Restricted secant varieties of Grassmannians are constructed from sums points corresponding to $k$-planes with the restriction that their intersection has a prescribed dimension. We study dimensions restricted and relate them analogous question for secants via an incidence variety construction. define notion expected dimension give formula all holds if Baur-Draisma-deGraaf Conjecture on non-def...

The paper is concerned with the numerical solution of non-linear conservation laws, and the contribution biomechanical models of spine and of loaded wrist are formulated and analysed. The models are based on a contact problem in non-linear elastic rheology. The stress–strain relation is derived from a positive definite strain energy density function. For a weak solution of the problem, a variat...

We find minimal generators for the ideals of secant varieties of Segre varieties in the cases of σk(P 1 × P n × P ) for all k, n,m, σ2(P n × P m × P p × P ) for all n,m, p, r (GSS conjecture for four factors), and σ3(P n ×P m ×P ) for all n,m, p and prove they are normal with rational singularities in the first case and arithmetically Cohen-Macaulay in the second two.

We introduce and discuss a condition generalizing one of the Archimedean properties characterizing parabolas. Archimedes was familiar with the following property of parabolas: If for any two points A, B on a parabola we denote by S the area of the region between the parabola and the secant AB, and by T the maximum of the area of the triangle ABC, where C is a point on the parabola between A and...

A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction of a quantity that combines gain and phase information for each system in the cascade. For linear one-dimensional systems, the known result is recovered exactly. © 2005 Elsevier B.V. All rights reserved.