critical behavior of the annealed ising model on random regular graphs in 17 the authors have defined an annealed ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2 regular graphs then in 11 we generalized their results to the class of all random regular graphs in this paper we study the critical behavior of this model in particular we determine the critical exponents and prove a non standard limit theorem that the magnetization scaled by n 3 4 converges to a specific random variable with n the number of vertices of random regular graphs

algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

the additivity of traces in triangulated categories abstract we explain a fundamental additivity theorem for euler characteristics and generalized trace maps in triangulated categories the proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation the refinement consists of several new axioms relating products and distinguished triangles the axioms hold in the examples and shed light on generalized homology and cohomology theories

quotients of absolute galois groups which determine the entire galois cohomology for a prime power q pd and a field f containing a root of unity of order q we show that the galois cohomology ring h g f mathbb z q is determined by a quotient g f 3 of the absolute galois group gf related to its descending q central sequence conversely we show that g f 3 is determined by the lower cohomology of gf this is used to give new examples of pro p groups which do not occur as absolute galois groups of fields

artin tate motivic sheaves with finite coefficients over an algebraic variety we propose a construction of a tensor exact category fxm of artin tate motivic sheaves with finite coefficients z m over an algebraic variety x over a field k of characteristic prime to m in terms of etale sheaves of z m modules over x among the objects of fxm in addition to the tate motives z m j there are the cohomological relative motives with compact support mccm y x of varieties y quasi finite over x exact functors of inverse image with respect to morphisms of algebraic varieties and direct image with compact supports with respect to quasi finite morphisms of varieties y x act on the exact categories fxm assuming the existence of triangulated categories of motivic sheaves dm x z m over algebraic varieties x over k and a weak version of the six operations in these categories we identify fxm with the exact subcategory in dm x z m consisting of all the iterated extensions of the tate twists mccm y x j of the motives mccm y x an isomorphism of the z m modules ext between the tate motives z m j in the exact category fxm with the motivic cohomology modules predicted by the beilinson lichtenbaum etale descent conjecture recently proved by voevodsky rost et al holds for smooth varieties x over k if and only if the similar isomorphism holds for artin tate motives over fields containing k when k contains a primitive m root of unity the latter condition is equivalent to a certain koszulity hypothesis as shown in our previous paper positselski mixed artin tate motives with finite coefficients mosc math j 11 2011 317 402

pseudo transient continuation for nonlinear transient elasticity this paper demonstrates how pseudo transient continuation improves the efficiency and robustness of a newton iteration within a non linear transient elasticity simulation pseudo transient continuation improves efficiency by enabling larger time steps than possible with a newton iteration robustness improves because pseudo transient continuation recovers the convergence of newton s method when the initial iterate is not within the region of local convergence we illustrate the benefits of pseudo transient continuation on a non linear transient simulation of a buckling cylinder including a comparison with a line search based newton iteration

the group sk 2 of a biquaternion algebra m rost has proved the existence of an exact sequence relating the group sk1 kernel of the reduced norm for k1 of a biquaternion algebra d whose center is a field f with galois cohomology groups of f in this paper we relate the group sk2 kernel of the reduced norm for k2 of d with galois cohomology of f through an exact sequence

the replica symmetric solution for potts models on d regular graphs we establish an explicit formula for the limiting free energy density log partition function divided by the number of vertices for ferromagnetic potts models on uniformly sparse graph sequences converging locally to the d regular tree for d even covering all temperature regimes this formula coincides with the bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d regular tree the so called replica symmetric solution for uniformly random d regular graphs we further show that the replica symmetric bethe formula is an upper bound for the asymptotic free energy for any model with permissive interactions

the group of k1 zero cycles on the second generalized severi brauer variety of an algebra of index 4 abstract in this manuscript it is shown that the group of k 1 zero cycles on the second generalized severi brauer variety of an algebra a of index 4 is given by elements of the group k 1 a together with a square root of their reduced norm utilizing results of krashen concerning exceptional isomorphisms we translate our problem to the computation of cycles on involution varieties work of chernousov and merkurjev then gives a means of describing such cycles in terms of clifford and spin groups and corresponding r equivalence classes we complete our computation by giving an explicit description of these algebraic groups

