some fixed point results on l embedded banach spaces abstract in this paper we prove that w fixed point property and w fixed point property are equivalent concepts for l embedded banach spaces which are duals of m embedded spaces similar results will be obtained with respect to the normal structure these equivalences will be applied to establish new fixed point results for different examples we will also prove the existence of fixed points for both nonexpansive and asymptotically regular mappings defined on subsets of l embedded banach spaces which are sequentially compact for the abstract measure topology we will check that our results do not hold in the case of the weak topology

a renorming in some banach spaces with applications to fixed point theory abstract we consider a banach space x endowed with a linear topology and a family of seminorms r k which satisfy some special conditions we define an equivalent norm on x such that if c is a convex bounded closed subset of x which is relatively sequentially compact then every nonexpansive mapping t c c has a fixed point as a consequence we prove that if g is a separable compact group its fourier stieltjes algebra b g can be renormed to satisfy the fpp in case that g t we recover p k lin s renorming in the sequence space l 1 moreover we give new norms in l 1 with the fpp we find new classes of nonreflexive banach spaces with the fpp and we give a sufficient condition so that a nonreflexive subspace of l 1 can be renormed to have the fpp

spaces of compact operators on a hilbert space with the fixed point property abstract every non reflexive subspace of k h the space of compact operators on a hilbert space h contains an asymptotically isometric copy of c 0 this along with a result of besbes shows that a subspace of k h has the fixed point property if and only if it is reflexive

galois groups of some vectorial polynomials previously nice vectorial equations were constructed having various finite classical groups as galois groups here such equations are constructed for the remaining classical groups the previous equations were genus zero equations the present equations are strong genus zero

spectral super elements for wave propagation in structures with local non uniformities the spectral element method for the analysis of wave propagation in structures is extended by the introduction of a super element concept to handle local regions of non uniformity the region of interest is meshed with conventional finite elements and its stiffness and mass matrices dynamically condensed leaving only the connection degrees of freedom these are further condensed to just waveguide connectivities thus making the element suitable for assembly with other spectral elements the formulation is verified by comparison with 2 d finite element solutions examples of its use in waveguides with cracks holes and extended joints are demonstrated

fourier stieltjes algebras and measure algebras on compact right topological groups abstract let g be an admissible compact hausdorff right topological group that is a group with a hausdorff topology such that for each a g the map g g a is continuous and the set of a g such that the map g a g is continuous is dense in g such groups arise in the study of distal flows in this paper we study the fourier stieltjes algebra b g the linear span of the continuous positive definite functions on g we show that b g is isomorphic with the fourier stieltjes algebra of an associated compact topological group this result is then applied to obtain some geometric properties including the weak and weak fixed point properties on b g we also study some related properties on the measure algebra m g

isometric copies of c0 and l in duals of banach spaces abstract let x be a banach space then x contains an isometric copy of l if and only if x contains an asymptotically isometric copy of c0

modelling turbulence induced vibration of pipes with a spectral finite element method the vibration of pipes is studied here using the arnold warburton theory for thin shells and a simplified theory valid in a lower frequency regime the vibrational response is described numerically with the spectral finite element method sfem which uses the exact solutions of the equations of motion as basis functions for turbulence excitation the set of basis functions was extended to include particular solutions which model a spatially distributed excitation an efficient numerical solution to homogeneous random excitation is presented and the results compare favourably with wind tunnel measurements

renormings and the fixed point property in non commutative l1 spaces abstract let m be a finite von neumann algebra it is known that l 1 m and every non reflexive subspace of l 1 m fail to have the fixed point property for non expansive mappings fpp we prove a new fixed point theorem for this class of mappings in non commutative l 1 m banach spaces which lets us obtain a sufficient condition such that a closed subspace of l 1 m can be renormed to satisfy the fpp as a consequence we deduce that the predual of every atomic finite von neumann algebra can be renormed with the fpp

