energetic bem fem coupling for wave propagation in 3d multidomains summary starting from a recently developed energetic space time weak formulation of boundary integral equations for wave propagation problems a coupling algorithm is presented which allows a flexible use of fems and bems as local discretization techniques emphasis is given to theoretical and experimental analysis of the stability of the proposed method several numerical results on model problems are presented and discussed showing that both bounded and unbounded three dimensional domains can be efficiently addressed copyright 2013 john wiley sons ltd

on the product of a nilpotent group and a group with non trivial center abstract it is proved that a finite group g a b which is a product of a nilpotent subgroup a and a subgroup b with non trivial center contains a non trivial abelian normal subgroup

finite groups whose element orders are consecutive integers there are various characterizations of groups by conditions on the orders of its elements for example in 8 1 the finite groups all of whose elements have prime power order have been classified in 2 16 181 some simple groups have been characterized by conditions on the orders of its elements and b h neumann 12 has determined all groups whose elements have orders 1 2 and 3 the latter groups are oc3 groups in the sense of the following

a characterization of the finite simple groups abstract in this paper we obtain a quantitative characterization of all finite simple groups let t g denote the set of indices of maximal subgroups of group g and let p g be the smallest number in t g we have the following theorems theorem 2 let n and g be finite simple groups if n divides g p n p g and t n t g then or and 2 11 or 2 and 3 theorem 3 let n be a finite simple and let g be a finite group if g n and t g t n then g n

the diameter of the commuting graph of a finite group with trivial centre abstract the commuting graph of a finite group with trivial centre is examined it is shown that the connected components of have diameter at most 10

boundary elements with mesh refinements for the wave equation the solution of the wave equation in a polyhedral domain in mathbb r 3 admits an asymptotic singular expansion in a neighborhood of the corners and edges in this article we formulate boundary and screen problems for the wave equation as equivalent boundary integral equations in time domain study the regularity properties of their solutions and the numerical approximation guided by the theory for elliptic equations graded meshes are shown to recover the optimal approximation rates known for smooth solutions numerical experiments illustrate the theory for screen problems in particular we discuss the dirichlet and neumann problems as well as the dirichlet to neumann operator and applications to the sound emission of tires

prime power graphs for groups of lie type abstract we associate a weighted graph g to each finite simple group g of lie type we show that with an explicit list of exceptions g determines g up to isomorphism and for these exceptions g nevertheless determines the characteristic of g this result was motivated by algorithmic considerations we prove that for any finite simple group g of lie type input as a black box group with an oracle to compute the orders of group elements g and the characteristic of g can be computed by a monte carlo algorithm in time polynomial in the input length the characteristic is needed as part of the input in a previous constructive recognition algorithm for g

characterization of the alternating group by its non commuting graph abstract let g be any non abelian group and z g be its center the non commuting graph g of g is the simple graph whose vertex set is g z g with two vertices x and y adjacent whenever x y x y we prove that if g is isomorphic to the non commuting graph of the alternating group a n n 4 then g a n this result together with a recent one due to solomon and woldar gives a complete positive answer to a conjecture proposed in a abdollahi s akbari h r maimani non commuting graph of a group j algebra 298 2006 468 492 if s is any finite non abelian simple group such that s g for some group g then g s

on element orders in covers of finite simple classical groups abstract we show that finite simple symplectic groups of dimension at least 6 finite simple orthogonal groups of dimension at least 7 and finite simple unitary groups of dimension at least 4 except for u 5 2 have the following property if such a group g defined over a field of characteristic p acts on a vector space over a field of positive characteristic other than p then the corresponding semidirect product contains an element whose order is distinct from the order of any element of g

galerkin finite element methods with symmetric pressure stabilization for the transient stokes equations stability and convergence analysis we consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient stokes equation the analysis is valid for a class of symmetric pressure stabilization operators but also for standard inf sup stable velocity pressure spaces without stabilization provided the initial data are chosen as a specific method dependent ritz projection we get unconditional stability and optimal convergence for both pressure and velocity approximations in natural norms for arbitrary interpolations of the initial data a condition between the space and time discretization parameters has to be verified in order to guarantee pressure stability

the graph of atomic divisors and recognition of finite simple groups abstract the spectrum g of a finite group g is the set of orders of elements of g we present a polynomial time algorithm that given a finite set m of positive integers outputs either an empty set or a finite simple group g in the former case there is no finite simple group h with m h while in the latter case m g and m h for all finite simple groups h with h g

