desingularization of quasi excellent schemes in characteristic zero grothendieck proved in ega iv that if any integral scheme of finite type over a locally noetherian scheme x admits a desingularization then x is quasi excellent and conjectured that the converse is probably true we prove this conjecture for noetherian schemes of characteristic zero namely starting with the resolution of singularities for algebraic varieties of characteristic zero we prove the resolution of singularities for noetherian quasi excellent q schemes

on the spectrum of finite rooted homogeneous trees abstract in this paper we study the adjacency spectrum of families of finite rooted trees with regular branching properties in particular we show that in the case of constant branching the eigenvalues are realized as the roots of a family of generalized fibonacci polynomials and produce a limiting distribution for the eigenvalues as the tree depth goes to infinity we indicate how these results can be extended to periodic branching patterns and also provide a generalization to higher order simplicial complexes

computing tight upper bounds on the algebraic connectivity of certain graphs a generalized bethe tree is a rooted unweighted tree in which vertices at the same level have the same degree let b be a generalized bethe tree the algebraic connectivity of the generalized bethe tree b a tree obtained from the union of b and a tree t isomorphic to a subtree of b such that the root vertex of t is the root vertex of b a tree obtained from the union of r generalized bethe trees joined at their respective root vertices a graph obtained from the cycle cr by attaching b by its root to each vertex of the cycle and a tree obtained from the path pr by attaching b by its root to each vertex of the path is the smallest eigenvalue of a special type of symmetric tridiagonal matrices in this paper we first derive a procedure to compute a tight upper bound on the smallest eigenvalue of this special type of matrices finally we apply the procedure to obtain a tight upper bound on the algebraic connectivity of the above mentioned graphs

sur une conjecture de kato et kuzumaki concernant les hypersurfaces de fano resume nous montrons que le corps qp et les corps de nombres totalement imaginaires verifient la propriete c 1 conjecturee par kato et kuzumaki en 1986 autrement dit si k est l un de ces corps et f k x0 xn est un polynome homogene de degre d 6 n tout element de k s ecrit comme produit de normes depuis des extensions finies de k dans lesquelles f admet un zero non trivial nous etablissons aussi la conjecture d ax sur les corps pseudo algebriquement clos parfaits pour les corps dont le groupe de galois absolu est un pro p groupe

bi discontinuous time step integration algorithms part 2 second order equations abstract in this paper bi discontinuous time step integration algorithms for linear second order equations are investigated the second order equations are manipulated directly both the initial and final displacement and velocity are only weakly enforced at the beginning and at the end of the time interval as a result there may be discontinuous jumps for both the displacement and velocity at the two ends of the time interval if the displacement is assumed to be a polynomial of degree n 1 within the time interval there are n 4 unknowns in the formulation it is found that the order of accuracy would be at least n 1 for displacement and n for velocity in general it is shown that the relevant algorithmic parameters for the second order equations can be related to the algorithmic parameters presented in part 1 of this paper for the first order equations unconditionally stable higher order accurate time step integration algorithms with controllable numerical dissipation equivalent to the generalized pade approximations with an order of accuracy 2 n 3 can then be constructed systematically the weighting parameters and the corresponding weighting functions are given explicitly it is also shown that the accuracy of the particular solutions is compatible with the accuracy of the homogeneous solutions if the proposed weighting functions are employed

third order complex time step methods for transient analysis abstract using complex time steps and the method for the first order differential equations third order accurate a stable step by step time integration algorithms with controllable numerical dissipation are constructed for transient analysis the results at two sub step locations are evaluated and combined linearly with the corresponding weighting factors to give higher order accurate results at the end of a time step the sub step locations and the weighting factors are complex numbers the amplification factors at infinity are controlled by another algorithmic parameter a fourth order accurate algorithm is obtained when 1 the algorithmic characteristics and the computational procedure for the present third order algorithms are discussed equivalent algorithms and comparisons with other algorithms are given the present algorithms are found to be competitive with the other third and fourth order accurate algorithms