there is an equivalent norm on l1 that has the fixed point property abstract let k 8 k 1 8 k for all k n and let be the equivalent norm of l 1 defined by a n sup k n k n k a n for all x a n l 1 we prove that l 1 has the fixed point property for nonexpansive self mappings

failure of the fpp inside an asymptotically isometric free copy of c0 abstract we produce an equivalent renorming of c 0 which fails to contain an asymptotically isometric copy of c 0 yet all of its infinite dimensional subspaces fail to have the fixed point property for nonexpansive mappings on closed bounded convex subsets

order asymptotically isometric copies of l l1 and c0 in banach function spaces abstract we investigate order asymptotically isometric copies of c 0 l and l 1 in kothe spaces firstly we prove a number of general relations between them and we discuss what happens with such copies while passing to kothe dual spaces or vice versa passing to preduals finally we apply the results to characterize certain classes of kothe spaces as orlicz spaces calderon lozanovski spaces orlicz lorentz spaces and musielak orlicz spaces with such copies

split embedding problems over complete domains we prove that every finite split embedding problem is solvable over the field k x1 x n of formal power series in n 2 variables over an arbitrary field k as well as over the field quot a x 1 x n of formal power series in n 1 variables over a noetherian integrally closed domain a this generalizes a theorem of harbater and stevenson who settled the case k x1 x 2

asymptotically isometric copies ofc0in banach spaces abstract if is an uncountable set then any equivalent renorming of c 0 contains an asymptotically isometric copy of c 0 if y is an infinite dimensional closed subspace of c 0 then y contains an asymptotically isometric copy of c 0 if x and y are two infinite dimensional banach spaces and if x contains an asymptotically isometric copy of c 0 then the injective tensor product of x and y x e y contains a complemented asymptotically isometric copy of c 0 similarly if x contains an asymptotically isometric copy of c 0 then the lebesgue bochner space l p 0 1 x contains a complemented asymptotically isometric copy of c 0

renormings and fixed point property in non commutative l1 spaces ii affine mappings abstract in this paper we prove that every noncommutative l 1 space associated to a finite von neumann algebra can be renormed to satisfy the fixed point property for nonexpansive affine mappings particular examples are l 1 r where r is the hyperfinite i i 1 factor and the function spaces l 1 0 1 and l 1 for any finite measure space this property does not hold for the usual 1 norm

the fundamental group of affine curves in positive characteristic abstract it is shown that the commutator subgroup of the fundamental group of a smooth irreducible affine curve over an uncountable algebraically closed field k of positive characteristic is a profinite free group of rank equal to the cardinality of k

renormings of c0 and the fixed point property it is unknown whether all renormings of c0 fail the fixed point property fpp or not in this note we give a sufficient condition for a renorming of c0 to fail the fpp which is more general than the previously known ones in fact the condition is satisfied for all renormings of c0 we know it also allows us to show that for some usual renormings of c0 not only the whole space but all its infinite dimensional subspaces fail the fpp

algebraic curves with many automorphisms abstract let x be a projective geometrically irreducible non singular algebraic curve of genus g 2 defined over an algebraically closed field k of odd characteristic p let aut x be the group of all automorphisms of x which fix k element wise it is known that if aut x 8 g 3 then the p rank equivalently the hasse witt invariant of x is zero this raises the problem of determining the minimum value function f g such that whenever aut x f g then x has zero p rank for even g we prove that f g 900 g 2 the odd genus case appears to be much more difficult although for any genus g 2 if aut x has a solvable subgroup g such that g 252 g 2 then x has zero p rank and g fixes a point of x our proofs use the hurwitz genus formula and the deuring shafarevich formula together with a few deep results from group theory characterizing finite simple groups whose sylow 2 subgroups have a cyclic subgroup of index 2 we also point out some connections with the abhyankar conjecture and the katz gabber covers

