organizing the arithmetic of elliptic curves abstract suppose that e is an elliptic curve defined over a number field k p is a rational prime and k is the maximal z p power extension of k in previous work b mazur k rubin elliptic curves and class field theory in ta tsien li ed proceedings of the international congress of mathematicians icm 2002 vol ii higher education press beijing 2002 pp 185 195 b mazur k rubin pairings in the arithmetic of elliptic curves in j cremona et al eds modular curves and abelian varieties progress in mathematics vol 224 2004 pp 151 163 we discussed the possibility that much of the arithmetic of e over k i e the mordell weil groups and their p adic height pairings the shafarevich tate groups and their cassels pairings over all finite extensions of k in k can be described efficiently in terms of a single skew hermitian matrix with entries drawn from the iwasawa algebra of k k in this paper using work of nekovar j nekovar selmer complexes preprint available at http www math jussieu fr nekovar pu we show that under not too stringent conditions such an organizing matrix does in fact exist we also work out an assortment of numerical instances in which we can describe the organizing matrix explicitly

iterative space marching method for compressible sub trans and supersonic flows anewiterativefully coupledimplicitspace marching method isproposedforsolving thetwo dimensionalsteady eulerequationsforcompressiblee owsatmach numbers ranging from subsonic to supersonic aspecial treatment of the streamwise pressure gradient component permits us to calculate both supersonic e ow regions where the euler equations are hyperbolic and subsonic regions where the equations reveal elliptic properties to take into account the elliptic effects of subsonic and transonic e ows space marching sweeps are carried out iteratively a new parabolic pressure correction procedure is developed to accelerate the convergence rate this procedure can be applied for subsonic and transonic regimes and is consistent with the characteristic analysis of the euler equations ateach marching station a newton iterativetechniqueisused tosolvethenonlinearsystem ofequations in a fully coupled manner to resolve strong shocks and contact discontinuities as well as smooth e owe elds with high accuracy implicit symmetric second order total variation diminishing and upwind second order richardson schemes are employed to approximate the transverse and streamwise derivatives respectively the method is tested on theproblem ofthee owin a ductwith a circulararcbump fordifferentmach numberregimes numerical calculations show that the method is accurate is robust and can efe ciently be applied for calculating subsonic transonic and supersonic e ows without streamwise separation

modular elliptic curves and fermat s last theorem when andrew john wiles was 10 years old he read eric temple bell s the last problem and was so impressed by it that he decided that he would be the first person to prove fermat s last theorem this theorem states that there are no nonzero integers a b c n with n 2 such that an bn cn the object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular fermat s last theorem follows as a corollary by virtue of previous work by frey serre and ribet

locally monotonic regression the concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of the signal the median filter is a suboptimal smoother under this measure of smoothness since a filter pass does necessarily yield a locally monotonic output even if a locally monotonic output does result there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal locally monotonic regression is a technique for the optimal smoothing of finite length discrete real signals under such a criterion a theoretical framework in which the existence of locally monotonic regression is proved and algorithms for their computation are given regression is considered as an approximation problem in r sub n the criterion of approximation is derived from a semimetric and the approximating set is the collection of signals sharing the property of being locally monotonic

second p descents on elliptic curves let p be a prime and let c be a genus one curve over a number field k representing an element of order dividing p in the shafarevich tate group of its jacobian we describe an algorithm which computes the set of d in the shafarevich tate group such that pd c and obtains explicit models for these d as curves in projective space this leads to a practical algorithm for performing explicit 9 descents on elliptic curves over q

on the modularity of elliptic curves over q wild 3 adic exercises in this paper building on work of wiles wi and of wiles and one of us r t tw we will prove the following two theorems see 2 2 theorem a if e q is an elliptic curve then e is modular theorem b if gal q q gl2 f5 is an irreducible continuous representation with cyclotomic determinant then is modular we will first remind the reader of the content of these results and then briefly outline the method of proof if n is a positive integer then we let 1 n denote the subgroup of sl2 z consisting of matrices that modulo n are of the form 1 0 1

