torsion in the cohomology of congruence subgroups of sl 4 z and galois representations abstract we report on the computation of torsion in certain homology theories of congruence subgroups of sl 4 z among these are the usual group cohomology the tate farrell cohomology and the homology of the sharbly complex all of these theories yield hecke modules we conjecture that the hecke eigenclasses in these theories have attached galois representations the interpretation of our computations at the torsion primes 2 3 5 is explained we provide evidence for our conjecture in the 15 cases of odd torsion that we found in levels 31

solving homogeneous linear equations over gf 2 via block wiedemann algorithm we propose a method of solving large sparse systems of homogeneous linear equations over g f 2 the field with two elements we modify an algorithm due to wiedemann a block version of the algorithm allows us to perform 32 matrix vector operations for the cost of one the resulting algorithm is competitive with structured gaussian elimination in terms of time and has much lower space requirements it may be useful in the last stage of integer factorization we address here the problem of solving a large sparse system of homogeneous linear equations over gf 2 the field with two elements one important application which motivates the present work arises in integer factorization during the last stage of most integer factorization algorithms we are presented with a large sparse integer matrix and are asked to find linear combinations of the columns of this matrix which vanish modulo 2 for example 7 the matrix may have 100 000 columns with an average of 15 nonzero entries per column for this application we would like to obtain several solutions because a given solution will lead to a nontrivial factorization with probability 112 with n independent solutions our probability of finding a factorization rises to 1 2 structured gaussian elimination can be used 7 but as problems get larger it may become infeasible to store the matrices obtained in the intermediate stages of gaussian elimination the wiedemann algorithm 9 71 has smaller storage requirements one need only store a few vectors and an encoding of a sparse matrix not a dense matrix as occurs in gaussian elimination after fillin and it may have fewer computational steps since one takes advantage of the sparseness of the matrix but its efficiency is hampered by the fact that the algorithm acts on only one bit at a time in the present paper we work with blocks of vectors at a single time by treating 32 vectors at a time on a machine with 32 bit words we can perform 32 matrix vector products at once thus considerably decreasing the cost of indexing this can be viewed as a block wiedemann algorithm the main technical difficulty is in obtaining the correct generalization of the berlekamp massey algorithm to a block version namely a multidimensional version of the extended euclidean algorithm received by the editor november 20 1991 and in revised form july 24 1992 1991 mathematics subject classijication primary 15a33 11y05 11 04 15 04 1994 amencan mathernat cal soc ety 0025 571 8 94 1 oo 25 per page

ldpc codes over the bec bounds and decoding algorithms the performance of maximum likelihood ml decoding on the binary erasure channel for finite length low density parity check ldpc codes from two random ensembles is studied a tightened union type upper bound on the ml decoding error probability based on the precise coefficients of the average weight spectrum is presented for ldpc codes from the gallager ensemble and the richardson urbanke ensemble new upper bounds on the ml decoding performance based on computing the rank of submatrices of the code parity check matrix are derived a new lower bound on the ml decoding threshold followed from the latter error probability bound is obtained an improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well a new low complexity near ml decoding algorithm for quasi cyclic ldpc codes is proposed and simulated its performance is compared to the simulated belief propagation and ml decoding performance and simulated performance of the best known improved iterative decoding techniques as well as with the derived upper bounds on the ml decoding performance and with decoding thresholds obtained by the density evolution technique

refined analysis to the extended tower number field sieve abstract the hardness of discrete logarithm problem over finite fields is the security foundation of many cryptographic protocols when the characteristic of the finite field is medium or large the state of art algorithms for solving the corresponding problem are the number field sieve and its variants in 2016 kim and barbulescu presented the extended tower number field sieve which achieves a new complexity in the medium prime case and imposes a new estimation of the security of concrete parameters in certain cryptosystems such as pairing based cryptosystems in this paper a refined analysis to this algorithm is given as follows firstly a uniform formula is given for the total complexity of the extended tower number field sieve for a given polynomial selection method this formula can directly give the complexity in this case then a method is proposed to improve the computation in the smoothing phase by exploring subfield structures when the extension degree is composite at last the complexity of the descent phase is analyzed when sieving over degree one polynomials and high degree polynomials respectively and it is shown still negligible compared to the improved smoothing phase

