morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

collisions and phase vortex interactions in dissipative ginzburg landau dynamics in this paper we describe a natural framework for the vortex dynamics in the parabolic complex ginzburg landau equation in r this general setting does not rely on any assumption of well preparedness and has the advantage to be valid even after collision times we analyze carefully collisions leading to annihilation a new phenomenon is identified the phase vortex interaction related to persistence of low frequency oscillations and leading to an unexpected drift in the motion of vortices

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

there are genus one curves of every index over every infinite finitely generated field every nontrivial abelian variety over a hilbertian field in which the weak mordellweil theorem holds admits infinitely many torsors with period any n 1 which is not divisible by the characteristic the corresponding statement with period replaced by index is plausible but much more challenging we show that for every infinite finitely generated field k there is an elliptic curve e k which admits infinitely many torsors with index any n 1

the iwasawa main conjecture for semistable abelian varieties over function fields we prove the iwasawa main conjecture over the arithmetic mathbb z p extension for semistable abelian varieties over function fields of characteristic p 0

boundary element analysis for the helmholtz eigenvalue problems with a multiply connected domain for a helmholtz eigenvalue problem with a multiply connected domain the boundary integral equation approach as well as the boundary element method is shown to yield spurious eigenvalues even if the complex valued kernel is used in such a case it is found that spurious eigenvalues depend on the geometry of the inner boundary demonstrated as an analytical case the spurious eigenvalue for a multiply connected problem with its inner boundary as a circle is studied analytically by using the degenerate kernels and circulants an annular case can be studied analytically in a discrete system and can be treated as a special case the proof for the general boundary instead of the circular boundary is also derived the burton miller method is employed to eliminate spurious eigenvalues in the multiply connected case moreover a modified method considering only the real part formulation is provided five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary good agreement between analytical prediction and numerical results are found

motivic cohomology over dedekind rings we study properties of bloch s higher chow groups on smooth varieties over dedekind rings we prove the vanishing of open image in new window for i n and the existence of a gersten resolution for open image in new window if the residue characteristic is p we also show that the bloch kato conjecture implies the beilinson lichtenbaum conjecture open image in new window an identification open image in new window for m invertible and a gersten resolution with arbitrary finite coefficients over a complete discrete valuation ring of mixed characteristic 0 p we construct a map from motivic cohomology to syntomic cohomology which is a quasi isomorphism provided the bloch kato conjecture holds

hasse principles for higher dimensional fields for rather general excellent schemes x k kato deflned complexes of gerstenbloch ogus type involving the galois cohomology groups of all residue flelds of x for arithmetically interesting schemes i e schemes over global or local flelds or over their rings of integers he developed a web of conjectures on some of these complexes generalizing the fundamental exact sequence of brauer groups for a global fleld he proved these conjectures for low dimensions we prove kato s conjecture with inflnite coe cients over number flelds in particular it gives a hasse principle for function flelds f over a number fleld k involving the corresponding function flelds fv over the completions kv of k we get a conditional result over global flelds k of positive characteristic assuming resolution of singularities this is unconditional for dim x 3 due to recent results on resolution there are also applications to other cases considered by kato

on some invariants of fields of characteristic p 0 abstract let k be a field of characteristic p 0 k n the k vector space of n differential forms and k n k n d k n 1 the artin schreier operator given by x d x 1 x 1 d x n x n x p x d x 1 x 1 d x n x n let h p n 1 k coker and define p k min m h p m 1 k 0 we show that for any finite extension l k p k p l p k 1

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

hida families and rational points on elliptic curves let e be an elliptic curve over q of conductor n mp having a prime p n of multiplicative reduction because e is modular it corresponds to a normalised weight two eigenform on 0 n whose q expansion is denoted f n anq letx hom z p z p z p 1 z zp which contains z as a dense subset by associating to k z the character x xk 2 denote by a u the ring of cp valued p adic analytic functions on a compact open subset u of x hida s theory associates to f a neighborhood u of 2 x which can be assumed for simplicity to be contained in the residue class of 2 modulo p 1 and a formal q expansion

nonequilibrium phenomena outlines and bibliographies of a workshop the following is a set of outlines and bibliographies for lectures presented at a summer workshop on nonequilibrium phenomena held from june 22 to july 3 1981 at the institute for theoretical physics in santa barbara these outlines were distributed to the participants in lieu of formal proceedings and they are being presented for publication in the same form in the belief that the information they contain will be useful to a wider audience it should be clearly stated however that the compilation is an informal one which does not claim to be a complete survey of the subject