mathematical programming algorithms for regression based nonlinear filtering in r sup n this paper is concerned with regression under a sum of partial order constraints examples include locally monotonic piecewise monotonic runlength constrained and unimodal and oligomodal regression these are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis it is shown that under a least absolute error criterion these problems can be transformed into appropriate finite problems which can then be efficiently solved via dynamic programming techniques although the result does not carry over to least squares regression hybrid programming algorithms can be developed to solve least squares counterparts of certain problems in the class

the fontaine mazur conjecture for gl _2 introduction 641 1 breuil mezard conjecture and the p adic local langlands 644 1 1 the breuil mezard conjecture 644 1 2 review of colmez s functor 647 1 3 hilbert samuel multiplicities 650 1 4 representations and pseudo representations 653 1 5 gl2 qp representations mod p 657 1 6 local patching and multiplicities 661 1 7 from pseudo representations to representations 669 2 modularity via the breuil mezard conjecture 675 2 1 quaternionic forms 675 2 2 global patching and multiplicities 677 2 3 the breuil mezard conjecture 686 addendum to ki 1 687 references 689

weak continuity with structural constraints nonlinear regression and nonlinear regularization are two powerful approaches to segmentation and nonlinear filtering in this correspondence we propose a hybrid approach that effectively combines the best of both worlds and can be efficiently implemented via the viterbi algorithm

diagonal cycles and euler systems ii the birch and swinnerton dyer conjecture for hasse weil artin l functions this article establishes new cases of the birch and swinnerton dyer conjecture in analytic rank 0 for elliptic curves over mathbb q viewed over the fields cut out by certain self dual artin representations of dimension at most 4 when the associated l function vanishes to even order ge 2 at its central point two canonical classes in the corresponding selmer group are constructed and shown to be linearly independent assuming the non vanishing of a garrett hida p adic l function at a point lying outside its range of classical interpolation the key tool for both results is the study of certain p adic families of global galois cohomology classes arising from gross kudla schoen diagonal cycles in a tower of triple products of modular curves

the relation between flux vector splitting and parabolized schemes abstract the relationship between pns and thin layer navier stokes algorithms is used to develop traditional as well as new pns procedures the use of characteristics based flux vector splitting gives rise to a parabolized system that is based on the predominant physics of the flow while pressure gradient based flux vector splitting is shown to give the traditional parabolized scheme of vigneron comparisons with tlns results show the characteristics based pns system gives results that are at least as accurate as the more traditional pressure gradient split pns system the use of a safety factor in the pressure gradient splitting is shown to cause inaccuracies and should be avoided the interpretation of pns procedures as the first sweep of a tlns adi procedure also suggests an obvious global pressure iteration method that is mathematically well posed and hence leads to an efficient rapidly converging global iteration procedure

the local root number of elliptic curves with wild ramification let e be an elliptic curve over a number field f the root number is conjecturally the sign of the functional equation of l function of e f it is defined as the product of local signs over all places of f the purpose of this paper is to describe this local sign by the coefficients of a weierstras equation of e

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

module de congruences pour gl 2 d un corps imaginaire quadratique et theorie d iwasawa d un corps cm biquadratique

newman polynomials with prescribed vanishing and integer sets with distinct subset sums we study the problem of determining the minimal degree d m of a polynomial that has all coefficients in 0 1 and a zero of multiplicity m at 1 we show that a greedy solution is optimal precisely when m 5 mirroring a result of boyd on polynomials with 1 coefficients we then examine polynomials of the form e e xe 1 where e is a set of m positive odd integers with distinct subset sums and we develop algorithms to determine the minimal degree of such a polynomial we determine that d m satisfies inequalities of the form 2m c1m d m 103 96 2m c2 last we consider the related problem of finding a set of m positive integers with distinct subset sums and minimal largest element and show that the conway guy sequence yields the optimal solution for m 9 extending some computations of lunnon

lower upper implicit scheme for high speed inlet analysis on developpe une methode numerique d analyse du champ d ecoulement non visqueux d une entree a grande vitesse par resolution des equations d euler le schema se revele efficace et robuste aussi bien pour les faibles nombres de mach que pour les ecoulements transsoniques

