Historical Development of the BFGS Secant Method and Its Characterization Properties by Joanna Maria Papakonstantinou The BFGS secant method is the preferred secant method for finite-dimensional unconstrained optimization. The first part of this research consists of recounting the historical development of secant methods in general and the BFGS secant method in particular. Many people believe t...

We propose an exact solution to a linear two-level system with the existence of special hyperbolic secant external field and elucidate its transition dynamics. then extend model nonlinear case show that nonlinearity will significantly affect As increases, Landau–Zener–Stückelberg–Majorana interference fringes can be constructive up energy level in adiabatic limit splits into three levels. For f...

In this paper, authors examine flows with a finite hyperbolic chain-recurrent set without heteroclinic intersections on arbitrary closed n-manifolds. For such flows, the existence of dual attractor and repeller is proved. These points are separated by (n−1)-dimensional sphere, which secant for wandering trajectories in complement to repeller. The study flow dynamics makes it possible obtain top...

We determine a Gröbner basis for the secant ideal of the toric ideal associated to the second hypersimplex ∆(2, n), with respect to any circular term order. The Gröbner basis of the secant ideal requires polynomials of odd degree up to n. This shows that the circular term order is 2-delightful, resolving a conjecture of Drton, Sturmfels, and the author. The proof uses Gröbner degenerations for ...

This work demonstrates the attractivity of alpha-skew hyperbolic secant distribution, a new skewed distribution based on technique and distribution. In first part, we determine its main features, including cumulative function, modality, non-central moments, skewness, kurtosis, moment generating function characteristic function. The remaining part is devoted to model applicability in statistical...

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 study the potential for controlled transfer of population to biexciton state a semiconductor quantum dot coupled with metal nanoparticle, under influence an electromagnetic pulse hyperbolic secant shape, and derive analytical solutions density matrix equations, both zero nonzero energy shift. These lead efficient state, various interparticle distances, including relatively small values. In c...