In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

We consider the nonlinear Klein-Gordon equation∂t2u(x,t)−∂x2u(x,t)+αu(x,t)=±|u(x,t)|p−1u(x,t) on a periodic metric graph (necklace graph) for p>1 with Kirchhoff conditions at vertices. Under suitable assumptions frequency we prove existence and regularity of infinitely many spatially localized time-periodic solutions (breathers) by variational methods. Compared to previous results obtained via ...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

Excited state properties of one-dimensional molecular materials are dominated by many-body interactions resulting in strongly bound confined excitons. These effects cannot be neglected or treated as a small perturbation and should be appropriately accounted for by electronic structure methodologies. We use adiabatic time-dependent density functional theory to investigate the electronic structur...

This paper investigates the efficient parallelization of algorithms with strong stability guarantees to factor dense symmetric indefinite matrices. It shows how the bounded Bunch-Kaufman algorithm may be efficiently parallelized, and then how its performance can be enhanced by using exhaustive block searching techniques, which is effective in keeping most symmetric interchanges within the curre...

Self-consistent calculations using the Perdew-Zunger self-interaction correction (PZ-SIC) to local density and gradient dependent energy functionals are presented for the binding energy and equilibrium geometry of small molecules as well as energy barriers of reactions. The effect of the correction is to reduce binding energy and bond lengths and increase activation energy barriers when bond br...

Orbital energies, ionization potentials, molecular constants, potential energy curves, and the excitation spectrum of O(2) are calculated using time-dependent density functional theory (TDDFT) with Tamm-Dancoff approximation (TDA). The calculated negative highest occupied molecular orbital energy (-epsilon(HOMO)) is compared with the energy difference ionization potential for five exchange corr...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

In 2012 Bryson, Ono, Pitman and Rhoades showed how the generating functions for certain strongly unimodal sequences are related to quantum modular mock forms. They proved some parity results conjectured mod 4 congruences coefficients of these functions. 2016 Kim, Lim Lovejoy obtained similar odd-balanced made conjectures. We prove all conjectures Andrews spt-function theta Our method proof invo...