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

a variety associated to an algebra with involution abstract a variety iv a is canonically associated to a central simple algebra a with orthogonal involution of the first kind the properties of this variety are the main topic of this paper the paper is divided into two parts we first define this variety to be the subvariety of the grassmannian of the n dimensional subspaces of the n2 dimensional vector space a consisting of all the n dimensional right ideals i of a such that i i 0 the geometric properties of iv a are investigated in particular the generic property of this variety is identified further the kernel of the scalar extension map br f br k where k is the function field of iv a is also computed lastly a criterion on the embeddability of the field k into the function field of the brauer severi variety of a is given in the second part the quillen k theory of iv a is computed the k theory result then leads to an index reduction formula for the function field k

reconstructing function fields from rational quotients of mod ell galois groups in this paper we develop the main step in the global theory for the mod ell analogue of bogomolov s program in birational anabelian geometry for higher dimensional function fields over algebraically closed fields more precisely we show how to reconstruct a function field k of transcendence degree ge 5 over an algebraically closed field up to inseparable extensions from the mod ell abelian by central galois group of k endowed with the collection of mod ell rational quotients

triple massey products of weight 1 n 1 in galois cohomology abstract fix an arbitrary prime p let f be a field containing a primitive p th root of unity with absolute galois group g f and let h n denote its mod p cohomology group h n g f z p z the triple massey product abbreviated 3mp of weight n k m n 3 is a partially defined multi valued function h n h k h m h n k m 1 in this work we prove that for an odd prime p any defined 3mp of weight 1 k 1 contains zero

the six operations in equivariant motivic homotopy theory abstract we introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks x g where g is a linearly reductive linear algebraic group we extend to this equivariant setting the main foundational results of motivic homotopy theory the unstable purity and gluing theorems of morel voevodsky and the stable ambidexterity theorem of ayoub our proof of the latter is different than ayoub s and is of interest even when g is trivial using these results we construct a formalism of six operations for equivariant motivic spectra and we deduce that any cohomology theory for g schemes that is represented by an absolute motivic spectrum satisfies descent for the cdh topology

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

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

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

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

stable homotopy groups of spheres we discuss the current state of knowledge of stable homotopy groups of spheres we describe a computational method using motivic homotopy theory viewed as a deformation of classical homotopy theory this yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90 as an application we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90 except for dimension 4 the method relies more heavily on machine computations than previous methods and is therefore less prone to error the main mathematical tool is the adams spectral sequence

ising models on power law random graphs we study a ferromagnetic ising model on random graphs with a power law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite degree exponent 2 for which the random graph has a tree like structure for this we closely follow the analysis by dembo and montanari ann appl probab 20 2 565 592 2010 which assumes finite variance degrees 3 adapting it when necessary and also simplifying it when possible our results also apply in cases where the degree distribution does not obey a power law

a point collocation method based on reproducing kernel approximations a reproducing kernel particle method with built in multiresolution features in a very attractive meshfree method for numerical solution of partial differential equations the design and implementation of a galerkin based reproducing kernel particle method however faces several challenges such as the issue of nodal volumes and accurate and efficient implementation of boundary conditions in this paper we present a point collocation method based on reproducing kernel approximations we show that in a point collocation approach the assignment of nodal volumes and implementation of boundary conditions are not critical issues and points can be sprinkled randomly making the point collocation method a true meshless approach the point collocation method based on reproducing kernel approximations however requires the calculation of higher order derivatives that would typically not be required in a galerkin method a correction function and reproducing conditions that enable consistency of the point collocation method are derived the point collocation method is shown to be accurate for several one and two dimensional problems and the convergence rate of the point collocation method is addressed copyright 2000 john wiley sons ltd

a mean field spin glass with short range interactions we formulate and study a spin glass model on the bethe lattice appropriate boundary fields replace the traditional self consistent methods they give our model well defined thermodynamic properties we establish that there is a spin glass transition temperature above which the single site magnetizations vanish and below which the edwards anderson order parameter is strictly positive in a neighborhood below the transition temperature we use bifurcation theory to establish the existence of a nontrivial distribution of single site magnetizations two properties of this distribution are studied the leading perturbative correction to the gaussian scaling form at the transition and the nonperturbative behavior of the tails