root numbers and ranks in positive characteristic abstract for a global field k and an elliptic curve e over k t silverman s specialization theorem implies rank e k t rank e t k for all but finitely many t p 1 k if this inequality is strict for all but finitely many t the elliptic curve e is said to have elevated rank all known examples of elevated rank for k q rest on the parity conjecture for elliptic curves over q and the examples are all isotrivial some additional standard conjectures over q imply that there does not exist a non isotrivial elliptic curve over q t with elevated rank in positive characteristic an analogue of one of these additional conjectures is false inspired by this for the rational function field k u over any finite field with characteristic 2 we construct an explicit 2 parameter family e c d of non isotrivial elliptic curves over k t depending on arbitrary c d such that under the parity conjecture each e c d has elevated rank

analogue p adique du theoreme de turrittin et le theoreme de la monodromie p adique 1 rappel de quelques resultats sur la structure p adique d un point singulier d une equation differentielle 322 2 cas d une pente entiere 327 3 cas d une pente fractionnaire premiere a p 333 4 cas d un rang premier a p 335 5 cas general 339 6 l exemple mx 1 3 343 7 la theorie des modules et l implication dr pst 346

a generalized mazur s theorem and its applications we generalize a theorem of mazur concerning the universal norms of an abelian variety over a d p extension of a complete local field then we apply it to the proof of a control theorem for abelian varieties over global function fields

analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real part dual bem it has been found recently that the multiple reciprocity method mrm chen and wong engng anal boundary elements 1997 20 1 25 33 chen processings of the fourth world congress on computational mechanics onate e idelsohn sr eds argentina 1998 106 chen and wong j sound vibration 1998 217 1 75 95 or real part bem liou chen and chen j chinese inst civil hydraulics 1999 11 2 299 310 in chinese results in spurious eigenvalues for eigenproblems if only the singular ut or hypersingular lm integral equation is used in this paper a circular cavity is considered as a demonstrative example for an analytical study based on the framework of the real part dual bem the true and spurious eigenvalues can be separated by using singular value decomposition svd to understand why spurious eigenvalues occur analytical derivation by discretizing the circular boundary into a finite degree of freedom system is employed resulting in circulants for influence matrices based on the properties of the circulants we find that the singular integral equation of the real part bem for a circular domain results in spurious eigenvalues which are the zeros of the bessel functions of the second kind y k while the hypersingular integral equation of the real part bem results in spurious eigenvalues which are the zeros of the derivative of the bessel functions of the second kind yn k it is found that spurious eigenvalues exist in the real part bem and that they depend on the integral representation one uses singular or hypersingular single layer or double layer no matter what the given types of boundary conditions for the interior problem are furthermore spurious modes are proved to be trivial in the circular cavity through analytical derivations numerically they appear to have the same nodal lines of the true modes after normalization with respect to a very small nonzero value two examples with a circular domain including the neumann and dirichlet problems are presented the numerical results for true and spurious eigensolutions match very well with the theoretical prediction copyright 2000 john wiley sons ltd

solutions for nonlinear convection in the presence of a lateral boundary abstract a method is described for calculating steady state patterns in large scale nonlinear systems taking into account the effect of a lateral boundary and without the need for extensive numerical calculations the key feature is the determination of the phase shift of the nonlinear periodic form distant from the boundary as a function of wavelength this is found by analyzing the solution close to the boundary where floquet theory is used to describe the departure of the solution from its periodic form for a restricted band of wavelengths lying within the eckhaus boundary dual solutions for the phase shift are found one of which corresponds to an unstable state results are presented here for the one dimensional swift hohenberg equation in a semi infinite domain but in principle the method can be applied to more general pattern forming systems the results are compared with the predictions of weakly nonlinear theory and with nonlinear computations on a large but finite domain

proof of an exceptional zero conjecture for elliptic curves over function fields based on the analogy between number fields and function fields of one variable over finite fields we formulate and prove an analogue of the exceptional zero conjecture of mazur tate and teitelbaum for elliptic curves defined over function fields the proof uses modular parametrization by drinfeld modular curves and the theory of non archimedean integration as an application we prove a refinement of the birch swinnerton dyer conjecture if the analytic rank of the elliptic curve is zero

