k theory of log schemes ii log syntomic k theory abstract we prove that suitably truncated topological log syntomic etale homotopy k theory of proper semistable schemes in mixed characteristic surjects onto the kummer log etale p adic k theory of the generic fiber as a corollary we get that the log syntomic etale cohomology is a direct factor of the log syntomic etale cohomology of homotopy k theory sheaves the proofs use p adic hodge theory computations of p adic nearby cycles

a general solution for the free vibration of rectangular plates resting on uniform elastic edge supports abstract in this paper it is shown how the superposition method is employed to obtain accurate solutions for the free vibration frequencies and mode shapes of rectangular plates resting on elastic edge supports the analysis is completely general in that uniform elastic rotational and translational supports of any stiffness magnitudes are considered to act simultaneously along each of the four edges eight stiffness coefficients being required to define the problem it is shown how all of the classical boundary conditions are approached when the coefficients are allowed to take on appropriate limits a limited number of plots of fundamental mode eigenvalues vs stiffness coefficients are presented for square plate problems of special interest to the author s knowledge this represents the first accurate comprehensive treatment of this problem to appear in the literature

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

on a conjecture of vorst let k be an infinite perfect field of positive characteristic such that strong resolution of singularities holds over k we prove that a localization of a d dimensional commutative k algebra r of finite type is kd 1 regular if and only if it is regular this partially affirms a conjecture of vorst

zeta functions of regular arithmetic schemes at s 0 lichtenbaum conjectured in 22 the existence of a weil etale cohomology in order to describe the vanishing order and the special value of the zeta function of an arithmetic scheme x at s 0 in terms of euler poincare characteristics assuming the conjectured finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over spec z in particular we compute uncon ditionally the right weil etale cohomology of number rings and projective spaces over number rings we state a precise version of lichtenbaum s con jecture which expresses the vanishing order resp the special value of the zeta function x s at s 0 as the rank resp the determinant of a single perfect complex of abelian groups r w c x z then we relate this conjecture to soule s conjecture and to the tamagawa number conjecture lichtenbaum s conjecture for projective spaces over the ring of integers of an abelian number field follows

milnor k theory of rings higher chow groups and applications if r is a smooth semi local algebra of geometric type over an infinite field we prove that the milnor k group kmn r surjects onto the higher chow group chn r n for all n 0 our proof shows moreover that there is an algorithmic way to represent any admissible cycle in chn r n modulo equivalence as a linear combination of symbolic elements defined as graphs of units in r as a byproduct we get a new and entirely geometric proof of results of gabber kato and rost related to the gersten resolution for the milnor k sheaf furthermore it is also shown that in the semi local pid case we have under some mild assumptions an isomorphism some applications are also given

the k theory of fields in characteristic p we show that for a field k of characteristic p h i k n is uniquely p divisible for i n we use higher chow groups as our definition of motivic cohomology this implies that the natural map k n m k k n k from milnor k theory to quillen k theory is an isomorphism up to uniquely p divisible groups and that k n m k and k n k are p torsion free as a consequence one can calculate the k theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de rham witt sheaves for example k n x p r 0 for n dimx another consequence is gersten s conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p as the last consequence bloch s cycle complexes localized at p satisfy all beilinson lichtenbaum milne axioms for motivic complexes except possibly the vanishing conjecture

motivic periods and grothendieck arithmetic invariants abstract we construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers for the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective showing that a suitable betti de rham realization of 1 motives is fully faithful we can verify this period conjecture in several cases the divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical grothendieck period conjecture for algebraic cycles on smooth and proper schemes these divisibility properties are treated in an appendix by b kahn extending previous work of bloch and colliot thelene raskind

