rationality problem of three dimensional monomial group actions abstract let k be a field of characteristic not two and k x y z the rational function field over k with three variables x y z let g be a finite group acting on k x y z by monomial k automorphisms we consider the rationality problem of the fixed field k x y z g under the action of g namely whether k x y z g is rational that is purely transcendental over k or not we may assume that g is a subgroup of gl 3 z and the problem is determined up to conjugacy in gl 3 z there are 73 conjugacy classes of g in gl 3 z by results of endo miyata voskresenski lenstra saltman hajja kang and yamasaki 8 conjugacy classes of 2 groups in gl 3 z have negative answers to the problem under certain monomial actions over some base field k and the necessary and sufficient condition for the rationality of k x y z g over k is given in this paper we show that the fixed field k x y z g under monomial action of g is rational over k except for possibly negative 8 cases of 2 groups and unknown one case of the alternating group of degree four moreover we give explicit transcendental bases of the fixed fields over k for the unknown case we obtain an affirmative solution to the problem under some conditions in particular we show that if k is quadratically closed field then k x y z g is rational over k we also give an application of the result to 4 dimensional linear noether s problem

retract rational fields abstract let k be an infinite field the notion of retract k rationality was introduced by saltman in the study of noether s problem and other rationality problems we will investigate the retract rationality of a field in this paper theorem 1 let k k l be fields if k is retract k rational and l is retract k rational then l is retract k rational theorem 2 for any finite group g containing an abelian normal subgroup h such that g h is a cyclic group for any complex representation g gl v the fixed field c v g is retract c rational theorem 3 if g is a finite group then all the sylow subgroups of g are cyclic if and only if c m g is retract c rational for all g lattices m for all short exact sequences 0 c m m 0 because the unramified brauer group of a retract c rational field is trivial theorems 2 and 3 generalize previous results of bogomolov and barge respectively see theorems 5 9 and 6 1

on rayleigh waves in incompressible orthotropic elastic solids in this paper the secular equation for the rayleigh wave speed in an incompressible orthotropic elastic solid is obtained in a form that does not admit spurious solutions it is then shown that inequalities on the material constants that ensure positive definiteness of the strain energy function guarantee existence and uniqueness of the rayleigh wave speed finally an explicit formula for the rayleigh wave speed is obtained

the rationality problem for finite subgroups of gl4 q abstract let g be a finite subgroup of gl 4 q the group g induces an action on q x 1 x 2 x 3 x 4 the rational function field of four variables over q theorem the fixed subfield q x 1 x 2 x 3 x 4 g f q x 1 x 2 x 3 x 4 f f for any g is rational i e purely transcendental over q except for two groups which are images of faithful representations of c 8 and c 3 c 8 into gl 4 q both fixed fields for these two exceptional cases are not rational over q there are precisely 227 such groups in gl 4 q up to conjugation the answers to the rationality problem for most of them were proved by kitayama and yamasaki 2009 ky except for four cases we solve these four cases left unsettled by kitayama and yamasaki thus the whole problem is solved completely

finite element formulations for non steady state large viscoplastic deformation different mechanical formulations are employed for calculation of the large deformations occurring in metal forming processes eulerian and updated lagrangian descriptions valid for viscoplastic materials are presented in view of the numerical tests which were carried out the eulerian formulation associated with an implicit integration scheme which proved to be numerically accurate and reliable is shown to be preferable

a velocity based approach including acceleration to the finite element computation of viscoplastic problems we present a velocity based approach including acceleration to the finite element computation of metal forming problems based on the viscoplastic norton hoff law in order to reduce computational cost we suggest substituting the classical solution procedure based on standard newton raphson method for solving the set of non linear equations with a new one which needs only one computation inside a time step and which is based on the linearization of the non linear equations over time the new procedure was introduced as an option in the existing computer code forge2 some examples are used for comparison between the classical procedure and the new one they show that the new procedure is stable and accurate and in comparison to the classical one it reduces the total number of resolutions of linear systems therefore significant computer time reduction can be expected for 3 d problems

