7,463 research outputs found
Matrix interpretation of multiple orthogonality
In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence
relation in terms of type II multiple orthogonal polynomials.We rewrite
this recurrence relation in matrix form and we obtain a three-term recurrence
relation for vector polynomials with matrix coefficients. We present a matrix
interpretation of the type II multi-orthogonality conditions.We state a Favard
type theorem and the expression for the resolvent function associated to the
vector of linear functionals. Finally a reinterpretation of the type II Hermite-
Padé approximation in matrix form is given
Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method
We describe a sparse grid collocation algorithm to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method may be in applications by computing the nonlinear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with 2, 4, and 6 countries (i.e., up to 12 continuous state variables).
Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method
We describe a sparse grid collocation algorithm to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method may be in applications by computing the nonlinear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with 2, 4, and 6 countries (i.e., up to 12 continuous state variables).
Hyperspherical harmonics for tetraatomic systems
A recursion procedure for the analytical generation of hyperspherical harmonics for tetraatomic systems, in terms of row-orthonormal hyperspherical coordinates, is presented. Using this approach and an algebraic Mathematica program, these harmonics were obtained for values of the hyperangular momentum quantum number up to 30 (about 43.8 million of them). Their properties are presented and discussed. Since they are regular at the poles of the tetraatomic kinetic energy operator, are complete, and are not highly oscillatory, they constitute an excellent basis set for performing a partial wave expansion of the wave function of the corresponding Schrödinger equation in the strong interaction region of nuclear configuration space. This basis set is, in addition, numerically very efficient and should permit benchmark-quality calculations of state-to-state differential and integral cross sections for those systems
Recursive regularization step for high-order lattice Boltzmann methods
A lattice Boltzmann method (LBM) with enhanced stability and accuracy is
presented for various Hermite tensor-based lattice structures. The collision
operator relies on a regularization step, which is here improved through a
recursive computation of non-equilibrium Hermite polynomial coefficients. In
addition to the reduced computational cost of this procedure with respect to
the standard one, the recursive step allows to considerably enhance the
stability and accuracy of the numerical scheme by properly filtering out second
(and higher) order non-hydrodynamic contributions in under-resolved conditions.
This is first shown in the isothermal case where the simulation of the doubly
periodic shear layer is performed with a Reynolds number ranging from to
, and where a thorough analysis of the case at is
conducted. In the latter, results obtained using both regularization steps are
compared against the BGK-LBM for standard (D2Q9) and high-order (D2V17 and
D2V37) lattice structures, confirming the tremendous increase of stability
range of the proposed approach. Further comparisons on thermal and fully
compressible flows, using the general extension of this procedure, are then
conducted through the numerical simulation of Sod shock tubes with the D2V37
lattice. They confirm the stability increase induced by the recursive approach
as compared with the standard one.Comment: Accepted for publication as a Regular Article in Physical Review
On models of the braid arrangement and their hidden symmetries
The De Concini-Procesi wonderful models of the braid arrangement of type
are equipped with a natural action, but only the minimal model
admits an `hidden' symmetry, i.e. an action of that comes from its
moduli space interpretation. In this paper we explain why the non minimal
models don't admit this extended action: they are `too small'. In particular we
construct a {\em supermaximal} model which is the smallest model that can be
projected onto the maximal model and again admits an extended action.
We give an explicit description of a basis for the integer cohomology of this
supermaximal model.
Furthermore, we deal with another hidden extended action of the symmetric
group: we observe that the symmetric group acts by permutation on the
set of -codimensionl strata of the minimal model. Even if this happens at a
purely combinatorial level, it gives rise to an interesting permutation action
on the elements of a basis of the integer cohomology
Gaussian Bounds for Noise Correlation of Functions
In this paper we derive tight bounds on the expected value of products of
{\em low influence} functions defined on correlated probability spaces. The
proofs are based on extending Fourier theory to an arbitrary number of
correlated probability spaces, on a generalization of an invariance principle
recently obtained with O'Donnell and Oleszkiewicz for multilinear polynomials
with low influences and bounded degree and on properties of multi-dimensional
Gaussian distributions. The results derived here have a number of applications
to the theory of social choice in economics, to hardness of approximation in
computer science and to additive combinatorics problems.Comment: Typos and references correcte
Discrete Fourier Analysis and Chebyshev Polynomials with Group
The discrete Fourier analysis on the
-- triangle is deduced from the
corresponding results on the regular hexagon by considering functions invariant
under the group , which leads to the definition of four families
generalized Chebyshev polynomials. The study of these polynomials leads to a
Sturm-Liouville eigenvalue problem that contains two parameters, whose
solutions are analogues of the Jacobi polynomials. Under a concept of
-degree and by introducing a new ordering among monomials, these polynomials
are shown to share properties of the ordinary orthogonal polynomials. In
particular, their common zeros generate cubature rules of Gauss type
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