stabilized mixed hp bem for frictional contact problems in linear elasticity we analyze stabilized mixed hp boundary element methods for frictional contact problems for the lame equation the stabilization technique circumvents the discrete inf sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables we prove a priori convergence rates in the case of tresca friction using gauss legendre lagrange polynomials as test and trial functions for the lagrange multiplier additionally a residual based a posteriori error estimate for a more general class of discretizations is derived it in particular applies to discretizations based on bernstein polynomials for the discrete lagrange multiplier which we also analyze the discretization and the a posteriori error estimate are extended to the case of coulomb friction several numerical experiments underline our theoretical results demonstrate the behavior of the method and its insensitivity to the scaling and perturbations of the stabilization term

time integration schemes for the finite element dynamic signorini problem a large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic signorini problem we classify the different discretizations into four groups the first three groups correspond to different ways of enforcing the contact condition exact enforcement enforcement with penalty and enforcement with contact condition in velocity the fourth approach is based on a modification of the mass matrix numerical simulations on two one dimensional benchmark problems with analytical solutions illustrate the properties of representative methods within each class focusing first on spurious oscillations triggered by contact and then on energy behavior after multiple impacts selected schemes are also tested on a two dimensional benchmark

new criteria for the solvability of finite groups see 6 or 7 p 291 it has been conjectured that a group is solvable if and only if it has a hall 2 subgroup and a hall 3 subgroup see 11 we verify this conjecture for groups whose composition factors are known simple groups along the way we also verify for groups whose composition factors are known simple groups a conjecture of hall s that if a group has a hall

hall subgroups and π separable groups abstract let g be a finite group and a set of primes in this paper some new criteria for separable groups and solvable groups in terms of hall subgroups are proved the main results are the following theorem g is a separable group if and only if 1 g satisfies e and e 2 g satisfies e q and e p for all p q theorem g is a separable group if and only if 1 g satisfies e and e 2 g satisfies e p q for all p and q

time domain boundary elements for dynamic contact problems abstract this article considers a unilateral contact problem for the wave equation the problem is reduced to a variational inequality for the dirichlet to neumann operator for the wave equation on the boundary which is solved in a saddle point formulation using boundary elements in the time domain as a model problem also a variational inequality for the single layer operator is considered a priori estimates are obtained for galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area where the existence of solutions to the continuous problem is known numerical experiments demonstrate the performance of the proposed mixed method they indicate the stability and convergence beyond flat geometries

criteria for the solubility and non simplicity of finite groups abstract some criteria of the non simplicity of a finite group by graph theoretical terms are derived this is then used to establish conditions under which a finite group is soluble

on thompsonʼs conjecture for some finite simple groups in this article we prove a conjecture of j g thompson for an infinite class of simple groups of lie type more precisely we show that every finite group g with the property z g 1 and cs g cs psln q is necessarily isomorphic to psln q note that cs g is the set of lengths of conjugacy classes of g

non commuting graph of a group abstract let g be a non abelian group and let z g be the center of g associate a graph g called non commuting graph of g with g as follows take g z g as the vertices of g and join two distinct vertices x and y whenever x y y x we want to explore how the graph theoretical properties of g can effect on the group theoretical properties of g we conjecture that if g and h are two non abelian finite groups such that g h then g h among other results we show that if g is a finite non abelian nilpotent group and h is a group such that g h and g h then h is nilpotent

the characterization of psl 2 q by its element orders abstract we show that the simple groups psl 2 q q 9 are characterized by their element orders

two variational inequality problems for the wave equation in a half space an important problem in the theory of elasticity is the dynamic planestrain type crack problem the subject of dynamic cracks in solids has received much attention in the past two decades see freund 4 poruchikov 11 and walton and herrmann 17 most of the work done however has not explicitly imposed the physical condition that the two faces of the crack do not interpenetrate this type of condition is known as a unilateral constraint imposing this type of condition amounts to imposing certain inequalities on the displacements or tractions to the problem problems in elasticity involving the contact of two elastic bodies give another example of problems with unilateral constraints imposed on boundaries see kikuchi and oden 7 a particular case of a contact problem is the punch problem which consists of a rigid body the punch indenting an elastic halfspace while static contact problems have been studied extensively see kikuchi and oden 7 the case of dynamic contact problems has not been studied nearly as much there is no work to our knowledge on the dynamic crack problem taking into account the condition of noninterpenetration the mathematical formulation of the dynamic crack and punch problems with unilateral constraints involve the dynamic equations of linear elasticity in this paper we consider two simplified dynamic problems with unilateral constraints obtained when the elasticity equations are replaced by a single wave equation although these simplified problems have no physical meaning we will still call them the crack and punch problems respectively

