Frequent oscillation in a nonlinear partial difference equation

This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.      

A new trend in the synergistic extraction of rare-earth(III) complexes with various β-diketones and 1,10-phenanthroline

The synergistic extraction of rare-earth (RE) [La(III), Sm(III), Tb(III) and Lu(III)] complexes, with three β-diketones (HA) [hexafluoroacetylacetone (Hhfa), pivaloyl-trifluoroacetone (Hpta) and benzoylacetone] in the presence of a bidentate ligand (S), 1,10-phenanthroline, in benzene was investigated. The general composition of the adducts formed is expressed as RE(A)₃S. RE(A)₃(S)₂ is also observed in La-Hhfa, La-Hpta and Sm-Hhfa systems. The adduct formation contains β_s,1 and β_s,2 and the synergistic extraction constants K_ex,s,1 were determined. The trend of these constants is discussed in terms of the RE(III), β-diketone, neutral bidentate ligand and organic solvent.     

Infrared,matrix i.r. and Raman spectra of hexachloro-2-propanol

The i.r. spectra of the alcohol CCl₃CHOHCCl₃ have been recorded in the gaseous and solid phases, in argon, krypton, nitrogen and carbon monoxide matrices and in various solutions. Raman spectra of the solid alcohol and its solutions were also recorded. Assignments of the vibration bands are made on the basis of an approximate normal coordinate calculation. The alcohol exhibits two conformers in the vapour phase and in solutions; the relative stabilities of these conformers are discussed. When the temperature is varied, a reversible interconversion between two species of the alcohol occurs in nitrogen matrices. The self-association tendency of the alcohol is very weak.     

Infrared and Raman spectra of magnesium ammonium phosphate hexahydrate (struvite) and its isomorphous analogues. IX: Spectra of protiated and partially deuterated cubic magnesium caesium phosphate hexahydrate

Infrared and Raman spectra of cubic magnesium caesium phosphate hexahydrate, MgCsPO₄·6H₂O (cF100), and its partially deuterated analogues were analyzed and compared to the previously studied spectra of the hexagonal analogue, MgCsPO₄·6H₂O (hP50). The vibrational spectra of the cubic and hexagonal dimorphic analogues are similar, especially in the regions of HOH stretching and bending vibrations. In the difference IR spectrum of the slightly deuterated analogue (<5% D), one distinctive band appears at 2260 cm⁻¹ with a small shoulder at around 2170 cm⁻¹, but only one band is expected in the region of the OD stretchings of isotopically isolated HDO molecules. The small weak band could possibly result from second-order transitions (a combination of HDO bending and some libration of the same species) rather than statistical disorder of the water molecules. By comparing the IR spectra in the region of external vibrations of water molecules of the protiated compound recorded at RT (room temperature) and at LNT (liquid nitrogen temperature) and those in the series of the partially deuterated analogues, it can be stated with certainty that the bands at 924 and 817 cm⁻¹ result from librations of water molecules, rocking and wagging respectively. And the band at 429 cm⁻¹ can be safely attributed to a stretching Mg–O_w mode. In the ν₃(PO₄) and ν₄(PO₄) region in the infrared spectra, one band in each is observed, at 995 and 559 cm⁻¹, respectively. In the region of the ν₁ modes, in the Raman spectrum of the protiated compound, one very intense band was observed at 930 cm⁻¹ which is only insignificantly shifted to 929 cm⁻¹ in the spectrum of the perdeuterated compound. The band at 379 cm⁻¹ in the Raman spectrum could be assigned to the ν₂(PO₄) modes. With respect to the phosphate ion vibrations, the comparison between the two polymorphic forms of MgCsPO₄·6H₂O and their deuterated compounds shows that ν₁(PO₄) and ν₃(PO₄) appear at lower wavenumbers in the cubic phase than in the hexagonal phase. These data are in full agreement with the lower repulsion potential at the cubic lattice sites compared with that for the hexagonal lattice sites.     