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

minimum stiffness location of point support for control of fundamental natural frequency of rectangular plate by rayleigh ritz method abstract the rayleigh ritz method is employed to determine the minimum stiffness location of the elastic point support for raising the fundamental natural frequency of a rectangular plate to the second frequency of the unsupported plate which usually is the upper limit of the first frequency for a single support based on the optimal design of the support position the minimum stiffness can be obtained numerically by solving a characteristic eigenvalue sub problem in the rayleigh ritz procedure the boundary characteristic orthogonal polynomials are used for the admissible functions several typical examples of plate structures with the additional point supports are analyzed in detail and the results prove that the proposed method is very effective in the solution to the optimal design of the supports it will be shown that elastic supports can be designed like rigid ones for the purpose of increasing the fundamental natural frequency of a rectangular plate

optimization of support positions to maximize the fundamental frequency of structures in this paper the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure both elastic and rigid supports are taken into account first the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method by means of the shape functions of the finite element method closed form sensitivity formulations are developed straightforwardly then a heuristic approach called evolutionary shift method is presented for optimizing support positions with a fixed grid mesh scheme based on the design sensitivity analysis the support with the highest efficiency is shifted in priority along the elementary edges with the interval step of the elementary size to facilitate the convergence of the process the interpolation technique is employed to evaluate the solution more accurately finally three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method copyright 2004 john wiley sons ltd

rost nilpotence and higher unramified cohomology abstract we develop an approach to proving the rost nilpotence principle involving higher unramified cohomology along with a decomposition of the diagonal technique we use this to prove the principle for certain threefolds over a perfect field

theoremes de dualite pour les corps de fonctions sur des corps locaux superieurs let k be the function field of a smooth projective curve x over a higher dimensional local field k we define tate shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of k coming from a closed point of x we establish duality theorems between tate shafarevich groups for finite groups schemes and for tori

gersten s conjecture for thek theory with torsion coefficients of a discrete valuation ring between quillen k groups induced by the obvious inclusion functors are all zero in 6 quillen proved this conjecture if r is essentially of finite type over a field in the case of discrete valuation rings this conjecture reduces to conjecture let r be a discrete valuation ring with residue field k and field of fractions f then for all q z 0 the transfer map which is defined since every k vector space is of finite projective dimension as an r module k k k r is zero equivalently the map r ec f induced by the ring homomorphism r p f is injective a third equivalent formulation is that the boundary map

optimal support positions for a structure to maximize its fundamental natural frequency abstract a procedure and related theories are developed to find loci of optimal support positions for a structure to maximize its fundamental eigenvalue by increasing the support stiffness the concept of limit eigenvalue which is the upper bound of fundamental eigenvalue achieved by adding supports is introduced a condition is derived on which the fundamental eigenvalue can be reached to its limit eigenvalue a sensitivity formula of eigenvalues with respect to the change of support positions is also derived to set up an optimization problem and to obtain its optimal support positions it is found that the loci of m supports start from the maximum displacement position of the structure s first eigenfunction and end at certain positions on the nodal line of its m 1 th eigenfunction if the fundamental eigenvalue can reach its limit eigenvalue the suggested method is tested to find the loci for a beam and a plate structure

vibration of isotropic and composite plates using computed shape function and its application to elastic support optimization abstract vibration of plates with various boundary and internal support conditions is analyzed based on classical thin plate theory and the rayleigh ritz approach to satisfy the support conditions a new set of admissible functions namely the computed shape functions is applied to each of the two orthogonal in plane directions similar to conventional finite element shape functions parameters associated with each term of the proposed functions represent the actual displacements of the plates thus making the method easily applicable to a wide range of support conditions including continuous or partial edge supports and discrete internal supports the method can also be applied to plates consisting of rectangular segments like an l shape plate which sub domains can be formulated using the computed shape functions and subsequently assembled in the usual finite element manner unlike many other admissible functions proposed in the literature however the computed shape functions presented herein are c1 continuous and involve no complicated mathematical functions they can be easily computed a priori by means of a continuous beam computer program and only the conventional third order beam shape functions are involved in subsequent formulation in all the examples given herein only a few terms of these functions are sufficient to obtain accurate frequencies thus demonstrating its computational effectiveness and accuracy the method is further extended to the study of optimal location and stiffness of discrete elastic supports for maximizing the fundamental frequency of plates unlike rigid point supports with infinite stiffness which optimal locations have been studied by many researchers only discrete supports with a finite stiffness is considered in this paper the optimal location and stiffness of discrete supports are determined for isotropic plates and laminated plates with various stacking sequences which results are presented for the first time in literature