maximal subloops of finite simple moufang loops abstract we classify the maximal subloops of finite simple non associative moufang loops up to conjugacy with respect to automorphisms

analysis of the modified mass method for the dynamic signorini problem with coulomb friction the aim of the present work is to analyze the modified mass method for the dynamic signorini problem with coulomb friction we prove that the space semidiscrete problem is equivalent to an upper semicontinuous one sided lipschitz differential inclusion and is therefore well posed we derive an energy balance next considering an implicit time integration scheme we prove that under a cfl type condition on the discretization parameters the fully discrete problem is well posed for a fixed discretization in space we also prove that the fully discrete solutions converge to the space semidiscrete solution when the time step tends to zero

a characterization of the prime graphs of solvable groups abstract let g denote the set of prime divisors of the order of a finite group g the prime graph of g denoted g is the graph with vertex set g with edges p q e g if and only if there exists an element of order pq in g in this paper we prove that a graph is isomorphic to the prime graph of a solvable group if and only if its complement is 3 colorable and triangle free we then introduce the idea of a minimal prime graph we prove that there exists an infinite class of solvable groups whose prime graphs are minimal we prove the 3k conjecture on prime divisors in element orders for solvable groups with minimal prime graphs and we show that solvable groups whose prime graphs are minimal have fitting length 3 or 4

predator prey cycles from resonant amplification of demographic stochasticity we present the simplest individual level model of predator prey dynamics and show via direct calculation that it exhibits cycling behavior the deterministic analogue of our model recovered when the number of individuals is infinitely large is the volterra system with density dependent prey reproduction which is well known to fail to predict cycles this difference in behavior can be traced to a resonant amplification of demographic fluctuations which disappears only when the number of individuals is strictly infinite our results indicate that additional biological mechanisms such as predator satiation may not be necessary to explain observed predator prey cycles in real finite populations

integer polynomials with roots mod p for all primes p abstract let f x be an integer polynomial which is a product of two irreducible factors assume that f x has a root mod p for all primes p if the splitting field of f x over the rationals is a cyclic extension of the stem fields then the galois group of f x over the rationals is soluble and of bounded fitting length moreover the fixed groups of the stem extensions are in some sense unique

stochastic resonance in overdamped two coupled anharmonic oscillators abstract we consider the overdamped version of two coupled anharmonic oscillators with the external periodic force f sin t and gaussian noise term t added to one of the two state variables of the system linear stability analysis is carried out in the absence of external periodic force and noise then the system with external periodic force only and noise term only are studied in the noise free system four period t orbits are found to co exist one in each of the four wells for small values of forcing amplitude f for fixed values of other parameters at a critical value of f f c cross well periodic orbit appears f c is found to increase with increase in the coupling strength in the absence of forcing the system is found to exhibit intermittent jumping motion between two wells above a particular value of noise strength d d c the noise induced jumping behaviour is characterized by first passage time and residence time distributions next the influence of noise in the presence of the external periodic force is numerically studied the system is found to exhibit stochastic resonance behaviour the observed stochastic resonance dynamics is characterized using power spectrum signal to noise ratio and residence time distribution the plot of maximal lyapunov exponent versus noise strength has shown a stochastic resonance profile the occurrence of stochastic resonance is studied by varying the forcing frequency and the coupling strength finally the influence of addition of external periodic force and noise term to different state variables is also presented

coupling discontinuous galerkin methods and retarded potentials for transient wave propagation on unbounded domains this work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities to do so we propose to combine a discretization based on a discontinuous galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain the coupling formula enforces a discrete energy identity ensuring the stability under the usual cfl condition in the interior moreover the scheme allows to use a smaller time step in the interior domain yielding to quasi optimal discretization parameters for both methods the aliasing phenomena introduced by the local time stepping are reduced by a post processing by averaging in time obtaining a stable and second order consistent in time coupling algorithm we compute the numerical rate of convergence of the method for an academic problem the numerical results show the feasibility of the whole discretization procedure

co degrees of irreducible characters in finite groups abstract for a character of a finite group g the number a g ker 1 is called the co degree of the object of this paper is to study the connection between the structure of a finite group and the co degrees of its irreducible characters

