a vertex formalism for local ruled surfaces we develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a calabi yau threefold our construction is based on large n duality and localization with respect to a degenerate torus action we also discuss potential generalizations of our formalism to a broader class of calabi yau threefolds using the same underlying principles

an obstruction based approach to the kochen specker theorem in isham and butterfield 1998 int j theor phys 37 2669 733 it was shown that the kochen specker theorem can be written in terms of the non existence of global elements of a certain varying set over the category of boolean subalgebras of projection operators on some hilbert space in this paper we show how obstructions to the construction of such global elements arise and how this provides a new way of looking at proofs of the theorem

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a first order system least squares method for the helmholtz equation we present a first order system least squares fosls method for the helmholtz equation at high wave number k which always leads to a hermitian positive definite algebraic system by utilizing a non trivial solution decomposition to the dual fosls problem which is quite different from that of the standard finite element methods we give an error analysis to the h p version of the fosls method where the dependence on the mesh size h the approximation order p and the wave number k is given explicitly in particular under some assumption of the boundary of the domain the l 2 norm error estimate of the scalar solution from the fosls method is shown to be quasi optimal under the condition that k h p is sufficiently small and the polynomial degree p is at least o log k numerical experiments are given to verify the theoretical results

first order least squares method with weakly imposed boundary condition for convection dominated diffusion problems we present and analyze a first order least squares method for convection dominated diffusion problems which provides robust l 2 a priori error estimate for the scalar variable even if the given data f l 2 the novel theoretical approach is to rewrite the method in the framework of discontinuous petrov galerkin dpg method and then show numerical stability by using a key equation discovered by gopalakrishnan and qiu 2014 this new approach gives an alternative way to do numerical analysis for least squares methods for a large class of differential equations we also show that the condition number of the global matrix is independent of the diffusion coefficient a key feature of the method is that there is no stabilization parameter chosen empirically in addition dirichlet boundary condition is weakly imposed numerical experiments verify our theoretical results and in particular show our way of weakly imposing dirichlet boundary condition is essential to the design of least squares methods numerical solutions on subdomains away from interior layers or boundary layers have remarkable accuracy even on coarse meshes which are unstructured quasi uniform

an analysis of the practical dpg method we give a complete error analysis of the discontinuous petrov galerkin dpg method accounting for all the approximations made in its practical implementation specifi cally we consider the dpg method that uses a trial space consisting of polynomials of degree p on each mesh element earlier works showed that there is a trial to test operator t which when applied to the trial space defines a test space that guarantees stability in dpg formulations this operator t is local it can be applied element by element however an infinite dimensional problem on each mesh element needed to be solved to apply t in prac tical computations t is approximated using polynomials of some degree r p on each mesh element we show that this approximation maintains optimal convergence rates provided that r 2 p n where n is the space dimension two or more for the laplace equation we also prove a similar result for the dpg method for linear elasticity remarks on the conditioning of the stiffness matrix in dpg methods are also included

proposed experimental tests of the bell kochen specker theorem for a two particle two state system sets of compatible propositions exist for which quantum mechanics and noncontextual hidden variable theories make conflicting predictions for every individual system whatever its quantum state this permits a simple all or nothing state independent experimental verification of the bell kochen specker theorem

the number of ramified covering of a riemann surface by riemann surface interpreting the number of ramified covering of a riemann surface by riemann surfaces as the relative gromov witten invariants and applying a gluing formula we derive a recursive formula for the number of ramified covering of a riemann surface by riemann surface with elementary branch points and prescribed ramification type over a special point

isogeometric residual minimization method igrm with direction splitting for non stationary advection diffusion problems abstract in this paper we propose a novel computational implicit method which we call isogeometric residual minimization igrm with direction splitting the method mixes the benefits resulting from isogeometric analysis implicit dynamics residual minimization and alternating direction solver we utilize tensor product b spline basis functions in space implicit second order time integration schemes residual minimization in every time step and we exploit kronecker product structure of the matrix to employ linear computational cost alternating direction solver we implement an implicit time integration scheme and apply for each space direction a stabilized mixed method based on residual minimization we show that the resulting system of linear equations has a kronecker product structure which results in a linear computational cost of the direct solver even using implicit time integration schemes together with the stabilized mixed formulation we test our method on three advection diffusion computational examples including model membrane problem the circular wind problem and the simulations modeling pollution propagating from a chimney