on the statistical optimality of locally monotonic regression locally monotonic regression is a recently proposed technique for the deterministic smoothing of finite length discrete signals under the smoothing criterion of local monotonicity locally monotonic regression falls within a general framework for the processing of signals that may be characterized in three ways regressions are given by projections that are determined by semimetrics the processed signals meet shape constraints that are defined at the local level and the projections are optimal statistical estimates in the maximum likelihood sense the authors explore the relationship between the geometric and deterministic concept of projection onto generally nonconvex sets and the statistical concept of likelihood with the object of characterizing projections under the family of the p semi metrics as maximum likelihood estimates of signals contaminated with noise from a well known family of exponential densities

calculation of supersonic flows with strong viscous inviscid interaction a procedure for the calculation of strong viscous inviscid interactions in two dimension al laminar super sonic flows with and without separation is described the equations solved are the so called parabolized navier stokes equations the streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propagation of information global iteration is utilized to repeatedly update the pressure field from an initial guess until convergence is achieved the numerical scheme employed is a new alternating direction explicit ade procedure which is used as an alternative to the more difficult to program multigrid strategy to accelerate convergence results are presented for flows past two flat plate related bodies he calculation of supersonic flows in which rapid changes in geometry or boundary condition occur often requires techniques other than classical prandtl boundary layer theory or other solution methods suitable for weakly interacting flows the reason for this is that at high reynolds number rapid changes in geometry or boundary condition induce large changes in the properties of the bound ary layer over a very short length scale when this occurs the phenomenon of upstream influence wherein information is propagated in the upstream direction becomes important this type of flow is referred to as a strongly interacting flow methods that treat such flows as initial value problems are not suitable because they are boundary value in nature in the predominant flow direction in this paper a procedure for two dimensional supersonic strongly interacting flows is developed which utilizes the parabolized or reduced navier stokes equations we will employ the former term here for simplicity it will be as sumed that x and y are nearly streamwise and stream normal directions respectively with special treatment of the pressure gradient term dp dx in the streamwise momentum equation one can develop a procedure which is well suited for calculating weakly interacting flows 1 4 in order to calculate strongly interacting flows a means for propagating information in the upstream direction is required this can be satisfied by utilizing a forward difference for the stream wise pressure gradient in subsonic flows where upstream influence is important even if the viscous inviscid interaction is weak a forward difference of px has been shown by rubin5 to allow the calculation of such flows lin and rubin6 later successfully applied forward differencing of px to a supersonic flow with weak interaction in that study forward differencing was utilized throughout the flowfield including the supersonic flow in the present technique for ward differencing of px is applied only in the subsonic por

lulu operators and discrete pulse transform for multidimensional arrays the lulu operators for sequences that is ln un and their compositions are extended to multidimensional arrays in a way which preserves their essential properties e g consistent separation total variation and shape preservation the power of the operators is demonstrated by deriving the discrete pulse transform dpt which is a hierarchical decomposition of the input array into pulses similar to its 1 d counterpart this transform satisfies a basic consistency property

piecewise and local image models for regularized image restoration using cross validation we describe two broad classes of useful and physically meaningful image models that can be used to construct novel smoothing constraints for use in the regularized image restoration problem the two classes termed piecewise image models pims and focal image models lims respectively capture unique image properties that can be adapted to the image and that reflect structurally significant surface characteristics members of the pim and lim classes are easily formed into regularization operators that replace differential type constraints we also develop an adaptive strategy for selecting the best pim or lim for a given problem from among the defined class and we explain the construction of the corresponding regularization operators considerable attention is also given to determining the regularization parameter via a cross validation technique and also to the selection of an optimization strategy for solving the problem several results are provided that illustrate the processes of model selection parameter selection and image restoration the overall approach provides a new viewpoint on the restoration problem through the use of new image models that capture salient image features that are not well represented through traditional approaches