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

broken replica symmetry bounds in the mean field spin glass model by using a simple interpolation argument in previous work we have proven the existence of the thermodynamic limit for mean field disordered models including the sherrington kirkpatrick model and the derrida p spin model here we extend this argument in order to compare the limiting free energy with the expression given by the parisi ansatz and including full spontaneous replica symmetry breaking our main result is that the quenched average of the free energy is bounded from below by the value given in the parisi ansatz uniformly in the size of the system moreover the difference between the two expressions is given in the form of a sum rule extending our previous work on the comparison between the true free energy and its replica symmetric sherrington kirkpatrick approximation we give also a variational bound for the infinite volume limit of the ground state energy per site

the group finite element formulation abstract the introduction of trial solutions for groups of variables within a finite element formulation is shown to provide a significant economy with no loss of accuracy for steady solutions of the two dimensional burgers equations with linear rectangular elements the application of the group finite element to the convective term produces a threefold reduction in execution time with a small improvement in accuracy operation count estimates indicate even larger economies in three dimensions or if higher order nonlinearities occur or if higher order shape functions are used applications of the group formulation are described for inviscid and viscous laminar and turbulent separated and unseparated and incompressible and compressible flows

a cohomological classification of vector bundles on smooth affine threefolds we give a cohomological classification of vector bundles of rank 2 on a smooth affine threefold over an algebraically closed field having characteristic unequal to 2 as a consequence we deduce that cancellation holds for rank 2 vector bundles on such varieties the proofs of these results involve three main ingredients first we give a description of the first nonstable a1 homotopy sheaf of the symplectic group second these computations can be used in concert with f morel s a1 homotopy classification of vector bundles on smooth affine schemes and obstruction theoretic techniques stemming from a version of the postnikov tower in a1 homotopy theory to reduce the classification results to cohomology vanishing statements third we prove the required vanishing statements

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

ising critical exponents on random trees and graphs we study the critical behavior of the ferromagnetic ising model on random trees as well as so called locally tree like random graphs we pay special attention to trees and graphs with a power law offspring or degree distribution whose tail behavior is characterized by its power law exponent 2 we show that the critical inverse temperature of the ising model equals the hyperbolic arctangent of the reciprocal of the mean offspring or mean forward degree distribution in particular the critical inverse temperature equals zero when tau in 2 3 where this mean equals infinity

antiferromagnetic potts model on the erdős renyi random graph we study the antiferromagnetic potts model on the poissonian erd s renyi random graph by identifying a suitable interpolation structure and an extended variational principle together with a positive temperature second moment analysis we prove the existence of a phase transition at a positive critical temperature upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution recovered in the framework of derrida ruelle probability cascades and from an entropy positivity argument

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

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

a point collocation method for geometrically nonlinear membranes abstract this paper describes the development of a numerical model for geometrically nonlinear membranes and evaluates its performance for membranes at static equilibrium the scheme has several features not commonly seen in structural finite element analysis the point collocation method group formulation and a staggered mesh in the point collocation finite element method the partial differential equations are solved at each node instead of by integrating over elements the group formulation simplifies the handling of nonlinearities by interpolating the nonlinear products of variables as opposed to seeking the product of independently interpolated variables the domain is discretized with a staggered mesh of linear triangles and associated polygons two sequential gradient recovery operations are performed first the gradients of the linear triangles are calculated and converted to stresses then polygon derivative shape functions derived in this paper are used to determine the internal forces from the stress gradients the resulting system of nonlinear equations is solved with a jacobian free newton krylov solver the code is first verified using the patch test and the method of manufactured solutions then the results are validated using experimental data and benchmark code results in the literature for the hencky problem a circular membrane with a fixed perimeter and uniform inflation pressure the observed rates of convergence for both displacement and radial strain were two for the configurations and grids used in this investigation the scheme was suitable for accurately predicting sub hyperelastic deformations