cohomology with twisted one dimensional coefficients for congruence subgroups of sl4 z and galois representations abstract we extend the computations in 2 3 4 to find the cohomology in degree five of a congruence subgroup of sl 4 z with coefficients in a field twisted by a nebentype character along with the action of the hecke algebra on the cohomology this is the top cuspidal degree for each hecke eigenclass we find we produce the unique galois representation that appears to be attached to it the computations require serious modifications to our previous algorithms nontrivial coefficients add a layer of complication to our data structures new possibilities must be taken into account in the galois finder the code that finds the galois representations we have improved the galois finder to report when the attached galois representation is uniquely determined by our data

reciprocity laws and galois representations recent breakthroughs suppose f x is a monic irreducible polynomial with integer coefficients if p is a prime number then reducing the coefficients of f x modulo p gives a new polynomial fp x which may be reducible we say that f x is split modulo p if fp x is the product of distinct linear factors example 1 1 1 the polynomial f x x2 1 is split modulo 5 since f5 x x 2 x 3 mod 5 but it is not split modulo 7 since f7 x is irreducible nor is it split modulo 2 since f2 x x 1 2 mod 2 has a repeated factor the first few p for which x2 1 is split modulo p are 5 13 17 29 37 41 53

parafermions and surface exponents of self dual z n spin models from conformal invariance the author studies the critical behaviour of a family of self dual two dimensional spin models with z n symmetry n or 8 in its hamiltonian formulation using the relations between the mass gap amplitudes of the hamiltonian in a finite strip and the critical exponents he estimates the anomalous dimensions of the parafermions occurring in the underlying field theory as well as the surface exponents

galois representations and torsion in the coherent cohomology of hilbert modular varieties let f be a totally real number eld and let p be a prime unramied in f we prove the existence of galois pseudo representations attached to modp m hecke eigenclasses of paritious weight occurring in the coherent cohomology of hilbert modular varieties forf of level prime to p

solving linear equations over gf 2 block lanczos algorithm abstract we propose a method of solving large sparse systems of linear equations over gf 2 the field with two elements we use the lanczos algorithm modified in two ways a lookahead lanczos algorithm is needed for the problem of dividing by an inner product whose value happens to be 0 a block version of the algorithm allows us to perform 32 matrix vector operations for the cost of one the resulting algorithm is competitive with structured gaussian elimination in terms of time and has much lower space requirements it may be useful in the last stage of integer factorization

on torsion in the cohomology of locally symmetric varieties the main result of this paper is the existence of galois representations associated with the mod p or mod p m cohomology of the locally symmetric spaces for gln over a totally real or cm eld proving conjectures of ash and others following an old suggestion of clozel recently realized by harris lan taylor thorne for characteristic 0 cohomology classes one realizes the cohomology of the locally symmetric spaces for gln as a boundary contribution of the cohomology of symplectic or unitary shimura varieties so that the key problem is to understand torsion in the cohomology of shimura varieties thus we prove new results on the p adic geometry of shimura varieties of hodge type namely the shimura varieties become perfectoid when passing to the inverse limit over all levels at p and a new period map towards the ag variety exists on them called the hodge tate period map it is roughly analogous to the embedding of the hermitian symmetric domain which is roughly the inverse limit over all levels of the complex points of the shimura variety into its compact dual the hodge tate period map has several favorable properties the most important being that it commutes with the hecke operators away from p for the trivial action of these hecke operators on the ag variety and that automorphic vector bundles come via pullback from the ag variety

euclid s algorithm and the lanczos method over finite fields this paper shows that there is a close relationship between the euclidean algorithm for polynomials and the lanczos method for solving sparse linear systems especially when working over finite fields it uses this relationship to account rigorously for the appearance of self orthogonal vectors arising in the course of the lanczos algorithm it presents an improved lanczos method which overcomes problems with self orthogonality and compares this improved algorithm with the euclidean algorithm

solving sparse linear equations over finite fields a coordinate recurrence method for solving sparse systems of linear equations over finite fields is described the algorithms discussed all require o n 1 omega n 1 log k n 1 field operations where n 1 is the maximum dimension of the coefficient matrix omega is approximately the number of field operations required to apply the matrix to a test vector and the value of k depends on the algorithm a probabilistic algorithm is shown to exist for finding the determinant of a square matrix also probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error