higher order accurate time step integration algorithms by post integration techniques in this paper a framework to construct higher order accurate time step integration algorithms based on the post integration techniques is presented the prescribed initial conditions are naturally incorporated in the formulations and can be strongly or weakly enforced the algorithmic parameters are chosen such that unconditionally a stable higher order accurate time step integration algorithms with controllable numerical dissipation can be constructed for linear problems besides it is shown that the order of accuracy for non linear problems is maintained through the relationship between the present formulation and the runge kutta method the second order differential equations are also considered numerical examples are given to illustrate the validity of the present formulation copyright 2001 john wiley sons ltd

r equivalence in adjoint classical groups over fields of virtual cohomological dimension 2 let f be a field of characteristic not 2 whose virtual cohomological dimension is at most 2 let g be a semisimple group of adjoint type defined over f let rg f denote the normal subgroup of g f consisting of elements r equivalent to identity we show that if g is of classical type not containing a factor of type d n g f rg f 0 if g is a simple classical adjoint group of type d n we show that if f and its multi quadratic extensions satisfy strong approximation property then g f rg f 0 this leads to a new proof of the r triviality of f rational points of adjoint classical groups defined over number fields

the spectra of a graph obtained from copies of a generalized bethe tree abstract we generalize the concept of a bethe tree as follows we say that an unweighted rooted tree is a generalized bethe tree if in each level the vertices have equal degree if b k is a generalized bethe tree of k levels then we characterize completely the eigenvalues of the adjacency matrix and laplacian matrix of a graph b k r obtained from the union of r copies of b k and the cycle c r connecting the r vertex roots moreover we give results on the multiplicity of the eigenvalues on the spectral radii and on the algebraic conectivity

design spaces measures and metrics for evaluating quality of time operators and consequences leading to improved algorithms by design illustration to structural dynamics for the first time for time discretized operators we describe and articulate the importance and notion of design spaces and algorithmic measures that not only can provide new avenues for improved algorithms by design but also can distinguish in general the quality of computational algorithms for time dependent problems the particular emphasis is on structural dynamics applications for the purpose of illustration and demonstration of the basic concepts the underlying concepts can be extended to other disciplines as well for further developments in time discretized operators and or for evaluating existing methods from the established measures for computational algorithms the conclusion that the most effective in the sense of convergence namely the stability and accuracy and complexity namely the algorithmic formulation and algorithmic structure computational algorithm should appear in a certain algorithmic structure of the design space amongst comparable algorithms is drawn with this conclusion and also with the notion of providing new avenues leading to improved algorithms by design as an illustration a novel computational algorithm which departs from the traditional paradigm in the sense of lms methods with which we are mostly familiar with and widely used in commercial software is particularly designed into the perspective design space representation of comparable algorithms and is termed here as the forward displacement non linearly explicit l stable fdel algorithm which is unconditionally consistent and does not require non linear iterations within each time step from the established measures for comparable algorithms simply for illustration purposes the resulting design of the fdel formulation is then compared with the commonly advocated explicit central difference method and the implicit newmark average acceleration method alternately the same conclusion holds true against controllable numerically dissipative algorithms which pertain to the class of linear multi step lms methods for assessing both linear and non linear dynamic cases the conclusions that the proposed new design of the fdel algorithm which is a direct consequence of the present notion of design spaces and measures is the most effective algorithm to date to our knowledge in comparison to the class of second order accurate algorithms pertaining to lms methods for routine and general non linear dynamic situations is finally drawn through rigorous numerical experiments

signless laplacians of finite graphs we survey properties of spectra of signless laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix for regular graphs the whole existing theory of spectra of the adjacency matrix and of the laplacian matrix transfers directly to the signless laplacian and so we consider arbitrary graphs with special emphasis on the non regular case the results which we survey old and new are of two types a results obtained by applying to the signless laplacian the same reasoning as for corresponding results concerning the adjacency matrix b results obtained indirectly via line graphs among other things we present eigenvalue bounds for several graph invariants an interpretation of the coefficients of the characteristic polynomial a theorem on powers of the signless laplacian and some remarks on star complements

unramified class field theory of arithmetical surfaces let k be an algebraic number field 9k its ring of integers and v a non empty open subscheme of spec ck let x be a projective smooth geometrically irreducible scheme over k and x a regular proper flat scheme over v such that x x vk x the purpose of this paper is to give an explicit description of the abelian fundamental groups ab x and 7t b x using some idele class groups attached to x and x by a k theoretical method its outline is as follows in general for a noetherian scheme z and i 0 or 1 we define the group ski z to be the cokernel of