reflexivity and the fixed point property for nonexpansive maps abstract connections between reflexivity and the fixed point property for nonexpansive self mappings of nonempty closed bounded convex subsets of a banach space are investigated in particular it is shown that l 1 for uncountable sets and l cannot even be renormed to have the fixed point property as a consequence if an orlicz space on a finite measure space that is not purely atomic is endowed with the orlicz norm the orlicz space has the fixed point property exactly when it is reflexive

resolution of singularities and modular galois theory i shall sketch a brief history of the desingularization problem from riemann thru zariski to hironaka including the part i played in it and the work on galois theory which this led me to and how that caused me to search out many group theory gurus i shall also formulate several conjectures and suggest numerous thesis problems

energy flow models from finite element analysis computationally efficient methods are described by which the results of a finite element analysis of a system may be post processed to form energy flow models yielding time and perhaps frequency average subsystem energies as well as input and dissipated powers the methods are particularly efficient for excitation which is spatially distributed or broadband e g rain on the roof or if the frequency average response is required first a method based on a global finite element analysis is presented this involves a global modal decomposition and a reordering of the subsequent numerical calculations the properties of the distribution of the excitation and the system s mass and stiffness lead to subsystem force distribution mass distribution and stiffness distribution matrices the response is given by a sum of terms involving the interaction of a pair of global modes the contribution of each pair depending on the appropriate elements of the distribution matrices frequency averaging is performed by separating the resulting frequency dependent terms and integrating in most practical cases this integration can be done analytically next an alternative method involving component mode synthesis is described in this individual finite element analyses are performed for each subsystem using here the fixed interface method these are then assembled to perform a global modal analysis with the order of the model being much reduced the consequent results are then post processed in the same way finally a system comprising three coupled plates is presented as a numerical example

dynamic behaviour of structures in large frequency range by continuous element methods abstract the continuous element method is presented in the context of the harmonic response of beam assemblies a general formulation is described from the displacement solution of the elementary problem a direct computation of elementary dynamic stiffness matrices is presented in the present formulation distributed loadings are taken into account in the case of more complex geometries for which many coupling phenomena occur an explicit formulation is no more conceivable in this case a numerical approach is presented this approach allows an algorithmic computation of exact dynamic stiffness matrices this method called numerical continuous element allows one to consider the coupled vibrations of curved beams and those of helical beams the validation of this numerical method is achieved by comparisons with the harmonic response of various beams obtained by a finite element approach finally a comparison between eigenfrequencies obtained experimentally and numerically for a straight beam and a helical beam has been made to evaluate the performances of the method

polynomials with psl 2 monodromy let k be a field of characteristic p 0 let q be a power of p and let u be transcendental over k we determine all polynomials f k x k x p of degree q q 1 2 for which the galois group of f x u over k u has a transitive normal subgroup isomorphic to psl 2 q subject to a certain ramification hypothesis as a consequence we describe all polynomials f k x such that deg f is not a power of p and f is functionally indecomposable over k but f decomposes over an extension of k moreover except for one ramification configuration which is handled in a companion paper with rosenberg we describe all indecomposable polynomials f k x such that deg f is not a power of p and f is exceptional in the sense that x y is the only absolutely irreducible factor of f x f y which lies in k x y it is known that when k is finite a polynomial f is exceptional if and only if it induces a bijection on infinitely many finite extensions of k

cyclic quotients of transitive groups abstract let a be a transitive subgroup of s n we show that the largest cyclic quotient of a has order at most n this can be interpreted as an equivalent result about extensions of constants in the galois closure of a covering of curves over a finite field we also prove that the point stabilizer in a finite primitive permutation group always has a faithful orbit

