Volume 59, Issue 10

First, applying the Jacobi elliptic sine function expansion, basic travelling wave solutions of some nonlinear evolution equations are obtained. Second, according to the formal invariance of nonlinear evolution equations, the sister travelling wave solutions, which have the same wave speed as the basic ones, are derived. Finally, we show that a suitable linear combination of these two solutions results in a combined travelling wave solution, whose wave speed is different from those of the basic and sister travelling wave solutions. The combination of travelling wave solutions to nonlinear evolution equations must satisfy certain conditions. - PACS: 03.65.Ge.

Using the B¨acklund transformation and a variable separation approach with some arbitrary functions, three new types of solutions of the sine-Gordon system have been obtained. The excitations are localized as well as non-localized. E.g. solitoffs, dromions, multidromions, lumps, breathers, instantons, multivalued solitary waves, doubly periodic waves, etc., can be constructed on the basis of selecting the arbitrary functions properly. Also the interaction properties for all the possible localized excitations are of interest. In this paper, we discuss two elastic interactions. - PACS Ref: 05.45.Yv, 02.30.Jr, 02.30.Ik.

We provide evidence of the nonintegrability of a recently proposed model for water waves in 2+1 dimensions: we show that under a nonlinear time transformation, a certain reduction of this partial differential equation is mapped to an ordinary differential equation which does not have the Painlev´e property. This is in contrast to what happens in the case of the Camassa-Holm equation. Also, and again in contrast to the case of the Camassa-Holm equation, the equation under study fails to admit Dirichlet series solutions. - MSC2000 classification scheme numbers: 35Q51, 35Q58, 37K10.

The multi-linear variable separation approach is applied to a differential-difference asymmetric Nizhnik-Novikov-Veselov equation. It is found that the solution formula ANNV equation is rightly the semi-discrete form of the continuous one which describes some types of special solutions for many (2+1)-dimensional continuous systems. Moreover, it is different but similar to that of a special differential-difference Toda system. Thus abundant semi-discrete localized coherent structures of the ANNV equation are easily constructed by appropriately selecting the arbitrary functions appearing in the final solution formula. A concrete method to construct multiple localized discrete excitations with and without completely elastic interaction properties are discussed. It is found that for some types of bounded solitoff modes, they can exchange solitoffs, move in new different directions, extend the lengths of solitoffs, etc. after finishing their interactions. - PACS numbers: 0230, 0220, 0540

We report on thermal microscopy and low frequency dielectric relaxation of a liquid crystal formed by mixing cholesterol with 1-hexadecanol. Though both components are non-mesogenic, the mixture is found to exhibit a smectic A phase. A 1 V p-p a. c signal of 100 kHz was used to study the dielectric response, while the frequency was varied from 5 Hz to 10 MHz for relaxation studies. The dielectric loss in the smectic A phase exhibits a single Debye-type off-centered relaxation in the MHz region. The temperature variation of the relaxation frequency is presented by Arrhenius plots, and the corresponding activation energy is estimated. The temperature variation of the dielectric strength (Δε =ε 0 −ε ∞ ) and the distribution parameter α in the smectic phase are estimated. The mesomorphic behavior of binary systems, where both components are non-mesomorphic, is discussed.

Electron paramagnetic resonance of γ -irradiated single crystals of Nα -monochloroacetyl-α-aminoisobutyric acid were investigated at room temperature and 130 K. The paramagnetic center as attributed to the (CH 3 ) 2 ˙CCOOH radical.

EPR spectra of VO 2+ ions in di-sodium tartrate, [Na 2 C 4 H 4 O 6 ], single crystal and powder spectra have been studied at room temperature. The angular variation of the EPR spectra has shown that three different VO 2+ complexes are located in different chemical environments, and each environment contains two magnetically inequvalent sites. The spin Hamiltonian parameters are determined, and these parameters have been used to assess the bonding coefficients of the VO 2+ ion in the di-sodium tartrate lattice. The parallel and perpendicular components of axially symmetric g and hyperfine tensors are evaluated. The results are discussed.

Results of dielectric studies of three 4,4’-di-n-alkyl-azoxybenzenes (nAOB) and 4,4’-di-n-alkoxyazoxybenzenes (nOAOB), n = 5, 6 and 7, are presented. The nAOB compounds exhibit positive, and the nOAOBs negative dielectric anisotropy in the nematic phase. In the smectic A phase of 7AOB the anisotropy changes its sign, whereas in the smectic C phase of 7OAOB it persists negative; moreover, in the latter case the perpendicular component of the permittivity increases with respect to the value of the nematic phase. This may be due to parallel dipole-dipole correlation of the perpendicular components involved by the layer arrangements in both smectic phases. For all substances a systematic decrease of the permittivity components with chain length was observed. Different types of smectic order in the 7th members of both series are discussed in relation to the mean-field theory developed recently by Govind and Madhusudana. The dielectric relaxation times and activation enthalpies characterizing the molecular rotation around the principal inertia axes are given.

