This paper studies the dimension of secant varieties to Segre varieties. The problem is cast both in the setting of tensor algebra and in the setting of algebraic geometry. An inductive procedure is built around the ideas of successive specializations of points and projections. This reduces the calculation of the dimension of the secant variety in a high dimensional case to a sequence of calcul...

We give an almost asymptotically sharp bound for the non-secant defectiveness and identifiability of Segre–Veronese varieties. also provide new examples defective varieties, implement our methods in Magma. Finally, we two applications techniques: classify possibly singular 2-secant toric surfaces study secant Losev–Manin spaces.

We intend to give a classification of smooth nondegenerate projective varieties admitting extremal or next to extremal curvilinear secant subspaces. Gruson, Lazarsfeld and Peskine classified all projective integral curves with extremal secant lines. On the other hand, if a locally Cohen-Macaulay variety Xn ⊂ Pn+e of degree d meets with a linear subspace L of dimension β at finite points, then l...

In this work we study a class of Secant-like iterations for solving nonlinear and non-differentiable equations in Banach spaces. We consider a condition for divided differences which generalizes those usual ones, i.e, Lipschitz continuous and Hölder continuous conditions. A semilocal convergence result is obtained. For that, we use a technique based on a new system of recurrence relations to ob...

We show the secant variety of a linearly normal smooth curve of degree at least 2g + 3 is arithmetically Cohen-Macaulay, and we use this information to study the graded Betti numbers of the secant variety.

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds ...

Here we study (in positive characteristic) integral curves X ⊂ Pr with secant degree one, i.e., for which a general P ∈ Seck−1(X) is in a unique k-secant (k − 1)-dimensional linear subspace.

in this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. to approach this aim the analytical formulas of secant stiffness matrix are presented. the models were validated and used to perform inve...

This paper is concerned with an important theorem due to Fyodor L. Zak, which appeared in [Za1]: Let X ⊂ P be a (reduced and irreducible) subvariety. A k – secant space to X is a k – dimensional linear subspace of P which is spanned by k+1 points from X, the k – secant variety of X in P is the (closure of the) union of all the k – secant spaces of X. Zak denotes this space by S(X), we shall als...

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n2(logn)2+o(1)) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n2) integer operations. These algorithms are extremely simple, and fast fo...