patching and thickening problems in recent years much progress has been made on the structure of fundamental groups of algebraic curves by means of patching techniques in formal and rigid geometry a number of these results have concerned curves over algebraically closed fields of characteristic p e g the proofs of the abhyankar conjecture ra ha5 and of the geometric case of the shafarevich conjecture po1 ha6 and the realization of galois groups over projective curves sa1 st1 while the rigid approach to patching is often regarded as more intuitive than the formal approach its foundations are less well established but constructions involving the formal approach have tended to be technically more cumbersome the purpose of the current paper is to build on previous formal patching results in order to create a framework in which such constructions are facilitated in the process we prove a result asserting that singular curves over a field k can be thickened to curves over k t with prescribed behavior in a formal neighborhood of the singular locus and similarly for covers of curves afterwards we obtain applications to fundamental groups of curves over large fields the structure of the paper is as follows section 1 concerns patching problems for projective curves x over a power series ring r k t1 tn it is shown theorem 1 that giving a coherent projective module over x is equivalent to giving such modules compatibly on a formal neighborhood of each singular point of the closed fibre x and on the formal thickening along the complement of the singular locus s of x section 2 applies this to thickening problems in both the absolute and relative senses namely it shows theorem 3 that such an x can be constructed from its closed fibre x and from complete local thickenings near s such that x is a trivial deformation away from s moreover theorem 2 given a morphism x z and a thickening z of z such that the local thickenings near s are compatible with that of z there is a unique such thickening x of x that is compatible with the given data in section 3 these results are applied to the problem of thickening and deforming covers theorem 4 there combines the results of sections 1 and 2 to show that covers of reducible k curves can be thickened to covers of curves over k t and theorem 5 then shows how this can be used over large fields to

tchebotarev theorems for function fields abstract the central theme of the paper is the specialization of algebraic function field extensions our main results are tchebotarev type theorems for galois function field extensions finite or infinite over various base fields under some conditions we extend the classical finite field case to number fields p adic fields pac fields function fields x etc we also compare the tchebotarev conclusion existence of unramified local specializations with galois group any cyclic subgroup of the generic galois group up to conjugation to the hilbert specialization property for a function field extension with the tchebotarev property the exponent of the galois group is bounded by the l c m of the local specialization degrees local global questions arise for which we provide answers examples and counter examples

families of wildly ramified covers of curves in this paper i investigate wildly ramified g galois covers of curves inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i branched at exactly one point over an algebraically closed field k of characteristic p i answer a question of m raynaud by showing that proper families of such covers of a twisted projective line are isotrivial the method is to construct an affine moduli space for covers whose inertia group is of the form inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i there are two other applications of this space in the case that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i the first uses formal patching to compute the dimension of the space of nonisotrivial deformations of in terms of the lower jump of the filtration of higher inertia groups the second gives necessary criteria for good reduction of families of such covers these results will be used in a future paper to prove the existence of such covers with specified ramification data

galois groups of unramified covers of projective curves in characteristicp abstract we show several results concerning the finite groups that occur as galois groups of unramified covers of projective curves in characteristic p in particular we prove that every finite group with g generators occurs over some curve of genus g this implies for example that every finite simple group occurs in genus 2 by similar methods we obtain several other families of groups which occur in genus 2 in addition we show that if a group g occurs over some curve of genus g then it must occur over almost all curves of genus g or greater the results are obtained using formal patching

asymptotically isometric copies of c0 and l1 in bochner spaces abstract let x be a banach space and be a finite measure space it is shown that if 1 p resp 1 p l p x contains asymptotically isometric copies of c 0 resp l 1 if and only if x does

spectral finite elements for vibrating rods and beams with random field properties the classical stochastic helmholtz equation grasps through the random field of the refraction index the spatial variability in the mass density but not the variability in elastic moduli or geometric parameters in contradistinction to this restriction the present analysis accounts for the spatial randomness of mass density as well as those of elastic properties and cross sectional geometric properties of rods undergoing longitudinal vibrations and of timoshenko beams in flexural vibrations all the material variabilities are described here by random fourier series with a typical average characteristic size of inhomogeneity d which is either smaller comparable to or larger than the wavelength the third length scale entering the problem but kept constant is the rod or beam length we investigate the relative effects of random noises in all the material parameters on the spectral stiffness matrices associated with rods and beams for a very wide range of frequencies

