The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

Let p be an odd prime and {χ(m) = (m/p)}, m = 0,1, . . . ,p − 1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m,p)= 1. We study the relation between the Gauss and the quadratic Gauss sums. It is shown that the quadratic Gauss sumsG(k;p) are equal to the Gauss sums G(k,χ) that correspond to this ...

The post-optimality analysis of a tetrahedral formation flying optimal control problem is considered. In particular, this four-spacecraft orbit insertion problem is transcribed to a nonlinear programming problem (NLP) using a direct method called the Gauss pseudospectral method. The Karush-Kuhn-Tucker (KKT) conditions for this NLP are then derived and are compared to the conditions obtained via...

In this paper we introduce a process we have called “Gauss-Seidelization” for solving nonlinear equations. We have used this name because the process is inspired by the well-known Gauss-Seidel method to numerically solve a system of linear equations. Together with some convergence results, we present several numerical experiments in order to emphasize how the Gauss-Seidelization process influen...

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss-Manin connection are integral linear combinations of the weights which define the local system.

We study the biharmonic stress-energy tensor S2 of Gauss map. Adding few assumptions, the Gauss map with vanishing S2 would be harmonic.

for 12386 A Comparison Theorem of the Improving Gauss-Seidel method for H-matrix and its Comparison Matrix Authors: liying Sun, xingye xu Affiliations: Math Dept.of Guangdong Education Institute, Math Dept. of Guangdong Education Institute

We give an estimate of the Gauss curvature for minimal surfaces in R m whose Gauss map omits more than m(m + 1)=2 hyperplanes in P m?1 (C).