high order hierarchical a and l stable integration methods numerical integration of stiff first order systems of differential equations is considered it is shown how a c continuous polynomial time discretization in conjunction with a weighted residual method can be used to derive methods corresponding to the diagonal and first subdiagonal pade approximants in this manner a stable schemes of order 2k and l stable schemes of order 2k l are obtained at least for k 4 the methods are hierarchical in the sense that a scheme with a given accuracy embraces the equations of all lower order methods that have the same stability type

a generalization of serre s condition mathrm f f with applications to the finiteness of unramified cohomology in this paper we introduce a condition mathrm f m on a field k for a positive integer m that generalizes serre s condition f and which still implies the finiteness of the galois cohomology of finite galois modules annihilated by m and algebraic k tori that split over an extension of degree dividing m as well as certain groups of etale and unramified cohomology various examples of fields satisfying mathrm f m including those that do not satisfy f are given

comparison of some single step methods for the numerical solution of the structural dynamic equation this paper compares the performance of the ss22 and ss23 references 1 and 2 single step algorithms for the numerical solution of the second order structural dynamic equation and a related new algorithm ss32b applied to the equivalent first order system with sine and step forcing functions various aspects of stability relevant to these equations are discussed

class field theory for open curves over p adic fields we introduce the idele class group for quasi projective curves over p adic fields and show that the kernel of the reciprocity map is divisible this extends saito s class field theory for projective curves saito in j number theory 21 44 80 1985

weighting parameters for unconditionally stable higher order accurate time step integration algorithms part 2 second order equations in this paper unconditionally stable higher order accurate time step integration algorithms suitable for linear second order differential equations based on the weighted residual method are presented the second order equations are manipulated directly as in part 1 of this paper instead of specifying the weighting functions the weighting parameters are used to control the algorithm characteristics the algorithms are at least nth order accurate if the numerical solution for displacement is approximated by a polynomial of degree n 1 with n undetermined coefficients by choosing the weighting parameters carefully the order of accuracy can be improved the generalized pade approximations for the second order equations are considered the ultimate spectral radius is an algorithmic parameter by relating the approximate solutions to the equivalent formulations presented in part 1 of this paper the required weighting parameters are found explicitly any set of linearly independent functions can be used to construct the corresponding weighting functions from the weighting parameters the stabilizing weighting functions for the weighted residual method are found explicitly to ensure higher order accuracy in the general solution the accuracy of the particular solution due to excitation is also examined copyright 1999 john wiley sons ltd

a family of single step houbolt time integration algorithms for structural dynamics a new family of implicit single step time integration methods is presented for solving structural dynamics problems the proposed method is unconditionally stable second order accurate and asymptotically annihilating it is spectrally equivalent to houbolt s method but is cast in single step form rather than multi step form thus the new algorithm computationally is more convenient an explicit predictor correcter algorithm is presented based upon the new implicit scheme the explicit algorithm is spectraily equivalent to the central difference method the two new algorithms are merged into an implicit explicit method resulting in an improved algorithm for solving structural dynamics problems composed of soft and stiff domains numerical results are presented demonstrating the improved performance of the new implicit explicit method compared to previously developed implicit explicit schemes for structural dynamics

a time integration algorithm for linear transient analysis based on the reproducing kernel method in this paper a new algorithm based on the reproducing kernel method is presented for linear transient analysis using very large time steps in the conventional time integration methods the required accuracy is always achieved by either decreasing the size of time steps or increasing the order of approximations the proposed method however does not require a restriction on the size of the time step the required approximating functions for integration of governing equations are determined using the concept of reproduction of the solution within each time step a recurrence relationship is obtained through solving the governing equation by the point collocation based reproducing kernel method within the time step in collocation points the values of external excitation can be obtained either through the approximation between the values at the beginning and the end of each time step or assigning the exact values of the external force hence one advantage of this new method is the independency of the sampling rates of external excitation from the size of the time step the proposed method is applied for solving first and second order differential equations and advantages of the method are illustrated through a number of numerical examples