spurious and true eigensolutions of helmholtz bies and bems for a multiply connected problem the spurious eigenvalues of an annular domain have been verified for the singular and hypersingular boundary element methods bems and circumvented by using the burton miller approach do they also occur in other formulations continuous formulations such as the singular and hypersingular boundary integral equations bies the null field bies and the fictitious bies or such discrete formulations as the null field bems and the fictitious bems for the ten formulations of the multiply connected problem the study of otherwise the same issues is continued in the present paper by using the degenerate kernels and the fourier series it is demonstrated analytically for the six continuous formulations of bies that spurious eigensolutions depend on the geometry of the inner boundary but not on that of the outer boundary this conclusion can be extended to the six discrete formulations of bems to filter out the spurious eigenvalues the chief combined helmholtz integral equation formulation method is used here instead of the burton miller approach the optimum number and appropriate positions of the chief points are also addressed it is then shown that in the null field and fictitious bems the spurious and true eigenvalues can be detected and distinguished by using the singular value decomposition updating techniques in conjunction with the fredholm alternative theorem illustrative examples show the validity of the proposed methodologies

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

filtrations de type hasse arf et monodromie p adique one proves the crew tsuzuki p adic local monodromy conjecture for local fields of characteristic p 0

cohomology of arithmetic families of γ modules we prove the niteness of the cohomology and the iwasawa cohomology of arithmetic families of modules using this niteness theorem we show that a family of galois representations that is densely pointwise rened in the sense of mazur is actually trianguline as a family over a large subspace in the case of the colemanmazur eigencurve we determine the behavior at all classical points

logarithmic hodge witt sheaves on normal crossing varieties in this paper we define two kinds homological and cohomological of etale logarithmic hodge witt sheaves on normal crossing varieties over a perfect field of positive characteristic and discuss some fundamental properties in particular puity and duality

p adic deformation of algebraic cycle classes we study the p adic deformation properties of algebraic cycle classes modulo rational equivalence we show that the crystalline chern character of a vector bundle on the closed fibre lies in a certain part of the hodge filtration if and only if rationally the class of the vector bundle lifts to a formal pro class in k theory on the p adic scheme

the effect of distant side walls on the evolution and stability of finite amplitude rayleigh benard convection a recent study by cross et al 1980 has described a class of finite amplitude phase winding solutions of the problem of two dimensional rayleigh benard convection in a shallow fluid layer of aspect ratio 2 l 1 confined laterally by rigid side walls these solutions arise at rayleigh numbers r r 0 o l 1 where r 0 is the critical rayleigh number for the corresponding infinite layer nonlinear solutions of constant phase exist for rayleigh numbers r r 0 o l 2 but of these only the two that bifurcate at the lowest value of r are stable to two dimensional linearized disturbances in this range daniels 1978 in the present paper one set of the class of phase winding solutions is found to be stable to two dimensional disturbances for certain values of the prandtl number of the fluid and for stress free horizontal boundaries the results predict that to preserve stability there must be a continual readjustment of the roll pattern as the rayleigh number is raised with a corresponding increase in wavelength proportional to r r 0 these solutions also exhibit hysteresis as the rayleigh number is raised and lowered for other values of the prandtl number the number of rolls remains unchanged as the rayleigh number is raised and the wavelength remains close to its critical value it is proposed that the complete evolution of the flow pattern from a static state must take place on a number of different time scales of which t o r r 0 1 and t o r r 0 2 are the most significant when t o r r 0 1 the amplitude of convection rises from zero to its steady state value but the final lateral positioning of the rolls is only completed on the much longer time scale t o r r 0 2

a p adic local monodromy theorem we produce a canonical filtration for locally free sheaves on an open p adic annulus equipped with a frobenius structure using this filtration we deduce a conjecture of crew on p adic differential equations analogous to grothendieck s local monodromy theorem also a consequence of results of andre and of mebkhout namely given a finite locally free sheaf on an open p adic annulus with a connection and a compatible frobenius structure the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix

the iwasawa main conjectures for gl2 we prove the one two and three variable iwasawa greenberg main conjectures for a large class of modular forms that are ordinary with respect to an odd prime p the method of proof involves an analysis of an eisenstein ideal for ordinary hida families for gu 2 2

