exact inference on the random effects model for meta analyses with few studies we describe an exact unconditional non randomized procedure for producing confidence intervals for the grand mean in a normal normal random effects meta analysis the procedure targets meta analyses based on too few primary studies 7 say to allow for the conventional asymptotic estimators e g dersimonian and laird 1986 or non parametric resampling based procedures e g liu et al 2017 meta analyses with such few studies are common with one recent sample of 22 453 heath related meta analyses finding a median of 3 primary studies per meta analysis davey et al 2011 reliable and efficient inference procedures are therefore needed to address this setting the coverage level of the resulting ci is guaranteed to be above the nominal level up to monte carlo error provided the meta analysis contains more than 1 study and the model assumptions are met after employing several techniques to accelerate computation the new ci can be easily constructed on a personal computer simulations suggest that the proposed ci typically is not overly conservative we illustrate the approach on several contrasting examples of meta analyses investigating the effect of calcium intake on bone mineral density

complexes de chaines etales et courbes de deligne lusztig abstract in a first part we lift the usual constructions of functors between derived categories of etale sheaves over schemes with a sheaf of algebras to pure derived categories for varieties with finite group actions we recover in a more functorial way rickard s construction we apply this to the case of deligne lusztig varieties and show that broue s conjecture holds for curves the additional ingredient we need is obtained from an easy property of the cohomology of etale covers of the affine line

numerical investigation on the stability of singular driven cavity flow by applying the singularity subtraction technique to the unsteady driven cavity problem the stability of the impulsively started flow is investigated without smoothing the corner singularity a second order spectral projection method allows localization of the critical reynolds number for the first hopf bifurcation in the interval 8017 6 8018 8

accurate three dimensional lid driven cavity flow a chebyshev collocation method in space is introduced which allows an accurate calculation of three dimensional lid driven cavity flows the time integration is carried out by an adams bashforth backward euler scheme the accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field this way the most severe discontinuities in the boundary conditions which arise along the lines where moving and stationary walls meet are taken care of analytically and thus do not spoil the numerical part of the solution calculations are carried out for no slip boundary conditions at the cavity end walls as well as for periodic end wall conditions in general the spatial accuracy is better than fifth order for rigid end wall conditions the accuracy is reduced near the end walls to o n 3 2 but recovers in the bulk tabulated data are provided for the most interesting flow properties

fourier transforms and frobenius eigenvalues for finite coxeter groups abstract lusztig s classification of the unipotent characters of a finite chevalley or steinberg group involves a certain non abelian fourier transformation we construct analogous transformations for the suzuki and ree groups based on a set of axioms derived from lusztig s theory of character sheaves we also determine fourier matrices for the spetses in the sense of broue michel and the second author associated with twisted dihedral groups this completes the determination of fourier matrices for all spetses associated with finite coxeter groups we end by collecting common properties of these fourier matrices and the eigenvalues of frobenius of character sheaves and unipotent characters

translation by the full twist and deligne lusztig varieties abstract we prove several conjectures about the cohomology of deligne lusztig varieties invariance under conjugation in the braid group behaviour with respect to translation by the full twist parity vanishing of the cohomology for the variety associated with the full twist in the case of split groups of type a and using previous results of the second author this implies broue michel s conjecture on the disjointness of the cohomology for the variety associated to any good regular element that conjecture was inspired by broue s abelian defect group conjecture and the specific form broue conjectured for finite groups of lie type 4 reves 1 et 2

the development version of the chevie package of gap3 abstract i describe the current state of the development version of the chevie package which allows to transform the theories of coxeter groups reductive algebraic groups complex reflection groups hecke algebras braid monoids etc into actual computations examples are given showing the code to check some results of lusztig

minimal length elements in twisted conjugacy classes of finite coxeter groups let w be a finite coxeter group and let f be an automorphism of w that leaves the set of generators of w invariant we establish certain properties of elements of minimal length in the f conjugacy classes of w that allow us to define character tables for the corresponding twisted iwahori hecke algebras these results are extensions of results obtained by geck and pfeiffer in the case where f is trivial