the norsett time integration methodology for finite element transient analysis this paper presents a set of methods for time integration of problems arising from finite element semidiscretizations the purpose is to obtain computationally efficient methods which possess higher order accuracy and controllable dissipation in the spurious high modes the methods are developed and analysed by a general collocation methodology which leads to the class of norsett approximants an algorithmic parameter is used to achieve an effective control over numerical dissipation moreover a simple and efficient implementation scheme is presented at each time step algorithms based on p order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix in this way a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval to demonstrate the performance of the proposed algorithms a wide experimental evaluation is carried out on typical test problems in finite element transient analysis

cycles on curves over global fields of positive characteristic let k be a global field of positive characteristic and let x spec k be a smooth projective curve we study the zero dimensional cycle group v x ker sik 1 x k 1 k and the one dimensional cycle group w x coker k 2 k h 0 zar x k 2 addressing the conjecture that v x is torsion and w x is finitely generated the main idea is to use abhyankar s theorem on resolution of singularities to relate the study of these cycle groups to that of the k groups of a certain smooth projective surface over a finite field

weighting parameters for time step integration algorithms with predetermined coefficients in this paper the effect of using the predetermined coefficients in constructing time step integration algorithms is investigated both first and second order equations are considered the approximate solution is assumed to be in a form of polynomial in the time domain it can be related to the truncated taylor s series expansion of the exact solution therefore some of the coefficients can be predetermined from the known initial conditions if there are m predetermined coefficients and r unknown coefficients in the approximate solution the unknowns can be solved by the weighted residual method the weighting parameter method is used to investigate the resultant algorithm characteristics it is shown that the formulation is consistent with a minimum order of accuracy m r the maximum order of accuracy achievable is m 2r unconditionally stable algorithms exist if m r for first order equations and m 1 r for second order equations hence the dahlquist s theorem is generalized algorithms equivalent to the pade approximations and unconditionally stable algorithms equivalent to the generalized pade approximations are constructed the corresponding weighting parameters and weighting functions for the pade and generalized pade approximations are given explicitly copyright 2000 john wiley sons ltd

how to render second order accurate time stepping algorithms fourth order accurate while retaining the stability and conservation properties abstract for a fairly general class of second order accurate algorithms a sub stepping procedure is described which achieves fourth order accuracy while retaining the stability conservation properties and implementation of the underlying second order method two features render the proposed approach especially attractive from a computational perspective over conventional fourth order methods first the improved fourth order accuracy is attained merely by two additional residual evaluations with no changes in the implementation of the underlying second order method in particular no additional storage or extra computations of high order gradients are required second for hamiltonian systems the stability properties and possible conservation properties of the underlying second order method such as energy momentum and symplectic character are preserved the new technique is applied to a number of standard algorithms for elastodynamics structural and rigid body dynamics in particular when applied to the recently proposed second order accurate energy momentum method this approach results in a fourth order accurate energy linear and angular momentum conserving algorithm for general hamiltonian systems

zero cycles sur les fibrations au dessus d une courbe de genre quelconque resume soit x une variete propre et lisse sur un corps de nombres k des conjectures sur l image du groupe de chow des zero cycles de x dans le produit des memes groupes sur tous les completes de k ont ete proposees par colliot thelene kato et saito nous demontrons ces conjectures pour l espace total de fibrations en varietes rationnellement connexes verifiant l approximation faible au dessus de courbes dont le groupe de tate shafarevich est fini sous une hypothese d abelianite sur les fibres singulieres

a sharp lower bound for the least eigenvalue of the signless laplacian of a non bipartite graph we prove that the minimum value of the least eigenvalue of the signless laplacian of a connected non bipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices

unconditionally stable collocation algorithms for second order initial value problems abstract in this paper unconditionally stable higher order accurate time step integration algorithms suitable for second order initial value problems in collocation form are presented the second order equations are manipulated directly if the approximate solution is expressed as a polynomial of degree n 1 there are n unknowns to be determined after taking into account the two given initial conditions it is well known that by suppressing the residuals of the governing equations at n distinct collocation points only the resultant algorithms are only conditionally stable in this paper linear combinations of the residuals at n 1 distinct collocation points are used to solve for the n unknowns the collocation points and the relative weights between the residuals are derived from the weighted residual method the weighting functions are arbitrary polynomials of degree not exceeding n 1 to control the accuracy and stability properties of the resultant algorithms the reduced integration technique is used to evaluate the integrals in the formulation once the reduced integration rules are decided the equivalent collocation form can be derived it is found that the resultant algorithms cast in the collocation form are easy to implement and can be used to tackle non linear problems directly numerical examples are given to illustrate the validity of the present formulation