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

construction of unipotent galois extensions and massey products abstract for all primes p and for all fields we find a sufficient and necessary condition of the existence of a unipotent galois extension of degree p 6 the main goal of this paper is to describe an explicit construction of such a galois extension over fields admitting such a galois extension this construction is surprising in its simplicity and generality the problem of finding such a construction has been left open since 2003 recently a possible solution of this problem gained urgency because of an effort to extend new advances in galois theory and its relations with massey products in galois cohomology

maximum independent sets on random regular graphs we determine the asymptotics of the independence number of the random d regular graph for all d geq d 0 it is highly concentrated with constant order fluctuations around n alpha c log n for explicit constants alpha d and c d our proof rigorously confirms the one step replica symmetry breaking heuristics for this problem and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs

gibbs states and the set of solutions of random constraint satisfaction problems abstract an instance of a random constraint satisfaction problem defines a random subset the set of solutions of a large product space x n the set of assignments we consider two prototypical problem ensembles random k satisfiability and q coloring of random regular graphs and study the uniform measure with support on s as the number of constraints per variable increases this measure first decomposes into an exponential number of pure states clusters and subsequently condensates over the largest such states above the condensation point the mass carried by the n largest states follows a poisson dirichlet process for typical large instances the two transitions are sharp we determine their precise location further we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem the degree of correlation naturally affects the performances of many search sampling algorithms empirical evidence suggests that local monte carlo markov chain strategies are effective up to the clustering phase transition and belief propagation up to the condensation point finally refined message passing techniques such as survey propagation may also beat this threshold message passing algorithms phase transitions random graphs

universality of the mean field for the potts model we consider the potts model with q colors on a sequence of weighted graphs with adjacency matrices a n allowing for both positive and negative weights under a mild regularity condition on a n we show that the mean field prediction for the log partition function is asymptotically correct whenever mathrm tr a n 2 o n in particular our results are applicable for the ising and the potts models on any sequence of graphs with average degree going to infty using this we establish the universality of the limiting log partition function of the ferromagnetic potts model for a sequence of asymptotically regular graphs and that of the ising model for bi regular bipartite graphs in both ferromagnetic and anti ferromagnetic domain we also derive a large deviation principle for the empirical measure of the colors for the potts model on asymptotically regular graphs

zero cycles on homogeneous varieties abstract in this paper we study the group a 0 x of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety x to do this we translate rational equivalence of 0 cycles on a projective variety into r equivalence on symmetric powers of the variety for certain homogeneous varieties we then relate these symmetric powers to moduli spaces of etale subalgebras of central simple algebras which we construct this allows us to show a 0 x 0 for certain classes of homogeneous varieties for groups of each of the classical types extending previous results of swan karpenko of merkurjev and of panin

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 u invariant of function fields of curves over complete discretely valued fields abstract let k be a complete discretely valued field with residue field if char k 0 char 2 and 2 d we prove that there exists an integer n depending on d such that the u invariant of any function field in one variable over k is bounded by n the method of proof is via introducing the notion of uniform boundedness for the p torsion of the brauer group of a field and relating the uniform boundedness of the 2 torsion of the brauer group to the finiteness of the u invariant we prove that the 2 torsion of the brauer group of function fields in one variable over k is uniformly bounded

on the behaviour of brauer p dimensions under finitely generated field extensions abstract the present paper shows that if q p or q 0 where p is the set of prime numbers then there exist characteristic q fields e q k k n of brauer dimension brd e q k k and infinite absolute brauer p dimensions abrd p e q k for all p p not dividing q 2 q this ensures that brd p f q k p q 2 q for every finitely generated transcendental extension f q k e q k we also prove that each sequence a p b p p p satisfying the conditions a 2 b 2 and 0 b p a p equals the sequence abrd p e brd p e p p for a field e of characteristic zero