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

eliminating gibbs phenomena a non linear petrov galerkin method for the convection diffusion reaction equation abstract in this article we consider the numerical approximation of the convection diffusion reaction equation one of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection dominated case can lead to non physical oscillations in the numerical approximation often referred to as gibbs phenomena the idea of this article is to consider the approximation problem as a residual minimization in dual norms in l q type sobolev spaces with 1 q we then apply a non standard non linear petrov galerkin discretization that is applicable to reflexive banach spaces such that the space itself and its dual are strictly convex similar to discontinuous petrov galerkin methods this method is based on minimizing the residual in a dual norm replacing the intractable dual norm by a suitable discrete dual norm gives rise to a non linear inexact mixed method this generalizes the petrov galerkin framework developed in the context of discontinuous petrov galerkin methods to more general banach spaces for the convection diffusion reaction equation this yields a generalization of a similar approach from the l 2 setting to the l q setting a key advantage of considering a more general banach space setting is that in certain cases the oscillations in the numerical approximation vanish as q tends to 1 as we will demonstrate using a few simple numerical examples

crosswind smear and pointwise errors in streamline diffusion finite element methods for a model convection dominated singularly perturbed convection diffusion prob lem it is shown that crosswind smear in the numerical streamline diffusion finite element method is minimized by introducing a judicious amount of artificial crosswind diffusion the ensuing method with piecewise linear elements converges with a pointwise accuracy of almost h 5 4 under local smoothness assumptions 1 introduction the streamline diffusion method is a finite element method for convection dominated convection diffusion problems which combines formal high accuracy with decent stability properties the method was introduced in the case of stationary problems by hughes and brooks 7 cf raithby and torrance 14 and wahlbin 15 for earlier thoughts in this direction the mathematical analysis of the method was started in johnson and navert 8 and continued with extensions to e g time dependent problems in navert 12 johnson navert and pitkaranta 9 and johnson and saranen 10 in these papers local error estimates in l2 of order o h k 1 2 in regions of smoothness with piecewise polynomial finite elements of degree k were derived together with estimates stating as a typical example that in the zero diffusion limit a sharp discontinuity in the exact solution across a streamline will be captured in a numerical crosswind layer of width 0 h1 2 essentially the purpose of the present paper is first to improve the result just mentioned on numerical crosswind smear to 0 h3 4 the improvement from 0 h1 2 to 0 h3 4 is obtained by adding a small amount 0 h3 2 of artificial crosswind diffusion to the method in the piecewise linear case k 1 this does not destroy the known o h3 2 accuracy in l2 in smooth regions using our first result we then obtain our second main result localized pointwise error estimates of order 0 h5 4 in regions of smoothness the previously known best pointwise error estimate in the piecewise linear situation is 0 h1 2 another consequence is a global l estimate of order 0 h 2 in the presence of typical crosswind and downwind singularities we shall consider the model problem of finding u u x y such that

colouring the rational quantum sphere and the kochen specker theorem we review and extend recent findings of godsil and zaks who published a constructive colouring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the sphere exactly one ray is red one white and one black they also showed that any consistent colouring of the real sphere requires an additional colour we discuss some of the consequences for the kochen specker theorem

a combinatorial approach to nonlocality and contextuality so far most of the literature on quantum contextuality and the kochen specker theorem seems either to concern particular examples of contextuality or be considered as quantum logic here we develop a general formalism for contextuality scenarios based on the combinatorics of hypergraphs which significantly refines a similar recent approach by cabello severini and winter csw in contrast to csw we explicitly include the normalization of probabilities which gives us a much finer control over the various sets of probabilistic models like classical quantum and generalized probabilistic in particular our framework specializes to quantum nonlocality in the case of bell scenarios which arise very naturally from a certain product of contextuality scenarios due to foulis and randall in the spirit of csw we find close relationships to several graph invariants the recently proposed local orthogonality principle turns out to be a special case of a general principle for contextuality scenarios related to the shannon capacity of graphs our results imply that it is strictly dominated by a low level of the navascues pironio acin hierarchy of semidefinite programs which we also apply to contextuality scenarios