solving initial value problems by differential quadrature method part 1 first order equations in this paper the differential quadrature method is used to solve first order initial value problems the initial condition is given at the beginning of a time interval the time derivative at a sampling grid point within the time interval can be expressed as a weighted linear sum of the given initial condition and the function values at the sampling grid points within the time interval the order of accuracy and the stability property of the quadrature solutions depend on the locations of the sampling grid points it is shown that the order of accuracy of the quadrature solutions at the end of a time interval can be improved to 2n 1 or 2n if the n sampling grid points are chosen carefully in fact the approximate solutions are equivalent to the generalized pade approximations the resultant algorithms are therefore unconditionally stable with controllable numerical dissipation the corresponding sampling grid points are found to be given by the roots of the modified shifted legendre polynomials from the numerical examples the accuracy of the quadrature solutions obtained by using the proposed sampling grid points is found to be better than those obtained by the commonly used uniformly spaced or chebyshev gauss lobatto sampling grid points copyright 2001 john wiley sons ltd

voevodsky s motives and weil reciprocity we describe somekawa s k group associated to a finite collection of semiabelian varieties or more general sheaves in terms of the tensor product in voevodsky s category of motives while somekawa s definition is based on weil reciprocity voevodsky s category is based on homotopy invariance we apply this to explicit descriptions of certain algebraic cycles

on the equivalence of the time domain differential quadrature method and the dissipative runge kutta collocation method numerical solutions for initial value problems can be evaluated accurately and efficiently by the differential quadrature method unconditionally stable higher order accurate time step integration algorithms can be constructed systematically from this framework it has been observed that highly accurate numerical results can also be obtained for non linear problems in this paper it is shown that the algorithms are in fact related to the well established implicit runge kutta methods through this relation new implicit runge kutta methods with controllable numerical dissipation are derived among them the non dissipative and asymptotically annihilating algorithms correspond to the gauss methods and the radau iia methods respectively other dissipative algorithms between these two extreme cases are shown to be b stable or algebraically stable as well and the order of accuracy is the same as the corresponding radau iia method through the equivalence it can be inferred that the differential quadrature method also enjoys the same stability and accuracy properties copyright 2001 john wiley sons ltd

high order integration of smooth dynamical systems theory and numerical experiments this paper describes a new class of algorithms for integrating linear second order equations and those containing smooth non linearities the algorithms are based on a combination of ideas from standard newmark integration methods and extrapolation techniques for the algorithm to work the underlying newmark method must be stable second order accurate and produce asymptotic error expansions for response quantities containing only even ordered terms it is proved that setting the newmark parameter equal to 1 2 gives a desirable asymptotic expansion irrespective of the setting for numerical experiments are conducted for one linear and two non linear applications

unconditionally stable higher order accurate collocation time step integration algorithms for first order equations abstract in this paper unconditionally stable higher order accurate time step integration algorithms for linear first order differential equations based on the collocation method are presented the amplification factor at the end of the spectrum is a controllable algorithmic parameter the collocation parameters for unconditionally stable higher order accurate algorithms are found to be given by the roots of a polynomial in terms of the ultimate amplification factor in general when the numerical solution is approximated by a polynomial of degree n this approximation is at least n th order accurate however by using the above collocation parameters the order of accuracy can be improved to 2 n 1 or 2 n the approximate solutions are found to be equivalent to the generalized pade approximations furthermore it is shown that the accuracy of the particular solution due to excitation given by the present method is compatible with the homogeneous solutions no modification of the collocation parameters is required

