Volume 62, Issue 3-4

In this paper, we formulate a method wherein we harness the results of the Painlevé analysis to generate the solutions of the (2+1)-dimensional Ablowitz-Kaup-Newell-Segur system completely in terms of the arbitrary functions. This method is mainly based on the results of the truncated Painlevé expansion. Different types of interactions among dromions are deeply understood both analytically and numerically. Especially, different from the traditional viewpoint, we point out that the soliton (dromion) fission and fusion may be an approximate phenomenon.

The question concerning the extent of the local spacetime has often been raised. At what circumsolar distance the well known Robertson-Walker spacetime of our expanding universe may become a valid approximation? Inside of that distance a local Schwarzschild metric, which permits to explain the Keplerian motions of planets within the frame of general relativity, must be applicable.We briefly analyze the historical answer to that question given by Einstein, Straus and their followers and show that till now this answer is unsatisfactory in many respects. We revisit the problem of local spacetime geometries in the light of their effects on local photon propagation in view of the radiopropagation phenomena detected with the NASA spaceprobes PIONEER-10/11, waiting for a satisfying answer for several decades now. Comparing radiosignals outgoing from the earth to the probe and ingoing again from the probe to the receiver on earth do show anomalous frequency shifts which presently find no explanation by anomalous non-Newtonian decelerations of these probes. Therefore we study cosmological conditions for the transfer of radiosignals between the earth and these distant probes based on time dependent local spacetime geometries. First we study the cosmological redshift of radiophotons during their propagation to the spaceprobe and show that this shift in fact explains the registered PIONEER phenomenon under the assumption that the full cosmological expansion of the universe also takes place locally. Though yielding the right magnitude, one finds that this assumption leads to a redshift instead of the observed blueshift. We then, however, show that theoretically motivated forms of time dependent local spacetime metrices in fact lead to a blueshift of the needed magnitude. The appropriate local space vacuole is characterized by a Schwarzschild metric of a central mass increasing with cosmic time. Though it is clear that further studies of this effect have to be carried out to give more credit and verification to this hypothetical result, nevertheless more careful hightech radiotracking of freely flying spaceprobes may do a usefull job in confirming a completely unexpected, but cosmologically highly relevant phenomenon.

The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

In this paper, a protocol which can be used in multi-user quantum signature is proposed. The scheme of signature and verification is based on the correlation of Greenberger-Horne-Zeilinger (GHZ) states and the controlled quantum teleportation. Different from the digital signatures, which are based on computational complexity, the proposed protocol has perfect security in the noiseless quantum channels. Compared to previous quantum signature schemes, this protocol can verify the signature independent of an arbitrator as well as realize multi-user signature together. - PACS numbers: 03.67.Dd; 03.67.-a

Conventional solutions of the (Mean) King’s problem without using entanglement have been investigated by P. K. Aravind, Z. Naturforsch. 58a, 682 (2003). We report that the upper bound for the success probability claimed is not valid in general but we give a condition for the claim to be justified.

The oxide complexation chemistry in molten tetrachloroaluminate salts and ionic liquids is discussed with respect to what possible structures may be formed in addition to [AlCl 4 ] − : [Al 2 OCl 6 ] 2− , [Al 3 OCl 8 ] − , [Al 2 O 2 Cl 4 ] 2− , [Al 3 O 2 Cl 6 ] − and [Al 4 O 2 Cl 10 ] 2− . Ab initio molecular orbital calculations are carried out on these various aluminium chloride and oxochloride ions, in assumed isolated gaseous free ionic state, by use of the Gaussian 03W program at the restricted Hartree-Fock (HF) level and with the 6-31+G(d,p) basis set.Without any pre-assumed symmetries and with tight optimization convergence criteria and by using the modified GDIIS algorithm, the model calculations generally converge. The structures and their binding energies are presented. The expected geometries are supported, with one exception perhaps being the [Al 2 OCl 6 ] 2− ion, that gave a linear Al-O-Al bonding system of staggered AlCl 3 -groups (approximate D3d symmetry), in analogy to the linear Al-O-Al geometry of the analogous [Al 2 OF 6 ] 2− ion, found previously. The calculations include determination of the vibrational harmonic normal modes and the infrared and Raman spectra (vibrational band wavenumbers and intensities), without any empiric adjustments of the harmonic force constants, using constants directly predicted from the Gaussian 03W program. Previously obtained IR absorption and Raman scattering spectra of melts are assigned, by comparing to the ab initio quantum mechanical vibrational analysis results. It is concluded that the small oxide content commonly found in basic and neutral tetrachloroaluminate melts, most probably consists of [Al 4 O 2 Cl 10 ] 2− ions, and the vibrational spectra are given.

Electronic absorption and Raman spectra of solid and molten Cs 2 NaHoCl 6 elpasolite have been measured in the temperature range 20 - 780 ◦ C. The Raman spectra of the solid indicate that there is no phase transition above room temperature. It appears, that the internal vibrational modes of the solid are transferred into the melt, indicating that the [HoCl 6 ] 3 − “octahedra” are the predominant species. The 5 G 6 ← 5 I 8 and 3 H 6 ← 5 I 8 hypersensitive transitions of Ho(III) in elpasolite have been studied and analyzed in terms of the ligand field splittings of these states in the octahedral [HoCl 6 ] 3 − field. The temperature-induced changes in the spectra are attributed to the presence of “hot” bands arising from sets (“zones”) of energy levels in the ground 5 I 8 state. The continuous and smooth spectral changes observed upon melting indicate the presence of [HoCl 6 ] 3− octahedra in both phases.