conformal theory of spin correlations in the semi infinite 3 state potts and self dual zn models in the conformal theory the magnetization operator of the critical 3 state potts or self dual z3 model is degenerate at level 6 solving a sixth order differential equation the authors calculate the bulk 4 spin correlation function and the spin spin correlation function in the half space the spin spin correlation function of the semi infinite self dual zn model is also obtained for arbitrary n both free and fixed spin boundary conditions are considered

two dimensional semi infinite multicritical ising models the order parameter correlation functions of the z2 invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi infinite plane constrained to fixed or free boundary conditions these yield the corresponding universal surface exponents which distinguish the behaviour between even and odd critical models we also make explicit the interplay between duality and boundary conditions

galois representations attached to tensor products of arithmetic cohomology abstract we compute the action of hecke operators on tensor products of cohomology classes of lower congruence subgroups of sl n z in trivial weight we use this computation to prove that if each representation in a collection of galois representations is attached to a cohomology class of a lower congruence subgroup in trivial weight then a sum of certain twists of the representations consistent with the main conjectures of 5 10 is also attached to such a cohomology class

on the equivalence between berlekamp s and euclid s algorithms corresp it is shown that berlekamp s iterative algorithm can be derived from a normalized version of euclid s extended algorithm simple proofs of the results given recently by cheng are also presented

parallel computation of polynomial gcd and some related parallel computations over abstract fields several fundamental problems of computations with polynomials and structured matrices are well known for their resistance to effective parallel solution this includes computing the gcd the 1cm and the resultant of two polynomials as well as any selected entry of either the extended euclidean scheme for these polynomials or the pade approximation table associated to a fixed power series the solution of the berlekamp massey problem of recovering the n coefficients of a linear recurrence sequence from its first 2n terms the solution of a toeplitz linear system of equations computing the ranks and the null spaces of toeplitz matrices and several other computations with toeplitz hankel vandermonde and cauchy generalized hilbert matrices and with matrices having similar structures our algorithms enable us to reach new record estimates for randomized parallel arithmetic complexity of all these computations over any field of constants that is o log n h time and o n2 log log n log n h g arithmetic processors where n is the input size g varies from 1 to 2 and h varies from 2 to 4 depending on the computational problem and on the fixed field of constants the estimates include the cost of correctness tests for the solution the results have further applications to many related computations over abstract fields and rely on some new techniques in particular on recursive pade approximation and regularization of pade approximation via randomization which might be of some independent technical interest in particular an auxiliary algorithm computes over any field the coefficients of a polynomial from the power sums of its zeros which is an important problem of algebraic coding

worst case complexity bounds on algorithms for computing the canonical structure of infinite abelian groups and solving systems of linear diophantine equations an o s 5 m s 2 elementary operations algorithm for computing the canonical structure of infinite abelian groups represented by a matrix of size s is presented also given is an algorithm for solving systems of linear diophantine equations say ax b in o s 3 376 log sm s 2 s 2 m s elementary operations where s is the size of a and s is the size of b the upper bounds mentioned above improve the results given by chou and collins in siam j comput 11 1982 pp 687 708

additive preconditioning and aggregation in matrix computations we combine our novel svd free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations our analysis and experiments show the power of our algorithms guide us in selecting most effective policies of preconditioning and aggregation and provide some new insights into these and related subjects compared to the popular svd based multiplicative preconditioners our additive preconditioners are generated more readily and for a much larger class of matrices furthermore they better preserve matrix structure and sparseness and have a wider range of applications e g they facilitate the solution of a consistent singular linear system of equations and of the eigenproblem

modular representations of gl 3 fp symmetric squares and mod p cohomology of gl 3 z abstract we prove certain cases of nonabelian reciprocity between mod p galois representations and hecke eigenclasses in the mod p cohomology of gl 3 z using the symmetric square liftings from gl 2 and congruences on hecke eigenvalues we need to develop some modular representation theory for gl 3 z p in some cases we also need to invoke certain computer calculations to finish the proof

