on the eisenstein cohomology of arithmetic groups the cohomology h gamma e of an arithmetic subgroup gamma of a connected reductive algebraic group g defined over some algebraic number field f can be interpreted in terms of the automorphic spectrum of gamma with this framework in place there is a sum decomposition of the cohomology into the cuspidal cohomology i e classes represented by cuspidal automorphic forms for g and the so called eisenstein cohomology constructed as the span of appropriate residues or derivatives of eisenstein series attached to cuspidal automorphic forms on the levi components of proper parabolic f subgroups of g the main objective of this paper is to isolate a specific structural part in the eisenstein cohomology this pertains to regular eisenstein cohomology classes attached to cuspidal automorphic representations whose archimedean component is tempered it is shown that the cohomological degree of these classes is bounded from below by the constant q 0 g mathbb r 1 2 dim x g mathbb r rk g mathbb r rk k mathbb r where k mathbb r denotes a maximal compact subgroup of the real lie group g mathbb r where x g mathbb r is the associated symmetric space this investigation has various applications one of these is a vanishing result for the cohomology in the generic case i e where the representation determining the coefficient system e has regular highest weight in degrees below q 0 g mathbb r this is a sharp bound depending only on the underlying real lie group g mathbb r corollary 5 6 proposition 5 8 this result is supplemented by a qualitative structural result in the description of the cohomology in higher degrees by means of regular eisenstein cohomology classes

on the cuspidal cohomology of arithmetic groups it is the main objective of this paper to show a vanishing result for cuspidal cohomology of arithmetic groups in classical groups g defined over some number field k our approach relies on the fact that cuspidal automorphic forms are nonsingular in the sense of howe this result puts a strong constraint on the archimedean components of irreducible cuspidal automorphic representations of g that can possibly contribute to the cuspidal cohomology combining this with the classification of vogan zuckerman of unitary representations with nonzero cohomology provides a constant r 0 g k only depending on g k below which the cuspidal cohomology vanishes we will give a formula for this constant for each classical group of type i in the classification scheme due to weil we conclude with making this result explicit for some split classical groups over a totally real algebraic number field

inference in linear time series models with some unit roots this paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots our motivating example is a vector autoregression with some unit roots in the companion matrix which might include polynomials in time as regressors in the general formulation the variable might be integrated or cointegrated of arbitrary orders and might have drifts as well we show that parameters that can be written as coefficients on mean zero nonintegrated regressors have jointly normal asymptotic distributions converging at the rate t 2 in general the other coefficients including the coefficients on polynomials in time will have nonnormal asymptotic distributions the results provide a formal characterization of which t or f tests such as granger causality tests will be asymptotically valid and which will have nonstandard limiting distributions

boundary and eisenstein cohomology of mathrm sl _3 mathbb z sl3 z in this article several cohomology spaces associated to the arithmetic groups mathrm sl 3 mathbb z and mathrm gl 3 mathbb z with coefficients in any highest weight representation mathcal m lambda have been computed where lambda denotes their highest weight consequently we obtain detailed information of their eisenstein cohomology with coefficients in mathcal m lambda when mathcal m lambda is not self dual the eisenstein cohomology coincides with the cohomology of the underlying arithmetic group with coefficients in mathcal m lambda in particular for such a large class of representations we can explicitly describe the cohomology of these two arithmetic groups we accomplish this by studying the cohomology of the boundary of the borel serre compactification and their euler characteristic with coefficients in mathcal m lambda at the end we employ our study to discuss the existence of ghost classes

some advanced concepts in discrete aerodynamic sensitivity analysis abstract 1 0 introduction an efficient incremental iterative approach for dif ferentiating advanced flow codes is successfully demon strated on a 2d inviscid model problem the methodemploys the reverse mode capability of the automatic differentiation software tool adifor 3 0 and isproven to yield accurate first order aerodynamic sensi tivity derivatives a substantial reduction in cpu timeand computer memory is demonstrated in comparisonwith results from a straight forward black box t everse mode application of adifor 3 0 to the same flowcode an adifor assisted procedure for accurate sec ond order aerodynamic sensitivity derivatives is suc cessfidly verified on an inviscid transonic lifting airfoilexample problem the method requires that first orderderivatives are calculated first using both the fonvard direct and reverse adjoint procedures then a veryefficient non iterative calculation of all second orderderivatives can be accomplished accurate second de rivatives le the complete hessian matrices of lift wave drag and pitching moment coefficients are calcu lated with respect to geometric shape angle of attack and freestream mach numbercomputing sensitivity derivatives sds from high fidelity nonlinear cfd codes is an enabling technologyfor design of advanced concept vehicles in recent yearssignificant progress has been achieved in the efficientcalculation of accurate sds from these cfd codes the automatic differentiation ad software tooladifor automatic differentiation of fortran has been proven an effective tool for extracting aerody namlc