mixed initial boundary value problems for hyperbolic equations with constant coefficients we shall investigate the well posedness and regularity of mixed initialboundary value problems for constant coefficient strictly hyperbolic equations in a quarter space mibvp the interface is a smooth compact manifold which divides the flat boundary into two regions in this paper existence and uniqueness theorems are proved for a large class of such problems for hyperbolic equations of arbitrary order these are based on the study of a new class of pseudo differential operators o which could naturally be called hyperbolic pseudo d f erential operators a second paper will contain results on regularity for this class of problems and it will give an asymptotic expansion of the trace of the solution near the interface an example of a mibvp is the wave equation with mixed dirichletneumann boundary conditions in three spatial dimensions it is given by the equations

a simplicity criterion for finite groups abstract given a finite groupg let e g denote the set of all orders of elements ing in this paper we investigate the relation between the number of primes and that of composite numbers in e g and obtain a criterion for the simplicity of finite groups

coherent configurations associated with ti subgroups let x be a coherent configuration associated with a transitive group g in terms of the intersection numbers of x a necessary condition for the point stabilizer of g to be a ti subgroup is established furthermore under this condition x is determined up to isomorphism by the intersection numbers it is also proved that asymptotically this condition is also sufficient more precisely an arbitrary homogeneous coherent configuration satisfying this condition is associated with a transitive group the point stabilizer of which is a ti subgroup as a byproduct of the developed theory recent results on pseudocyclic and quasi thin association schemes are generalized and improved in particular it is shown that any scheme of prime degree p and valency k is associated with a transitive group whenever p 1 6k k 1 2

finite nonsolvable groups in which only two nonlinear irreducible characters have equal degrees abstract y berkovich et al proc amer math soc 115 1992 955 959 classified finite groups in which the degrees of the nonlinear irreducible characters are distinct theorem 24 7 from y berkovich j algebra 184 1996 584 603 contains the classification of solvable groups in which only two nonlinear irreducible characters have equal degrees d 1 groups in this paper we obtain the classification of nonsolvable d 1 groups completing the classification of d 1 groups our proof depends on the classification of finite simple groups the results of the important paper illinois j math 33 no 1 1988 103 131 on rational simple groups play a key role as well

on thompson s conjecture abstract let g be a finite group and n g n n g has a conjugacy class c such that c n professor j g thompson has conjectured that if g be a finite group with z g 1 and m a nonabelian simple group satisfying that n g n m then g m we have proved that if m is a sporadic simple group then thompson s conjecture is correct in this paper we shall further prove that if m is a finite simple group having at least three prime graph components then the conjecture is also correct

stochastic resonance without an external periodic drive in a simple prey predator model we have investigated the effect of noise on a simple prey predator model where the oscillations are triggered by the internal dynamics of the system without the aid of any external periodic drive we report the occurrence of stochastic resonancelike behavior in this system which does not have a threshold or a potential barrier in the absence of an external drive

the validity of johnson nedelec s bem fem coupling on polygonal interfaces in this short article we prove that the classical one equation or johnson nedelec coupling of finite and boundary elements can be applied with a lipschitz coupling interface because of the way it was originally approached from the analytical standpoint this bem fem scheme required smooth boundaries and hence produced a consistency error in the finite element part with a variational argument we prove that this requirement is not needed and that stability holds for all pairs of discrete space as it inherits the underlying ellipticity of the problem

on sharp characters of rank 2 with rational values abstract for a finite group g and its character let l be the set of distinct values of on non identity elements of g and f l 1 denote the monic polynomial of least degree having l as its set of roots blichfeldt a theorem concerning the invariants of linear homogeneous groups with some applications to substitution groups trans amer math soc 5 1904 461 466 2 showed that f l 1 g is a rational integer cameron and kiyota sharp character of finite groups j algebra 115 1988 125 143 called the pair g l sharp if g f l 1 and posed the problem of determining all the l sharp pairs g for a given set l for several cases those problems have already been studied by many authors our purpose is to determine the sharp pairs of types 2 1 and 1 2 having non trivial center

local high order regularization and applications to hp methods we develop a regularization operator based on smoothing on a spatially varying length scale this operator is defined for functions u l 1 and has approximation properties that are given by the local sobolev regularity of u and the local smoothing length scale additionally the regularized function satisfies inverse estimates commensurate with the approximation orders by combining this operator with a classical h p interpolation operator we obtain an h p clement type quasi interpolation operator i e an operator that requires minimal smoothness of the function to be approximated but has the expected approximation properties in terms of the local mesh size and polynomial degree as a second application we consider residual error estimates in h p boundary element methods that are explicit in the local mesh size and the local approximation order

