In this paper, I propose some problems, of topological nature, on the energy functional associated to the Dirichlet problem −∆u = f(x, u) in Ω, u|∂Ω = 0. Positive answers to these problems would produce innovative multiplicity results on this Dirichlet problem. In the present very short paper, I wish to propose some problems, of topological nature, on the energy functional associated to the Dir...

Recently, Bennett arononled that he proved a conjecture of Sierpinski on triangular numbers. In this paper, we firstly modified the mistakes in reference [7] of Bennett and [8] of Chen and Fang, and then using Störmer’s theorem of the solutions of Pell equation, and a deep result of primitive divisor of Bilu, Hanrot and Voutier, we proved that there do not exist four distinct triangular numbers...

We discuss the converse of a theorem of Potter stating that if the matrix equation AB = ωBA is satisfied with ω a primitive qth root of unity, then Aq+Bq = (A+B)q. We show that both conditions have to be modified to get a converse statement and we present a characterization when the converse holds for these modified conditions and q = 3 and a conjecture for the general case. We also present som...

There is a need for brief screening instruments for autistic spectrum disorders (ASD) that can be used by frontline healthcare professionals to aid in the decision as to whether an individual should be referred for a full diagnostic assessment. In this study we evaluated the ability of a short form of the Autism Spectrum Quotient (AQ) questionnaire, the 10 item AQ-10, to correctly classify indi...

Anthraquinone (AQ) (9,10-anthracenedione) is an important compound in commerce. Many structurally related AQ derivatives are medicinal natural plant products. Examples include 1-hydroxyanthraquinone (1-OH-AQ) and 2-hydroxyanthraquinone (2-OH-AQ), which are also metabolites of AQ. Some commercial AQ is produced by the oxidation of anthracene (AQ-OX). In the recent past, the anthracene used was d...

There is a need for brief screening instruments for autistic spectrum disorders (ASD) that can be used by frontline healthcare professionals to aid in the decision as to whether an individual should be referred for a full diagnostic assessment. In this study we evaluated the ability of a short form of the autism spectrum quotient (AQ) questionnaire, the 10 item AQ-10, to correctly classify indi...

We investigated the free corrosion potential at an interface between Al electrode and aqueous NaCl solution (NaCl(aq)) under acidic conditions via density functional theory combined with effective screening medium reference interaction site model (ESM-RISM). Firstly, potentials for anodic cathodic reactions were obtained from grand profile as a function of electron chemical interface. Thereafte...