application of an automatic differentiation method to a 2d navier stokes cfd code abstract the adifor2 0 automatic differentiator is applied to the flomgem flow solver along with the grid generator hyperg2 the flomgem is an advanced navier stokes cfd code for airfoil computations which employs multigrid method the hyperg2 is a two dimensional hyperbolic grid generator for generating a c mesh both non geometric and geometric sensitivity derivative codes are obtained the sensitivity derivatives via automatic differentiation are presented and compared with divided difference generated derivatives the study shows that an automatic differentiation method gives accurate derivative values in an efficient manner

the dihedral lie algebras and galois symmetries of pi_1 l mathbb p 0 infty cup mu_n we describe the image of the absolute galois group acting on the pro l completion of the fundamental group of the mathbb g m minus n th roots of unity we relate the structure of the image with geometry and topology of modular varieties for the congruence subgroups gamma 1 m n of rm gl m mathbb z for m 1 2 3 ldots

variable fidelity aerodynamic optimization for turbulent flows using a discrete adjoint formulation an aerodynamic shape optimization methodology based on a discrete adjoint solver for navier stokes flows is described the flow solver at the heart of this optimization process is a reynolds averaged navier stokes code for multiblock structured grids it uses osher s approximate riemann solver and the algebraic turbulence model of baldwin lomax a corresponding discrete navier stokes adjoint solver is derived analytically it has to calculate accurately the jacobian including the effect of the turbulence modeling the shape deformations

on the non vanishing of the first betti number of hyperbolic three manifolds we show the non vanishing of cohomology groups of sufficiently small congruence lattices in sl 1 d where d is a quaternion division algebra defined over a number field e contained inside a solvable extension of a totally real number field as a corollary we obtain new examples of compact arithmetic hyperbolic three manifolds with non torsion first homology group confirming a conjecture of waldhausen the proof uses the characterisation of the image of solvable base change by the author and the construction of cusp forms with non zero cusp cohomology by labesse and schwermer

asymptotic normality when regressors have a unit root under fairly general conditions ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables standard formulas may be used to calculate a consistent estimate of the asymptotic variance covariance matrix of the estimated parameter vector even if the disturbances are conditionally heteroskedastic and autocorrelated so inference may proceed in the usual way the key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero copyright 1988 by the econometric society

the cointegrated vector autoregressive model with general deterministic terms abstract in the cointegrated vector autoregression cvar literature deterministic terms have until now been analyzed on a case by case or as needed basis we give a comprehensive unified treatment of deterministic terms in the additive model x t z t y t where z t belongs to a large class of deterministic regressors and y t is a zero mean cvar we suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent as well as an algorithm for deriving the additive model parameters from the extended model parameters we derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms in particular we give conditions under which the estimators are asymptotically mixed gaussian such that associated tests are 2 distributed

a comparison of optimization based approaches for a model computational aerodynamics design problem abstract the objective of this paper is to compare three optimization based methods for solving aerodynamic design problems we use the euler equations for one dimensional duct flow as a model problem the optimization methods are i the black box method with finite difference gradients ii a modification where gradients are found by an algorithm based on the implicit function theorem and iii an all atonce method where the flow and design variables are simultaneously altered the three methods are applied to the model problem and compared for efficiency robustness and implementation difficulty we also show that the black box implicit gradient method is equivalent to applying the variational or optimal control approach to design optimization directly to the discretized analysis problem rather than to the continuous problem as is usually done the black box method with implicit gradients seems to provide a good compromise of features and can be retrofitted to most existing analysis codes to turn them into design codes although the all at once method was found to be less robust than the black box methods when it succeeded it was considerably more efficient

modular representations of gl 3 fp symmetric squares and mod p cohomology of gl 3 z abstract we prove certain cases of nonabelian reciprocity between mod p galois representations and hecke eigenclasses in the mod p cohomology of gl 3 z using the symmetric square liftings from gl 2 and congruences on hecke eigenvalues we need to develop some modular representation theory for gl 3 z p in some cases we also need to invoke certain computer calculations to finish the proof

