Volume 59, Issue 9

A new Jacobi elliptic function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi elliptic function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi elliptic functions m→1 or 0, the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions are also found.

Two higher homologues of N(p-n-nonyloxybenzylidene)p-n-alkylanilines, viz. the 9O.m series with m = 12 and 16, are synthesised and characterised by thermal microscopy, differential scanning calorimetry and density studies. The compounds exhibit the phase variants smectic-A, smectic-B and smectic-G. Density studies reveal the first order nature of the isotropic to smectic-A and smectic-A to smectic-B transitions. An estimate of the pressure dependence of the phase transition temperature, using volume and enthalpy data, is presented. A comparison of these results with those reported on nO.m and other liquid crystalline compounds is presented.

The isotropic Compton profile of mercury has been measured, using 661.65 keV gamma-rays from a 20 Ci 137 Cs source. To extract the true experimental Compton line shape, besides the usual systematic corrections we have incorporated for the first time the background correction due to bremsstrahlung radiation generated by photo and Compton electrons. Theoretical computations have been carried out, using the renormalised-free-atom (RFA) for the electron configuration 4f 14 5d 10 6s 2 and free electron models. It is found that the present experimental data with bremsstrahlung background correction are in better agreement with the RFA calculations. This work suggests the incorporation of the bremsstrahlung background correction in Compton scattering experiments of heavy materials using high-energy gamma-ray sources.

The pore size of white cement samples is studied by the melting behaviour of water confined in it, using 1 H NMR cryopormetry. The influence of the preparing method and antifreeze admixture on the pore size and distribution in cement samples is investigated at 283 K. The addition of an antifreeze admixture [containing 1% Sika Rapid 2 by weight of the dry cement] influences the porosity. In wet prepared samples we observed a significant increase in the quantity of mesopores between 0.8 and 5 nm and a smaller increase of mesopores between 5 and 10 nm, when compared to cement without admixture. The compressive strength is related to the porosity of the cement. Therefore the cement with Sika Rapid 2, wet prepared at 278 K shows a higher strength than all other measured samples.

The paper presents the results of viscosity measurements performed on 1,2-hexanediol in water and n-, s- and t-butanol solutions in the whole range of concentrations, at different temperatures. The activation energy for viscous flow of the solutions and the viscosity excess, were determined.

The spin Hamiltonian parameters anisotropic g factors g||, g ⊥ and hyperfine structure constants A|| and A ⊥ , as well as the local structure of the trigonal Co 2+ center in Bi 4 Ge 3 O 12 (BGO) are theoretically investigated by the perturbation formulas of the spin Hamiltonian parameters for a 3d 7 ion in trigonal symmetry, based on the cluster approach. It is found that the impurity Co 2 + substituting the host Bi 3 + undergoes an off-center displacement ΔZ(≈ −0.132 Å ) away from the center of the oxygen octahedron along the C 3 axis. The spin Hamiltonian parameters based on the above displacement show reasonable agreement with the observed values. The results are discussed.

The analysis based on Rüdenberg’s well-known letter of 1951, which has been outlined for molecules in a preceding contribution, has now been transfered to translational periodic systems in one, two, or three dimensions. Entitled “On the Three- and Four-Center Integrals in Molecular Quantum Mechanics”, this letter explicitly presents two approximations only for four-center repulsion integrals. When applied to some types of three-center repulsion integrals, however, these two recipes still imply considerable oversimplifications. Using both one-electron and two-electron routes of Rüdenberg’s expansion, such shortcomings can be avoided strictly. Starting from a simple “Unrestricted and Combined” (U&C) approximation scheme introduced elsewhere, an improved “Restricted and Combined” (R&C) approximation picture for Fock-matrix elements now will be outlined, which does not tolerate any unnecessary oversimplifications. Although the simplicity of the U&C scheme is lost in this case, R&C-approximated Fock-matrix elements still can be constructed from one- and twocenter integrals alone in an effective way. Moreover, due to their dependence on a single geometric parameter, all types of two-center integrals can be calculated in advance for about one hundred fixed interatomic distances at the desired level of sophistication, and stored once and for all. A cubic spline algorithm may be taken to interpolate the actual integral value from each precomputed list.

A harmonic interpolation of a polygon (for odd and even numbers of points forming the polygon) used in computer graphics is derived from the primary permutation matrix using the spectral decomposition of the matrix. This is a technique to draw closed curves. We compare these curves with Bézier curves. We also show situations where the harmonic interpolation of a polygon is a more suitable alternative to B´ezier curves. Trigonometric Interpolation is another technique to draw curves. The relationship between trigonometric interpolation and harmonic interpolation is discussed.

A theoretical scheme for controlled and secure direct communication is proposed. The communication is based on GHZ state and controlled quantum teleportation. After insuring the security of the quantum channel (a set of qubits in the GHZ state), Alice encodes the secret message directly on a sequence of particle states in the GHZ state and transmits them to Bob, supervised by Charlie using controlled quantum teleportation. Bob can read out the encoded messages directly by the measurement on his qubits. In this scheme, the controlled quantum teleportation transmits Alice’s message without revealing any information to a potential eavesdropper. Because there is not a transmission of the qubit carrying the secret messages between Alice and Bob in the public channel, it is completely secure for controlled and direct secret communication if a perfect quantum channel is used. The feature of this scheme is that the communication between two sides depends on the agreement of a third side.

The complex formation between cobalt(II) and chloride and bromide ions in molten calcium nitrate tetrahydrate at different temperatures has been studied by a spectrophotometric technique. Addition of halide ions to cobalt(II) nitrate solution in calcium nitrate tetrahydrate caused a pronounced shift of the absorption maximum toward lower energies and a large increase of absorption intensity, indicating a change from octahedral to a tetrahedral co-ordination. The change of co-ordination depends on temperature and halide concentration. Stability constants for the [Co(NO 3 ) 4 ] 2 −, [Co(NO 3 ) 2 X 2 ] 2 − and [CoX 4 ] 2 − complexes at 40 and 70 ◦C and the corresponding species spectra are reported.

A previously presented quantum-chemical scheme has been used to calculate the lattice energies of borazine (B 3 N 3 H 6 ), the low pressure polymorph of benzene (C 6 H 6 ), and of borazine in the lowpressure benzene lattice utilizing some frequently used semiempirical methods (CNDO/2, INDO, MINDO/3, MNDO, AM1, PM3, MSINDO). With all methods the lattice energy of the title compound was found to be less favourable than that of isoelectronic benzene, which offers an explanation of the significantly lower melting point of B 3 N 3 H 6 . Calculation of the lattice energy of borazine in the crystal lattice of the low-pressure modification of benzene revealed that the interactions between the molecules in this environment are not so stabilizing as those in its own lattice. This is predominantly due to a less favourable contribution of the dispersion energy. The semiempirical results have qualitatively been confirmed by quantum-chemical calculations on small molecular clusters at the MP2/6-31+G*//HF/6-31+G* level of ab initio theory. In these calculations we assumed pairwise additivity of the intermolecular interactions and calculated the energy of interaction between a reference molecule and all those neighbours to which the shortest intermolecular distance does not exceed 3Å.

Viscosity and molar conductance of Bu 4 NBPh 4 , Bu 4 NClO 4 , [Cu(CH 3 CN) 4 ]ClO 4 , NaClO 4 and NaBPh 4 have been measured in the concentration ranges 0.02 - 0.5 mol dm −3 and 0.0005 - 0.0065 mol dm −3 at 298.15 K in AN + DMF mixtures containing 0, 10, 20, 40, 60, 75, 80, 90, and 100 mol % DMF. The viscosity data have been analyzed by the extended form of the Jones-Dole equation in the form: (η/η0) = 1+AC 1/2 +BC+DC 2 to evaluate B and D parameters and the conductance data by the Shedlovsky equation to evaluate Λ o and K A values of the salts. Ionic viscosity B-coefficients (B ± ) and ionic molar conductances (λ◦ i ) have been calculated by using Bu 4 NBPh 4 as a reference electrolyte. Solvated radii (r i ) for Na + , Cu + and ClO 4 − have been estimated by using Gill’s modification of Stokes’ law. The variation of B ± and r i as a function of mol % DMF shows that both Na + and Cu + are highly solvated in AN + DMF mixtures over the entire composition region. The solvation passes through a maximum between 40 to 80 mol % DMF. Both Na + and Cu + are more strongly solvated between 40 to 80 mol % DMF. Cu + is relatively more strongly solvated than Na + in AN + DMF mixtures. ClO 4 − shows poor solvation in AN + DMF mixtures.

The force constants of the internal coordinates of nonlinear XY 2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.