A series of liposomes has been studied by the Fluorescence Recovery after Photobleaching technique using confocal scanning laser microscopy. Both mobile and immobile specimens of lipid membranes have been examined. The specimens consisted of liposomal suspensions incorporating mixtures of the phospholipids dioleoyl phosphatidylcholine (DOPC) and distearoyl phosphatidylcholine (DSPC) with the aminolipid dihexadecanol glycerophospho-ethanolamine (DHPE). The measurements reported provide information about the effective diffusion coefficients, which vary from 0.2 · 10 −10 cm 2 s −1 to 3.2 · 10 −10 cm 2 s −1 . They were highly dependent on the ratio DSPC:DOPC. A simple theoretical model of 1-D diffusion was applied for the calculation of the effective diffusion coefficients. The measurements show that it is possible to use straightforward procedures with an unmodified commercial confocal microscope to determine diffusion coefficients of biological specimens.

The high-order perturbation formulas of the spin Hamiltonian (SH) parameters g-shift Δg (=g−g s ) and the hyperfine structure constant A for a 3d 3 ion in cubic octahedra are established, based on the two mechanism model. In this model, not only the contributions from the conventional crystal-field (CF) mechanism, but also those from the charge-transfer (CT) mechanism are taken into account. These formulas are applied to the investigation of the SH parameters of cubic V 2+ , Cr 3+ and Mn 4+ centers in MgO and CaO. Based on these studies, the sign of Δg due to the CT mechanism is opposite to that due to the CF mechanism, while the signs of the A factor due to the CF and CT mechanisms are equal. The theoretical results, including the contributions from the CF and CT mechanisms, agree better with the observed values than those containing only the conventional CF mechanism.

In an earlier work it was demonstrated that the Zenkevich index U provides a measure of the intramolecular energy of an organic molecule, and that - in the case of alkanes - it is related to the Wiener index. We now show that U is much closer related to the recently introduced variable Wiener index W λ : Within sets of isomeric alkanes, the relation between U and W λ is linear, the (U,W λ )-points forming several, mutually parallel, lines. Each such line pertains to a group of isomers possessing a fixed number of methyl groups. There exists a critical value of the parameter λ for which all the (U,W λ )-lines coalesce, in which case the relation between U and W λ becomes independent of the number of methyl groups. Approximate analytical expressions for the (U,W λ )-dependence are deduced.

The relation between Pauling and Coulson bond orders in benzenoid hydrocarbons is examined. The carbon-carbon bonds of benzenoid hydrocarbons have to be classified into three classes, depending on the number of attached hydrogen atoms. Within each class the correlation between the bond orders is linear. The results can be used to rationalize the recently discovered correlation between the energy and electron contents of rings. An approximate expression for the total π-electron energy is also deduced.

A UV and visible spectrophotometric study was made in order to prove the existence of Nd 2+ and clarify the equilibrium among Nd metal, Nd 2+ , and Nd 3+ in LiCl-KCl eutectic melt. Spectra assigned to Nd 2+ were observed for NdCl 2 in (LiCl-KCl)eut. and Nd- NdCl 3 in (LiCl-KCl)eut. melts. Black corrosion products were observed on the surface of the glass cells used for the measurements, where the spectra assigned to Nd 2+ were observed. X-ray diffraction measurements and electron-probe micro-analyses of the corroded glass cells revealed that the corrosion products contained NdOCl.

We have investigated the electrochemical behaviour of lanthanum ions in a eutectic molten mixture of LiCl and KCl, using linear sweep voltammetry, as well as semi-integration and semi-differentiation of cyclic voltammograms. It was found that the reduction of La 3+ is quasi-reversible, and that the obtained diffusion coefficient of La 3+ is consistent with that estimated from thermodynamic data. The electrochemical reduction, diffusion of La 3+ in LiCl-KCl, and the structure and stability of the complex ion are discussed.

In a paper, published in 1997 by L. Corry, J. Renn, and J. Stachel, it is claimed that the recently discovered printer’s proofs of Hilbert’s 1915 paper on the general theory of relativity prove that Hilbert did not anticipate Einstein in arriving at the correct form of the gravitational field equations, as it is widely believed, but that only after having seen Einstein’s final paper did Hilbert amend his published version with the correct form of the gravitational field equations. However, because a crucial part of the printer’s proofs of Hilbert’s paper had been cut off by someone, a fact not mentioned in the paper by Corry, Renn, and Stachel, the conclusion drawn by Corry, Renn, and Stachel is untenable and has no probative value. I rather will show that the cut off part of the proofs suggests a crude attempt by some unknown individual to falsify the historical record.