cohomology of units and l values at zero let klk be a finite galois extension of number fields with galois group g and let s be a finite g stable set of primes of k containing all archimedean primes we denote the g module of s units of k by e es and let as be the kernel of the augmentation map zs z which sends each basis element p c s to 1 we are concerned with invariants of k k which are associated to a g homomorphism p as e inducingq0 as cq0e these invariants were defined by tate ta2 and chinburg chl when s is large i e when s contains all ramified primes of k k and the s class group cl cls of k is trivial there are two of them and each is a function of the complex characters x of g the first aw has a x equal to the tate regulator at x divided by the leading coefficient c x of the taylor expansion at s 0 of the artin l function l s x with the euler factors at primes of s omitted according to stark s conjecture st in tate s form a takes algebraic values which satisfy a o x5 a x

free vibration of non circular cylindrical shells with longitudinal interior partitions abstract an analysis is presented for the free vibration of a simply supported non circular cylindrical shell with longitudinal interior partitions for this purpose the governing equations of vibration of a non circular cylindrical shell including a plate as special case are written in a matrix differential equation by using the transfer matrix in the circumferential direction once the matrix has been determined the entire structure matrix is obtained by the product of the transfer matrix of the shell and the point matrix at the joint of the structure matrix the method is applied to approximately elliptical cylindrical shells with an interior plate and the natural frequencies and the mode shapes of vibration are calculated numerically giving the results

experimentally friendly geometrical criteria for entanglement a simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement its generalization gives a necessary and sufficient condition it is linked with a family of entanglement identifiers which is strictly richer than the family of entanglement witnesses

the iwasawa conjecture for totally real fields let f be a totally real number field let p be a prime number and for any integer n let fun denote the group of nth roots of unity let 41 be a p adic valued artin character for f and let f be the extension of f attached to 4 i e so that 4 is the character of a faithful representation of gal f f we will assume that f is also totally real for a number field k let k denote the cyclotomic zp extension of k following greenberg we say that 4 is of type s if f n fc f and of type w if 4 is one dimensional with f p c fcc deligne and ribet in dr following kubota and leopoldt for the case f q have proved the existence of a p adic l function associated to a one dimensional artin character 4 with f totally real this function lp s 4 is continuous for s e zp 1 and even at s 1 if 4 is not trivial and satisfies the following interpolation property

stickelberger elements fitting ideals of class groups of cm fields and dualisation in this paper we systematically construct abelian extensions of cm fields over a totally real field whose stickelberger elements are not in the fitting ideals of the class groups our evidence indicates that pontryagin duals of class groups behave better than the class groups themselves we also explore the behaviour of fitting ideals under projective limits and dualisation in a somewhat broader context

non commutative fitting invariants and annihilation of class groups abstract one can associate to each finitely presented module m over a commutative ring r an r ideal fitt r m which is called the zeroth fitting ideal of m over r and which is an important natural invariant of m we generalize this notion to o orders in separable algebras where o is a complete commutative noetherian local ring as an application we construct annihilators of class groups assuming the validity of the equivariant tamagawa number conjecture for a certain motive attached to a galois cm extension of number fields

on the non abelian brumer stark conjecture and the equivariant iwasawa main conjecture we show that for an odd prime p the p primary parts of refinements of the imprimitive non abelian brumer and brumer stark conjectures are implied by the equivariant iwasawa main conjecture eimc for totally real fields crucially this result does not depend on the vanishing of the relevant iwasawa mu invariant in combination with the authors previous work on the eimc this leads to unconditional proofs of the non abelian brumer and brumer stark conjectures in many new cases

computing fitting ideals of iwasawa modules this paper determines in an equivariant sense the fitting ideals of several iwasawa modules including the most canonical one the connection between the modules themselves which are usually not of finite projective dimension and the required auxiliary modules of finite projective dimension is made rather explicit the resulting fitting ideals look like stickelberger ideals and there is a close relation with recent work of kurihara as an application we obtain new evidence in favor of the brumer stark conjecture

congruences between derivatives of abelian l functions at s 0 let k k be a finite abelian extension of global fields we prove that a natural equivariant leading term conjecture implies a family of explicit congruence relations between the values at s 0 of derivatives of the dirichlet l functions associated to k k we also show that these congruences provide a universal approach to the refined abelian stark conjectures formulated by inter alia stark gross rubin popescu and tate we thereby obtain the first proofs of amongst other things the rubin stark conjecture and the refined class number formulas of both gross and tate for all extensions k k in which k is either an abelian extension of or is a function field

free vibrations of circular cylindrical shells with an interior plate using the receptance method this paper describes the method to analyze the free vibrations of simply supported cylindrical shells with an interior rectangular plate by using the receptance method this method is based on the ratio of a deflection or slope response to a harmonic force or moment at the joint after finding the free vibrational characteristics of the simply supported plate and shell before combination the frequency equation of the combined system is obtained by considering the continuity conditions at the joint between the plate and the shell when the line load and moment applied along the joint are assumed as the dirac delta and sinusoidal function the continuity conditions at the joint are proven to be satisfied the numerical results are compared with published works and experimental results in order to show the validity of the formulation and that the analytical results agree with those from other methods