koszulity of cohomology k π 1 ness quasi formality abstract this paper is a greatly expanded version of 37 section 9 11 a series of definitions and results illustrating the thesis in the title where quasi formality means vanishing of a certain kind of massey multiplications in the cohomology is presented in particular we include a categorical interpretation of the koszulity implies k 1 claim discuss the differences between two versions of massey operations and apply the derived nonhomogeneous koszul duality theory in order to deduce the main theorem in the end we demonstrate a counterexample providing a negative answer to a question of hopkins and wickelgren about formality of the cochain dg algebras of absolute galois groups thus showing that quasi formality cannot be strengthened to formality in the title assertion

counting in two spin models on d regular graphs supported in part by alfred p sloan research fellowship supported in part by department of defense ndseg fellowships

analysis of thin shells by the element free galerkin method a meshless approach to the analysis of arbitrary kirchhoff shells by the element free galerkin efg method is presented the shell theory used is geometrically exact and can be applied to deep shells the method is based on moving least squares approximant the method is meshless which means that the discretization is independent of the geometric subdivision into finite elements the satisfaction of the c1 continuity requirements is easily met by efg since it requires only c1 weights therefore it is not necessary to resort to mindlin reissner theory or to devices such as discrete kirchhoff theory the requirements of consistency are met by the use of a polynomial basis of quadratic or higher order a subdivision similar to finite elements is used to provide a background mesh for numerical integration the essential boundary conditions are enforced by lagrange multipliers membrane locking which is due to different approximation order for transverse and membrane displacements is removed by using larger domains of influence with the quadratic basis and by using quartic polynomial basis which can prevent membrane locking completely it is shown on the obstacle course for shells that the present technique performs well

motivic decomposition of isotropic projective homogeneous varieties we give a decomposition of the chow motive of an isotropic projective homogeneous variety of a semisimple algebraic group in terms of twisted motives of simpler projective homogeneous varieties as an application we prove a generalization of rost s nilpotence theorem

r equivalence in spinor groups the notion of r equivalence in the set x f of f points of an algebraic variety x defined over a field f was introduced by manin in 11 and studied for linear algebraic groups by colliot thelene and sansuc in 3 for an algebraic group g defined over a field f the subgroup rg f of r trivial elements in the group g f of all f points is defined as follows an element g belongs to rg f if there is a rational morphism f al g over f defined at the points 0 and 1 such that f o 1 and f 1 g in other words g can be connected with the identity of the group by the image of a rational curve the subgroup rg f is normal in g f and the factor group g f rg f g f r is called the group of r equivalence classes the group of r equivalence classes is very useful while studying the rationality problem for algebraic groups the problem to determine whether the variety of an algebraic group is rational or stably rational we say that a group g is r trivial if g e r 1 for any field extension e f if the variety of a group g is stably rational over f then g is r trivial thus if one can establish non triviality of the group of r equivalence classes g e r just for one field extension e f the group g is not stably rational over f the group of r equivalence classes for adjoint semisimple classical groups was computed in 15 this computation was used to obtain examples of non rational adjoint algebraic groups consider simply connected algebraic groups of classical types let g gl1 a be the algebraic group of invertible elements of a central simple f algebra a of dimension n2 and let h sl1 a be the subgroup in g of the reduced norm 1 elements the group h is a simply connected group of inner type a 1 v voskresenskiy 29 has shown that the natural homomorphism ax k1 a induces an isomorphism

algebraic morava k theories for any prime q and positive integer t we construct a spectrum k t in the stable homotopy category of schemes over a field k equipped with an embedding k in classical homotopy theory the realization of k t is known as morava k theory the algebraic content lies in the fact that these spectra are defined as the homotopy limit of a tower whose cofibers are appropriate suspensions of the motivic eilenberg maclane spectra which are known to represent motivic cohomology in the stable homotopy category of schemes

gibbs measures over locally tree like graphs and percolative entropy over infinite regular trees consider a statistical physical model on the d regular infinite tree t d described by a set of interactions phi let g n be a sequence of finite graphs with vertex sets v n that locally converge to t d from phi one can construct a sequence of corresponding models on the graphs g n let mu n be the resulting gibbs measures here we assume that mu n converges to some limiting gibbs measure mu on t d in the local weak sense and study the consequences of this convergence for the specific entropies v n 1 h mu n we show that the limit supremum of v n 1 h mu n is bounded above by the percolative entropy h textit perc mu a function of mu itself and that v n 1 h mu n actually converges to h textit perc mu in case phi exhibits strong spatial mixing on t d when it is known to exist the limit of v n 1 h mu n is most commonly shown to be given by the bethe ansatz percolative entropy gives a different formula and we do not know how to connect it to the bethe ansatz directly we discuss a few examples of well known models for which the latter result holds in the high temperature regime