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

l functions with large analytic rank and abelian varieties with large algebraic rank over function fields the goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of l functions allows one to produce many examples of l functions over function fields vanishing to high order at the center point of their functional equation conjectures of birch and swinnerton dyer bloch and beilinson relate the orders of vanishing of some of these l functions to mordell weil groups and other groups of algebraic cycles for certain abelian varieties of high analytic rank we are also able to prove the conjecture of birch and swinnerton dyer thus establishing the existence of large mordell weil groups in those cases in the rest of this section we state the main results of the paper

isogeometric analysis of large deformation thin shells using rht splines for multiple patch coupling we present an isogeometric thin shell formulation for multi patches based on rational splines over hierarchical t meshes rht splines nitsche s method is employed to efficiently couple the patches the rht splines have the advantages of allowing a computationally feasible local refinement are free from linear dependence possess high order continuity and satisfy the partition of unity and non negativity in addition the c1c1 continuity of the rht splines avoids the rotational degrees of freedom the good performance of the present method is demonstrated by a number of numerical examples

addendum to values of zeta functions of varieties over finite fields the original article it amer j math bf 108 1986 no 2 297 360 expressed the special values of the zeta function of a variety over a finite field in terms of the widehat bbb z cohomology of the variety as the article was being completed september 1983 lichtenbaum conjectured the existence of complexes of sheaves bbb z r extending the sequence bbb z bbb g m 1 ldots the complexes given by bloch s higher chow groups are known to satisfy most of the axioms for bbb z r using lichtenbaum s weil e tale topology we can now give a beautiful restatement of the main theorem of the original article in terms of bbb z cohomology groups

pontryagin duality for iwasawa modules and abelian varieties we prove a functional equation for two projective systems of finite abelian p groups an and bn endowed with an action of z d such that an can be identified with the pontryagin dual of bn for all n let k be a global field let l be a z d extension of k d 1 unramified outside a finite set of places let a be an abelian variety over k we prove an algebraic functional equation for the pontryagin dual of the selmer group of a

numerical implementation of the edem for modified helmholtz bvps on annular domains in a recent paper by the current authors a new methodology called the extended domain eigenfunction method edem was proposed for solving elliptic boundary value problems on annular like domains in this paper we present and investigate one possible numerical algorithm to implement the edem this algorithm is used to solve modified helmholtz bvps on annular like domains two examples of annular like domains are studied the results and performance are compared with those of the well known boundary element method bem the high accuracy of the edem solutions and the superior efficiency of the edem over the bem make edem an excellent alternate candidate to use in the animation industry where speed is a predominant requirement and by the scientific community where accuracy is the paramount objective

extended domain eigenfunction method edem a study of ill posedness and regularization the extended domain eigenfunction method edem proposed for solving elliptic boundary value problems on annular like domains requires an inversion process the procedure thus represents an ill posed problem whose numerical solution involves an ill conditioned system of equations in this paper the ill posed nature of edem is studied and numerical solutions based on regularization schemes are considered it is shown that the edem solution methodology lends itself naturally to a formulation in terms of the well known iterative landweber method and the more general and faster converging semi iterative regularization schemes theoretical details and numerical results of the regularization schemes are presented for the case of the two dimensional laplace operator on annular domains

elliptic curves with large rank over function fields we produce explicit elliptic curves over fp t whose mordell weil groups have arbitrarily large rank our method is to prove the conjecture of birch and swinnerton dyer for these curves or rather the tate conjecture for related elliptic surfaces and then use zeta functions to determine the rank in contrast to earlier examples of shafarevitch and tate our curves are not isotrivial asymptotically these curves have maximal rank for their conductor motivated by this fact we make a conjecture about the growth of ranks of elliptic

on symmetric power l invariants of iwahori level hilbert modular forms we compute the arithmetic cal l invariants of greenberg benois of twists of symmetric powers of p adic galois representations attached to iwahori level hilbert modular forms under some technical conditions our method uses the automorphy of symmetric powers and the study of analytic galois representations on p adic families of automorphic forms over symplectic and unitary groups combining these families with some explicit plethysm in the representation theory of rm gl 2 we construct global galois cohomology classes with coefficients in the symmetric powers and provide formulae for the cal l invariants in terms of logarithmic derivatives of hecke eigenvalues