an approach to the theoretical background of statistical energy analysis applied to structural vibration rayleigh s classical approach to the study of vibration of systems having a finite number of degrees of freedom is applied to the problem of coupling of subsystems in a complicated structure in order to probe the regions of applicability of the approach to vibration analysis usually known as statistical energy analysis sea the classical method has advantages of simplicity and rigor over previous approaches to the background of sea in certain cases and provides extensions and simplifications in several areas of the theory it also suggests modifications to sea modeling strategy depending on the type of coupling involved even when that coupling is weak so that earlier analyses might be thought to apply

local rotundity structure of generalized orlicz lorentz sequence spaces abstract we give some criteria for extreme points and strong u points in generalized orlicz lorentz sequence spaces which were introduced in p foralewski h hudzik l szymaszkiewicz on some geometric and topological properties of generalized orlicz lorentz sequence spaces math nachr in press cf g g lorentz an inequality for rearrangements amer math monthly 60 1953 176 179 m nawrocki the mackey topology of some f spaces ph d dissertation adam mickiewicz university poznan 1984 in polish some examples show that in these spaces the notion of the strong u point is essentially stronger than the notion of the extreme point this paper is related to the results from a kaminska extreme points in orlicz lorentz spaces arch math 55 1990 173 180 see remark 1

galois theory over rings of arithmetic power series let r be a domain complete with respect to a norm which denes a non discrete topology on r we prove that the quotient eld of r is ample generalizing a theorem of pop we then consider the case where r is a ring of arithmetic power series which are holomorphic on the closed disc of radius 0 r 1 around the origin and apply the above result to prove that the absolute galois group of the quotient eld of r is semi free this strengthens a theorem of harbater who solved the inverse galois problem over these elds

response variance prediction in the statistical energy analysis of built up systems in the statistical energy analysis sea of high frequency noise and vibration a complex engineering structure is represented as an assembly of subsystems the response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem and these energies are found by employing the principle of power balance strictly the computed energy is an average taken over an ensemble of random structures and for many years there has been interest in extending the sea prediction to the variance of the energy a variance prediction method for a general built up structure is presented here closed form expressions for the variance are obtained in terms of the standard sea parameters and an additional set of parameters alpha k that describe the nature of the power input to each subsystem k and alpha ks that describe the nature of the coupling between subsystems k and s the theory is validated by comparison with monte carlo simulations of plate networks and structural acoustic systems

dual fixed point property on spaces of continuous functions under equivalent norms abstract a banach space x is said to have the fixed point property if for every closed convex bounded subset c x and for every t c c nonexpansive there is a fixed point a banach space is said to have the dual fixed point property if its dual space x verifies the fixed point property it is a fact that c 0 k fails the dual fixed point property for every locally compact hausdorff set k in this article we study the fulfilment of the dual fixed point property under equivalent norms we prove that c 0 k can be renormed to have the dual fixed point property if and only if k is a countable set in this case we prove that this renorming can be achieved as close to the standard norm on c 0 k as we like for the banach mazur distance we further obtain the corresponding weak fixed point property stability coefficient regarding the duality c 0 k c 0 k it will be displayed that the value of this stability coefficient strongly depends on the distribution of the accumulation points of k finally we prove that the dual fixed point property is completely unstable for the banach mazur distance in most of nonreflexive banach spaces

asymptotically isometric copies of c0 and l1 in certain banach spaces abstract if x is a separable banach space then x contains an asymptotically isometric copy of l1 if and only if there exists a quotient space of x which is asymptotically isometric to c0 if x is an infinite dimensional normed linear space and y is any banach space containing an asymptotically isometric copy of c0 then l x y contains an isometric copy of l if x and y are two infinite dimensional banach spaces and y contains an asymptotically isometric copy of c0 then k w x y contains a complemented asymptotically isometric copy of c0