a dual petrovgalerkin finite element method for the convectiondiffusion equation we present a minimum residual finite element method based on a dual petrovgalerkin formulation for convectiondiffusion problems in a higher order adaptive continuous galerkin setting the method borrows concepts from both the discontinuous petrovgalerkin dpg method by demkowicz and gopalakrishnan 2011 and the method of variational stabilization by cohen dahmen and welper 2012 and it can also be interpreted as a variational multiscale method in which the fine scales are defined through a dual orthogonality condition a key ingredient in the method is the proper choice of dual norm used to measure the residual and we present two choices which are observed to be robust in both convection and diffusion dominated regimes as well as a proof of stability for quasi uniform meshes and a method for the weak imposition of boundary conditions numerically obtained convergence rates in 2d are reported and benchmark numerical examples are given to illustrate the behavior of the method

a robust petrov galerkin discretisation of convection diffusion equations a petrov galerkin discretisation is studied of an ultra weak variational formulation of the convection diffusion equation in a mixed form to arrive at an implementable method the truly optimal test space has to be replaced by its projection onto a finite dimensional test search space to prevent that this latter space has to be taken increasingly large for vanishing diffusion a formulation is constructed that is well posed in the limit case of a pure transport problem numerical experiments show approximations that are very close to the best approximations to the solution from the trial space uniformly in the size of the diffusion term

two simple proofs of the kochen specker theorem a new proof of the kochen specker theorem uses 33 rays instead of 117 in the original proof if the number of dimensions is increased from 3 to 4 only 24 rays are needed

density conditions for quantum propositions as has already been pointed out by birkhoff and von neumann quantum logic can be formulated in terms of projective geometry in three dimensional hilbert space elementary logical propositions are associated with one dimensional subspaces corresponding to points of the projective plane it is shown that starting with three such propositions corresponding to some basis u v w successive application of the binary logical operation x y x y generates a set of elementary propositions which is countable infinite and dense in the projective plane if and only if no vector of the basis u v w is orthogonal to the other ones

greechie diagrams nonexistence of measures in quantum logics and kochen specker type constructions we use greechie diagrams to construct finite orthomodular lattices realizable in the orthomodular lattice of subspaces in a three dimensional hilbert space such that the set of two valued states is not large i e full separating unital nonempty resp we discuss the number of elements of such orthomodular lattices of their sets of ortho generators and of their subsets that do not admit a large set of two valued states we show connections with other results of this type

shifted genus expanded w algebra and shifted hurwitz numbers we construct the shifted genus expanded w algebra which is isomorphic to the central subalgebra a of infinite symmetric group algebra and to the shifted schur symmetrical function algebra defined by okounkov and olshanskii as an application we get some differential equations for the generating functions of the shifted hurwitz numbers thus we can express the generating functions in terms of the shifted genus expanded cut and join operators

the p and hp versions of the finite element method for problems with boundary layers we study the uniform approximation of boundary layer functions exp x d for x 0 1 d 0 1 by the p and hp versions of the finite element method for the p version with fixed mesh we prove super exponential convergence in the range p 1 2 e 2d we also establish for this version an overall convergence rate of o p 1 ln p in the energy norm error which is uniform in d and show that this rate is sharp up to the ln p term when robust estimates uniform in d 0 1 are considered for the p version with variable mesh i e the hp version we show that exponential convergence uniform in d 0 1 is achieved by taking the first element at the boundary layer to be of size o pd numerical experiments for a model elliptic singular perturbation problem show good agreement with our convergence estimates even when few degrees of freedom are used and when d is as small as e g 10 8 they also illustrate the superiority of the hp approach over other methods including a low order h version with optimal exponential mesh refinement the estimates established in this paper are also applicable in the context of corresponding spectral element methods

proof of the labastida marino ooguri vafa conjecture based on large n chern simons topological string duality in a series of papers 37 21 19 j m f labastida m marino h ooguri and c vafa conjectured certain remarkable new algebraic structure of link invariants and the existence of infinite series of new integer invariants in this paper we provide a proof of this conjecture moreover we also show these new integer invariants vanish at large genera

curves in calabi yau threefolds and topological quantum field theory we continue our study of the local gromov witten invariants of curves in calabi yau threefolds we define relative invariants for local theory which give rise to a 1 1 dimensional topological quantum field theory tqft taking values in the ring mathbb q t the associated frobenius algebra over mathbb q t is semisimple consequently we obtain a structure result for the local invariants as an easy consequence of our structure formula we recover the closed formulas for the local invariants in the case where either the target genus or the degree equals 1