mathematical analysis and numerical study to free vibrations of annular plates using biem and bem in this paper the spurious eigenequations for annular plate eigenproblems by using biem and bem are studied in the continuous and discrete systems since any two boundary integral equations in the plate formulation 4 equations can be chosen 6 c options can be considered instead of only two approaches single layer and double layer methods or singular and hypersingular equations which are adopted for the eigenproblems of the membrane and acoustic problems the occurring mechanism of the spurious eigenequation for annular plates in the complex valued formulations is studied analytically for the continuous system degenerate kernels for the fundamental solution and the fourier series expansion for the circular boundary density are employed to derive the true and spurious eigenequations analytically for the discrete system the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the true and spurious eigenequations true eigenequation depends on the specified boundary condition while spurious eigenequation is embedded in each formulation it is found that the spurious eigenvalue for the annular plate is the true eigenvalue of the associated interior problem with an inner radius of the annular domain also we provide three methods svd updating technique burton and miller method and chief method to suppress the occurrence of the spurious eigenvalues several examples were demonstrated to check the validity of the formulations copyright 2005 john wiley sons ltd

free vibration analysis of circular plates with multiple circular holes using indirect biems in this paper a semi analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and fourier series all the kernels in the indirect formulation are expanded into degenerate form by uniformly collocating points on the boundary a linear algebraic system can be constructed the direct searching approach is adopted to determine the natural frequency through singular value decomposition svd after determining the unknown fourier coefficients the corresponding mode shape is obtained by using the indirect boundary integral formulations the results of the annular plate as a special case are compared with the analytical solution to verify the validity of the present method for the cases of circular plates with multiple circular holes the results are also compared with those of finite element method fem using abaqus besides the effect of eccentricity of the hole on the natural frequencies is also considered good accuracy high rate of convergence and computational efficiency are the main features of the present method due to the semianalytical procedure r 2007 elsevier ltd all rights reserved

on the brauer group of a surface artin and tate 15 5 1 have shown in 1966 the existence of a canonical skew symmetric pairing on the non p part of br x whose kernel is exactly the set of divisible elements it follows from this fact that if the non p part of br x is finite then its order is a square or twice a square a few years later manin published examples of rational surfaces that is surfaces birational over k to the projective plane with brauer groups equal to z 2z it is only in 1996 that the examples of manin were revisited by urabe who found a mistake in them for rational surfaces the brauer group is relatively easy to understand and urabe 16 remark after 1 17 showed improving on a result of milne 9 that the brauer group of a rational surface has order a square in 17 0 3 urabe then proves in full generality that when p 2 the 2 part of br x modulo its divisible subgroup has order a square thus to complete the proof of theorem 1 it remains to treat the case where p 2 and x k is not rational as we remarked above it was wrongly assumed for about 30 years that br x was not always a square our method of proof provides for any p that the 2 part of br x has order a square via the knowledge of the 2 part

a boundary integral algorithm for the laplace dirichlet neumann mixed eigenvalue problem we present a novel integral equation algorithm for evaluation of zaremba eigenvalues and eigenfunctions that is eigenvalues and eigenfunctions of the laplace operator with mixed dirichlet neumann boundary conditions of course slight modifications of our algorithms are also applicable to the pure dirichlet and neumann eigenproblems expressing the eigenfunctions by means of an ansatz based on the single layer boundary operator the zaremba eigenproblem is transformed into a nonlinear equation for the eigenvalue for smooth domains the singular structure at dirichlet neumann junctions is incorporated as part of our corresponding numerical algorithm which otherwise relies on use of the cosine change of variables trigonometric polynomials and to avoid the gibbs phenomenon that would arise from the solution singularities the fourier continuation method fc the resulting numerical algorithm converges with high order accuracy without recourse to use of meshes finer than those resulting from the cosine transformation for non smooth lipschitz domains in turn an alternative algorithm is presented which achieves high order accuracy on the basis of graded meshes in either case smooth or lipschitz boundary eigenvalues are evaluated by searching for zero minimal singular values of a suitably stabilized discrete version of the single layer operator mentioned above the stabilization technique is used to enable robust non local zero searches the resulting methods which are fast and highly accurate for high and low frequencies alike can solve extremely challenging two dimensional dirichlet neumann and zaremba eigenproblems with high accuracies in short computing times enabling in particular evaluation of thousands of eigenvalues and corresponding eigenfunctions for a given smooth or non smooth geometry with nearly full double precision accuracy