on noether s problem for central extensions of symmetric and alternating groups for a field k and a finite group g acting regularly on a set of indeterminates x xg g g let k g denote the invariant field k x g we first prove for the alternating group an that if n is odd then q an is rational over q an 1 we then obtain an analogous result where an is replaced by an arbitrary finite central extension of either an or sn valid over q n for suitable n concrete applications of our results yield 1 a new proof of maeda s result on the rationality of q x1 x5 a5 q 2 an affirmative answer to noether s problem over q for both a5 and s5 3 an affirmative answer to noether s problem over c for every finite central extension group of either an or sn with n 5

on the third and fourth order constants of incompressible isotropic elasticity consider the constitutive law for an isotropic elastic solid with the strain energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain the stress strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit for this purpose use of the logarithmic strain tensor is of particular value it enables the limiting values of all nine fourth order elastic constants in the incompressible limit to be evaluated precisely and rigorously in particular it is explained why the three constants of fourth order incompressible elasticity and d are of the same order of magnitude several examples of application of the results follow including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation

generic extensions and generic polynomials for linear algebraic groups abstract we construct generic extensions and polynomials for certain linear algebraic groups over finite fields in particular we show the existence of generic polynomials for the cyclic group c 2 m in characteristic p for all odd primes p

explicit secular equations for surface waves in monoclinic materials with the symmetry plane x1 0 x2 0 or x3 0 the traditional way of deriving the secular equation for surface waves propagating in the direction of the x1axis in an anisotropic elastic halfspace x20 is to find a general steadystate solution f

a unified formalism for elastostatics or steady state motion of compressible or incompressible anisotropic elastic materials abstract for a two dimensional deformation of an anisotropic elastic material the lekhnitski formalism applies to elastostatics only it does not apply to steady state motion such as surface waves or a moving line dislocation the stroh formalism applies to elastostatics as well as steady state motion however it does not apply to an incompressible material because some of the elastic stiffnesses become unbounded in the incompressible limit modifying a new formalism studied recently a more explicit and remarkably simple expression of the matrices in the new formalism is given and a unified formalism that is applicable to elastostatics as well as steady state motion of a compressible or incompressible anisotropic elastic material is obtained as an application the secular equation is presented for surface waves propagating in a monoclinic material with the symmetry plane at x 3 0 that has a more explicit expression than what is available in the literature for a general anisotropic elastic material explicit expressions are obtained for the sextic equation for the eigenvalues p and the eigenvectors b and a for any steady state wave speed the explicit expressions recover results related to one component surface waves when the material is incompressible it is shown that the eigenvalues p remain complex for elastostatics we also show that when the material is incompressible a monoclinic material with the symmetry plane at x 3 0 behaves like that of an orthotropic material

analytical and numerical investigation of strain hardening viscoplastic thick walled cylinders under internal pressure by using sequential limit analysis plastic limit load of strain hardening viscoplastic thick walled cylinders subjected to internal pressure is investigated numerically and analytically in the paper the paper applies sequential limit analysis to deal with the quasi static problem involving hardening material properties and weakening behavior corresponding to the strain rate sensitivity and widening deformation by sequential limit analysis the paper treats the plasticity problems as a sequence of limit analysis problems stated in the upper bound formulation rigorous upper bounds are acquired iteratively through a computational optimization procedure with the internal pressure factor as the objective function especially rigorous validation was conducted by numerical and analytical studies of thick walled cylinders in terms of the plastic limit load as well as the onset of instability it is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions 2007 elsevier b v all rights reserved

noether s problem for p groups with a cyclic subgroup of index p2 abstract let k be any field and g be a finite group let g act on the rational function field k x g g g by k automorphisms defined by g x h x g h for any g h g noether s problem asks whether the fixed field k g k x g g g g is rational purely transcendental over k we will prove that if g is a non abelian p group of order p n n 3 containing a cyclic subgroup of index p 2 and k is any field containing a primitive p n 2 th root of unity then k g is rational over k as a corollary if g is a non abelian p group of order p 3 and k is a field containing a primitive p th root of unity then k g is rational