a class of discontinuous petrov galerkin methods part iv the optimal test norm and time harmonic wave propagation in 1d the phase error or the pollution effect in the finite element solution of wave propagation problems is a well known phenomenon that must be confronted when solving problems in the high frequency range this paper presents a new method with no phase errors for one dimensional 1d time harmonic wave propagation problems using new ideas that hold promise for the multidimensional case the method is constructed within the framework of the discontinuous petrov galerkin dpg method with optimal test functions we have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm in this paper we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm this is answered in the specific case of the helmholtz equation with l 2 norm as the energy norm we obtain uniform stability with respect to the wave number we illustrate the method with a number of 1d numerical experiments using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally a 1d theoretical stability analysis is also developed

all loop topological string amplitudes from chern simons theory we demonstrate the equivalence of all loop closed topological string amplitudes on toric local calabi yau threefolds with computations of certain knot invariants for chern simons theory we use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera in particular we explicitly compute the topological string amplitudes for open image in new window 2 up to degree 12 and open image in new window 1 open image in new window 1 up to total degree 10 to all genera this also leads to certain novel large n dualities in the context of ordinary superstrings involving duals of type ii superstrings on local calabi yau three folds without any fluxes

the dpg method for the stokes problem we discuss well posedness and convergence theory for the dpg method applied to a general system of linear partial differential equations pdes and specialize the results to the classical stokes problem the stokes problem is an iconic troublemaker for standard bubnov galerkin methods if discretizations are not carefully designed they may exhibit non convergence or locking by contrast dpg does not require us to treat the stokes problem in any special manner we illustrate and confirm our theoretical convergence estimates with numerical experiments

a robust dpg method for convection dominated diffusion problems ii adjoint boundary conditions and mesh dependent test norms we introduce a dpg method for convection dominated diffusion problems the choice of a test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter demkowicz and heuer 2011 18 we propose a new inflow boundary condition which regularizes the adjoint problem allowing the use of a stronger test norm the robustness of the method is proven and numerical experiments demonstrate the method s robust behavior

exceptional and non crystallographic root systems and the kochen specker theorem the kochen specker theorem states that a 3 dimensional complex euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables the orthogonal projectors cannot be assigned with 0 and 1 values in a classically consistent way this paper shows that the irreducible root systems of exceptional and of non crystallographic types are useful in constructing such configurations in other dimensions the cases e 6 and e 7 lead to new examples while f 4 e 8 and h 4 yield a new interpretation of the known ones the described configurations have an additional property they are saturated i e the tuples of mutually orthogonal lines being partially ordered by inclusion yield a poset with all maximal elements having the same cardinality the dimension of space

explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements we derive new trace inequalities for nurbs mapped domains in addition to sobolev type inequalities we derive discrete trace inequalities for use in nurbs based isogeometric analysis all dependencies on shape size polynomial degree and the nurbs weighting function are precisely specified in our analysis and explicit values are provided for all bounding constants appearing in our estimates as hexahedral finite elements are special cases of nurbs our results specialize to parametric hexahedral finite elements and our analysis also generalizes to t spline based isogeometric analysis we compare the bounding constants appearing in our explicit trace inequalities with numerically computed optimal bounding constants and we discuss application of our results to a laplace problem we finish this paper with a brief exploration of so called patch wise trace inequalities for isogeometric analysis

adaptive streamline diffusion finite element methods for stationary convection diffusion problems adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed the underlying discretization scheme is the shock capturing streamline diffusion method the adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed a priori error estimates are used to show that the algorithms are efficient in a certain sense

hodge gue correspondence and the discrete kdv equation we prove the conjectural relationship recently proposed in dubrovin and yang commun number theory phys 11 311 336 2017 between certain special cubic hodge integrals of the gopakumar marino vafa type gopakumar and vafa in adv theor math phys 5 1415 1443 1999 marino and vafa in contemp math 310 185 204 2002 and gue correlators and the conjecture proposed in dubrovin et al adv math 293 382 435 2016 that the partition function of these hodge integrals is a tau function of the discrete kdv hierarchy

the gromov witten potential of a point hurwitz numbers and hodge integrals hurwitz numbers which count certain covers of the projective line or equivalently factorizations of permutations into transpositions have been extensively studied for over a century the gromov witten potential f of a point the generating series for descendent integrals on the moduli space of curves is a central object of study in gromov witten theory we define a slightly enriched gromov witten potential g including integrals involving one lambda class and show that after a non trivial change of variables g h in positive genus where h is a generating series for hurwitz numbers we prove a conjecture of goulden and jackson on higher genus hurwitz numbers which turns out to be an analogue of a genus expansion ansatz of itzykson and zuber as consequences we have new combinatorial constraints on f and a much more direct proof of the ansatz of itzykson and zuber we can produce recursions and explicit formulas for hurwitz numbers the algorithm presented proves all such recursions as examples we present surprisingly simple new recursions in genus 0 to 3 similar recursions should exist for all genera as we expect this paper also to be of interest to combinatorialists we have tried to make it as self contained as possible including reviewing some results and definitions well known in algebraic and symplectic geometry and mathematical physics 2000 mathematical subject classification primary 14h10 81t40 secondary 05c30 58d29

lower bounds for enumerative counts of positive genus real curves abstract we transform the positive genus real gromov witten invariants of many real orientable symplectic threefolds into signed counts of curves these integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints we conclude with some implications and related conjectures for hodge integrals

discrete least squares finite element methods abstract a finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators 1 the differential operator defining the spatial boundary value problem and 2 a riesz map on the test space the resulting linear system is overdetermined two different approaches for solving the system are suggested although others are discussed 1 solving the associated normal equation with linear solvers for symmetric positive definite systems e g cholesky factorization and 2 solving the overdetermined system with orthogonalization algorithms e g qr factorization the finite element assembly algorithm for each of these approaches is described in detail the normal equation approach is usually faster for direct solvers and requires less storage the second approach reduces the condition number of the system by a power of two and is less sensitive to round off error the rectangular stiffness matrix of second approach is demonstrated to have condition number o h 1 for a variety of formulations of poisson s equation the stiffness matrix from the normal equation approach is demonstrated to be related to the monolithic stiffness matrices of least squares finite element methods and it is proved that the two are identical in some cases an example with poisson s equation indicates that the solutions of these two different linear systems can be nearly indistinguishable if round off error is not an issue and rapidly converge to each other the orthogonalization approach is suggested to be beneficial for problems which induce poorly conditioned linear systems experiments with poisson s equation in single precision arithmetic as well as the linear acoustics problem near resonance in double precision arithmetic verify this conclusion the methodology described here is an outgrowth of the discontinuous petrov galerkin dpg methodology of demkowicz and gopalakrishnan 2015 the strength of dpg is highlighted throughout however the majority of theory presented is more general extensions to constrained minimization principles are also considered throughout but are not analyzed in experiments

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

the symplectic sum formula for gromov witten invariants in the symplectic category there is a connect sum operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds this paper establishes a formula for the gromov witten invariants of a symplectic sum z x y in terms of the relative gw invariants of x and y several applications to enumerative geometry are given gromov witten invariants are counts of holomorphic maps into symplectic manifolds to define them on a symplectic manifold x w one introduces an almost complex structure j compatible with the symplectic form w and

analysis of the dpg method for the poisson equation we give an error analysis of the recently developed dpg method applied to solve the poisson equation and a convection diffusion problem we prove that the method is quasioptimal error estimates in terms of both the mesh size h and the polynomial degree p for various element shapes can be derived from our results results of extensive numerical experiments are also presented

relative gromov witten invariants we define relative gromov witten invariants of a symplectic manifold relative to a codimension two symplectic submanifold these invariants are the key ingredients in the symplectic sum formula of ip4 the main step is the construction of a compact space of v stable maps simple special cases include the hurwitz numbers for algebraic curves and the enumerative invariants of caporaso and harris

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

algebraic partial boolean algebras partial boolean algebras first studied by kochen and specker in the 1960s provide the structure for bell kochen specker theorems which deny the existence of non contextual hidden variable theories in this paper we study partial boolean algebras which are algebraic in the sense that their elements have coordinates in an algebraic number field several of these algebras have been discussed recently in a debate on the validity of bell kochen specker theorems in the context of finite precision measurements the main result of this paper is that every algebraic finitely generated partial boolean algebra b t is finite when the underlying space is three dimensional answering a question of kochen and showing that conway and kochen s infinite algebraic partial boolean algebra has minimum dimension this result contrasts the existence of an infinite non algebraic b t generated by eight elements in an abstract orthomodular lattice of height 3 we then initiate a study of higher dimensional algebraic partial boolean algebras first we describe a restriction on the determinants of the elements of b t that are generated by a given set t we then show that when the generating set t consists of the rays spanning the minimal vectors in a real irreducible root lattice b t is infinite just if that root lattice has an a5 sublattice finally we characterize the rays of b t when t consists of the rays spanning the minimal vectors of the root lattice e8