on derivatives of artin l series we present a universal theory of refined stark conjectures we give evidence in support of these explicit and very general conjectures including a full proof in several important cases and explain the connection to previous conjectures of bloch and kato of lichtenbaum and of serre and tate we also deduce a wide range of unconditional consequences of these results concerning the annihilation as galois modules of ideal class groups by explicit elements constructed from the values of higher order derivatives of non abelian artin l series

on a conjecture of brumer in a series of papers iwasawa proposed and studied analogues for number fields of constructions due to weil for curves over finite fields cf 11 in particular he conjectured an analogue for weil s theorem relating the zeta function of a non singular curve over a finite field with the characteristic polynomial of its frobenius automorphism one strong piece of evidence for this came from the classical theorem of stickelberger however iwasawa s original conjecture was proved for f q in mw without use of stickelberger s theorem for a general totally real number field brumer proposed a generalization of stickelberger s theorem in w2 we proved iwasawa s conjecture for an arbitrary totally real field and here we use this to recover a version of brumer s conjecture we note however that iwasawa s conjecture alone is not sufficient to prove our theorem owing to the phenomenon of trivial zeroes the reason is that in iwasawa theory one habitually interpolates the special values of lfunctions which are imprimitive the key part of this paper is the development of a technique introduced in w2 of adjoining an auxiliary variable to the p adic b functions in a way that permits the study of these primitive lfunctions i am grateful to the referee for correcting some obscure arguments let f be a totally real number field and let k be a cm field which is

on the equivariant tamagawa number conjecture in tame cm extensions let l k be a finite galois cm extension with galois group g the equivariant tamagawa number conjecture etnc for the pair h 0 rm spec l 0 mathbb z g naturally decomposes into p parts where p runs over all rational primes if p is odd these p parts in turn decompose into a plus and a minus part let l k be tame above p we show that a certain ray class group of l defines an element in k 0 mathbb z p g mathbb q p which is determined by a corresponding stickelberger element if and only if the minus part of the etnc at p holds for this we use the lifted root number conjecture for small sets of places which is equivalent to the etnc in the number field case for abelian g we show that the minus part of the etnc at p implies the strong brumer stark conjecture at p we prove the minus part of the etnc at p for almost all primes p

equivariant epsilon constants discriminants and etale cohomology let l k be a finite galois extension of number fields we formulate and study a conjectural equality between an element of the relative algebraic k group k 0 mathbb z mathrm gal l k mathbb r which is constructed from the equivariant artin epsilon constant of l k and a sum of structural invariants associated to l k the precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the tamagawa number conjecture of bloch and kato as formulated by flach and the second named author should be compatible with the functional equation of the associated l function we show that more concretely our conjecture also suggests a completely systematic refinement of the central approach and results of classical galois module theory in particular the evidence for our conjecture that we present here already strongly refines many of the main results of galois module theory

integrality of stickelberger elements and the equivariant tamagawa number conjecture let l k be a nite galois cm extension of number elds with galois group g in an earlier paper the author has de ned a module sku l k over the center of the group ring zg which coincides with the sinnott kurihara ideal if g is abelian and in particular contains many stickelberger elements it was shown that a certain conjecture on the integrality of sku l k implies the minus part of the equivariant tamagawa number conjecture at an odd prime p for an in nite class of non abelian galois cm extensions of number elds which are at most tamely rami ed above p provided that iwasawa s invariant vanishes here we prove a relevant part of this integrality conjecture which enables us to deduce the equivariant tamagawa number conjecture from the vanishing of for the same class of extensions

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

prediction of the vibroacoustic behavior of a submerged shell with non axisymmetric internal substructures by a condensed transfer function method the vibroacoustic behavior of axisymmetric stiffened shells immersed in water has been intensively studied in the past on the contrary little attention has been paid to the modeling of these shells coupled to non axisymmetric internal frames indeed breaking the axisymmetry couples the circumferential orders of the fourier series and considerably increases the computational costs in order to tackle this issue we propose a sub structuring approach called the condensed transfer function ctf method that will allow assembling a model of axisymmetric stiffened shell with models of non axisymmetric internal frames the ctf method is developed in the general case of mechanical subsystems coupled along curves a set of orthonormal functions called condensation functions which depend on the curvilinear abscissa along the coupling line is considered this set is then used as a basis for approximating and decomposing the displacements and the applied forces at the line junctions thanks to the definition and calculation of condensed transfer functions for each uncoupled subsystem and by using the superposition principle for passive linear systems the behavior of the coupled subsystems can be deduced a plane plate is considered as a test case to study the convergence of the method with respect to the type and the number of condensation functions taken into account the ctf method is then applied to couple a submerged non periodically stiffened shell described using the circumferential admittance approach caa with internal substructures described by finite element method fem the influence of non axisymmetric internal substructures can finally be studied and it is shown that it tends to increase the radiation efficiency of the shell and can modify the vibrational and acoustic energy distribution