quenched central limit theorems for the ising model on random graphs the main goal of the paper is to prove central limit theorems for the magnetization rescaled by sqrt n for the ising model on random graphs with n vertices both random quenched and averaged quenched measures are considered we work in the uniqueness regime beta beta c or beta 0 and b ne 0 where beta is the inverse temperature beta c is the critical inverse temperature and b is the external magnetic field in the random quenched setting our results apply to general tree like random graphs as introduced by dembo montanari and further studied by dommers and the first and third author and our proof follows that of ellis in mathbb z d for the averaged quenched setting we specialize to two particular random graph models namely the 2 regular configuration model and the configuration model with degrees 1 and 2 in these cases our proofs are based on explicit computations relying on the solution of the one dimensional ising models

the weak limit of ising models on locally tree like graphs we consider the ising model with inverse temperature and without external field on sequences of graphs g n which converge locally to the k regular tree we show that for such graphs the ising measure locally weakly converges to the symmetric mixture of the ising model with boundary conditions and the boundary conditions on the k regular tree with inverse temperature in the case where the graphs g n are expanders we derive a more detailed understanding by showing convergence of the ising measure conditional on positive magnetization sum of spins to the measure on the tree

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

factor models on locally tree like graphs we consider homogeneous factor models on uniformly sparse graph sequences converging locally to a unimodular random tree t and study the existence of the free energy density the limit of the log partition function divided by the number of vertices n as n tends to infinity we provide a new interpolation scheme and use it to prove existence of and to explicitly compute the quantity subject to uniqueness of a relevant gibbs measure for the factor model on t by way of example we compute for the independent set or hard core model at low fugacity for the ferromagnetic ising model at all parameter values and for the ferromagnetic potts model with both weak enough and strong enough interactions even beyond uniqueness regimes our interpolation provides useful explicit bounds on in the regimes in which we establish existence of the limit we show that it coincides with the bethe free energy functional evaluated at a suitable fixed point of the belief propagation bethe recursions on t in the special case that t has a galton watson law this formula coincides with the nonrigorous bethe prediction obtained by statistical physicists using the replica or cavity methods thus our work is a rigorous generalization of these heuristic calculations to the broader class of sparse graph sequences converging locally to trees we also provide a variational characterization for the bethe prediction in this general setting which is of independent interest

r equivalence and special unitary groups abstract a norm homomorphism for the group of r equivalence classes of all simply connected semisimple classical algebraic groups is constructed the group of r equivalence classes for special unitary groups su b is computed it is proved that the variety of su b is rational if ind b 3 and the stable birational type of su b depends only on the brauer class of b and does not depend on the involution

information theoretic thresholds from the cavity method abstract vindicating a sophisticated but non rigorous physics approach called the cavity method we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models we work out several concrete applications of these general results for instance we pinpoint the exact condensation phase transition in the potts antiferromagnet on the random graph thereby improving prior approximate results contucci et al 2013 34 further we prove the conjecture from krzakala et al 2007 55 about the condensation phase transition in the random graph coloring problem for any number q 3 of colors moreover we prove the conjecture on the information theoretic threshold in the disassortative stochastic block model decelle et al 2011 35 additionally our general result implies the conjectured formula for the mutual information in low density generator matrix codes montanari 2005 73

on motivic decompositions arising from the method of bialynicki birula recently v chernousov s gille and a merkurjev have obtained a decomposition of the motive of an isotropic smooth projective homogeneous variety analogous to the bruhat decomposition using the method of a bialynicki birula and a corollary which is essentially due to s del bano i generalize this decomposition to the case of a possibly anisotropic smooth projective variety homogeneous under the action of an isotropic reductive group this answers a question of n karpenko