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

surface subgroups of kleinian groups with torsion we prove that every finitely generated kleinian group that contains a finite non cyclic subgroup either is finite or virtually free or contains a surface subgroup hence every arithmetic kleinian group contains a surface subgroup

increasing the number of fibered faces of arithmetic hyperbolic 3 manifolds we exhibit a closed hyperbolic 3 manifold which satisfies a very strong form of thurston s virtual fibration conjecture in particular this manifold has finite covers which fiber over the circle in arbitrarily many ways more precisely it has a tower of finite covers where the number of fibered faces of the thurston norm ball goes to infinity in fact faster than any power of the logarithm of the degree of the cover and we give a more precise quantitative lower bound the example manifold m is arithmetic and the proof uses detailed number theoretic information at the level of the hecke eigenvalues to drive a geometric argument based on fried s dynamical characterization of the fibered faces the origin of the basic fibration m s 1 is the modular elliptic curve e x 0 49 which admits multiplication by the ring of integers of q 7 we first base change the holomorphic differential on e to a cusp form on gl 2 over k q 3 and then transfer over to a quaternion algebra d k ramified only at the primes above 7 the fundamental group of m is a quotient of the principal congruence subgroup of o d of level 7 to analyze the topological properties of m we use a new practical method for computing the thurston norm which is of independent interest we also give a noncompact finite volume hyperbolic 3 manifold with the same properties by using a direct topological argument

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

implicit flux split schemes for the euler equations progress in the development of implicit algorithms for the euler equations using the flux vector splitting method is described comparisons of the relative efficiency of relaxation and spatially split approximately factored methods on a vector processor for transonic and supersonic twodimensional channel flows are made a hybrid threedimensional algorithm is developed that uses relaxation in one coordinate direction and approximate factorization in the crossflow plane the scheme is completely vectorizable and recovers conventional space marching schemes for fully supersonic flows the method is applied to a forebody shape in supersonic flow with an embedded pocket of subsonic flow

aerodynamic shape optimization using preconditioned conjugate gradient methods in an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure it is demonstrated that preconditioned conjugate gradient like methodologies dramatically decrease the computational efforts required for such procedures the design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric naca 0012 airfoil in inviscid transonic flow and at zero degrees angle of attack the complete surface shape is represented using a bezier bernstein polynomial

representations des groupes reductifs p adiques et de leurs sous groupes distingues cocompacts resume soient g et h deux groupes reductifs p adiques et h g une isogenie centrale a silberger a prouve qu une representation complexe admissible irreductible de g a pour restriction via une representation admissible semi simple de longueur finie de h nous prouvons que reciproquement toute representation complexe admissible irreductible de h est facteur direct d une telle restriction et s etend en une representation admissible d un sous groupe ouvert d indice fini de g nous etendons la portee de ces resultats en les reliant aux proprietes algebriques des categories de representations lisses de g et h let g h be reductive p adic groups and h g a central isogeny a silberger has proved that any admissible irreducible complex representation of g restricts via to a direct sum of finitely many admissible irreducible representations of h we prove that conversely any admissible irreducible complex representation of h occurs as a direct summand of such a restriction and extends to an admissible representation of a finite index open subgroup of g we extend those results by linking them with algebraic properties of the categories of smooth representations of g and h

a multidisciplinary optimization using semi analytical sensitivity analysis procedure and multilevel decomposition abstract this paper addresses the development of a multidisciplinary optimization procedure using an efficient semi analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles a semi analytical sensitivity analysis procedure is developed for aerodynamic design sensitivities accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique the optimization problem with the integration of aerodynamics and structures is decomposed into two levels optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level aerodynamic analysis is performed by solving the three dimensional parabolized navier stokes equations a nonlinear programming technique and an approximate analysis procedure are used for optimization the procedure developed is applied to design the wing of a high speed aircraft results obtained show significant improvements in the wing aerodynamic and structural performance when compared to a reference or baseline wing configuration the use of the semi analytical sensitivity technique provides significant computational savings

