In this paper we study the dimension of secant varieties of Segre-Veronese varieties P × P embedded by the morphism given by O(1, 2). Given the dimensions m, n, we provide two functions s(m, n) and s(m, n), such that the s secant variety is nondefective, i.e. it has the expected dimension, if s ≤ s(m, n) or s ≥ s(m, n). Finally, we present a conjecturally complete list of defective secant varie...

An all-optical Orthogonal Frequency Division Multiplexing communication system at 2 THz is modeled using photonic crystal fiber of length 1km, and the performance of four carrier waveforms hyperbolic secant, square of hyperbolic secant, square and sinusoidal is evaluated using standard metrics such as eye diagram and bit error rate. From the above mentioned valuations, one can deduce the minima...

We establish basic techniques for studying the ideals of secant varieties of Segre varieties. We solve a conjecture of Garcia, Stillman and Sturmfels on the generators of the ideal of the first secant variety in the case of three factors and solve the conjecture set-theoretically for an arbitrary number of factors. We determine the low degree components of the ideals of secant varieties of smal...

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...

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. derive estimators parameters using modified maximum likelihood methodology and explore properties so obtained. show that proposed are more efficient robust than commonly used least square estimators. also develop relevant test hypothesis...