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

the index calculus method using non smooth polynomials we study a generalized version of the index calculus method for the discrete logarithm problem in f q when q p n p is a small prime and n the database consists of the logarithms of all irreducible polynomials of degree between given bounds the original version of the algorithm uses lower bound equal to one we show theoretically that the algorithm has the same asymptotic running time as the original version the analysis shows that the best upper limit for the interval coincides with the one for the original version the lower limit for the interval remains a free variable of the process we provide experimental results that indicate practical values for that bound we also give heuristic arguments for the running time of the waterloo variant and of the coppersmith method with our generalized database

recognizing badly presented z modules finitely generated z modules have canonical decompositions when such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition this is the algorithm for computing the smith normal form of an integer matrix we discuss algorithms for smith normal form computation and present practical algorithms which give excellent performance for modules arising from badly presented abelian groups we investigate such issues as congruential techniques sparsity considerations pivoting strategies for gauss jordan elimination lattice basis reduction and computational complexity our results which are primarily empirical show dramatically improved performance on previous methods

efficient maximum likelihood decoding of ldpc codes over the binary erasure channel we propose an efficient maximum likelihood ml decoding algorithm for decoding low density parity check ldpc codes over the binary erasure channel bec we also analyze the computational complexity of the proposed algorithm

representation theory and homological stability abstract we introduce the idea of representation stability and several variations for a sequence of representations v n of groups g n a central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability this makes it possible to extend classical theorems of homological stability to a much broader variety of examples representation stability also provides a framework in which to find and to predict patterns from classical representation theory littlewood richardson and murnaghan rules stability of schur functors to cohomology of groups pure braid torelli and congruence groups to lie algebras and their homology to the equivariant cohomology of flag and schubert varieties to combinatorics the n 1 n 1 conjecture the majority of this paper is devoted to exposing this phenomenon through examples in doing this we obtain applications theorems and conjectures beyond the discovery of new phenomena the viewpoint of representation stability can be useful in solving problems outside the theory in addition to the applications given in this paper it is applied by church ellenberg farb in preparation 20 to counting problems in number theory and finite group theory representation stability is also used by church 2012 19 to give broad generalizations and new proofs of classical homological stability theorems for configuration spaces on oriented manifolds

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

hermite normal form computation using modulo determinant arithmetic this paper describes a new class of hermite normal form solution procedures which perform modulo determinant arithmetic throughout the computation this class of procedures is shown to possess a polynomial time complexity bound which is a function of the length of the input string computational results are also given

galois representations with conjectural connections to arithmetic cohomology in this paper we extend a conjecture of a ash and w sinnott relating niveau 1 galois representations to the mod p cohomology of congruence subgroups ofsln z to include galois representations of higher niveau we then present computational evidence for our conjecture in the case n 3 in the form of three dimensional galois representations which appear to correspond to cohomology eigenclasses as predicted by the conjecture our examples include galois representations with nontrivial weight and level as well as irreducible three dimensional representations that are in no obvious way related to lower dimensional representations in addition we prove that certain symmetric square representations are actually attached to cohomology eigenclasses predicted by the conjecture

resolutions of the steinberg module for gl n abstract we give several resolutions of the steinberg representation st n for the general linear group over a principal ideal domain in particular over z we compare them and use these results to prove that the computations in avner ash et al 2011 agm11 are definitive in particular in avner ash et al 2011 agm11 we use two complexes to compute certain cohomology groups of congruence subgroups of sl 4 z one complex is based on voronoi s polyhedral decomposition of the symmetric space for sl n r whereas the other is a larger complex that has an action of the hecke operators we prove that both complexes allow us to compute the relevant cohomology groups and that the use of the voronoi complex does not introduce any spurious hecke eigenclasses

analysis of coppersmith s block wiedemann algorithm for the parallel solution of sparse linear systems by using projections by a block of vectors in place of a single vector it is possible to parallelize the outer loop of iterative methods for solving sparse linear systems we analyze such a scheme proposed by coppersmith for wiedemann s coordinate recurrence algorithm which is based in part on the krylov subspace approach we prove that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors our analysis is valid for fields of entries that have sufficiently large cardinality our analysis also deals with an arising subproblem of solving a singular block toeplitz system by use of the theory of toeplitz like matrices

cohomology of congruence subgroups of sl4 z iii in two previous papers we computed cohomology groups h 5 0 n c for a range of levels n where 0 n is the congruence subgroup of sl 4 consisting of all matrices with bottom row congruent to 0 0 0 mod n in this note we update this earlier work by carrying it out for prime levels up to n 211 this requires new methods in sparse matrix reduction which are the main focus of the paper our computations involve matrices with up to 20 million nonzero entries we also make two conjectures concerning the contributions to h 5 0 n for n prime coming from eisenstein series and siegel modular forms