a restriction on centralizers in finite groups abstract for a given m 1 we consider the finite non abelian groups g for which c g g g m for every g g z g we show that the order of g can be bounded in terms of m and the largest prime divisor of the order of g our approach relies on dealing first with the case where g is a non abelian finite p group in that situation if we take m p k to be a power of p we show that g p 2 k 2 with the only exception of q 8 this bound is best possible and implies that the order of g can be bounded by a function of m alone in the case of nilpotent groups

a galerkin bem for transient acoustic scattering by an absorbing obstacle this paper deals with the numerical resolution of the so called time domain boundary integral equations the scattering problem by an absorbing obstacle serves as the model for this discussion a new system of retarded potential boundary integral equations rpbie is set up to solve the problem using an energy identity we are able to prove the unconditional stability for standard conforming galerkin approximation of the rpbie the actual space time boundary elements are described in some detail and their implementation has confirmed that stability in a wide range of situations and for large run times never reached before

a residual a posteriori error estimate for the time domain boundary element method this article investigates residual a posteriori error estimates and adaptive mesh refinements for time dependent boundary element methods for the wave equation we obtain reliable estimates for dirichlet and acoustic boundary conditions which hold for a large class of discretizations efficiency of the error estimate is shown for a natural discretization of low order numerical examples confirm the theoretical results the resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems

non abelian sylow subgroups of finite groups of even order we have been able to prove that every nonabelian sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution the proof depends upon the consequences of the classification of finite simple groups the purpose of this note is to announce 4 main theorem every nonabelian sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution let g be a finite group and g the prime graph of g g is the graph such that the vertex set is the set of prime divisors of g and two distinct vertices p and r are joined by an edge if and only if there exists an element of order pr in g let n g be the number of connected components of g and dg p r the distance between two vertices p and r of g it has been proved that n g 6 in 12 10 11 9 theorem 1 let g be a finite group of even order and p a prime divisor of g if dg 2 p 2 then a sylow p subgroup of g is abelian theorem 1 is a restatement of the main theorem in terms of the prime graph g corollary 1 let g be a finite group of even order and p a prime divisor of g if is a connected component of g p not containing 2 then a sylow r subgroup of g is abelian for any r there is a certain relation between a subgraph g p of g and brauer characters of p modular representations of g see 3 theorem 2 let g be a finite nonabelian simple group and p an odd prime divisor of g then dg 2 p 1 or 2 provided dg 2 p the significance of the prime graphs of finite groups can be found in 1 3 5 6 7 8 14 15 we apply the classification of finite simple groups see 1 2 4 7 10 13 it has been proved that a minimal counterexample to theorem 1 received by the editors october 20 1997 1991 mathematics subject classification primary 20d05 20d06 20d20

on finite factorizable groups in this paper we use freely the recent classification theorem for finite simple groups from the early stages of finite group theory finite factorizable groups satisfying h were studied by many authors in 1904 burnside 6 proved the solvability of groups factorizable by two prime power subgroups many years later wielandt 29 proved the solvability of finite groups factorizable by two nilpotent subgroups of relatively prime orders kegel extended wielandt s result in the case that both subgroups a and b are nilpotent without restrictions the second author in 121 classified finite factorizable groups of type h where a and b are solvable subgroups results on groups satisfying h can be found in 3 4 10 12 19 20 291 and in other papers on finite factorizable groups theorem 1 1 and corollary 1 2 of this paper state the final solution to the problem of classifying groups of type h we prove the following

mixed interpretation and extensions of the equivalent mass matrix approach for elastodynamics with contact the present paper highlights the idea that the mass redistribution technique introduced by khenous and co workers 2006 17 18 for elastodynamics with impact can be reinterpreted as a mixed formulation in displacements and velocities in which a special compatibility condition is enforced such a formulation opens the route to various extensions and to variational integrators for impact problems potentially with variational time adaption those ideas are exemplified in the design of such integrators and various mass redistribution schemes

a wave problem in a half space with a unilateral constraint at the boundary in this paper we study the following problem let omega be a half space of mathbb r n defined by omega x x x n in mathbb r x n where x x ldots x n 1 is the usual notation and let there be given functions u 0 in h 1 omega and u 1 in l 2 omega we assume that u 0 x n 0 is nonnegative and similarly partial u 0 partial x n x n 0 which is a priori an element of h 1 2 mathbb r n 1 is nonnegative

