Structural and electrical characteristics of rare earth simple perovskite oxide La0.57Nd0.1Pb0.33Mn0.8Ti0.2O3

Polycrystalline La_0.57Nd_0.1Pb_0.33Mn_0.8Ti_0.2O₃ (LNPMT) is prepared by the solid-state reaction technique. The formation of single phase material was confirmed by X-ray diffraction studies, and it was found to be a rhombohedral phase at room temperature. The impedance plane plot shows semicircle arcs at different temperatures and an electrical equivalent circuit has been proposed to explain the impedance results. The frequency dependent conductivity spectra follow the universal power law. The activation energy deduced from analysis of the imaginary part of electric modulus and imaginary impedance is found to be ∼75 meV. Such a value of activation energy indicates that the conduction mechanism for the sample is due to electron hopping. The imaginary part of the electric modulus suggests that the relaxation describes the same mechanism at various temperatures.     

The effect of increasing the excitation level of the sodium atom on the structure of the NaArn polyatomic exciplexes

In this work, the geometrical structures, the formation energies, and electronic states of the Na(ms)Ar_n polyatomic exciplexes with m = 3-6 and n = 2-5 are studied by using a quantum-classical method. The interaction potential between an electronically excited sodium atom and argon atoms are calculated by using a one-electron model involving electron-Ar and electron-Na⁺ pseudopotentials, in which the Hamiltonian is diagonalized at every optimization step in the Basin Hopping algorithm. The relationship between the position of the electronically excited levels and the cluster geometry is investigated as a function of the excitation level and of the spatial extension of the excited electron orbital. We show that the equilibrium structures of the ground state Na(3s)Ar_n and those of the electronically excited states Na(4s)Ar_n, Na(5s)Ar_n, and Na(6s)Ar_n are significantly different. As a result of the detailed examination of the relationships between the geometrical structure and density distribution of the Na valence electron of the Na^∗Ar_n with n = 2-5 polyatomic exciplexes, we can see that for the Na(4s)Ar_n polyatomic exciplexes, the two extreme geometries, neutral Na(3s)Ar_n and ionic Na⁺Ar_n compete. It appears that none of them is the actual one. For Na(5s)Ar_n and Na(6s)Ar_n the valence electron is very weakly bound to the ionic core and described by a more diffused orbital so that the geometry and the formation energies of this excited state called Rydberg states converge towards those of the ionic cores.     

The Fibonacci sequence modulo π, chaos and some rational recursive equations

In this paper, we provide the closed form solution to the inter-related equations Both of these equations were suggested as open problems in the book by Kocic and Ladas [V.L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of High Order with Applications, Kluwer Academic, Dordrecht, 1993]. We also give the closed form solution to the equations studied by X. Li and D. Zhu [X. Li, D. Zhu, Two rational recursive sequences, Comput. Math. Appl. 47 (2004) 1487–1494].     

Rydberg states of small NaAr(n)* clusters

The 4s and 5s Rydberg excited states of NaAr(n)* clusters are investigated using a pseudopotential quantum-classical method. While NaAr(n) clusters in their ground state are known to be weakly bound van der Waals complexes with Na lying at the surface of the argon cluster, isomers in 4s or 5s electronically excited states of small NaAr(n)* clusters (n< or =10) are found to be stable versus dissociation. The relationship between electronic excitation and cluster geometry is analyzed as a function of cluster size. For both 4s and 5s states, the stable exciplex isomers essentially appear as sodium-centered structures with similar topologies, converging towards those of the related NaAr(n)+ positive ions when the excitation level is increased. This is consistent with a Rydberg-type picture for the electronically excited cluster, described by a central sodium ion solvated by an argon shell, and an outer diffuse electron orbiting around this NaAr(n)+ cluster core.     

One-Electron Pseudo-Potential Determination of Stable Isomers of the Li*Ar n Excited Clusters: Absorption Spectra

We present pseudo-potential calculations of geometrical structures of stable isomers of LiAr _n clusters with both an electronic ground state and excited states of the lithium atom. The Li atom is perturbed by argon atoms in LiAr _n clusters. Its electronic structure obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Li⁺Ar _n core, the Li⁺ and Ar atoms are replaced by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for the polarization and correlation of the inert core with the valence Lithium electron [J Chem Phys 116, 1839 1]. The geometry optimization of the ground and excited states of LiAr _n (n = 1–12) clusters is carried out via the Basin-Hopping method of Wales et al. [J Phys Chem 101, 5111 2; J Chem Phys 285, 1368 3]. The geometries of the ground and ionic states of LiAr _n clusters were used to determine the energy of the high excited states of the neutral LiAr _n clusters. The variation of the excited state energies of LiAr _n clusters as a function of the number of argon atoms shows an approximate Rydberg character, corresponding to the picture of an excited electron surrounding an ionic cluster core, is already reached for the 3s state. The result of optical transitions calculations shows that the absorption spectral features are sensitive to isomer structure. It is clearly the case for transitions close to the 2p levels of Li which are distorted by the cluster environment.     

Solvation of Na+ in argon clusters

The structures and stabilities of Ar(n)Na+ clusters (n < or = 54) are investigated using atomistic potentials fitted to reproduce ab initio calculations performed at the coupled-cluster level on the smaller clusters. Polarization effects are described using either the interaction between dipoles induced by the sodium ion, or a small charge transfer in the framework of a fluctuating charges model. In both models, extra three-body contributions of the Axilrod-Teller type are also included between the sodium ion and all pairs of argon atoms. The two models predict essentially similar growth patterns, and a transition in the metal ion coordination from 8 (square antiprism) to 12 (icosahedron) is seen to occur near n = 50, in response to the intrasolvent constraints.     

On the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearities

In this paper, we study the existence of positive solutions for the semilinear elliptic problem

     

Eigenvalues in Non-Linear Potential Theory

In this work, we study the existence of eigenvalues for a type of non-linear equations and we give some conditions to get positive eigenfunctions. Particularly, we show that under some appropriate conditions, the set of eigenvalues is an interval.     

Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map

Recently a new image encryption method based on DNA encoding and chaotic systems has been proposed. In this paper, several weaknesses of this cryptosystem are pointed out. Equivalent mathematical model of the cryptosystem is designed and algebraic analysis is given. Moreover reduction of the key space has been reached by finding equivalent keys. A recovering scheme is finally given with a lower complexity than the actual decryption scheme.