The “D” matrices for all states of the two fundamental representations and octet are shown in the generalized Euler angle parameterization. The raising and lowering operators are given in terms of linear combinations of the left invariant vector fields of the group manifold in this parameterization. Using these differential operators the highest weight state of an arbitrary irreducible represen...

Euler number of a binary image is a fundamental topological feature that remains invariant under translation, rotation, scaling, and rubber-sheet transformation of the image. In this work, a run-based method for computing Euler number is formulated and a new hardware implementation is described. Analysis of time complexity and performance measure is provided to demonstrate the efficiency of the...

The Euler characteristic heuristic has been proposed as a method for approximating the upper tail probability of the maximum of a random field with smooth sample path. When the random field is Gaussian, this method is proved to be valid in the sense that the relative approximation error is exponentially smaller. However, very little is known about the validly of the method when the random field...

In this manuscript we are interested in stored energy functionals W defined on the set of d × d matrices, which not only fail to be convex but satisfy limdet ξ→0+ W (ξ) = ∞. We initiate a study which we hope would lead to a theory for the existence and uniqueness of minimizers of functionals of the form E(u) = ∫ Ω (W (∇u) − F · u)dx, as well as their Euler–Lagrange equations. The techniques dev...

We present a streamline-upwind/Petrov±Galerkin (SUPG) algorithm for the solution of the compressible Euler equations at low Mach numbers. The Euler equations are written in terms of entropy variables which result in Jacobian matrices which are symmetric. We note that, in the low Mach number limit, the SUPG method with the standard choices for the stabilization matrix fail to provide adequate st...

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet Lfunctions in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz-Sarnak classification, these are believed to represent families of L-function with unitary symmetry. We here extend the formalism to families with ...

Two semi-implicit methods based on the splitting of the Euler equations ux into uid and acoustic parts applied to low Mach number ows are presented. The rst method is based on the splitting of slow and fast eigenvalues of the jacobian matrix of the uxes and a semi-implicit scheme is constructed by introducing only the fast eigenvalues in the implicit matrices. The second method is based on the ...

There is a large body of literature on the problem of stability for inviscid shock waves and in particular for gas dynamics, see [2, 17, 3, 5, 6, 9, 10, 16, 4, 7, 21, 12, 13, 1, 14, 15, 24]. The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function,” for the Euler equations of compressible gas dynamics. We describe two approaches to this problem. In the fir...

We introduce an affine extension of the Euler tensor which encompasses all of the inertia properties of interest in a convenient linear format, and we show how it transforms under affine maps. This result generalizes the standard theorems on the action of rigid transformations (translations and rotations) on inertia properties, allowing for stretch and shear components of the transformation. Mo...

We develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for rst-order advection-reaction equations on general multi-dimensional domains. Diierent tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes naturally incorporate innow boundary conditions into their formulations and do not ...