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

murthy s conjecture on 0 cycles we show that the levine weibel chow group of 0 cycles mathrm ch d a of a reduced affine algebra a of dimension d ge 2 over an algebraically closed field is torsion free among several applications it implies an affirmative solution to an old conjecture of murthy in classical k theory

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

rost nilpotence and etale motivic cohomology abstract a smooth projective scheme x over a field k is said to satisfy the rost nilpotence principle if any endomorphism of x in the category of chow motives that vanishes on an extension of the base field k is nilpotent we show that an etale motivic analogue of the rost nilpotence principle holds for all smooth projective schemes over a perfect field this provides a new approach to the question of rost nilpotence and allows us to obtain an elegant proof of rost nilpotence for surfaces as well as for birationally ruled threefolds over a field of characteristic 0

maximizing the natural frequency of a beam with an intermediate elastic support the minimum stiffness of a simple or point support that raises a natural frequency of a beam to its upper limit is investigated for different boundary conditions the approach produces the closed form solution for the minimum stiffness based on the derivative of a natural frequency with respect to the support position it is seen that when an intermediate elastic support is positioned properly the effect is similar to a rigid support the solution process also provides insight into the dynamics of a beam with an intermediate support for more general boundary conditions the resulting solutions can be used to guide the practical design of a support

a branch and bound algorithm for the maximum diversity problem this article begins with a review of previously proposed integer formulations for the maximum diversity problem mdp this problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized we propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the mdp empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium sized instances with 50 elements as well as some large sized instances with 100 elements we compare our method with the best previous linear integer formulation solved with the well known software cplex the comparison favors the proposed procedure

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

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

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

on the flexural vibration of rectangular plates approached by using simple polynomials in the rayleigh ritz method abstract sets of simple polynomials are proposed for use as admissible functions in the rayleigh ritz method for the study of the flexural vibration of rectangular plates the plates may be subject to a number of different complicating factors including the presence of in plane forces concentrated masses point and line spring supports and special orthotropy of the plate material the sets of polynomials are shown to be equivalent to the orthogonally generated polynomials used very successfully in earlier studies but are more easily generated and the subsequent evaluation of the integrals in the resulting eigenvalue problem are more simply performed numerical results are presented for several problems illustrating the applicability of the method and its accuracy

vibration analysis of rectangular plates with general elastic boundary supports abstract in this investigation the rayleigh ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so called residual displacement function at the edges as a result a drastic improvement of the convergence can be expected of the solution expressed as a series expansion in terms of the admissible functions perhaps more importantly this study has developed a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions several numerical examples are given to demonstrate the accuracy and convergence of the current solution

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

an iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives iterated greedy ig algorithms are based on a very simple principle are easy to implement and can show excellent performance in this paper we propose two new ig algorithms for a complex flowshop problem that results from the consideration of sequence dependent setup times on machines a characteristic that is often found in industrial settings the first ig algorithm is a straightforward adaption of the ig principle while the second incorporates a simple descent local search furthermore we consider two different optimization objectives the minimization of the maximum completion time or makespan and the minimization of the total weighted tardiness extensive experiments and statistical analyses demonstrate that despite their simplicity the ig algorithms are new state of the art methods for both objectives

comparison of dualizing complexes we prove that there is a map from bloch s cycle complex to kato s complex of milnor k theory which induces a quasi isomorphism from etale sheafified cycle complex to the gersten complex of logarithmic de rham witt sheaves next we show that the truncation of bloch s cycle complex at 3 is quasi isomorphic to spiess dualizing complex