division algebras over surfaces abstract we consider here a number of topics concerning the theory of division algebras over the function field of a surface one result relates the obstruction for ramification data to be from a division algebra and third etale cohomology another result shows this obstruction is always zero when the surface is spec of a regular local ring with some mild assumptions at the same time we study the brauer group of this function field as it relates to the brauer group of the function field of the henselization finally we prove a result which says that brauer group elements which look like they are of prime index q unequal to any characteristic must have all their ramification split by a cyclic galois extension of the same degree this last result requires a primitive q root of one

the construction of weight two arithmetic cohomology let x be a regular noetherian scheme in a letter to soul6 be beilinson conjectured for each non negative integer n the existence of complexes f n x of zariski sheaves on x whose hypercohomology should be in the same relation to algebraic k theory as classical cohomology is to topological ktheory and proposed certain properties that these complexes should satisfy this investigation was continued in l where the conjectured complexes were moved to the a at other points we work only up to 2torsion or up to torsion involving primes dividing the residue field characteristics there seems good reason to expect our complex f 2 x to in fact exactly satisfy all the axioms we now sketch the construction of f 2 x and recall the axioms let a be a regular noetherian ring let w s p e c a t z s p e c a t t t 1 let b bl b 2 b be a finite sequence of exceptional units of a i e b i and

division algebras with psl 2 q galois maximal subfields abstract if g is a finite group and k is a field then g is k admissible if there exists a g galois extension l k such that l is a maximal subfield of a k division algebra we prove that psl 2 7 is k admissible for any number field which either fails to contain 1 or which has two primes lying over the dyadic prime in addition psl 2 11 is shown to be admissible over q or any number field k with at least two extensions of the dyadic prime indeed there exist infinitely many linearly disjoint admissible extensions for these groups

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

frobenius groups and retract rationality abstract let k be any field g be a finite group acting on the rational function field k x g g g by h x g x h g for any h g g define k g k x g g g g noether s problem asks whether k g is rational purely transcendental over k a weaker notion retract rationality introduced by saltman is also very useful for the study of noether s problem we prove that if g is a frobenius group with abelian frobenius kernel then k g is retract k rational for any field k satisfying some mild conditions as an application we show that for any algebraic number field k for any frobenius group g with frobenius complement isomorphic to s l 2 f 5 there is a galois extension field k over k whose galois group is isomorphic to g i e the inverse galois problem is valid for the pair g k the same result is true for any non solvable frobenius group if k 8 is a cyclic extension of k

numerical formulations and algorithms for solving contact problems in metal forming simulation the problem of contact between a part and a tool or between two deforming bodies is analysed in view of metal forming processes for simplicity only the case of viscoplastic materials is considered the velocity formulation is presented the contact with a rigid tool is considered first and various forms of contact formulations are described nodal contact integral or discrete formulation with a penalty or with a lagrange multiplier method the time integration is considered which results in various explicit or implicit contact formulations a special attention is paid to the contact between two deforming bodies or to the self contact when a fold is generated in the work piece some 2 d and 3 d application examples illustrate the effectiveness of the proposed formulations and algorithms copyright 1999 john wiley sons ltd

rationality problem for transitive subgroups of s8 abstract for any field k and any transitive subgroup g of s 8 let g act naturally on k x 1 x 8 by permuting the variables we prove that under some minor conditions k x 1 x 8 g is always k rational except g is a 8 or g is isomorphic to pgl 2 7 we pay special attentions on the characteristic 2 cases

the gersten conjecture for milnor k theory we prove that the n th milnor k group of an essentially smooth local ring over an infinite field coincides with the n n motivic cohomology of the ring this implies levine s generalized bloch kato conjecture