resonant beam vibration a wave evolution analysis abstract in an attempt to verify the concept of wave mode duality and to understand the wave train closure principle in resonant beam vibration an elastically supported beam subjected to a swept sinusoidal force is investigated through a simulation of wave evolution from initial to final steady state response wave evolution is simulated in the superposition and the degenerate states according to the nature of wave reflection at the boundaries of the beam from the results resonance condition is established and the natural frequencies and mode shapes are calculated using a simply supported beam and a cantilever beam as examples the concept of wave mode duality at resonance is verified an examination of the wave train closure principle shows that although the frequency equations obtained by using the principle are identical to those derived from the wave evolution results the principle does not describe the realistic process of the formulation of vibration modes in general the waves described in the wave train closure principle are not physical but virtual waves that represent final steady state waves which can only be asymptotically approached in reality the principle can be used as a convenient technique to obtain vibration modes from the point of view of wave propagation

the daugavet property in the musielak orlicz spaces abstract we show that among all musielak orlicz function spaces on a finite non atomic complete measure space equipped with either the luxemburg norm or the orlicz norm the only spaces with the daugavet property are l 1 l l 1 1 l and l 1 l in particular we obtain complete characterizations of the daugavet property in the weighted interpolation spaces the variable exponent lebesgue spaces nakano spaces and the orlicz spaces

renormings failing to have asymptotically isometric copies of l1 or c0 abstract it is proved that every equivalent norm in l 1 is the starting point of a ray of norms which fail to have an asymptotically isometric copy of l 1 in the case where x is separable it is proved that the set of all equivalent norms in x which fail to have an asymptotically isometric copy of l 1 is residual similar results are obtained for the case of c 0 in particular we deduce that every separable banach space has an equivalent norm for which it fails to contain an asymptotically isometric copy of l 1 and c 0

almost locally free fields abstract using the positive solution of the general abhyankar s conjecture we prove that the fundamental group 1 c of the smooth connected affine curve c is almost free that is for each positive integer e and for almost all 1 e 1 c e in the sense of the haar measure the closed subgroup of 1 c generated by 1 e is profinite free on e generators this implies a theorem of harbater stevenson proved by other means that every finite embedding problem for 1 c is solvable if we restrict the problem to a suitable open subgroups

asymptotically isometric copies ofc0and renormings of banach spaces abstract if a banach space x contains an asymptotically isometric copy of c 0 then x fails to have weak normal structure consequently if x is an infinite dimensional subspace of c 0 then x fails to have weak normal structure also every equivalent renorming of c 0 for uncountable fails to have weak normal structure every separable banach space can be equivalently renormed so as not to contain an asymptotically isometric copy of c 0 every banach space with the generalized gossez lami dozo ggld property fails to contain a subspace isomorphic to c 0

normal subgroups of the algebraic fundamental group of affine curves in positive characteristic let 1 c be the algebraic fundamental group of a smooth connected affine curve defined over an algebraically closed field of characteristic p 0 of countable cardinality let n be a normal respectively characteristic subgroup of 1 c under the hypothesis that the quotient 1 c n admits an infinitely generated sylow p subgroup we prove that n is indeed isomorphic to a normal respectively characteristic subgroup of a free profinite group of countable cardinality as a consequence every proper open subgroup of n is a free profinite group of countable cardinality

fundamental group in positive characteristic abstract it is shown that the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic is profinite free of countable rank a description of the abelianizations of the fundamental groups of affine curves over an algebraically closed field of nonzero characteristic is also given

banach spaces with the daugavet property a banach space x is said to have the daugavet property if every operator t x x of rank 1 satisfies 11 id tl 1 fltil we show that then every weakly compact operator satisfies this equation as well and that x contains a copy of t1 however x need not contain a copy of l1 we also study pairs of spaces x c y and operators t x y satisfying i i j t i i 1 4 1f t i i where j x y is the natural embedding this leads to the result that a banach space with the daugavet property does not embed into a space with an unconditional basis in another direction we investigate spaces where the set of operators with f id tll 1 il t l i is as small as possible and give characterisations in terms of a smoothness condition

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation