We give explicit formulae for sums of even powers of secant and cosecant values in terms of Bernoulli numbers and central factorial numbers.

Maps between manifolds M → N (` > 0) have multiple points, and more generally, multisingularities. The closure of the set of points where the map has a particular multisingularity is called the multisingularity locus. There are universal relations among the cohomology classes represented by multisingularity loci, and the characteristic classes of the manifolds. These relations include the celeb...

We prove the Green–Lazarsfeld Secant Conjecture [GL1, Conjecture (3.4)] for extremal line bundles on curves of arbitrary gonality, subject to explicit genericity assumptions.

Let Gr(k, n) be the Plücker embedding of the Grassmann variety of projective k-planes in Pn. For a projective variety X, let σs(X) denote the variety of its s − 1 secant planes. More precisely, σs(X) denotes the Zariski closure of the union of linear spans of s-tuples of points lying on X. We exhibit two functions s0(n) ≤ s1(n) such that σs(Gr(2, n)) has the expected dimension whenever n ≥ 9 an...

The nonlinear behavior of spudcan foundation will lead to the decrease rotational stiffness spudcan, leading increase stress at critical member offshore jack-up drilling platform. Secant is used represent value linear model when soil changes from elastic elasto-plastic and then plastic. In this paper, “wished in-place” small strain finite element analysis (SSFE) simulate load-displacement respo...