bell kochen specker theorem for any finite dimension the bell kochen specker theorem against non contextual hidden variables can be proved by constructing a finite set of totally non colourable directions as kochen and specker did in a hilbert space of dimension n 3 we generalize kochen and specker s set to hilbert spaces of any finite dimension in a three step process that shows the relationship between different kinds of proofs continuum probabilistic state specific and state independent of the bell kochen specker theorem at the same time this construction of a totally non colourable set of directions in any dimension explicitly solves the question raised by zimba and penrose about the existence of such a set for n 5

local analysis of hdg methods for convection dominated diffusion problems in this paper we establish local error analysis of hybridizable discontinuous galerkin hdg methods for convection dominated diffusion equation in two types of subdomains away from the layers the first subdomain is of o log 1 h h 1 2 away from the interior layers and of o log 1 h h away from the boundary layers and the second one is of o away from the outflow of the boundary our local error bound for the first subdomain can be improved by a factor of log 1 h we use weighted estimates to prove the first result by constructing new weight functions and the inf sup condition of the bilinear form to prove the second one

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

the topological vertex we construct a cubic field theory which provides all genus amplitudes of the topological a model for all non compact toric calabi yau threefolds the topology of a given feynman diagram encodes the topology of a fixed calabi yau with schwinger parameters playing the role of kahler classes of the threefold we interpret this result as an operatorial computation of the amplitudes in the b model mirror which is the quantum kodaira spencer theory the only degree of freedom of this theory is an unconventional chiral scalar on a riemann surface in this setup we identify the b branes on the mirror riemann surface as fermions related to the chiral boson by bosonization

robust dpg method for convection dominated diffusion problems we propose and analyze a discontinuous petrov galerkin dpg method for convection dominated diffusion problems that provides robust l 2 error estimates for the field variables which are quasi optimal in the energy norm a key feature of the method is to construct test functions defined by a variational formulation with bilinear form test norm specifically designed for the goal of robustness a main theoretical ingredient is a stability analysis of the adjoint problem numerical experiments underline our theoretical results and in particular confirm robustness of the dpg method for well chosen test norms

localization and gluing of topological amplitudes we develop a gluing algorithm for gromov witten invariants of toric calabi yau threefolds based on localization and gluing graphs the main building block of this algorithm is a generating function of cubic hodge integrals of special form we conjecture a precise relation between this generating function and the topological vertex at fractional framing

kochen specker theorem for finite precision spin one measurements unsharp spin one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains if the uncertainty is below a certain level and if the distribution of measurement errors is covariant under rotations a kochen specker theorem for the unsharp spin observables follows there are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way

critical noncolorings of the 600 cell proving the bell kochen specker theorem aravind and lee elkin 1998 j phys a math gen 31 9829 34 gave a proof of the bell kochen specker theorem by showing that it is impossible to color the 60 directions from the center of a 600 cell to its vertices in a certain way this paper refines that result by showing that the 60 directions contain many subsets of 36 and 30 directions that cannot be similarly colored and so provide more economical demonstrations of the theorem further these subsets are shown to be critical in the sense that deleting even a single direction from any of them causes the proof to fail the critical sets of size 36 and 30 are shown to belong to orbits of 200 and 240 members respectively under the symmetries of the polytope a comparison is made between these critical sets and other such sets in four dimensions and the significance of these results is discussed

cyclic hodge integrals and loop schur functions abstract we conjecture an evaluation of three partition cyclic hodge integrals in terms of loop schur functions our formula implies the orbifold gromov witten donaldson thomas correspondence for toric calabi yau threefolds with transverse a n singularities we prove the formula in the case where one of the partitions is empty and thus establish the orbifold gromov witten donaldson thomas correspondence for local toric surfaces with transverse a n singularities