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

some remarks on the two variable main conjecture of iwasawa theory for elliptic curves without complex multiplication we establish several results towards the two variable main conjecture of iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields namely i the existence of an appropriate p adic l function building on works of hida and perrin riou ii the basic structure theory of the dual selmer group following works of coates hachimori venjakob et al and iii the implications of dihedral or anticyclotomic main conjectures with basechange the result of i is deduced from the construction of hida and perrin riou which in particular is seen to give a bounded distribution the result of ii allows us to deduce a corank formula for the p primary part of the tate shafarevich group of an elliptic curve in the z p 2 extension of an imaginary quadratic field finally iii allows us to deduce a criterion for one divisibility of the two variable main conjecture in terms of specializations to cyclotomic characters following a suggestion of greenberg as well as a refinement via basechange c 2011 elsevier inc all rights reserved

locally monotonic diffusion anisotropic diffusion affords an efficient adaptive signal smoothing technique that can be used for signal enhancement signal segmentation and signal scale space creation this paper introduces a novel partial differential equation pde based diffusion method for generating locally monotonic signals unlike previous diffusion techniques that diverge or converge to trivial signals locally monotonic lomo diffusion converges rapidly to well defined lomo signals of the desired degree the property of local monotonicity allows both slow and rapid signal transitions ramp and step edges while excluding outliers due to noise in contrast with other diffusion methods lomo diffusion does not require an additional regularization step to process a noisy signal and uses no ad hoc thresholds or parameters in the paper we develop the lomo diffusion technique and provide several salient properties including stability and a characterization of the root signals the convergence of the algorithm is well behaved nonoscillatory and is independent of the signal length in contrast with the median filter a special case of lomo diffusion is identical to the optimal solution achieved via regression experimental results validate the claim that lomo diffusion can produce denoised lomo signals with low error using less computation than the median order statistic approach

the use of domain decomposition in accelerating the convergence of quasihyperbolic systems this paper proposes an alternate form of the active domain method k nakahashi and e saitoh aiaa j 35 1280 1997 that is applicable to streamwise separated flows named the marching window the algorithm consists of performing pseudo time iterations on a minimal width subdomain composed of a sequence of cross stream planes of nodes the upstream boundary of the subdomain is positioned such that all nodes upstream exhibit a residual smaller than the user specified convergence threshold the advancement of the downstream boundary follows the advancement of the upstream boundary except in zones of significant streamwise ellipticity where a streamwise ellipticity sensor ensures its continuous progress compared to the standard pseudo time marching approach the marching window decreases the work required for convergence by up to 24 times for flows with little streamwise ellipticity and by up to eight times for flows with large streamwise separated regions storage is reduced by up to six times by not allocating memory to the nodes not included in the computational subdomain the marching window satisfies the same convergence criterion as the standard pseudo time stepping methods hence resulting in the same converged solution within the tolerance of the user specified convergence threshold the algorithm is not restricted to a discretization stencil and pseudo time stepping scheme in particular and is used here with the yee roe scheme and block implicit approximate factorization solving the favre averaged navier stokes fans equations closed by the wilcox k turbulence model the eigenstructure of the fans equations is also presented

local block relaxation method for the solution of equations of gasdynamics a new explicit pseudo time integration algorithm termed local block relaxation for the solution of the equations of gasdynamics in block structured domains is proposed the aim of the method is to reduce the computational costs in obtaining the numerical solution of complex flowfields attention is given to the definition of proper interface boundary conditions that ensure stability even if the smoothing of the solution is not synchronized in time among the blocks once stability is guaranteed oversmoothings can be performed in a restricted number of blocks namely those that exhibit a slower rate of convergence the method proposed is closely coupled with a standard multigrid cycle a theoretical analysis of the savings in computational work is presented so that the convergence speed up can be estimated a priori the strategy is shown to be effective in both two dimensional and three dimensional navier stokes simulations the present algorithm can be extended to a broad variety of numerical schemes based on explicit time integrations

parabolized navier stokes algorithm for solving supersonic flows with upstream influences a new parabolized navier stokes pns algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects innovative techniques are used to automatically detect and measure the extent of the embedded regions within the embedded regions the pns equations are globally iterated to duplicate the results that would be obtained with the complete navier stokes ns equations once an embedded region is computed the algorithm returns to the standard space marching pns mode until the next embedded region is encountered this procedure has been successfully incorporated into nasa s upwind pns code and it has been validated by its application to several two dimensional test cases all of these test cases include embedded regions that produce signie cant upstream effects the present numerical results arein excellent agreement with previous ns computations and experimental data in addition these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach

two variable p adic l functions attached to eigenfamilies of positive slope consider a classical cusp eigenform f n 1 a n f q n of weight k 2 for 0 n with a dirichlet character mod n and let l f s n 1 n a n f n s denote the l function of f twisted with an arbitrary dirichlet character for a prime number p 5 consider a family of cusp eigenforms f k of weight k k f k n 1 a n f k q n containing f f k such that the fourier coefficients a n f k are given by certain p adic analytic functions k a n f k the purpose of this paper is to construct a two variable p adic l function attached to coleman s family f k of cusp eigenforms of a fixed positive slope v p p 0 where p p k is an eigenvalue which depends on k of the atkin operator u u p our p adic l function interpolates the special values l f k s at points s k with s 1 2 k 1 we give a construction using the rankin selberg method and the theory of p adic integration on a profinite group y with values in an affinoid k algebra a where k is a fixed finite extension of q p our p adic l functions are p adic mellin transforms of certain a valued measures in their turn such measures come from eisenstein distributions with values in certain banach a modules m m n a of families of overconvergent forms over a

the alternating direction multi zone implicit method within the structured grid approach numerical solution of partial differential equations pde in complex regions requires the decomposition of the domain into several zones implicit solution methods of the discrete equations are preferred because of their superior numerical properties indeed many existing multi zone solution methods use implicit techniques but the zonal boundaries are updated explicitly the zonal boundaries are created between the zones in the process of domain decomposition but otherwise they are regular interior field points if only steady state solutions are sought the explicit calculation of the zonal boundaries usually effects only the convergence rate but not the accuracy of the solution however in time dependent cases this may degrade the time accuracy of the solution in the present work we propose a novel fully implicit method for solving sets of pde using multi zones and structured grids the method combines the zonal approach with the alternating direction implicit adi method and hence the method is referred to as the alternating direction multi zone implicit admzi method the key idea is the generation of different sets of zones for each stage factor of the adi method rather than using the same set of zones for all the stages consequently the adi sweeps are performed between physical boundaries so that zonal boundaries are avoided and the solution is fully implicit the admzi method can be applied to any set of pde that employs an adi or approximate factorization method typical examples include the time dependent compressible or incompressible navier stokes equations several conceptual examples and actual numerical test cases that solve the heat conduction equation confirm the versatility efficiency and accuracy of the admzi method

on l functions of elliptic curves and cyclotomic towers in this paper we shall strengthen a recent theorem of ralph greenberg 1 concerning l functions of elliptic curves and anticyclotomic towers let k be an imaginary quadratic field and m an abelian extension of k possibly of infinite degree we say that the extension m k is anticyclotomic if m is galois over q and if the nontrivial element of gal k q acts on gal m k by inversion now fix a finite set p of rational primes and consider the compositum in an algebraic closure of k of all anticyclotomic extensions of k which are unramified outside p we denote this compositum by l and refer to it as the maximal anticyclotomic extension of k unramified outside p the field l may also be described as the union of all ring class fields of k with conductor divisible only by primes in p class field theory shows that gal l k is isomorphic to the product of a finite group and the group

uniform distribution of heegner points let e be a modular elliptic curve over q of conductor n let k denote an imaginary quadratic field of discriminant d with n d 1 if p is a prime then there exists a unique zp extension k k such that gal k q acts nontrivially on gal k k the field k is called the anticyclotomic zp extension of k let e k denote the mordell weil group of e over k then a fundamental conjecture of mazur maz predicts that the size of e k is controlled by the prime factorization of n in k equivalently mazur s conjecture relates the size of the mordell weil group to the sign in the functional equation of certain l series the conjecture was verified by greenberg rohrlich and rubin in what mazur calls the exceptional case when e has complex multiplication by k more generally they settled the conjecture for certain abelian varieties with complex multiplication for a discussion of this cm case we refer the reader to gre roh and rub our goal in this paper is to treat the generic case which occurs either when e has no cm or when the field of complexmultiplications is distinct from k under certain conditions on e and k mazur s conjecture predicts that the group e k is finitely generated our main result asserts that this is in fact the case at least when p is an ordinary prime for e or when the class number of k is prime to p the main new ingredient we introduce is that of equidistribution following ideas used by ferrero andwashington to study the cyclotomic invariant more precisely we show that theheegner points associated to definite quaternion algebras are uniformly distributed on the components of a certain curve x and that the elements of a certain galois group act independently in a suitable sense this combined with a special value formula due to gross allows us to conclude that the special values of anticyclotomic l functions are almost always nonzero so that the statement about the mordell weil groups follows from the machinery of euler systems as developed by bertolini and darmon bd

