Finite groups whose character degree graphs coincide with their prime graphs

In the literature, there are several graphs related to a finite group G. Two of them are the character degree graph, denoted by ΔG), and the prime graph ΓG), In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.     

Quasi diabatic CASSCF state functions

A new method to determine quasi diabatic (QD) CASSCF states is presented. The adiabatic states are subjected to a unitary transformation resulting from diagonalization of a state-selection operator. The latter is constructed from the overlap of the adiabatic states with a suitable set of reference states. The multi-state (MS) CASPT2 method is used to account for the dynamical correlation effects in an approach where the QD-CASSCF wave functions are used as reference states. The procedure is applied to avoided crossings in excited states of BeH, LiO and ozone. The advantages of the proposed formulation are discussed.     

Synthesis and mechanical properties of mechanically alloyed Al-Cu-Fe quasicrystalline composites

Al-Cu-Fe alloys were prepared by mechanical alloying starting from elemental powders in a high-energy planetary ball mill. Three different alloy compositions with the same c _Cu : c _Fe ratio of 2:1 but different aluminium contents, that is Al₅₅Cu₃₀Fe₁₅, Al₆₃Cu₂₅Fe₁₂ and Al₇₀Cu₂₀Fe₁₀, were investigated. A sequence of solid-state reactions resulting in quasicrystalline phase formation in Al₆₃Cu₂₅Fe₁₂ proceeds during milling and during annealing of the as-milled powder. These reactions were studied by X-ray diffraction, transmission electron microscopy and differential scanning calorimetry. In order to form an aluminium-matrix composite, Al₆₃Cu₂₅Fe₁₂ single-phase quasicrystalline powders were blended with different amounts of aluminium. In an intermediate milling step the powder blend was homogenized. The powders were consolidated by hot extrusion. The bulk samples revealed a homogeneous dispersion of the particles in the matrix but a rather heterogeneous size distribution. The mechanical properties at room temperature were tested by constant-rate compression tests. A rule-of-mixtures dependence of the ultimate strength and the yield strength on the volume fraction of the quasicrystalline particles was found.     

The lowest electronic states of Ne2 +, Ar2 + and Kr2 +: comparison of theory and experiment

Non-relativistic configuration interaction (CI) ab initio calculations using large basis sets have been carried out to determine the potential curves of the first electronic states of Ne₂ ⁺, Ar₂ ⁺ and Kr₂ ⁺. The spin—orbit interaction was treated assuming that the spin—orbit coupling constant is independent of the internuclear separation (R). For Ar₂ ⁺, calculated dissociation energies and equilibrium separations are in good agreement with experimental results. The calculations for Ne₂ ⁺ suggest that the lowest vibrational level of the I(1/2u) ground state observed by threshold photoelectron spectroscopy by Hall et al. [1995, J. Phys. B: At. molec. opt. Phys., 28, 2435] and assigned to either ν = 0 or ν = 2 actually corresponds to ν = 4. The calculations also predict the I(1/2g) state of Ne₂ ⁺ and Ar₂ ⁺ to possess a double-well potential and that of Kr₂ ⁺ to be repulsive at short range and to only possess a single shallow well at large internuclear separation. The ab initio calculations provide an explanation for the observation made by Yoshii et al. [2002, J. chem. Phys., 117, 1517] that Kr₂ ⁺ and Xe₂ ⁺ dissociate after photoemission from the II(1/2u) state to the I(1/2g) state whereas Ar₂ ⁺ does not.     

Synthesis of novel 1,4 naphthoquinone-based molecules by an Ugi-type four-component reaction

In an attempt to further exploit multicomponent reactions in the field of 1,4 naphthoquinone-based compounds, we describe an Ugi-type multicomponent approach for the synthesis of novel 3-substituted 1,4 naphthoquinone molecules. The process relies on the execution of an enol-Ugi reaction between an enol-3-nitro-1,4 naphthoquinone with different secondary diamines and isocyanides. The novel methodology showed great chemical efficiency and versatility.     

Multiscale expansions in discrete world

In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.     

Determination of some trace metals with a new synthesized polymer resin by FAAS in various tea and herbal plants samples

In this work, a new polymer resin with a functional groups capable of holding trace metals has been synthesized. The structure of polymer resin has been examined by BET-N₂ method analyzer, IR spectrometer, scanning electron microscope (SEM) and elemental microanalyser. The synthesized polymer resin was used for the simultaneous separation and preconcentration of the trace metals from various tea and herbal plants samples. After extraction process, flame atomic absorption spectrometry (FAAS) was used to determine the trace metals. The analytical parameters and solid phase extraction (SPE) performance such as pH, sample volume, flow rates of sample, flow rates of eluent, concentration, volume and type of eluent and effect of interference ions, were investigated. The limits of detection (DL) of the SPE procedure for trace metals, were calculated to be (3s) in the range of 0.9?4.0 μg L^?1 (n = 21) and the factors of preconcentration (PF) were obtained at 200 for Cd, Co, Cu, Fe, Ni and Zn, and at 50 for Cr, Mn and Pb ions and the relative standard deviation (RSD) at ≤ 2% (n = 11).