on symmetric cauchy riemann manifolds the riemannian symmetric spaces play an important role in different branches of mathematics by definition a connected riemannian manifold m is called symmetric if to every a m there exists an involutory isometric diffeomorphism sa m m having a as isolated fixed point in m or equivalently if the differential dasa is the negative identity on the the tangent space ta tam of m at a in case such a transformation sa exists for a m it is uniquely determined and is the geodesic reflection of m about the point a as a consequence for every riemannian symmetric space m the group g gm generated by all symmetries sa a m is a lie group acting transitively on m in particular m can be identified with the homogeneous space g k for some compact subgroup k g using the elaborate theory of lie groups and lie algebras e cartan classified all riemannian symmetric spaces

periodic unsteady flow analysis using a diagonally implicit harmonic balance method an implicit harmonic balance method is applied to periodic unsteady flow problems diagonal terms of the harmonic source vector are treated implicitly and easily implemented on a diagonalized implicit solver that is very similar to a flow solver the multi grid performance and solution convergence of the present implicit harmonic balance method are investigated with a 2 d oscillating airfoil and a 3 d wing with pitching motion computational results are compared with results from explicit trials and a dual timestepping method in the time domain the present harmonic balance method provides fast and stable convergence characteristics regardless of the number of harmonics results show that the present method can largely reduce the computing time for unsteady flow problems compared to that necessary in the dual time stepping and explicit harmonic balance methods

solution of the euler equations for two dimensional transonic flow by a multigrid method the assumption of potential o w implies that the o w is irrotational this is not strictly correct when shock waves are present an exact description of transonic inviscid o w requires the solution of the euler equations the numerical solution of the euler equations for steady transonic o ws is therefore a problem of great interest to the aeronautical community it also presents a testing challenge to applied mathematicians and numerical analysts

a generalization of borel s theorem and microlocal gevrey regularity in involutive structures in this paper we use borel s procedure to construct gevrey approximate solutions of an initial value problem for involutive systems of gevrey complex vector fields as an application we describe the gevrey wave front set of the boundary values of approximate solutions in wedges w of gevrey involutive structures m v we prove that the gevrey wave front set of the boundary value is contained in the polar of a certain cone t w contained in rv tx where x is a maximally real edge of w we also prove a partial converse

singularities of the hypergeometric system associated with a monomial curve we compute using d module restrictions the slopes of the irregular hypergeometric system associated with a monomial curve we also study rational solutions and reducibility of such systems

existence of gevrey approximate solutions for certain systems of linear vector fields applied to involutive systems of first order nonlinear pdes abstract given a g s involutive structure m v a gevrey submanifold x m which is maximally real and a gevrey function u 0 on x we construct a gevrey function u which extends u 0 and is a gevrey approximate solution for v we then use our construction to study gevrey micro local regularity of solutions u c 2 r n of a system of nonlinear pdes of the form f j x u u x 0 j 1 n where f j x 0 are gevrey functions of order s 1 and holomorphic in 0 c c n the functions f j satisfy an involutive condition and d f 1 d f n 0

on microlocal analyticity and smoothness of solutions of first order nonlinear pdes we study the microlocal analyticity and smoothness of solutions u of of the nonlinear pde ut f x t u ux under some assumptions on the repeated brackets of the linearized operator and its conjugate

mappings and accuracy for chebyshev pseudo spectral approximations abstract the effect of mappings on the approximation by chebyshev collocation of functions which exhibit localized regions of rapid variation is studied a general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials a particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications it is shown that the mapped function can be approximated much more accurately by chebyshev polynomial approximations than the original function the effect on the approximation of introducing subdomains is also studied the accuracy of the pseudo spectral approximation is very sensitive to the location of the interface although this sensitivity is reduced when mappings are employed within the subdomains

demonstration of nonlinear frequency domain methods method in which users deliberately choose not to resolve temporal modes in the solution a variable time period method has been proposed such that the nonlinear frequency domain method can be applied to problems where the time period of the unsteadiness is either known or unknown a priori to validate the latter case results from this method have been compared with experimental results of vortex shedding in low reynolds number flows past cylinders validation of the first case utilizes experimental data of a pitching airfoil in transonic flow these comparisons demonstrate the efficiency of the nonlinear frequency domain method in representing complex nonlinear flow field physics with a limited number of temporal modes

compact implementation strategy for a harmonic balance method within implicit flow solvers a two step approximate factorization technique for implementing a computationally stable nonlinear unsteady frequency domain harmonic balance solution method within existing implicit computational fluid dynamic flow solver codes is presented the approach uses an explicit discretization of the harmonic balance source term and no new implicit code development is required both of these features enable the harmonic balance method to be implemented within existing implicit flow solver codes with minimal modification necessary to the underlying flow solver code the resulting harmonic balance solver can then be used for modeling nonlinear periodic unsteady flows the methodology is applied to the nasa overflow flow solver code and results are presented for transonic viscous flow past an unsteady pitching airfoil section

