Under an explicit positivity condition, we show the first secant variety of a linearly normal smooth variety is projectively normal, give results on the regularity of the ideal of the secant variety, and give conditions on the variety that are equivalent to the secant variety being arithmetically Cohen-Macaulay. Under this same condition, we then show that if X satisfies Np+2dim(X), then the se...

We draw here on the relation between the Cauchy and hyperbolic secant distributions to prove that the MLE of the scale parameter of Cauchy distribution is log-normally distributed and to study the properties of a Hodges-Lehmann type estimator for the scale parameter. This scale estimator is slightly biased but performs well even on small samples regardless of the location parameter. The asympto...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The notion of a secant for locally Lipschitz continuous functions is introduced and a new algorithm to locally minimize nonsmooth, nonconvex functions based on secants is developed. We demonstrate that the secants can be used to design an algorithm to find descent directions of locally Lipschitz continuous functions. This algorithm is applied to design a minimization method, called a secant met...

We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the classification of defective secant varieties of Segre-Veronese varieties with three or more factors.

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct. Keywords—Nonlinear equations, Secant method, Convergence order, Secant-like method.

This paper is devoted to the study of higher secant varieties of varieties of completely decomposable forms. The main goal is to develop methods to inductively verify the non-defectivity of such secant varieties. As an application of these methods, we will establish the existence of large families of non-defective secant varieties of “small” varieties of completely decomposable forms.

The article describes a certain computation method of -arcs to construct the number distinct in for . In this method, new approach employed compute and arcs respectively. This is based on choosing inequivalent classes } -secant distributions that 4-secant, 3-secant, 2-secant, 1-secant 0-secant each process. maximum size -arc has been constructed by tool deal with programming difficulties someti...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...