Sum-rules of the response potential in the strongly-interacting limit of DFT

The response part of the exchange-correlation potential of Kohn–Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.     

Acoustic energy relations in Mudejar-Gothic churches

Extensive objective energy-based parameters have been measured in 12 Mudejar-Gothic churches in the south of Spain. Measurements took place in unoccupied churches according to the ISO-3382 standard. Monoaural objective measures in the 125-4000 Hz frequency range and in their spatial distributions were obtained. Acoustic parameters: clarity C80, definition D50, sound strength G and center time Ts have been deduced using impulse response analysis through a maximum length sequence measurement system in each church. These parameters spectrally averaged according to the most extended criteria in auditoria in order to consider acoustic quality were studied as a function of source-receiver distance. The experimental results were compared with predictions given by classical and other existing theoretical models proposed for concert halls and churches. An analytical semi-empirical model based on the measured values of the C80 parameter is proposed in this work for these spaces. The good agreement between predicted values and experimental data for definition, sound strength, and center time in the churches analyzed shows that the model can be used for design predictions and other purposes with reasonable accuracy.     

Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards

We have compared the stability of two distinct atomic frequency standards. One is based on an atomic cold cloud of ¹³³Cs atoms in free expansion, interrogated by a Rabi resonance. The other standard is based on a thermal Cs beam interrogated by the separated oscillatory field method (Ramsey’s method). The atomic expanding cloud standard shows better stability and technical advances based on its simplicity.     

Exact solutions for a diffusion equation with a nonlinear external force

This work is devoted to investigate the solutions of the one-dimensional diffusion equation by taking the nonlinear external force F(x,t;ρ)=−k(t)x+K/x+κx|x|^α−1η[ρ(x,t)] into account. Our investigation is first performed by considering the case α=0 and η=1, which results in a Burgers like equation with a spatial and time dependent external force. After, we consider the case α≠0 and η=α+1 and show that the solution found may be expressed in terms of the q-exponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.     

Synthesis of New Iminosugar Derivatives Based on (S)-(1,2,3,6-Tetrahydropyridazin-3-yl)methanol

(S)-(1,2,3,6-Tetrahydropyridazin-3-yl)methanol was synthesized in two steps by the Diels-Alder reaction of penta-2,4-dien-1-ol with diethyl azodicarboxylate in the presence of (S)-BINOL as chiral catalyst. The subsequent Boc-protection of the 2-position of the pyridazine ring, ring-closing carbonylation of the hydroxy group, and deprotection afforded a bicyclic iminosugar analog. The structure of the isolated compounds was proved by NMR, IR, and mass spectra and elemental analyses.

     

Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

Optical activity and damage recovery of erbium implanted strontium titanate

Single crystalline SrTiO 3 samples were implanted with Er ions of 150 v keV at room temperature with fluences of 5 ‐ 10 14 and 5 ‐ 10 15 . Annealing treatments were carried out both in reducing and oxidising atmospheres to recover the implantation damage. Infrared 1.54 v m Er 3+ luminescence between the two lowest spin-orbit levels 4 I 13/2 M 4 I 15/2 as well as emission from higher excited states 4 S 3/2 M 4 I 15/2 , 4 F 9/2 M 4 I 15/2 and 4 S 3/2 M 4 I 13/2 were observed in the implanted samples with highest fluence, annealed either in air or in vacuum. Multiple site location of Er 3+ ion is discussed and compared with RBS/C and emission channelling results that indicate that Er goes to Sr and Ti sites.     

Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain

We study a semilinear elliptic equation of the form

On fractional integro-differential inclusions with state-dependent delay in Banach spaces

In this article we investigate the existence of solutions on a compact interval for the fractional integro-differential inclusions with state-dependent delay in Banach spaces when the delay is infinite. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values.     

On Dedekind Modules

In this article the authors give the relation between a finitely-generated torsionfree Dedekind module M over a domain R and prime submodules of the 𝒪(M)-module M and the ring 𝒪(M). They also prove that M is a finitely-generated torsionfree Dedekind module over a domain R if and only if every semi-maximal submodule of R-module M is invertible.