dispersivities ascend monotonically toward fickian asymptotes proportional to y

lorentzian lie n algebras we classify lie n algebras possessing an invariant lorentzian inner product we classify lie n algebras possessing an invariant lorentzian inner product

construction of units in integral group rings of finite nilpotent groups let u be the group of units of the integral group ring of a finite group g we give a set of generators of a subgroup b of u this subgroup is of finite index in u if g is an odd nilpotent group we also give an example of a 2 group such that b is of infinite index in u

isometry groups of lorentz manifolds soit v une variete de lorentz a n dimensions si v g est compacte analytique reelle simplement convexe alors le groupe d isometrie is v g est compact

solving a system of nonlinear integral equations by an rbf network in this paper a novel learning strategy for radial basis function networks rbfn is proposed by adjusting the parameters of the hidden layer including the rbf centers and widths the weights of the output layer are adapted by local optimization methods a new local optimization algorithm based on a combination of the gradient and newton methods is introduced the efficiency of some local optimization methods to update the weights of rbfn is studied in solving systems of nonlinear integral equations

units of p power order in principal p blocks of p constrained groups abstract let g be a finite group having a normal p subgroup n that contains its centralizer c g n and let r be a p adic ring it is shown that any finite p group of units of augmentation one in rg which normalizes n is conjugate to a subgroup of g by a unit of rg and if it centralizes n it is even contained in n

infinitely generated pseudocompact modules for finite groups and weiss theorem abstract one of the most beautiful results in the integral representation theory of finite groups is a theorem of a weiss that detects a permutation r lattice for the finite p group g in terms of the restriction to a normal subgroup n and the n fixed points of the lattice where r is a finite extension of the p adic integers using techniques from relative homological algebra we generalize weiss theorem to the class of infinitely generated pseudocompact lattices for a finite p group allowing r to be any complete discrete valuation ring in mixed characteristic a related theorem of cliff and weiss is also generalized to this class of modules the existence of the permutation cover of a pseudocompact module is proved as a special case of a more general result the permutation cover is explicitly described

numerical simulation of reaction diffusion neural dynamics models and their synchronization desynchronization application to epileptic seizures abstract cognitive disorders especially epilepsy are closely linked with synchronization desynchronization of neurons in the brain in this paper the dynamical modeling and behavior analysis of a fitzhugh nagumo neuron and also synchronization control of a network of fitzhugh nagumo neurons which promise the understanding of cognitive processing are studied to numerically simulate these models and in order to overcome their difficulties such as computational complexity multi dimensionality non linearity having large spatial and temporal domains and also having a discrete initial data we propose the use of a strongly meshless technique based on wendland compactly supported radial basis function in conjunction with an operator splitting algorithm the main advantage of the proposed algorithm is its computational complexity for example o n x 1 3 n x 2 3 of the inversion of all matrices which is much lower than the complexity of pure radial basis functions method o n x 1 3 n x 2 3 of the inversion of matrices numerical experiments are presented showing that the proposed approaches are extremely accurate and fast

isomorphisms of p adic group rings a long standing problem first posed by graham higman 15 and later by brauer 4 is the isomorphism problem for integral group rings given finite groups g and h is it true that zg zh implies g 2 h many authors have worked on this question but progress has been difficult 30 perhaps the best positive result was that of whitcomb in 1968 37 who showed that the implication g h holds for g metabelian dade 9 showed there were counterexamples even in the metabelian case if z were replaced by the family of all fields some mathematicians came to believe the problem was a kind of grammatical accident that counterexamples for z were surely there if difficult to find we ourselves began this investigation looking for counterexamples but found that they were indeed very difficult to find much more difficult than we had anticipated slowly we began to believe that at least some exciting positive results were possible in this paper we answer the isomorphism problem for finite p groups over the p adic integers z zcp and in a very strong way in the normalized units augmentation 1 of z pg there is only one con gay czu ss of groups of order g 1 this answers the isomorphism problem in the affirmative for finite p groups g over z or zp and in addition computes the entire picard group 2 of the category of z g modules in terms of automorphisms of g similarly we are able to settle the isomorphism problem for finite nilpotent groups and compute the associated semilocal picard groups we also treat more general coefficient domains namely integral domains s of characteristic 0 in which no rational prime divisor of the group order is invertible for the sg isomorphism problem and treat similar semilocal dedekind domains for the picard group computations the zassenhaus conjecture concerning the rational behavior of group ring automorphisms is verified for the nilpotent case in this general setting cf corollary 3 below over z we announce a positive answer to the isomorphism

cliff weiss inequalities and the zassenhaus conjecture abstract let n be a nilpotent normal subgroup of the finite group g assume that u is a unit of finite order in the integral group ring z g of g which maps to the identity under the linear extension of the natural homomorphism g g n we show how a result of cliff and weiss can be used to derive linear inequalities on the partial augmentations of u and apply this to the study of the zassenhaus conjecture this conjecture states that any unit of finite order in z g is conjugate in the rational group algebra of g to an element in g