irregular modified a hypergeometric systems a modified a hypergeometric system is a system of differential equations for the function f tw x where f y is a solution of an a hypergeometric system in n variables and w is an n dimensional integer vector which is called the weight vector we study the irregularity of modified systems by adapting to this case the notion of umbrella introduced by m schulze and u walther especially we study slopes and gevrey series solutions we develop some applications of this study under some conditions we give laplace integral representations of divergent series solutions of the modified system and we show that certain gevrey series solutions of the original a hypergeometric system along coordinate varieties are gevrey asymptotic expansions of holomorphic solutions of the a hypergeometric system

irregular hypergeometric systems associated with a singular monomial curve in this paper we study irregular hypergeometric systems defined by one row specifically we calculate slopes of such systems in the case of reduced semigroups we generalize the case studied by castro and takayama in all the cases we find that there always exists a slope with respect to a hyperplane of this system only in the case of an irregular system defined by a 1 x 2 integer matrix we might need a change of coordinates to study slopes at infinity in the other cases slopes are always at the origin defined with respect to a hyperplane we also compute all the l characteristic varieties of the system so we have a section of the grobner fan of the module defined by the hypergeometric system

gevrey solutions of irregular hypergeometric systems in two variables we describe the gevrey series solutions at singular points of the irregular hypergeometric system gkz system associated with an affine plane monomial curve we also describe the irregularity complex of such a system with respect to its singular support and in particular we prove using elementary methods that this irregularity complex is a perverse sheaf as assured by a theorem of z mebkhout

the a hypergeometric system associated with a monomial curve introduction inthis paper we make a detailed analysis of the hypergeometric system or gkz system associated with a monomial curve and integral hence resonant exponents we describe all rational solutions and show in theorem 1 10 that they are in fact laurent polynomials we also show that for any exponent there are at most two linearly independent laurent solutions and that the upper bound is reached if and only if the curve is not arithmetically cohen macaulay we then construct for all integral parameters a basis of local solutions in terms of the roots of the generic univariate polynomial 0 5 associated with we also determine in theorem 3 7 the holonomic rank r for all z 2 and show that d r d 1 where d is the degree of the curve moreover the value d 1 is attained only for those exponents for which there are two linearly independent rational solutions and therefore r d for all if and only if the curve is arithmetically cohen macaulay inorder to place these results intheir appropriate con text we recall the defin ition

fully implicit chebyshev time spectral method for general unsteady flows an efficient fully implicit chebyshev time spectral method tsm is developed to solve general unsteady flows with or without periodicity high accuracy of the chebyshev time spectral operator is d

a chebyshev spectral collocation method for solving burgers type equations in this paper we elaborated a spectral collocation method based on differentiated chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations the problem is reduced to a system of ordinary differential equations that are solved by runge kutta method of order four numerical results for the nonlinear evolution equations such as 1d burgers kdv burgers coupled burgers 2d burgers and system of 2d burgers equations are obtained the numerical results are found to be in good agreement with the exact solutions numerical computations for a wide range of values of reynolds number show that the present method offers better accuracy in comparison with other previous methods moreover the method can be applied to a wide class of nonlinear partial differential equations

approximate solutions and micro regularity in the denjoy carleman classes abstract we begin with a sequence m of positive real numbers and we consider the denjoy carleman class c m we show how to construct m approximate solutions for complex vector fields with c m coefficients we then use our construction to study micro local properties of boundary values of approximate solutions in general m involutive structures of codimension one where the approximate solution is defined in a wedge whose edge where the boundary value exists is a maximally real submanifold we also obtain a c m version of the edge of the wedge theorem

irregularity of hypergeometric systems via slopes along coordinate subspaces we study the irregularity sheaves attached to the a hypergeometric d module ma introduced by gel fand et al where a z d n is pointed of full rank and c more precisely we investigate the slopes of this module along coordinate subspaces in the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector l on torus equivariant generators to this end we introduce the a l umbrella a simplicial complex determined by a and l and identify its facets with the components of the associated graded ring we then establish a correspondence between the full a l umbrella and the components of the l characteristic variety of ma we compute in combinatorial terms the multiplicities of these components in the l characteristic cycle of the associated euler koszul complex identifying them with certain intersection multiplicities we deduce from this that slopes of ma are combinatorial independent of and in one to one correspondence with jumps of the a l umbrella this confirms a conjecture of sturmfels and gives a converse of a theorem of hotta ma is regular if and only if a defines a projective variety 1991 mathematics subject classification 13n10 14m25 16w70

on irregular binomial d modules we prove that a holonomic binomial d module m a i is regular if and only if certain associated primes of i determined by the parameter vector beta in mathbb c d are homogeneous we further describe the slopes of m a i along a coordinate subspace in terms of the known slopes of some related hypergeometric d modules that also depend on when the parameter is generic we also compute the dimension of the generic stalk of the irregularity of m a i along a coordinate hyperplane and provide some remarks about the construction of its gevrey solutions

mapped chebyshev pseudospectral method for unsteady flow analysis a mapped chebyshev pseudospectral method is developed as an accurate and yet efficient approach to solve unsteady flows preserving the conservation laws the method discretizes a spatial derivative term implicitly whereas a time derivative term is treated explicitly using the mapped chebyshev collocation operator because standard chebyshev points make the corresponding spectral derivative matrix ill conditioned due to uneven distribution of the chebyshev points clustered heavily toward the ends of the interval an inverse sine mapping function is applied to the chebyshev collocation operator so that the point distribution becomes more uniform in a time domain and mitigates numerical instabilities correspondingly computations of unsteady flows including the one dimensional burgers equation and two dimensional airfoil flows under oscillation and plunging motions are carried out numerical results of the present study are compared with those of the conventional time marching solution method and the ha

implementation of k w turbulence models in an implicit multigrid method three turbulence models using linear and nonlinear eddy viscosity formulations are implemented in an implicit multigrid method detailed techniques of implementation are presented and discussed freezing and limiting strategies are applied to improve robustness and convergence of the multigrid method the wilcox w shear stress transport and wilcox durbin wd models are first tested for flat plate flow and the results are in good agreement with the empirical correlations numerical results for unseparated and separated transonic flows show that the wd model using weakly nonlinear eddy viscosity is in better overall agreement with the experimental data particularly for the separated flows the present multigrid diagonalized alternating direction implicit method provides good convergence without any robustness problems

gevrey micro regularity for solutions to first order nonlinear pde abstract let x t r m r and u c 2 r m r we study the gevrey micro regularity of solutions u of the nonlinear equation u t f x t u u x where f x t 0 is a gevrey function of order s 1 and holomorphic in 0 we show that the gevrey wave front set of any c 2 solution u is contained in the characteristic set of the linearized operator l u t j 1 m f j x t u u x x j to achieve this we study the notion of gevrey approximate solutions a concept which we believe is of independent interest and could be applied to much more general situations

irregular hypergeometric d modules abstract we study the irregularity of hypergeometric d modules m a via the explicit construction of gevrey series solutions along coordinate subspaces in x c n as a consequence we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of m a given by m schulze and u walther 2008 in 23 still holds for any full rank integer matrix a we also provide a lower bound for the dimensions of the spaces of gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters holomorphic solutions of m a at nonsingular points can be understood as gevrey solutions of order one along x at generic points and so they are included as a particular case

hypergeometric d modules and twisted gaus manin systems abstract the euler koszul complex is the fundamental tool in the homological study of a hypergeometric differential systems and functions we compare euler koszul homology with d module direct images from the torus to the base space through orbits in the corresponding toric variety our approach generalizes a result by gel fand et al i m gel fand m m kapranov a v zelevinsky generalized euler integrals and a hypergeometric functions adv math 84 2 1990 255 271 mr mr1080980 92e 33015 thm 4 6 and yields a simpler more algebraic proof in the process we extend the euler koszul functor to a category of infinite toric modules and describe multigraded localizations of euler koszul homology

a rational spectral collocation method with adaptively transformed chebyshev grid points a spectral collocation method based on rational interpolants and adaptive grid points is presented the rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed chebyshev points the locations of the grid points are adapted to singularities of the underlying solution and the locations of these singularities are approximated by the locations of poles of chebyshev pade approximants numerical experiments on two time dependent problems one with finite time blow up and one with a moving front indicate that the method far outperforms the standard chebyshev spectral collocation method for problems whose solutions have singularities in the complex plane close to 1 1

computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors a harmonic balance technique for the analysis of unsteady flows about helicopter rotors in forward flight and hover is presented in this paper the aerodynamics of forward flight are highly nonlinear with transonic flow on the advancing blade subsonic flow on the retreating blade and stalled flow over the inner portion of the rotor nevertheless the unsteady flow is essentially periodic in time making it well suited for frequency domain analysis the present method uses periodic boundary conditions that allows one to model the flow field on a computational grid around a single helicopter blade no matter the actual blade count using this approach we compute several solutions each one corresponding to one of several instants in time over one period these time levels are coupled to each other through a spectral time derivative operator in the interior of the computational domain and through the far field and periodic boundary conditions around the boundary of the domain in this paper we apply the method to the three dimensional euler equations although the method can also be applied to three dimensional viscous flows and examine the steady and unsteady aerodynamics about wings and rotors