garside families and garside germs garside families have recently emerged as a relevant context for extending results involving garside monoids and groups which themselves extend the classical theory of generalized braid groups here we establish various characterizations of garside families that is equivalently various criteria for establishing the existence of normal decompositions of a certain type

affineness of deligne lusztig varieties for minimal length elements abstract we prove that the deligne lusztig varieties associated to elements of the weyl group which are of minimal length in their twisted class are affine our proof differs from the proof of he and orlik rapoport and it is inspired by the case of regular elements which correspond to the varieties involved in broue s conjectures

estimators for the one way random effects model with unequal error variances abstract using the random effects model yij i ij i 1 k j 1 ni where i and ij are normal with means zero and variances 2 and i 2 this article considers eight methods of estimating i 2 2 and thirteen corresponding procedures of estimating biases and mean squared errors mse s of these procedures are examined for variations in the magnitudes of the unknown parameters the sample sizes and the number of groups

the kinematic laplacian equation method a novel procedure for the navier stokes equations in the vorticity velocity formulation is presented the time evolution of the vorticity is solved as an ode problem on each node of the spatial discretization using at each step of the time discretization the spatial solution for the velocity field provided by a new pde expression called the kinematic laplacian equation kle this complete decoupling of the two variables in a vorticity in time velocity in space split algorithm reduces the number of unknowns to solve in the time integration process and also favors the use of advanced ode algorithms enhancing the efficiency and robustness of time integration the issue of the imposition of vorticity boundary conditions is addressed as well as the details of the implementation of the kle by isoparametric finite element discretization we shall see some validation results of the kle method applied to the classical case of a circular cylinder in impulsive started pure translational steady motion at several reynolds numbers in the range 5

cohomology of deligne lusztig varieties for short length regular elements in exceptional groups abstract we determine the cohomology of deligne lusztig varieties associated with some short length regular elements for split groups of type f 4 and e n as a byproduct we obtain conjectural brauer trees for the principal 14 block of e 7 and the principal 24 block of e 8

a note on words in braid monoids abstract the purpose of this note is to give a self contained apart from simple facts about coxeter groups and we hope a bit shorter and more understandable account of some results of c1 c2 on normal forms of braids which are themselves based on the papers d1 t in particular a motivation was to give a proof of proposition 5 1 that we use in b m some proofs and results from section 2 onwards seem to be new i thank several people for improvements from earlier versions of the manuscript m geck for pointing out some errors f digne for pointing out that some results don t need the braid group to be of finite type and j y hee for suggesting and providing further improvements in that direction

spectral element methods for elliptic problems in nonsmooth domains engineering applications frequently require the numerical solution of elliptic boundary value problems in irregularly shaped domains for smooth problems spectral element methods have proved very successful since they can accommodate fairly complicated geometries while retaining a rapid rate of convergence geometric singularities however often give rise to singular solutions the accuracy of the spectral element methods is then degraded and they offer no apparent advantage over low order finite element methods in many cases however the singular structure of the solution is known and its form may be exploited by the spectral element method among the various ways of doing so through supplementary basis functions eigenfunction expansions and graded meshes the method of auxiliary mapping proves to be particularly effective for certain simple cases the problem is transformed to a coordinate system in which the solution is analytic and exponential convergence is recovered even when this is not possible the singularity is usually much weaker after mapping so that other treatments are more effective in the new coordinate system in this paper we study different ways of treating singularities and in particular the method of auxiliary mapping coupled with the use of supplementary basis functions error estimates are presented explaining why the combined approach is more effective and these estimates are confirmed through a number of numerical experiments for the laplace poisson and helmholtz equations

maximum likelihood analysis for heteroscedastic one way random effects anova in interlaboratory studies summary this article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity following cochran 1937 journal of the royal statistical society4 supple 102 118 1954 biometrics10 101 129 1980 in proceedings of the 25th conference on the design of experiments in army research development and testing 21 33 and others this problem is formulated as a one way unbalanced random effects anova with unequal within group variances a reparametrization of the likelihood leads to simplified computations easier identification and interpretation of multimodality of the likelihood and through a non informative prior bayesian approach approximate confidence regions for the mean and between group variance