asymptotically exact a posteriori error estimators for first order div least squares methods in local and global l2 norm a new asymptotically exact a posteriori error estimator is developed for first order div least squares ls finite element methods let uh h be ls approximate solution for u au then e a1 2 h auh 0 is asymptotically exact a posteriori error estimator for a1 2 uuh 0 or a1 2 h 0 depending on the order of approximate spaces for and u for e to be asymptotically exact for a1 2 uuh 0 we require higher order approximation property for and vice versa when both au and are approximated in the same order of accuracy the estimator becomes an equivalent error estimator for both errors the underlying mesh is only required to be shape regular i e it does not require quasi uniform mesh nor any special structure for the underlying meshes confirming numerical results are provided and the performance of the estimator is explored for other choice of spaces for uh h

noncontextual hidden variables and physical measurements meyer phys rev lett 83 3751 1999 recently showed that the kochen specker theorem which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle can be effectively nullified if only finite precision measurements are considered we generalize this result one can ascribe consistent outcomes to a dense subset of the set of projection valued measurements or to a dense subset of the set of positive operator valued measurements on any finite dimensional system hence no kochen specker like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class

relative virtual localization and vanishing of tautological classes on moduli spaces of curves we prove a localization formula for the moduli space of stable relative maps as an application we prove that all codimension i tautological classes on the moduli space of stable pointed curves vanish away from strata corresponding to curves with at least i g 1 genus 0 components as consequences we prove and generalize various conjectures and theorems about various moduli spaces of curves due to getzler ionel faber looijenga pandharipande diaz and others this theorem appears to be the geometric content behind these results the rest is straightforward graph combinatorics the theorem also suggests the importance of the stratification of the moduli space by number of rational components

a simple proof of gopakumar vafa conjecture for local toric calabi yau manifolds we prove gopakumar vafa conjecture for local toric calabi yau manifolds it is also proven that the local gopakumar vafa invariants of a given class vanish at large genera

on the constants in hp finite element trace inverse inequalities we derive inverse trace inequalities for hp finite elements utilizing orthogonal polynomials we show how to derive explicit expressions for the constants when considering triangular and tetrahedral elements we also discuss how to generalize this technique to the general d simplex

a proof of a conjecture of marino vafa on hodge integrals where i c1 li is the first chern class of li and j cj e is the j th chern class of the hodge bundle hodge integrals arise in the calculations of gromov witten invariants by localization techniques 14 7 the explicit evaluation of hodge integrals is a difficult problem the hodge integrals involving only classes can be computed recursively by witten s conjecture 26 proven by kontsevich 13 algorithms of computing hodge integrals are described in 2 in 23 m marino and c vafa obtained a closed formula for a generating function of certain open gromov witten invariants some of which has been reduced to hodge integrals by localization techniques which are not fully clarified mathematically this leads to a conjectural formula of hodge integrals to state this formula we introduce some notation following 28 let

new separations in zero error channel capacity through projective kochen specker sets and quantum coloring we introduce two generalizations of kochen specker ks sets projective ks sets and generalized ks sets we then use projective ks sets to characterize all graphs for which the chromatic number is strictly larger than the quantum chromatic number here the quantum chromatic number is defined via a nonlocal game based on graph coloring we further show that from any graph with separation between these two quantities one can construct a classical channel for which entanglement assistance increases the one shot zero error capacity as an example we exhibit a new family of classical channels with an exponential increase

an adaptive stabilized conforming finite element method via residual minimization on dual discontinuous galerkin norms abstract we design and analyze a new adaptive stabilized finite element method we construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that has inf sup stability we formulate this residual minimization as a stable saddle point problem which delivers a stabilized discrete solution and a residual representation that drives the adaptive mesh refinement numerical results on an advection reaction model problem show competitive error reduction rates when compared to discontinuous galerkin methods on uniformly refined meshes and smooth solutions moreover the technique leads to optimal decay rates for adaptive mesh refinement and solutions having sharp layers

kochen specker vectors some reference citations in the text of this paper are incorrect and should be amended as listed below the reference list is correct as published page 1579 line 5 23 34 38 39 should read 23 34 35 36 page 1579 line 9 40 should read 37 page 1580 line 8 31 33 35 should read 31 33 38 page 1580 line 14 36 should read 39 page 1580 line 36 36 should read 39 page 1580 line 38 37 should read 40 page 1580 line 42 38 should read 35 page 1581 line 3 of caption 33 35 should read 33 38 page 1583 line 12 41 should read 42 page 1587 line 9 39 should read 36 page 1587 line 11 39 should read 36 page 1587 line 18 38 39 should read 35 36 page 1587 line 37 39 should read 36 page 1589 line 18 39 46 47 should read 36 46 47 page 1590 line 2 39 should read 36 age 1590 line 3 39 should read 36