on finite groups isospectral to simple classical groups the spectrum g of a finite group g is the set of element orders of g finite groups g and h are isospectral if their spectra coincide suppose that l is a simple classical group of sufficiently large dimension the lower bound varies for different types of groups but is at most 62 defined over a finite field of characteristic p it is proved that a finite group g isospectral to l cannot have a nonabelian composition factor which is a group of lie type defined over a field of characteristic distinct from p together with a series of previous results this implies that every finite group g isospectral to l is close to l namely if l is a linear or unitary group then l g autl in particular there are only finitely many such groups g for given l if l is a symplectic or orthogonal group then g has a unique nonabelian composition factor s and for given l there are at most 3 variants for s including s l

prime graph components of the simple groups of lie type over the field of even characteristic abstract we classify the connected components of the prime graphs of the simple groups of lie type over the field of even characteristic

further reflections on thompson s conjecture abstract let g be a finite group and let n g n n g has a conjugacy class c such that c n professor j g thompson has conjectured that if g is a finite group with z g 1 and m a non abelian simple group satisfying n g n m then g m we have proved previously that if m is a sporadic simple group or a simple group having its prime graph with at least three prime graph components then thompson s conjecture is correct in this paper we shall prove main theorem let g be a finite group with z g 1 and m g 2 q or g 2 2 where q 2 such that n g n m then g m

on torsion subgroups in integral group rings of finite groups the object of this article are torsion subgroups of the normalized unit group v zg of the integral group ring zg of a finite group g for specific subgroups w we study the gruenberg kegel graph w it is shown that the central elements of an isolated subgroup u of a group basis h of zg are the normalized units of its centralizer ring czg u moreover nv zg u nh u if g has elementary abelian sylow 2 subgroups of order at most 8 each finite 2 subgroup of v zg is rationally conjugate to a subgroup of g finally torsion subgroups of v zg in the case when g is a minimal simple group are considered it follows that if g is a simple group which admits a non trivial partition for each prime p the p rank of a torsion subgroup of v zg is bounded by that one of g

a criterion for the existence of normal π complements in finite groups abstract the purpose of this article is to prove using the classification of the finite simple groups the following conjecture let be a set of odd primes then a finite group is homogeneous if and only if it is closed using this several open problems can be settled including an affirmative answer to the following problem of baer let g be a finite group and g suppose that g is both homogeneous and homogeneous is g a direct product of a group and a group finally we note that the proof of the conjecture yields proof to some theorems proved earlier without using the classification of the finite simple groups

block separations and inclusions abstract we investigate the separation of characters by blocks at different primes and the inclusions of q blocks in p blocks viewed as sets of characters and use these notions to prove results on the structure of the corresponding groups in particular we provide a new criterion for the nilpotence of a finite group g based on the separation by principal blocks and we show that a condition on block unions has strong structural consequences

energy controlling time integration methods for nonlinear elastodynamics and low velocity impact it is now well established that discrete energy conservation dissipation plays a key role for the unconditional stability of time integration schemes in nonlinear elastodynamics in this paper from a rigorous conservation analysis of the hilber hughes taylor time integration scheme h hilber t hughes r taylor improved numerical dissipation for time integration algorithms in structural dynamics earthquake engrg struct dynam 5 1977 283 292 we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like j simo n tarnow the discrete energy momentum method conserving algorithms for nonlinear elastodynamics z angew math phys 43 1992 757 792 moreover we extend the technique proposed in o gonzalez exact energy and momentum conserving algorithms for general models in nonlinear elasticity comput methods appl mech engrg 190 13 14 2000 1763 1783 to provide energy controlling time integration schemes for frictionless contact problems enforcing the standard kuhn tucker conditions at time discretization points we also extend this technique to viscoelastic models numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis

space time adaptive finite elements for nonlocal parabolic variational inequalities abstract this article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction both in the domain and on the boundary for a large class of parabolic variational inequalities associated to the fractional laplacian we obtain a priori and a posteriori error estimates and study the resulting space time adaptive mesh refinement procedures particular emphasis is placed on mixed formulations which include the contact forces as a lagrange multiplier corresponding results are presented for elliptic problems our numerical experiments for 2 dimensional model problems confirm the theoretical results they indicate the efficiency of the a posteriori error estimates and illustrate the convergence properties of space time adaptive as well as uniform and graded discretizations