We present new algorithms for the solution of large structured Markov models whose innnitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shuue-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobi-style and Gauss-Seidel-style m...

We present new algorithms for the solution of large structured Markov models whose infinitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shuffle-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobi-style and Gauss-Seidel-styl...

A new algorithm for mesh simplification with triangle constriction is presented in this paper. Constricting error defined by a combination of square volume error variation with constraint (SVEC), shape factor and normal constraint factor of triangle. Gauss curvature factor of each constricted triangle is used to distinguish strong feature triangle or nonstrong feature triangle. The triangle whi...

S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive pr...

We present a number of classical proofs of the irreducibility of the n-th cyclotomic polynomial Φn(x). For n prime we present proofs due to Gauss (1801), in both the original and a simplified form, Kronecker (1845), and Schönemann/Eisenstein (1846/1850), and for general n proofs due to Dedekind (1857), Landau (1929), and Schur (1929). Let Φn(x) denote the n-th cyclotomic polynomial, defined by ...

We give the best possible upper bound on the number of exceptional values and totally ramified value number of the hyperbolic Gauss map for pseudo-algebraic Bryant surfaces and some partial results on the Osserman problem for algebraic Bryant surfaces. Moreover, we study the value distribution of the hyperbolic Gauss map for complete constant mean curvature one faces in de Sitter three-space.

Corrections to solar system gravity are derived for f(G) gravity theories, in which a function of the Gauss-Bonnet curvature term is added to the gravitational action. Their effects on Newton’s law, as felt by the planets, and on the frequency shift of signals from the Cassini spacecraft, are both determined. Despite the fact that the Gauss-Bonnet term is quadratic in curvature, the resulting c...

The goal of this paper is to describe Zermelo’s navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method in order to evaluate its control curvature. We will show that up to changing the Riemannian metric on the manifold the control curvature of Zermelo’s problem has a simple to handle expression which naturally leads to a generalization of the cl...

We give an expression, in terms of the so-called Hermitian intrinsic volumes, for the measure of the set of complex r-planes intersecting a regular domain in any complex space form. Moreover, we obtain two different expressions for the Gauss-BonnetChern formula in complex space forms. One of them expresses the Gauss curvature integral in terms of the Euler characteristic and some Hermitian intr...

To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the differential of the Gauss map of the underlying surface. The Gauss map assigns to each point in the surface the unit normal vector of the tangent plane to the surface...