decomposition matrices for low rank unitary groups we study the decomposition matrices of the unipotent blocks of finite special unitary groups sun q for unitary primes larger than n up to few unknown entries we give a complete solution for n 2 10 we also prove a general result for two column partitions when divides q 1 this is achieved using projective modules coming from the adic cohomology of deligne lusztig varieties

models and confidence intervals for true values in interlaboratory trials we consider the one way random effects model with unequal sample sizes and heterogeneous variances using the method of generalized confidence intervals we develop a new confidence interval procedure for the mean additionally we investigate two alternative models based on different sets of assumptions regarding between group variability and derive generalized confidence interval procedures for the mean these procedures are applicable to small samples statistical simulation is used to demonstrate that the coverage probabilities of these procedures are close enough to the nominal value so that they are useful in practice although the methods are quite general the procedures are explained with the backdrop of interlaboratory studies

coxeter orbits and brauer trees abstract we study the cohomology with modular coefficients of deligne lusztig varieties associated to coxeter elements under some torsion free assumption on the cohomology we derive several results on the principal l block of a finite reductive group g f q when the order of q modulo l is assumed to be the coxeter number these results include the determination of the planar embedded brauer tree of the block as conjectured by hiss lubeck and malle 1995 in 25 and the derived equivalence predicted by the geometric version of broue s conjecture broue and malle 1993 7

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

a mixed basis spectral projection method a new grid less no collocation spectral projection method is presented the unsteady navier stokes equations are approximated according to the variational framework of guermond and quartapelle which accommodates two vector spaces for the velocity fields obtained in the two half steps of the fractional step method but retains only one in the final solution algorithm two different bases built on legendre polynomials are used for the velocity and pressure to solve the corresponding helmholtz and poisson equations by direct spectral elliptic solvers interpolations pn and pn 2 are employed for velocity and pressure to satisfy the lbb stability requirement and a gauss legendre quadrature formula with 3 2n integration points is used to prevent aliasing error in the pseudospectral evaluation of the nonlinear terms a bdf second order time stepping is implemented to provide accurate numerical results about the stability of the singular driven cavity problem

confidence regions and intervals for meta analysis model parameters this article obtains confidence regions for the heteroscedastic one way random effects model s parameters the heteroscedastic one way random effects model the confidence regions are based on canonical representations of the restricted and profile likelihood functions in terms of independent normal random variables and 2 random variables these regions provide conservative confidence intervals for the common mean and heterogeneity variance mathematical details and the r code are available online as supplementary material

finite complex reflection arrangements are k pi 1 let v be a finite dimensional complex vector space and w gl v be a finite complex reflection group let v reg be the complement in v of the reflecting hyperplanes we prove that v reg is a k 1 space this was predicted by a classical conjecture originally stated by brieskorn for complexified real reflection groups the complexified real case follows from a theorem of deligne and after contributions by nakamura and orliksolomon only six exceptional cases remained open in addition to solving these six cases our approach is applicable to most previously known cases including complexified real groups for which we obtain a new proof based on new geometric objects we also address a number of questions about 1 w v the braid group of w this includes a description of periodic elements in terms of a braid analog of springer s theory of regular elements

accurate ω ψ spectral solution of the singular driven cavity problem this article provides accurate spectral solutions of the driven cavity problem calculated in the vorticity stream function representation without smoothing the corner singularities a prima facie impossible task as in a recent benchmark spectral calculation by primitive variables of botella and peyret closed form contributions of the singular solution for both zero and finite reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form the method employed is based on a split approach to the vorticity and stream function equations a galerkin legendre approximation of the problem for the perturbation and an evaluation of the nonlinear terms by gauss legendre numerical integration results computed for re 0 100 and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation chebyshev projection method the validity of the proposed singularity subtraction scheme for computing time dependent solutions is also established