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

transverse vibrations of a flexible beam sliding through a prismatic joint abstract in this paper the vibrations of an axially moving flexible beam sliding through an arbitrarily driven prismatic joint restricted to move on a horizontal plane are investigated upon considering the assumption of an euler bernoulli beam in addition to the effects of rotary inertia end mass and axial force in association with axial foreshortening the equations of motion and the associated boundary conditions of the dynamic system are derived by using the extended hamilton s principle forming a complex boundary value problem due to difficulties in finding an analytical solution the assumed modes method is utilized to obtain an approximate solution to the problem simulation results are presented for some typical kinematical inputs of the prismatic joint of the model

strata hasse invariants hecke algebras and galois representations we construct group theoretical generalizations of the hasse invariant on strata closures of the stacks mathop g hbox mathtt zip nolimits mu restricting to zip data of hodge type we obtain a group theoretical hasse invariant on every ekedahl oort stratum closure of a general hodge type shimura variety a key tool is the construction of a stack of zip flags mathop g hbox mathtt zipflag nolimits mu fibered in flag varieties over mathop g hbox mathtt zip nolimits mu it provides a simultaneous generalization of the classical case homogeneous complex manifolds studied by griffiths schmid and the flag space for siegel varieties studied by ekedahl van der geer four applications are obtained 1 pseudo representations are attached to the coherent cohomology of hodge type shimura varieties modulo a prime power 2 galois representations are associated to many automorphic representations with non degenerate limit of discrete series archimedean component 3 it is shown that all ekedahl oort strata in the minimal compactification of a hodge type shimura variety are affine thereby proving a conjecture of oort 4 part of serre s letter to tate on mod p modular forms is generalized to general hodge type shimura varieties

homological stability for completed homology we prove that the completed homology groups of mathrm gl n mathbf z in fixed degree stabilize as n goes to infinity we also prove that the action of hecke operators on stable cohomology is trivial in a precisely defined sense

modularity lifting beyond the taylor wiles method we prove new modularity lifting theorems for p adic galois representations in situations where the methods of wiles and taylor wiles do not apply previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology in practice this imposes several restrictions one must be in a shimura variety setting and the automorphic forms must be of regular weight at infinity in this paper we essentially show how to remove these restrictions our most general result is a modularity lifting theorem which on the automorphic side applies to automorphic forms on the group mathrm gl n over a general number field it is contingent on a conjecture which in particular predicts the existence of galois representations associated to torsion classes in the cohomology of the associated locally symmetric space we show that if this conjecture holds then our main theorem implies the following if e is an elliptic curve over an arbitrary number field then e is potentially automorphic and satisfies the sato tate conjecture in addition we also prove some unconditional results for example in the setting of mathrm gl 2 over mathbf q we identify certain minimal global deformation rings with the hecke algebras acting on spaces of p adic katz modular forms of weight 1 such algebras may well contain p torsion moreover we also completely solve the problem for p odd of determining the multiplicity of an irreducible modular representation overline rho in the jacobian j 1 n where n is the minimal level such that overline rho arises in weight two

bulk and surface critical behaviour at the conformal invariant point in the z5 model the author determines the bulk thermal and magnetic exponents at the conformal invariant point in the z5 model with a monte carlo based finite size calculation the results are in good agreement with the predictions of zamolodchikov and fateev 1985 the author also argues that the n 1 surface magnetic exponents xh j in the zn model are given by j n j n j 1 n 1 this prediction is also verified in a monte carlo finite size calculation for the z5 model

a constrained assumed modes method for solution of a new dynamic equation for an axially moving beam flexible beams with prismatic joints have complicated differential equations this complexity is mostly due to axial motion of the beam in the present research a horizontal flexible link sliding through a passive prismatic joint while attached to a rigid link of a robot moving in a vertical direction is considered a body coordinate system is used which aids in obtaining a new and rather simple form of the differential equation without the loss of generality to model the passive prismatic joint the motion differential equation is written in a form of virtual displacement next a solution method is presented for the lateral vibrations of the beam referred to as constrained assumed modes method unlike the traditional assumed modes method in the proposed constrained assumed modes method the assumed mode shapes do not each satisfy the geometrical boundary conditions of the point where passive prismatic joint is located instead by writing additional constraint equations the combination of the assumed modes will satisfy the geometrical boundary conditions at location of the passive prismatic joint two case studies for the effect of axial motion on lateral vibration of the beam are presented approximate analytical results are compared with fem results