the p adic gross zagier formula for elliptic curves at supersingular primes let p be a prime number and let e be an elliptic curve defined over of conductor n let k be an imaginary quadratic field with discriminant prime to pn such that all prime factors of n split in k b perrin riou established the p adic gross zagier formula that relates the first derivative of the p adic l function of e over k to the p adic height of the heegner point for k when e has good ordinary reduction at p in this article we prove the p adic gross zagier formula of e for the cyclotomic p extension at good supersingular prime p our result has an application for the full birch and swinnerton dyer conjecture suppose that the analytic rank of e over is 1 and assume that the iwasawa main conjecture is true for all good primes and the p adic height pairing is not identically equal to zero for all good ordinary primes then our result implies the full birch and swinnerton dyer conjecture up to bad primes in particular if e has complex multiplication and of analytic rank 1 the full birch and swinnerton dyer conjecture is true up to a power of bad primes and 2

nonlinear image estimation using piecewise and local image models we introduce a new approach to image estimation based on a flexible constraint framework that encapsulates meaningful structural image assumptions piecewise image models pims and local image models lims are defined and utilized to estimate noise corrupted images pims and lims are defined by image sets obeying certain piecewise or local image properties such as piecewise linearity or local monotonicity by optimizing local image characteristics imposed by the models image estimates are produced with respect to the characteristic sets defined by the models thus we propose a new general formulation for nonlinear set theoretic image estimation detailed image estimation algorithms and examples are given using two pims piecewise constant pico and piecewise linear pili models and two lims locally monotonic lomo and locally convex concave loco models these models define properties that hold over local image neighborhoods and the corresponding image estimates may be inexpensively computed by iterative optimization algorithms forcing the model constraints to hold at every image coordinate of the solution defines a nonlinear regression problem that is generally nonconvex and combinatorial however approximate solutions may be computed in reasonable time using the novel generalized deterministic annealing gda optimization technique which is particularly well suited for locally constrained problems of this type results are given for corrupted imagery with signal to noise ratio snr as low as 2 db demonstrating high quality image estimation as measured by local feature integrity and improvement in snr

high resolution shock capturing schemes for inviscid and viscous hypersonic flows abstract a class of high resolution implicit total variation diminishing tvd type algorithms suitable for transonic multidimensional euler and navier stokes equations has been extended to hypersonic computations the improved conservative shock capturing schemes are spatially second and third order and are fully implicit they can be first or second order accurate in time and are suitable for either steady or unsteady calculations enhancement of stability and convergence rate for hypersonic flows is discussed with the proper choice of the temporal discretization and implicit linearization these schemes are fairly efficient and accurate for very complex two dimensional hypersonic inviscid and viscous shock interactions this study is complemented by a variety of steady and unsteady viscous and inviscid hypersonic blunt body flow computations due to the inherent stiffness of viscous flow problems numerical experiments indicated that the convergence rate is in general slower for viscous flows than for inviscid steady flows