cohomologie des varietes de deligne lusztig abstract we study the cohomology of deligne lusztig varieties with aim the construction of actions of hecke algebras on such cohomologies as predicted by the conjectures of broue malle and michel ultimately aimed at providing an explicit version of the abelian defect conjecture we develop the theory for varieties associated to elements of the braid monoid and partial compactifications of them we are able to compute the cohomology of varieties associated to possibly twisted rank 2 groups and powers of the longest element w 0 some indeterminacies remain for g 2 we use this to construct hecke algebra actions on the cohomology of varieties associated to w 0 or its square for groups of arbitrary rank in the subsequent work f digne j michel endomorphisms of deligne lusztig varieties nagoya j math 183 2006 we construct actions associated to more general regular elements and we study their traces on cohomology

an algorithmic approach to perverse derived equivalences broue s conjecture for ω8 2 abstract following craven and rouquier s method 8 to tackle broue s abelian defect group conjecture we present two algorithms implementing that procedure in the case of principal blocks of defect d c l c l for a prime l the first describes a stable equivalence between b 0 g and b 0 n g d and the second tries to lift such a stable equivalence to a perverse derived equivalence as an application we show that broue s conjecture holds for the principal 5 block of the simple group 8 2

quotient of deligne lusztig varieties abstract we study the quotient of parabolic deligne lusztig varieties by a finite unipotent group u f where u is the unipotent radical of a rational parabolic subgroup p lu we show that in some particular cases the cohomology of this quotient can be expressed in terms of smaller parabolic deligne lusztig varieties associated to the levi subgroup l

parabolic subgroups of artin groups abstract let a be an artin system for x we denote by a x the subgroup of a generated by x such a group is called a parabolic subgroup of a we reprove van der lek s theorem a parabolic subgroup of an artin group is an artin group we give an algorithm which decides whether two parabolic subgroups of an artin group are conjugate let a be a finite type artin group and let a x be a parabolic subgroup with connected associated coxeter graph the quasi centralizer of a x in a is the set of in a such that x 1 x we prove that the commensurator of a x in a is equal to the normalizer of a x in a and that this group is generated by a x and the quasi centralizer of a x in a moreover if a x is not of type d l l 4 and l even then this group is generated by a x and the centralizer of a x in a

rigid geometry lefschetz verdier trace formula and deligne s conjecture in abstract algebraic geometry the lefschetz verdier trace formula expresses the global trace of an endomorphism induced on cohomology by a correspondence as a sum of local contributions called local terms near fixed points though the formula holds quite generally the explicit calculation of local terms is very hard to carry out and no good formula is known for general correspondences over the complex numbers a useful formula is known for a good class called weakly hyperbolic g m on the other hand in positive characteristics p deligne conjectured that the local terms would be much simplified if we composed a given correspondence with a high power of frobenius take a proper variety x over an algebraic closure k of a finite field fq a correspondence a y x xk x and a smooth qr k on an open set u of x fixed by a denote the inclusion by j and is invertible in k then

action du groupe des tresses sur une categorie we describe how to define by generators and relations an action of the braid group on a category more generally how to define a functor from a generalized positive braids monoid corresponding to a finite coxeter group to a monoidal category applications to constructions of bondal exceptional systems and of broue michel correspondences on flag manifolds are given

normalizers of parabolic subgroups in coxeter groups we shall describe a simple procedure for obtaining presentations of normalizers of parabolic subgroups of arbitrary coxeter groups in each case the normalizer is the semidirect product of the parabolic subgroup by a complement which acts by permuting the simple re ections this complement may be viewed in a natural way as a maximal subgroup of a certain groupoid for which we obtain a set of generators and de ning relations moreover the de ning relations are all derived from subgroupoids of ranks one and two so that the groupoid can be viewed as a generalization of a coxeter group