dynamic modelling and stability analysis of axially oscillating cantilever beams dynamic stability of an axially oscillating cantilever beam is investigated in this paper equations of motion for the axially oscillating beam are derived and transformed into dimensionless forms the equations include harmonically oscillating parameters which are related to the motion induced stiffness variation stability diagrams of the first and the second order approximate solutions are obtained by using the multiple scale perturbation method the stability diagrams show that there exist significant difference between the first and the second order approximate solutions it is also found that relatively large unstable regions exist around the first bending natural frequency twice the first bending natural frequency and twice the second being natural frequency the validity of the stability diagram is verified by direct numerical integrations of the equations of motion of the system

on the range of non vanishing p torsion cohomology for gln fp abstract the range of non vanishing of h gl n f p f p is not know in general in this paper we construct a cohomology class in h gl n f p f p of very low degree namely 2 p 2 and we prove that it is nonzero if p n

smith theory and hecke operators abstract of the connections between the cohomology of arithmetic groups and representations of galois groups some are known and more are conjectured this paper proves one of these conjectures for certain monomial galois representations let p be a prime we show that the representation of the absolute galois group of q induced from an f p valued ray class character of the cyclotomic field q p is attached to a hecke eigenclass in the mod p cohomology of a torsion free congruence subgroup m of gl p 1 z the method involves constructing an action of the hecke algebra on the fundamental exact sequence of smith theory arising from the action by conjugation of an element of order p in gl p 1 z on m

fast matrix rank algorithms and applications we consider the problem of computing the rank of an m n matrix a over a field we present a randomized algorithm to find a set of r rank a linearly independent columns in o vav p r field operations where vav denotes the number of nonzero entries in a and

on the boundary conditions for axially moving beams axially moving beam typed structures are of technical importance and present in a wide class of engineering problem as the axial speed of a beam may significantly affect the dynamic characteristics of the structure even at a low velocity it is important to accurately predict the dynamic characteristics and stability of such structures in most previous studies the net energy flux through the left end and right end boundaries of the finite beam over two simple supports has been implicitly assumed to be zero by completely ignoring the effects of its left incoming and right outgoing semi infinite beam parts or by applying fixed boundary conditions for its longitudinal vibration which seems to be very non realistic from the physical point of view thus this paper investigates the effects of the continuously incoming and outgoing semi infinite beam parts on the dynamic characteristics and stability of an axially moving beam by using the spectral element method the spectral element model is formulated from the equations of motion derived by using the hamilton s principle extended for the systems of changing mass it is numerically shown that the effects of the continuously incoming and outgoing semi infinite beam parts should be taken into account for further accurate prediction of the dynamic characteristics and stability for such axially moving beams

on a conjecture of ash abstract in this paper we prove a particular case of a conjecture of ash that states the existence of galois representations associated to hecke eigenclasses in cohomology

worst case complexity bounds on algorithms for computing the canonical structure of finite abelian groups and the hermite and smith normal forms of an integer matrix an o s 5 m s 2 algorithm for computing the canonical structure of a finite abelian group represented by an integer matrix of size s this is the smith normal form of the matrix is presented moreover an o s 3 m s 2 algorithm for computing the hermite normal form of an integer matrix of size s is given the upper bounds derived on the computational complexity of the algorithms above improve the upper bounds given by kannan and bachem in siam j comput 8 1979 pp 499 507 and chou and collins in siam j comput 11 1982 pp 687 708

fast evaluation of logarithms in fields of characteristic two a method for determining logarithms in gf 2 n is presented its asymptotic running time is o exp cn 1 3 log 2 3 n for a small constant c while by comparison adleman s scheme runs in time o exp c n 1 2 log 1 2 n the ideas give a dramatic improvement even for moderate sized fields such as gf 2 127 and make barely possible computations in fields of size around 2 400 the method is not applicable to gf q for a large prime q

asymptotically fast triangularization of matrices over rings this paper considers the problems of triangularizing and diagonalizing matrices over rings with particular emphasis on the integral case it begins with a description of fast algorithms for the computation of hermite and smith normal forms of integer matrices then it shows how to apply fast matrix multiplication techniques to the problem of triangularizing a matrix over a ring using elementary column operations these general results lead to an algorithm for triangularizing integer matrices that has a faster running time than the known hermite normal form algorithms the triangular matrix that is computed has small entries like the hermite normal form and will suffice for many applications