unconditionally stable time step integration algorithms based on hamilton s principle unconditionally stable time step integration algorithms derived from hamilton s principle are presented the corresponding constrained variations are assumed to be in the form of k k 1 to ensure vanishing variations at the ends of a time interval the initial conditions are strongly enforced in the formulation the order of accuracy can be 2n 1 or 2n where n is the number of unknown variables the ultimate spectral radii of the algorithms can be controlled directly the approximate solutions are in fact equivalent to the generalized pade approximations for linear second order differential equations hence hamilton s principle can be used to construct unconditionally stable higher order accurate time step integration algorithms directly as well provided the appropriate constrained variations are used

complex time step newmark methods with controllable numerical dissipation in this paper unconditionally stable higher order accurate time step integration algorithms with controllable numerical dissipation are presented the algorithms are based on the newmark method with complex time steps the ultimate spectral radius the sub step locations j and the weighting factors j are the algorithmic parameters for an algorithm that is 2n 1 th order accurate the sub step locations which may be complex are shown to be the roots of an nth degree polynomial the polynomial is given explicitly in terms of n and the weighting factors are then obtained by solving a system of n simultaneous equations it is further shown that the order of accuracy is increased by one for the non dissipative algorithms with 1 the stability properties of the present algorithms are studied it is shown that if the ultimate spectral radius is set between 1 and 1 the eigenvalues of the numerical amplification matrix are complex with magnitude less than or equal to unity the algorithms are therefore unconditionally c stable when the ultimate spectral radius is set to 0 or 1 the algorithms are found to be equivalent to the first sub diagonal and diagonal pade approximations respectively the present algorithms are more general as the numerical dissipation is controllable and are very suitable for parallel computers the accuracy of the excitation responses is found to be enhanced by the present complex time step procedure to maintain high order accuracy the excitation may need some modifications 1998 john wiley sons ltd

collocation methods with controllable dissipation for linear dynamics abstract this paper introduces a unified set of collocation methods for linear dynamics in which a parameter is used to control the position of the collocation points in this manner both a stable algorithms of order 2 p and l stable algorithms of order 2 p 1 are derived from collocation polynomials of degree p in addition algorithms with intermediate accuracy and stability properties are made available the effects of varying the algorithmic parameter are investigated with particular reference to the numerical dissipation of spurious high frequency modes numerical tests are reported which support the theoretical analysis and demonstrate the performance of the proposed algorithms

a unified set of single step asymptotic annihilation algorithms for structural dynamics when solving the equations of structural dynamics using direct time integration meth6ds algorithmic damping is useful in controlling spurious high frequency oscillations ideally an algorithm should possess asymptotic annihilation of the highfrequency response i e spurious oscillations in the high frequencies are eliminated after one time step in this paper a new class of asymptotic annihilation algorithms for structural dynamics is presented that possesses little numerical dissipation in the low frequency regime the algorithms are based upon using finite elements in time the displacement and velocity fields are interpolated independently using time discontinuous functions the equations of motion displacement velocity compatibility and the time continuity of displacement and velocity are satisfied weakly asymptotic annihilation is achieved by choosing the displacement and velocity fields to be of equal order algorithms of any desired order of temporal accuracy can be obtained by appropriate choice of the finite element interpolations in time an analysis of the proposed class of algorithms is given proving the asymptotic annihilation property and the spectral equivalence of the algorithms to the upper diagonal of the pad6 approximation table results from finite difference analyses are presented showing the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low frequency regime

time finite element methods for structural dynamics summary time finite element methods are developed for the equations of structural dynamics the approach employs the time discontinuous galerkin method and incorporates stabilizing terms having least squares form these enable a general convergence theorem to be proved in a norm stronger than the energy norm results are presented from finite difference analyses of the time discontinuous galerkin and least squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics these results show that for particular interpolations the time finite element method exhibits improved accuracy and stability

spectra of copies of a generalized bethe tree attached to any graph abstract a generalized bethe tree is a rooted unweighted tree in which vertices at the same level have the same degree let g be any connected graph let g b be the graph obtained from g by attaching a generalized bethe tree b by its root to each vertex of g we characterize completely the eigenvalues of the signless laplacian laplacian and adjacency matrices of the graph g b including results on the eigenvalue multiplicities finally for the laplacian and signless laplacian matrices we recall a procedure to compute a tight upper bound on the algebraic connectivity of g b as well as on the smallest eigenvalue of the signless laplacian matrix of g b whenever g is a non bipartite graph