the location of spring supports from measured vibration data detecting the position of supports within an elastic structure has many applications particularly when these supports are not fixed previous studies have presented methods for the detection of translational support locations in elastic structures based on the minimization of the difference between the measured and computed natural frequencies however these discrete supports were constrained to be at nodes of the finite element model of the elastic structure this required a fine mesh and the numerical computation of the eigenvalue derivative with respect to the support location this paper has the same purpose namely to identify the support locations but the position of the supports is now a continuous parameter when the support is located within an element the shape functions are used to produce the global stiffness matrix the advantage is that the support location now appears explicitly in the formulation of the problem and hence the analytical computation of the eigenvalue derivative is possible furthermore the mesh may be much more coarse requiring fewer degrees of freedom to detect the support locations with reduced computational effort the effect of identifying both the support stiffness and location is also discussed the proposed approach has been illustrated with simulated and experimental examples used in the earlier studies

iterated greedy for the maximum diversity problem abstract the problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best so far metaheuristics for the problem under consideration

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

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

the flexural vibration of rectangular plates with point supports abstract orthogonally generated polynomial functions are used in the lagrangian multiplier method to study the free flexural vibration problem of point supported thin flat rectangular plates the analysis applies to isotropic and specially orthotropic plates having any combination of clamped simply supported or free edges with arbitrarily located point supports and to plates which are continuous over line supports parallel to the plate edges numerical results are presented for a number of specific problems illustrating the accuracy and versatility of the approach and which include natural frequencies and nodal patterns for a point supported plate which is continuous over two perpendicular line supports

iterated tabu search for the maximum diversity problem in this paper we deal with the maximum diversity problem mdp which asks to select a specified number of elements from a given set so that the sum of distances between the selected elements is as large as possible we develop an iterated tabu search its algorithm for solving this problem we also present a steepest ascent algorithm which is well suited in application settings where solutions of satisfactory quality are required to be provided very quickly computational results for problem instances involving up to 5000 elements show that the its algorithm is a very attractive alternative to the existing approaches in particular we demonstrate the outstanding performance of its on the mdp instances taken from the literature for 69 such instances new best solutions were found

free vibration analysis of rectangular plates on elastic intermediate supports a procedure using the finite strip element method in combination with a spring system is proposed to treat the free vibration analysis of plates on elastic intermediate supports results indicate that the spring system can successfully simulate elastic intermediate supports such as point supports line supports local uniformly distributed supports and mixed edge supports from the results it is also evident that support stiffness and support areas have significant influence on the free vibration response of plates on line supports and local uniformly distributed supports

iterated greedy local search methods for unrelated parallel machine scheduling abstract this work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m parallel machines the most general variant of this problem is when the processing time depends on the machine to which each job is assigned to this case is known as the unrelated parallel machine problem similarly to most of the literature this paper deals with the minimization of the maximum completion time of the jobs commonly referred to as makespan c max many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time extensive computational campaigns show that these solutions are most of the time better than the current state of the art methodologies by a statistically significant margin

the minimum support stiffness required to raise the fundamental natural frequency of plate structures the minimum stiffness and optimum position of a flexible point support is calculated that raises the fundamental natural frequency of plate structures for a single support the maximum fundamental natural frequency of the supported structure is equal to the second natural frequency of the unsupported structure the structure is modelled using finite element analysis allowing a wide range of applications and boundary conditions if a support is positioned within a finite element then the shape functions are used to calculate the contribution of the support to the system stiffness and also the slope of the mode at the support efficient methods are used to calculate the minimum support stiffness required numerical results demonstrate that a system with flexible supports may be designed with the same fundamental natural frequency as that of a system with rigid supports examples of plate structures with one or two point supports are analysed and show that the method is efficient in these cases

the application of a new finite strip to the free vibration of rectangular plates of varying complexity abstract a new finite strip method is applied to the vibration of rectangular plates with complicated boundary and internal support conditions based on the classical thin plate theory and displacement formulation the new finite strip element is conforming with formula continuity the displacement function of the strip element is expressed as the product of cubic hermitian functions in the transverse direction and a set of computed static modes in the longitudinal direction by means of a continuous beam computer program these longitudinal modes can be computeda priori numerical examples are given to demonstrate the versatility accuracy and efficiency of the element