Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.

Hasse-Witt matrices, unit roots and period integrals

Abstract: Motivated by the work of Candelas, de la Ossa and Rodriguez-Villegas [6], we study the relations between Hasse-Witt matrices and period integrals of Calabi-Yau hypersurfaces in both toric varieties and partial flag varieties. We prove a conjecture by Vlasenko [23] on higher Hasse-Witt matrices for toric hypersurfaces following Katz's method of local expansion [14, 15]. The higher Hasse-Witt matrices also have close relation with period integrals. The proof gives a way to pass from Katz's congruence relations in terms of expansion coefficients [15] to Dwork's congruence relations [8] about periods.

On exact discretization of cubic-quintic Duffing oscillator

Abstract: Application of the intersection theory to the construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few exact discretizations of one-dimensional cubic and quintic Duffing oscillators sharing the form of the Hamiltonian and canonical Poisson bracket up to the integer scaling factor.

On Klein's Icosahedral Solution of the Quintic

Abstract: We present an exposition of the icosahedral solution of the quintic equation first described in Klein's classic work "Lectures on the icosahedron and the solution of equations of the fifth degree". Although we are heavily influenced by Klein we follow a slightly different approach which enables us to arrive at the solution more directly.

High accuracy quintic spline solution of fourth order two-point boundary value problems

Abstract: It has been known for a long time that quintic spline collocation for fourth order two-point boundary value problems: y (4)+p(x)y=q(x), a