Electron-vibration effects in Cs2SiF6 : Mn4+

We report a study of the ⁴ A _2g →² T _1g absorption band of Mn⁴⁺ in Cs₂SiF₆. The band shows several lines or groups of lines associated with transitions from the ⁴ A _2g ground state to the spin-orbit components (² T _1g )Γ₈ and (² T _1g )Γ₆ coupled to the three odd-parity vibrations v ₆(t _2u ), v ₄(t _1u ) and v ₃(t _1u ). The absorptions associated with the (² T _1g )Γ₈ electronic state have structure whereas those associated with the (² T _1g )Γ₆ do not. It is shown that the structure is a consequence of splitting of the Γ₈ × v vibronic multiplets by electron-vibration interaction. The intensity of the ⁴ A _2g →(² T _1g )Γ _i + v_j vibronic transitions are expressed in terms of a small number of parameters; two parameters for v(t _1u ) modes and three for v(t _2u ) modes. Plausible but not good fits to the low temperature Zeeman data and vibronic splitting patterns are obtained. The excitation spectrum of the Cs₂SiF₆ : Mn⁴⁺ in the region of the ⁴ A _2g →² E_g and ⁴ A _2g →² T _1g is recorded using a c.w. dye laser. This reveals numerous weaker lines involving combinational modes and even-parity modes v₅ (t _2g ), v ₂(e_g ) and v ₁(a _1g ). Several interesting electron-vibrational effects are observed. These are illustrated and discussed qualitatively.     

The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.     

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

New exact solutions of the space-time fractional cubic Schrodinger equation using the new type F-expansion method

In this study, a more general version of F-expansion method is proposed. With this offered method, more than one Jacobi elliptic functions are located in the solution function. We seek analytical solutions of the space-time fractional cubic Schrodinger equation by use of the new type of F-expansion method. Consequently, multifarious exact analytical solutions consisting of single, double, and multiple combined Jacobi elliptic functions solutions are acquired.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

Binding,Release and Functionalization of Intact Pnictogen Tetrahedra Coordinated to Dicopper Complexes

The bridging MeCN ligand in the dicopper(I) complexes [(DPFN)Cu₂(μ,η¹ : η¹-MeCN)][X]₂ (X=weakly coordinating anion, NTf₂ ( 1 a ), FAl[OC₆F₁₀(C₆F₅)]₃ ( 1 b ), Al[OC(CF₃)₃]₄ ( 1 c )) was replaced by white phosphorus (P₄) or yellow arsenic (As₄) to yield [(DPFN)Cu₂(μ,η² : η²-E₄)][X]₂ (E=P ( 2 a – c ), As ( 3 a – c )). The molecular structures in the solid state reveal novel coordination modes for E₄ tetrahedra bonded to coinage metal ions. Experimental data and quantum chemical computations provide information concerning perturbations to the bonding in coordinated E₄ tetrahedra. Reactions with N-heterocyclic carbenes (NHCs) led to replacement of the E₄ tetrahedra with release of P₄ or As₄ and formation of [(DPFN)Cu₂(μ,η¹ : η¹-^MeNHC)][X]₂ ( 4 a,b ) or to an opening of one E−E bond leading to an unusual E₄ butterfly structural motif in [(DPFN)Cu₂(μ,η¹ : η¹-E₄^DippNHC)][X]₂ (E=P ( 5 a,b ), E=As ( 6 )). With a cyclic alkyl amino carbene (^EtCAAC), cleavage of two As−As bonds was observed to give two isomers of [(DPFN)Cu₂(μ,η² : η²-As₄^EtCAAC)][X]₂ ( 7 a,b ) with an unusual As₄-triangle+1 unit.     

Structural properties of trans‐cyclohexane‐1,2‐diamine complexes of copper(II) and zinc(II) acesulfamates

The title compounds, trans‐bis(trans‐cyclohexane‐1,2‐diamine)bis(6‐methyl‐2,2,4‐trioxo‐3,4‐dihydro‐1,2,3‐oxathiazin‐3‐ido)copper(II), [Cu(C₄H₄NO₄S)₂(C₆H₁₄N₂)₂], (I), and trans‐diaquabis(cyclohexane‐1,2‐diamine)zinc(II) 6‐methyl‐2,2,4‐trioxo‐3,4‐dihydro‐1,2,3‐oxathiazin‐3‐ide dihydrate, [Zn(C₆H₁₄N₂)₂(H₂O)₂](C₄H₄NO₄S)₂·2H₂O, (II), are two‐dimensional hydrogen‐bonded supramolecular complexes. In (I), the Cu^II ion resides on a centre of symmetry in a neutral complex, in a tetragonally distorted octahedral coordination environment comprising four amine N atoms from cyclohexane‐1,2‐diamine ligands and two N atoms of two acesulfamate ligands. Intermolecular N—H...O and C—H...O hydrogen bonds produce R₂²(12) motif rings which lead to two‐dimensional polymeric networks. In contrast, the Zn^II ion in (II) resides on a centre of symmetry in a complex dication with a less distorted octahedral coordination environment comprising four amine N atoms from cyclohexane‐1,2‐diamine ligands and two O atoms from aqua ligands. In (II), an extensive two‐dimensional network of N—H...O, O—H...O and C—H...O hydrogen bonds includes R₂¹(6) and R₄⁴(16) motif rings.     

Functionalization of a cyclo‐P5 Ligand by Main‐Group Element Nucleophiles

Unprecedented functionalized products with an η⁴‐P₅ ring are obtained by the reaction of [Cp*Fe(η⁵‐P₅)] ( 1 ; Cp*=η⁵‐C₅Me₅) with different nucleophiles. With LiCH₂SiMe₃ and LiNMe₂, the monoanionic products [Cp*Fe(η⁴‐P₅CH₂SiMe₃)]^? and [Cp*Fe(η⁴‐P₅NMe₂)]^?, respectively, are formed. The reaction of 1 with NaNH₂ leads to the formation of the trianionic compound [{Cp*Fe(η⁴‐P₅)}₂N]^3?, whereas the reaction with LiPH₂ yields [Cp*Fe(η⁴‐P₅PH₂)]^? as the main product, with {[Cp*Fe(η⁴‐P₅)]₂PH}^2? as a byproduct. The calculated energy profile of the reactions provides a rationale for the formation of the different products.