Bright and dark solitons for the resonant nonlinear Schrödinger's equation with time-dependent coefficients

In this paper, the resonant nonlinear Schrödinger's equation is studied with five forms of nonlinearity. This equation is also considered with time-dependent coefficients and additionally time-dependent linear attenuation is considered. The ansatz method approach is used to carry out the integration. Both bright and dark soliton solutions are obtained in this paper. The constraint conditions for the existence of soliton solutions are also given.     

Soliton solutions of a BBM(m, n) equation with generalized evolution

We consider a BBM(m, n) equation which is a generalization of the celebrated Benjamin-Bona-Mahony equation with generalized evolution term. By using two solitary wave ansatze in terms of sech^p(x) and tanh^p(x) functions, we find exact analytical bright and dark soliton solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of existence of solitons are presented. Note that, it is always useful and desirable to construct exact analytical solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.     

Copper(I) Complex [Cu(ca<Subscript>2</Subscript>dapte)(NCS)] with the Flexible N<Subscript>2</Subscript>S<Subscript>2</Subscript> Schiff-base Tridentate Ligand: Synthesis,Characterization and Crystal Structure

Abstract  

New copper(I) complex involving the flexible N₂S₂ Schiff-base ligand ca₂dapte [Cu(ca₂dapte)(NCS)], [ca₂dapte = N,N′-bis-(cinnamaldehyde)-1,2-di(o-iminophenylthio)ethane], has been synthesized and structurally characterized by X-ray diffraction analysis. The coordination polyhedron around the Cu(I) center is best described as a distorted tetrahedron. The flexible N₂S₂ Schiff-base ligand ca₂dapte acts as a tridentate ligand via two S atoms and one N atom, while the NCS^- ligand is coordinated to the metal ion through its nitrogen atom. Crystal data: space group P-1, a = 10.7486(7), b = 12.3737(13), c = 12.7578(11) ?, α = 89.385(7), β = 68.527(7), γ = 66.190(8)°; V = 1425.8(2) ?³, Z = 2, R = 0.0417, wR ₂ = 0.0744.     

New charge transfer salts based on bis(ethylenedithio)tetrathiafulvalene (ET) and ferro- or antiferromagnetic oxalato-bridged dinuclear anions: syntheses, structures and magnetism of ET5[MM'(C2O4)(NCS)8] with MM' = Cr(III)Fe(III), Cr(III)Cr(III)

Electrochemical combination of the magnetic dinuclear anion [MM'(C2O4)(NCS)8](4-) (MM' = Cr(III)Cr(III), Cr(III)Fe(III)) with the ET organic pi-donor (ET = BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) gives rise to two new isostructural molecular hybrid salts ET5[MM'(C2O4)(NCS)8], with MM' = CrCr (1), CrFe (2). The molecular structure of compound 1 has been determined by single crystal X-ray diffraction. The particular arrangement of the organic units consists of an unprecedented two-dimensional organic sublattice nearly similar to that observed in kappa-phase structures. For both compounds, the magnetic susceptibility measurements indicate (i) the ET radicals do not contribute to the magnetic moment probably due to the presence of strong antiferromagnetic interaction between them, and (ii) in the anion, the magnetic coupling is antiferromagnetic for 1 (J = -3.65 cm(-1)) and ferromagnetic for 2 (J = 1.14 cm(-1), J being the parameter of the exchange Hamiltonian H = -2JS1S2). The field dependence of the magnetization of compound 2 at 2.0 K gives further evidence of the S = 4 ground-state arising from the interaction between S = 3/2 Cr(III) and S = 5/2 Fe(III). EPR measurements confirm the nature of the magnetic interactions and the absence of any contribution from the organic part, as observed from the static magnetic measurement. Conductivity measurements and electronic band structure calculations show that both salts are semiconductors with low activation energies.     

Theoretical investigation of the SO(2+) dication and the photo-double ionization spectrum of SO

Highly correlated ab initio methods were used in order to generate the potential energy curves of the electronic states of the SO(2+) dication and of the electronic ground state of the neutral SO molecule. These curves were used to predict the spectroscopic properties of this dication and to perform forward calculations of the double photoionization spectrum of SO. In light of spin-orbit calculations, the metastability of this doubly charged ion is discussed: for instance, the rovibrational levels of the X (1)Sigma(+) and A (3)Sigma(+) states are found to present relatively long lifetimes. In contrast, the other electronic excited states should predissociate to form S(+) and O(+) in their electronic ground states. The simulated spectrum shows structures due to transitions between the v=0 vibrational level of SO (X (3)Sigma(-)) and the vibrational levels below the barrier maximum of 11 of the calculated electronic states. The 2 (1)Sigma(+) electronic state of SO(2+) received further treatment: in addition to vibrational bands due to the below barrier energy levels of this electronic state, at least nine continuum resonances were predicted which are responsible for the special shape of the spectrum in this energy region. This work is predictive in nature and should stimulate future experimental investigations dealing with this dication.     

Dipotassium trimanganese(II) tetrakis(hydrogenphosphite), K2[Mn3(HPO3)4]

The title compound is a new mixed alkali/3d metal phosphite. It exhibits a layered structure formed by linear Mn₃O₁₂ trimer units which contain face‐sharing MnO₆ octahedra interconnected by (HPO₃)²⁻ phosphite oxoanions. The K⁺ cations located between the anionic [Mn₃(HPO₃)₄]²⁻ sheets are ninefold coordinated. The presence of the alkaline ion leads to the highest symmetry and shortest interlayer distance compared with two previous compounds showing the same anionic framework and having ammonium salts as cations. The compound crystallizes in the space group Rm, with two crystallographically independent Mn atoms occupying sites of m and 3m symmetry. All the other atoms, except for the phosphite O atoms, are located on special positions with 3m symmetry.     

Mixed integer formulations for the probabilistic minimum energy broadcast problem in wireless networks

In this paper we study a new variant of the minimum energy broadcast (MEB) problem, namely the probabilistic MEB (PMEB). The objective of the classic MEB problem is to assign transmission powers to the nodes of a wireless network is such a way that the total energy dissipated on the network is minimized, while a connected broadcasting structure is guaranteed by the assigned transmission powers. In the new variant of the problem treated in this paper, node failure is taken into account, aiming at providing solutions with a chosen reliability level for the broadcasting structure. Three mixed integer linear programming formulations for the new problem are presented, together with efficient formulation-dependent methods for their solution. Computational results are proposed and discussed. One method emerges as the most promising one under realistic settings. It is able to handle problems with up to fifty nodes.