a degeneration formula of gw invariants this is the sequel to the paper 23 in this paper we construct the virtual moduli cycles of the degeneration of the moduli of stable morphisms constructed in 23 we also construct the virtual moduli cycles of the moduli of relative stable morphisms of a pair of a smooth divisor in a smooth variety based on these we prove a degeneration formula of the gromov witten invariants

graph approach to quantum systems using a graph approach to quantum systems we show that descriptions of 3 dim kochen specker ks setups as well as descriptions of 3 dim spin systems by means of greechie diagrams a kind of lattice that we find in the literature are wrong correct lattices generated by mckay megill pavicic mmp hypergraphs and hilbert subspace equations are given to enable future exhaustive generation of 3 dim ks setups by means of our recently found stripping technique bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks orthogonal triples of elements up to 41 of them we obtain several new results on such lattices and hypergraphs in particular on properties such as superposition and orthoraguesian equations

three partition hodge integrals and the topological vertex we give a new proof of the equivalence between the cubic hodge integrals and the topological vertex in topological string theory a central role is played by the notion of generalized shift symmetries in a fermionic realization of the two dimensional quantum torus algebra these algebraic relations of operators in the fermionic fock space are used to convert generating functions of the cubic hodge integrals and the topological vertex to each other as a byproduct the generating function of the cubic hodge integrals at special values of the parameters overrightarrow w therein is shown to be a tau function of the generalized kdv aka gelfand dickey hierarchies

adaptive petrov galerkin methods for first order transport equations we propose stable variational formulations for certain linear unsymmetric operators with first order transport equations in bounded domains serving as the primary focus of this paper the central objective is to develop for such classes adaptive solution concepts with provable error reduction to adaptively resolve anisotropic solution features such as propagating singularities the presently proposed variational formulations allow in particular the employment of trial spaces spanned by directional representation systems since such systems typically given as frames are known to be stable only in l 2 special emphasis is placed on l 2 stable formulations the proposed stability concept is based on perturbations of certain ideal test spaces in petrov galerkin formulations see also l f demkowicz and j gopalakrishnan comput methods appl mech engrg 199 2010 pp 1558 1572 l demkowicz and j gopalakrishnan numer methods partial differential equations 27 2011 pp 70 105 j

a class of discontinuous petrov galerkin methods part i the transport equation considering a simple model transport problem we present a new finite element method while the new method fits in the class of discontinuous galerkin dg methods it differs from standard dg and streamline diffusion methods in that it uses a space of discontinuous trial functions tailored for stability the new method unlike the older approaches yields optimal estimates for the primal variable in both the element size h and polynomial degree p and outperforms the standard upwind dg method

hurwitz numbers and intersections on moduli spaces of curves 1 department of mathematics university of stockholm s 10691 stockholm sweden e mail teke matematik su se 2 higher college of mathematics independent university of moscow and institute for system research ras moscow russia e mail lando mccme ru 3 department of mathematics royal institute of technology s 10044 stockholm sweden e mail mshapiro math kth se 4 department of mathematics and department of computer science university of haifa haifa 31905 israel e mail alek mathcs haifa ac il

gromov witten donaldson thomas correspondence for toric 3 folds we prove the equivariant gromov witten theory of a nonsingular toric 3 fold x with primary insertions is equivalent to the equivariant donaldson thomas theory of x as a corollary the topological vertex calculations by agangic klemm marino and vafa of the gromov witten theory of local calabi yau toric 3 folds are proven to be correct in the full 3 leg setting

a primal dpg method without a first order reformulation abstract we show that it is possible to apply the dpg methodology without reformulating a second order boundary value problem into a first order system by considering the simple example of the poisson equation the result is a new weak formulation and a new dpg method for the poisson equation which has no numerical trace variable but has a numerical flux approximation on the element interfaces in addition to the primal interior variable

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

a hidden variables versus quantum mechanics experiment in the light of the bell kochen specker theorem we examine a feasible experimental test in order to discriminate between non contextual hidden variables and some probabilistic predictions of quantum mechanics

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100