非扩张映射和广义变分不等式的粘滞逼近法

应用已提出的非扩张映射的粘滞逼近方法,给定初值x_0∈C,考虑一般迭代过程{x_n},g(x_(n+1))=α_nf(x_n)+(1-α_n)SP_C(g(x_n)-λ_nAx_n),n≥0,其中{α_n}■(0,1),S:C→C是非扩张映射,C是实Hilbert空间H的非空闭凸子集.在{α_n}满足合适的条件下可证明,{x_n}强收敛到非扩张映射的不动点集和广义变分不等式解的公共元,且满足某变分不等式.     

Geometric approach to global asymptotic stability for the SEIRS models in epidemiology

In this paper, we present a more general criterion for the global asymptotic stability of equilibria for nonlinear autonomous differential equations based on the geometric criterion developed by Li and Muldowney. By applying this criterion, we obtain some results for the global asymptotic stability of SEIRS models with constant recruitment and varying total population size. Based on these results, we give a complete affirmative answer to Liu–Hethcote–Levin conjecture. Furthermore, an affirmative answer to Li–Graef–Wang–Karsai’s problem for SEIR model with permanent immunity and varying total population size is given.     

Reactive resonances in the photodissociation of symmetric triatomic molecules: an interpretation of collinear CO2 in terms of polar coordinates

We discuss the origin of reactive scattering resonances in absorption cross sections following the collinear photodissociation of symmetric triatomic molecules. The analysis of spectra for CO₂ dissociation, previously calculated by Kulander and Light, becomes very simple in terms of polar coordinates. Of particular interest is a symmetry effect which is not observable in ordinary scattering calculations.     

Thermal activation and thermal transfer of localized excitons in InAs self-organized quantum dots

We have investigated the temperature dependence of photoluminescence (PL) properties of a number of InAs/GaAs heterostructures with InAs layer thickness ranging from 0.5 monolayer (ML) to 3 ML. The temperature dependence of the InAs exciton energy and linewidth was found to display a significant difference when the InAs layer thickness is smaller or larger than the critical thickness around 1.7 ML, indicating spontaneous formation of quantum dots (QDs). A model, involving exciton recombination and thermal activation and transfer, is proposed to explain the experimental data. In the PL thermal quenching study, the measured thermal activation energies of different samples demonstrate that the InAs wetting layer may act as a barrier for thermionic emission of carriers in high quality InAs multilayers, while in InAs monolayers and submonolayers the carriers are required to overcome the GaAs barrier to thermally escape from the localized states.     

Investigation of electronic properties of alloyed double metal ring

The present work is a theoretical study of the electronic properties of alloyed double metal ring (ADMR) threaded by magnetic flux. The studied system is consisting of two rings connected parallel, with two different types of atomic sites. This work contains two parts. First is an analytical study of calculation of the energy spectrum, persistent current, Drude weight and low-field magnetic susceptibility of ADMR by the tight-binding method. Second is a computation study of electronic properties of the alloyed double metal ring by density functional theory (DFT). The latter part is considered as a complementary study of what was studied in the first part in order to determine the best materials which will be used to design alloyed double metal ring. Our results show that the on-site energies for both types of atoms, inter-ring coupling strength and hopping strengths play an interesting role in controlling the electronic properties.     

Origin of arrhythmias in a heart model

An investigation of the nonlinear dynamics of a heart model is presented. The model compartmentalizes the heart into one part that beats autonomously (the x oscillator), representing the pacemaker or SA node, and a second part that beats only if excited by a signal originating outside itself (the y oscillator), representing typical cardiac tissue. Both oscillators are modeled by piecewise linear differential equations representing relaxation oscillators in which the fast time portion of the cycle is modeled by a jump. The model assumes that the x oscillator drives the y oscillator with coupling constant $\alpha$. As $\alpha$ decreases, the regular behavior of y oscillator deteriorates, and is found to go through a series of bifurcations. The irregular behavior is characterized as involving a large amplitude cycle followed by a number n of small amplitude cycles. We compute critical bifurcation values of the coupling constant, ${\alpha }_n$, using both numerical methods as well as perturbations.