compact lorentz manifolds with local symmetry we prove a structure theorem for compact aspherical lorentz manifolds with abundant local symmetry if m is a compact aspherical real analytic complete lorentz manifold such that the isometry group of the universal cover has semisimple identity component then the local isometry orbits in m are roughly fibers of a fiber bundle a corollary is that if m has an open dense locally homogeneous subset then m is locally homogeneous acknowledgements i thank my dissertation advisor benson farb for his guidance and encouragement i also thank abdelghani zeghib with whom i had helpful conversations while working on this project in loving memory of laura sue jung kang

three dimensional metrics with a spherical homogeneous model one finds the moduli spaces of isocurved homogeneous metrics on s3 then one determines the germs of three dimensional analytic metrics with a spherical homogeneous model

some examples of picard groups of blocks abstract we calculate examples of picard groups for 2 blocks with abelian defect groups with respect to a complete discrete valuation ring these include all blocks with abelian 2 groups of 2 rank at most three with the exception of the principal block of j 1 in particular this shows directly that all such picard groups are finite and picent the group of morita auto equivalences fixing the centre is trivial these are amongst the first calculations of this kind further we prove some general results concerning picard groups of blocks with normal defect groups as well as some other cases

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

application of the multiquadric method for numerical solution of elliptic partial differential equations abstract we have used the multiquadric mq approximation scheme for the solution of elliptic partial differential equations with dirichlet and or neumann boundary conditions the scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering two dimensional laplace poisson and biharmonic equations describing the various physical processes have been taken as the test examples the agreement is found to be very good between the computed and exact solutions the method also provides an excellent approximation with a curved boundary

the parameter r2 in multiquadric interpolation the multiquadric mq method is an effective bivariate interpolant to three dimensional data xi yi zi where the xi yi are arbitrarily located in the plane the accuracy of the mq method is dependent on a user defined parameter r2 and most practitioners select r2 based upon the number of data points and the locations of the xi yi in the plane we observe that the optimal value of r2 is a strong function of the zi and that it is essentially independent of both the number and the locationsof the xi yi points contrary to some opinions we observe that the mq method can effectively interpolate to track data that is data sampled densely along tracks in the plane together with several other observations we present an algorithm that generally yields an effective value for r2

periodic geodesics and geometry of compact lorentzian manifolds with a killing vector field we study the geometry and the periodic geodesics of a compact lorentzian manifold that has a killing vector field which is timelike somewhere using a compactness argument for subgroups of the isometry group we prove the existence of one timelike non self intersecting periodic geodesic if the killing vector field is nowhere vanishing then there are at least two distinct periodic geodesics as a special case compact stationary manifolds have at least two periodic timelike geodesics we also discuss some properties of the topology of such manifolds in particular we show that a compact manifold m admits a lorentzian metric with a nowhere vanishing killing vector field which is timelike somewhere if and only if m admits a smooth circle action without fixed points

isometries of lorentz surfaces and convergence groups we study the isometry group of a globally hyperbolic spatially compact lorentz surface such a group acts on the circle and we show that when the isometry group acts non properly the subgroups of mathrm diff mathbb s 1 obtained are semi conjugate to subgroups of finite covers of mathrm psl 2 mathbb r by using convergence groups under an assumption on the conformal boundary we show that we have a conjugacy in mathrm homeo mathbb s 1

free nilpotent lie algebras admitting ad invariant metrics abstract in this work we find necessary and sufficient conditions for a free nilpotent or a free metabelian nilpotent lie algebra to be endowed with an ad invariant metric for such nilpotent lie algebras admitting an ad invariant metric the corresponding automorphisms groups are studied

a meshless method on non fickian flows with mixing length growth in porous media based on radial basis functions a comparative study the present study aims to introduce a solution for parabolic integro differential equations arising in heat conduction in materials with memory which naturally occur in many applications two radial basis functions rbfs collocation schemes are employed for solving this equation the first method tested is an unsymmetric method and the second one which appears to be more efficient is a symmetric one the convergence of these two schemes is accelerated as we use the cartesian nodes as the center nodes

the sylow subgroups of the absolute galois group gal q abstract we describe the l sylow subgroups of gal q for an odd prime l by observing and studying their decomposition as f z l where f is a free pro l group and z l are the l adic integers we determine the finite z l quotients of f and more generally show that every split embedding problem of z l groups for f is solvable moreover we analyze the z l action on generators of f

a kind of improved univariate multiquadric quasi interpolation operators in this paper a kind of improved univariate multiquadric quasi interpolation operators is proposed by using hermite interpolating polynomials error analysis shows that the convergence rate of the operators depends heavily on the shape parameter c which indicates that our operators could provide the desired smoothness and precision by choosing a suitable value of c numerical examples show that the operators provide a high degree of accuracy moreover operators are applied to the fitting of discrete solutions of initial value problems

numerical solution of the nonlinear klein gordon equation using radial basis functions the nonlinear klein gordon equation is used to model many nonlinear phenomena in this paper we propose a numerical scheme to solve the one dimensional nonlinear klein gordon equation with quadratic and cubic nonlinearity our scheme uses the collocation points and approximates the solution using thin plate splines tps radial basis functions rbf the implementation of the method is simple as finite difference methods the results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme