The goal of this note is to explain a derivation the formulas for local Euler obstructions determinantal varieties general, symmetric and skew-symmetric matrices, by studying invariant de Rham complex using character simple equivariant D-modules. These calculations are then combined with standard arguments involving Kashiwara's index formula description characteristic cycles implicit in work Bo...

We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of Hölder continuous coefficients as well as piecewise smooth drifts with smooth diffusion matrices. 1991 Mathematics Subject Classification. Primary 60H10; Secondary 65C30. December 22, 2016.

In this paper, A-factor circulant matrices with the structure of a circulant, but with the entries below the diagonal multiplied by the same factor A are introduced. Then the generalized rotation and hyperbolic matrices are defined, using an idea due to Ungar. Considering the exponential property of the generalized rotation and hyperbolic matrices, additive formulae for corresponding matrices a...

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices integration, we try to solve those FDEs. The method’s major objective transform FDE into system algebraic that straightforward with matrix techniques. are constructed using polynomials, which have fewer ...

A bstract We elaborate on the connection between Gel’fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations Feynman Integrals. propose a novel, more efficient algorithm to compute Macaulay matrices, which are used derive systems of differential equations. The matrices then employed obtain linear relations $$ \mathcal{A} <mml:math xmlns:mml="http:/...

Due to considerable recent interest in the use of density matrices for a wide variety of purposes, including quantum computation, we present a general method for their parameterizations in terms of Euler angles. We assert that this is of more fundamental importance than (as several people have remarked to us) “just another parameterization of the density matrix.” There are several uses to which...

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid bodies, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system are written. Then using the equivalence of EL and Newton–Euler (NE) equations, and the DeNOC m...

In the present work, the nonlinear equation of motion of Bernoulli-Euler beam is used for investigating the scalability of the shooting method. A parallel implementation of the complete process of computing the nonlinear frequency-response function is presented and its efficiency is studied. The process involves algebraic operations of sparse and dense matrices and also solutions of linear and ...

Recurrence relations are derived for constructing rotation matrices between complex spherical harmonics directly as polynomials of the elements of the generating3×3 rotation matrix, bypassing the intermediary of any parameters such as Euler angles. The connection to the rotation matrices for real spherical harmonics is made explicit. The recurrence formulas furnish a simple, efficient, and nume...

It is well-known that for each prime power q and for each d ∈ 2N, there exists a circulant weighing matrix of order q d+1−1 q−1 and weight q . We extend this result to show that there exist φ(d+1) 2 inequivalent circulant weighing matrices of order q d+1−1 q−1 and weight q , where φ is the Euler totient function. Further, we obtain a bound on the magnitude of the values taken by the cross-corre...