modularity of certain potentially barsotti tate galois representations where is the reduction of p these results were subject to hypotheses on the local behavior of p at x i e the restriction of p to a decomposition group at x and to irreducibility hypotheses on 1p in this paper we build on the methods of 461 451 and 121 and relax the hypotheses on local behavior in particular we treat certain adic representations which are not semistable at x but potentially semistable we do this using results of 61 generalizing a theorem of ramakrishna 321 see fontaine mazur 22 131 for a slightly different point of view the results in 61 show that certain potentially barsotti tate deformation problems are smooth allowing us to define certain universal deformations for with the necessary galoistheoretic properties to apply wiles method to carry out the proof that these deformations are indeed realized in the cohomology of modular curves i e that the universal deformation rings are hecke algebras we need to identify the corresponding cohomology groups and prove they have the modular theoretic properties needed to apply wiles method as in 151 and 121 the identification is made by matching local behavior of automorphic representations and galois representations via the local langlands correspondence together with fontaine s theory at the prime we work directly with cohomology of modular curves instead of

analysis of complex hypersonic flows with strong viscous inviscid interaction etude de deux methodes utilisees pour ameliorer la prevision de l interaction visqueuse non visqueuse dans les ecoulements hypersoniques

on the hida deformations of fine selmer groups abstract in this paper we study the fine selmer group of p adic galois representations and their deformations we show that for an infinite family of elliptic cuspforms if the invariant of the dual fine selmer group is zero for one member of the family then the same holds for all the other members further the invariants are equal for all but finitely many members in the family

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

on certain zeta functions attached to two hilbert modular forms i the case of hecke characters to make our exposition smooth let us first introduce some notational conventions for an algebraic number field k of finite degree we denote by jk the set of all embeddings of k into c and by ik the free z module generated by the elements of jk we then put rik ik0 r and cik ik0 c if p eapau e ik with a e jk and po e z we put xp fl xa pfor 0 x e k this is meaningful for p e cik if xa are all real and positive throughout the paper we denote by d the complex upper half plane and by f a totally real algebraic number field of degree n now the zeta function to be studied in this paper when suitably specialized has the form

ring theoretic properties of certain hecke algebras the purpose of this article is to provide a key ingredient of w2 by establishing that certain minimal hecke algebras considered there are complete intersections as is recorded in w2 a method going back to mazur m allows one to show that these algebras are gorenstein but for the complete intersection property a new approach is required the methods of this paper are related to those of chapter 3 of w2 the methods of section 3 of this paper are based on a previous approach of one of us a w we would like to thank henri darmon fred diamond and gerd faltings for carefully reading the first version of this article gerd faltings has also suggested a simplification of our argument as well as of the argument of chapter 3 of w2 and we would like to thank him for allowing us to reproduce these in the appendix to this paper r t would like to thank a w for his invitation to collaborate and for sharing his many insights into the questions considered r t would also like to thank princeton university universite de paris 7 and harvard university for their hospitality during this collaboration a w was supported by an nsf grant

on a conjecture of conrad diamond and taylor we prove a conjecture of conrad diamond and taylor on the size of certain deformation rings parametrizing potentially barsotti tate ga lois representations to achieve this we extend results of breuil and m ezard classifying galois lattices in semistable representations in terms of strongly divisible modules to the potentially crystalline case in hodge tate weights 0 1 we then use these strongly divisible modules to compute the desired deformation rings as a corollary we obtain new results on the modularity of potentially barsotti tate representations

notes on anomalies elliptic curves and the bs d conjecture we consider anomaly cancellation for gauge theories where the left handed chiral multiplets are in higher representations in particular if the left handed quarks and leptons transform under the triplet representation of and if the gauge group is compact then up to an overall scaling there is only one possible nontrivial assignment for the hypercharges if n 3 and two if n 9 otherwise there are infinitely many we use the mordell weil theorem mazur s theorem and the cremona elliptic curve database which uses kolyvagin s theorem on the birch swinnerton dyer conjecture to prove these statements

fast digital locally monotonic regression locally monotonic regression is the optimal counterpart of iterated median filtering in a previous paper restrepo and bovik see ibid vol 41 no 9 p 2796 2810 1993 developed an elegant mathematical framework in which they studied locally monotonic regressions in r sup n the drawback is that the complexity of their algorithms is exponential in n we consider digital locally monotonic regressions in which the output symbols are drawn from a finite alphabet and by making a connection to viterbi decoding provide a fast o a sup 2 spl alpha n algorithm that computes any such regression where a is the size of the digital output alphabet a stands for lomo degree and n is the sample size this is linear in n and it renders the technique applicable in practice