weil etale cohomology over finite fields we calculate the derived functors r for the base change from the weil etale site to the etale site for a variety over a finite field for smooth and proper varieties we apply this to express tate s conjecture and lichtenbaum s conjecture on special values of functions in terms of weil etale cohomology of the motivic complex n

integral motives and special values of zeta functions for each field k we define a category of rationally decomposed mixed motives with z coefficients when k is finite we show that the category is tannakian and we prove formulas relating the behaviour of zeta functions near integers to certain ext groups

lower bounds for the minima of certain symplectic and unitary group lattices we obtain lower bounds for the minimal norms in several families of integral lattices associated to the weil representations of finite symplectic and unitary groups ultimately these bounds come from elkies bounds for a certain family of mordell weil lattices of elliptic curves and from the minima of the barnes wall lattices

a new method for true and spurious eigensolutions of arbitrary cavities using the combined helmholtz exterior integral equation formulation method integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems radiation and scattering it was recently found that the real part boundary element method bem for the interior problem results in spurious eigensolutions if the singular ut or the hypersingular lm equation is used alone the real part bem results in spurious solutions for interior problems in a similar way that the singular integral equation ut method results in fictitious solutions for the exterior problem to solve this problem a combined helmholtz exterior integral equation formulation method cheef is proposed based on the cheef method the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully finally two examples for the eigensolutions of circular and rectangular cavities are considered the optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied also numerical experiments were designed to verify the analytical results it is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry while the nodal line of the rectangular is on a fixed position

etale duality for constructible sheaves on arithmetic schemes in this note we relate the following three topics for arithmetic schemes a general duality for etale constructible torsion sheaves a theory of etale homology and the arithmetic complexes of gersten bloch ogus type defined by k kato kct in brief there is an absolute duality using certain dualizing sheaves on these schemes we describe and characterize the dualizing sheaves to some extent relate them to symbol maps define etale homology via the dualizing sheaves and show that the niveau spectral sequence for the latter constructed by the method of bloch and ogus bo leads to the complexes defined by kato some of these relations may have been expected by experts and some have been used implicitly in the literature although we do not know any explicit reference for statements or proofs moreover the main results are used in a crucial way in a paper by two of us js so a major aim is to fill a gap in the literature and a special emphasis is on precise formulations including the determination of signs but the general picture developed here may be of interest itself

the de rham witt and z p cohomologies of an algebraic variety abstract we prove that for a smooth complete variety x over a perfect field h i x z p r hom d c b r 1 r w x r i where h i x z p r lim n h i r x et n r amer j math 108 2 1986 297 360 w x is the de rham witt complex on x ann scient ec num sup 12 1979b 501 661 and d c b r is the triangulated category of coherent complexes over the raynaud ring inst hautes etuder sci publ math 57 1983 73 212

a generalization of a theorem of imai and its applications to iwasawa theory it is proved that if k is a complete discrete valuation field of mixed characteristic 0 p with residue field satisfying a mild condition then any abelian variety over k with potentially good reduction has finite k k 1 p infty rational torsion subgroup this can be used to remove certain conditions assumed in some theorems in iwasawa theory

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

classicality for small slope overconvergent automorphic forms on some compact pel shimura varieties of type c we study the rigid cohomology of the ordinary locus in some compact pel shimura varieties of type c with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent hecke eigenforms this generalises work of coleman and is a first step in an ongoing project to extend the cohomological approach to classicality to higher dimensional shimura varieties

finite local monodromy of overconvergent unit root f isocrystals on a curve we prove that the category of p adic continuous representations of a fundamental group of a curve over a perfect field of a positive characteristic p with finite local monodromy is equivalent to that of overconvergent unit root f isocrystals on the curve to show the equivalence of categories we study the local theory and apply it to the global case

selmer groups over mathbb z _p d extensions consider an abelian variety a defined over a global field k and let l k be a mathbb z p d extension unramified outside a finite set of places of k with mathrm gal l k gamma let lambda gamma mathbb z p gamma denote the iwasawa algebra in this paper we study how the characteristic ideal of the lambda gamma module x l the dual p primary selmer group varies when l k is replaced by a strict intermediate mathbb z p e extension