normalisateur et groupe d artin de type spherique abstract let a s be an artin group and x a subset of s denote by ax the subgroup of a generated by x when a is of spherical type we prove that the normalizer and the commensurator of ax in a are equal and are the product of ax by the quasi centralizer of ax in a looking the associated monoids a and ax we described the quasi centralizer of ax in a thanks to results in coxeter groups these two results generalize earlier results of paris j algebra 196 1997 369 399 finally we compare in the spherical case the normalizer of a parabolic subgroup in the artin group and in the coxeter group

very high order compact finite difference schemes on non uniform grids for incompressible navier stokes equations this article presents a family of very high order non uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible navier stokes equations the high order compact schemes on non uniform grids developed in shukla and zhong r k shukla x zhong derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation j comput phys 204 2005 404 for linear model equations are extended to the full navier stokes equations in the vorticity and streamfunction formulation two methods for the solution of helmholtz and poisson equations using high order compact schemes on non uniform grids are developed the schemes are constructed so that they maintain a high order of accuracy not only in the interior but also at the boundary second order semi implicit temporal discretization is achieved through an implicit backward differentiation scheme for the linear viscous terms and an explicit adam bashforth scheme for the non linear convective terms the boundary values of vorticity are determined using an influence matrix technique the resulting discretized system with boundary closures of the same high order as the interior is shown to be stable when applied to the two dimensional incompressible navier stokes equations provided enough grid points are clustered at the boundary the resolution characteristics of the high order compact finite difference schemes are illustrated through their application to the one dimensional linear wave equation and the two dimensional driven cavity flow comparisons with the benchmark solutions for the two dimensional driven cavity flow thermal convection in a square box and flow past an impulsively started cylinder show that the high order compact schemes are stable and produce extremely accurate results on a stretched grid with more points clustered at the boundary

galerkin spectral method for the vorticity and stream function equations a galerkin legendre spectral method for the solution of the vorticity and stream function equations in uncoupled form under no slip conditions in a square domain is presented which fully exploits the separation of variables in the two elliptic problems benefits from a nonsingular influence matrix and is able to solve the singular driven cavity problem modulo gibbs phenomenon even without regularizing the boundary condition at the corners

perverse equivalences and broueʼs conjecture abstract we give a new approach to the construction of derived equivalences between blocks of finite groups based on perverse equivalences in the setting of broue s abelian defect group conjecture we provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with sylow subgroups elementary abelian of order 9 we also examine extensions to automorphism groups in a general setting

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

parabolic deligne lusztig varieties abstract motivated by the broue conjecture on blocks with abelian defect groups for finite reductive groups we study parabolic deligne lusztig varieties and construct on those which occur in the broue conjecture an action of a braid monoid whose action on their l adic cohomology will conjecturally factor through a cyclotomic hecke algebra in order to construct this action we need to enlarge the set of varieties we consider to varieties attached to a ribbon category this category has a garside family which plays an important role in our constructions so we devote the first part of our paper to the necessary background on categories with garside families

euler characteristic of analogues of a deligne lusztig variety for gln abstract we give a combinatorial formula to calculate the euler characteristic of an analogue of a deligne lusztig variety denoted y w g which is attached to an element w in the weyl group of g l n and g g l n the main theorem of this paper states that the euler characteristic of y w g only depends on the unipotent part of the jordan decomposition of g and the conjugacy class of w it generalizes the formula of the euler characteristic of springer fibers for type a

a transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular in this paper we propose an implicit high order compact hoc finite difference scheme for solving the two dimensional 2d unsteady navier stokes n s equations on irregular geometries on orthogonal grids our scheme is second order accurate in time and fourth order accurate in space it is used to solve three pertinent fluid flow problems namely the flow decayed by viscosity the lid driven square cavity and the flow in a constricted channel it is seen to efficiently capture both transient and steady state solutions of the n s equations with dirichlet as well as neumann boundary conditions apart from including the good features of hoc schemes our formulation has the added advantage of capturing transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variations detailed comparison data produced by the scheme for all the three test cases are provided and compared with analytical as well as established numerical results excellent comparison is obtained in all the cases