on the cuspidal cohomology of arithmetic subgroups of mathrm sl 2n and the first betti number of arithmetic 3 manifolds

eigenvalues of the laplacian the first betti number and the congruence subgroup problem theorem 1 1 let f be an arithmetic lattice in the real lie group so n 1 n 2 if n 7 then assume r does not come from the twisted forms 3 6d4 if n 3 and f comes from the units of a quaternion algebra over a number field l with a unique complex embedding then assume l has a subfield of index 2 then for some finite index congruence subgroup fo of r the commutator quotient is infinite equivalently 1 fo the first betti number of the manifold fo hn is nonzero when 1 so n 1 so n is the n dimensional hyperbolic space

mirror image distributions and the dickey fuller regression with a maintained trend abstract a puzzle of many empirical studies where dickey fuller regressions with a maintained trend are run is that the t test of the ar root and the trend t statistic frequently appear to be of equal magnitude but with opposite sign in this paper i demonstrate that when the true process contains a drift then the asymptotic distributions of the two statistics will be the mirror image of each other and even in finite samples this property will be predominant as long as the standardized drift is sufficiently strong

an approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives in this study involving advanced fluid flow codes an incremental iterative formulation also known as the delta or correction form together with the well known spatially split approximate factorization algorithm is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis for smaller 2d problems a direct method can be applied to solve these linear equations in either the standard or the incremental form in which case the two are equivalent iterative methods are needed for larger 2d and future 3d applications however because direct methods require much more computer memory than is currently available iterative methods for solving these equations in the standard form are generally unsatisfactory due to a lack of diagonal dominance and perhaps ill conditioning of the coefficient matrix this problem can be overcome when these equations are cast in the incremental form these and other benefits are discussed herein the methodology is successfully implemented and tested in 2d using an upwind cell centered finite volume formulation applied to the thin layer navier stokes equations results are presented for two sample airfoil problems 1 subsonic low reynolds number laminar flow and 2 transonic high reynolds number turbulent flow

sensitivity derivatives for three dimensional supersonic euler code using incremental iterative strategy in a recent work an incremental strategy was proposed to iteratively solve the very large systems of linear equations that are required to obtain quasianalytical sensitivity derivatives from advanced computational fluid dynamics cfd codes the technique was sucessfully demonstrated for two large two dimensional problems a subsonic and a transonic airfoil the principal feature of this incremental iterative stategy is that it allows the use of the identical approximate coefficient matrix operator and algorithm to solve the nonlinear flow and the linear sensitivity equations at convergence the accuracy of the sensitivity derivatives is not compromised this feature allows a comparatively straightforward extension of the methodology to three dimensional problems this extension is successfully demonstrated in the present study for a space marching solution of the three dimensional euler equations over a mach 2 4 blended wing body configuration

doubly cuspidal cohomology for principal congruence subgroups of gl 3 z the cohomology of arithmetic groups is made up of two pieces the cuspidal and noncuspidal parts within the cuspidal cohomology is a subspacethe f cuspidal cohomology spanned by the classes that generate representations of the associated finite lie group which are cuspidal in the sense of finite lie group theory few concrete examples of f cuspidal cohomology have been computed geometrically outside the cases of rational rank 1 or where the symmetric space has a hermitian structure this paper presents new computations of the f cuspidal cohomology of principal congruence subgroups f p of gl 3 2 of prime level p we show that the f cuspidal cohomology of f p vanishes for all p 19 with p 11 but that it is nonzero for p 11 we give a precise description of the f cuspidal cohomology for jt 11 in terms of the f cuspidal representations of the finite lie group gl 3 e 11 we obtained the result ultimately by proving that a certain large complex matrix m is rank deficient computation with the svd algorithm gave strong evidence that m was rank deficient but to prove it we mixed ideas from numerical analysis with exact computation in algebraic number fields and finite fields