The (v’ = 34, J’ = 14) level of the A 1 Σ + u electronic state of Na 2 has been selectively populated by excitation with the 578.1 nm line of a ring dye-laser with rhodamine 6G. Through collisions with ( 2 S 1/2 ) Na atoms, energy is transferred to neighbouring rotational levels in Na 2 , and the density of these levels is determined by observing the fluorescence to the electronic ground state. From previous measurements of the lifetime of the A 1 Σ + u state and new measurements of the intensities of collision-induced spectral lines, absolute collision cross-sections for all rotational transitions up to ΔJ = ±6 have been obtained; the total cross-section for all rotational transitions observed is: rot σtotal = 0.41 nm 2 .

A phase transition in [Cr(NH 3 ) 6 ](ClO 4 ) 3 at T h c = 293.5 K (on heating) and T c c = 293.0 K (on cooling) was determined by differential scanning calorimetry. The temperature dependences of the full width at half maximum of the bands connected with ρ r (NH 3 )F 1u and δ d (ClO)E modes suggest that the discovered phase transition is not connected with drastic changes in the speed of reorientational motions of the NH 3 ligands nor the ClO 4 − anions. Temperature dependence of the FT-FIR spectra and the diffraction patterns show that the discovered phase transition is caused by a change in the crystal structure.

The differential capacity at the electrode (Pt, Au)/ionic liquid interface of 18 ionic liquids (ILs), was measured applying chronoamperometry. The measurements were done by a two electrode system. The double layer capacity at the Pt/IL and Au/IL interface was 1 - 8 μF/cm 2 . The capacity, estimated from the impedance measurements, was approximately constant within a potential range of ca. 3 V.

In order to investigate the redox equilibrium of europium ions in molten NaCl-2CsCl, UV-Vis absorption spectrophotometry measurements were performed for Eu 2+ and Eu 3+ in molten NaCl - 2CsCl at 923 K under simultaneous electrolytic control of their ratio. Molar absorptivities of EuCl 3 and EuCl 2 in NaCl-2CsCl at 923 K were determined to be (420±21) M −1 cm −1 at 31200 cm −1 and (1130±56) M −1 cm −1 at 30300 cm −1 , respectively. The formal redox potential of the Eu 2+ /Eu 3+ couple in NaCl-2CsCl melt at 923 K was determined to be (−0.941 ±0.004) V vs. Cl 2 /Cl − by electromotive force measurements on varying concentration ratios of Eu 2+ and Eu 3+ , which were performed using a technique based on the combination of electrolysis and spectrophotometry. Cyclic voltammetry was also carried out in order to examine the characteristics of the voltammograms for the Eu 2+ /Eu 3+ couple in NaCl-2CsCl melt. The formal redox potential of the Eu 2+ /Eu 3+ couple determined by a spectroelectrochemical method agreed with that determined by cyclic voltammetry [(−0.946±0.008) V vs. Cl 2 /Cl − ]. The effects of temperature on the redox potential of the Eu 2+ /Eu 3+ couple in NaCl-2CsCl, NaCl-KCl, LiCl-KCl, and CsCl melts were studied by cyclic voltammetry in the range from 923 to 1123 K.

This paper continues our research program on lanthanide halide-alkali metal halide systems. Differential scanning calorimetry (DSC) was used to investigate the phase equilibria of the CeBr 3 -KBr system. This system is characterized by the two congruently melting compounds K 3 CeBr 6 and K 2 CeBr 5 and the three eutectics located at the CeBr 3 mole fractions 0.193 (837 K), 0.295 (855 K) and 0.555 (766 K). K 3 CeBr 6 forms at 775 K and melts congruently at 879 K with the related enthalpies 54.5 and 41.7 kJ mol −1 , respectively. K 2 CeBr 5 melts congruently at 874 K with the enthalpy 82.4 kJ mol −1 . The electrical conductivity was measured of all CeBr 3 -KBr mixtures and of the pure components down to temperatures below solidification. The experimental determinations were conducted over the entire composition range in steps of about 10 mol%. The specific electrical conductivity decrease with increasing CeBr 3 concentration, with significantly larger conductivity changes in the potassium bromide-rich region. The results are discussed in terms of possible complex formation.

Electronic absorption spectra of gaseous chlorine and their saturated solutions in molten alkali chlorides were studied in wide ranges of temperature and wavelength. It was found that gaseous chlorine has a wide absorption band between 20 000 and 43 500 cm −1 . There is a tendency to both widening of the band and shifting of the absorption maximum to the short-waves region with rising temperature. The absorption bands of saturated solutions of chlorine in all molten alkali chlorides show a maximum in the neighborhood of 30 000 cm −1 . A good correlation was found between the optical density of molten salt-Cl 2 systems and the solubility of chlorine.

Using standard standing wave microwave X-band techniques, and by following Gopala Krishna’s single frequency (9.90 GHz) concentration variational method, the dielectric relaxation times (τ) and dipole moments (μ) of binary mixtures of different molar concentrations of ethanol (EtOH) in binary mixtures of N-methylacetamide (NMA) and ethanol in benzene solutions at 25, 30, 35 and 40 ◦C have been calculated. The activation parameters (ΔH ε , ΔF ε , ΔS ε ) for the dielectric relaxation process of binary mixtures containing 30 mol% of EtOH have been calculated at 25, 30, 35 and 40 ◦ C and compared with the corresponding viscosity parameters. A good agreement between the free energy of activation from these two sets of values shows that the dielectric relaxation process, like the viscous flow, can be treated as a rate process. From relaxation time behaviour of NMA and EtOH binary mixtures in benzene solution, solute-solute and solute-solvent types of the molecular association have been predicted.

The EPR g-shift Δg (≈ g−g e ) of the metal-cyanide cluster [Cr(CN) 6 ] 3− is calculated by high-order perturbation formulas based on both the crystal-field (CF) and charge-transfer (CT) mechanisms (the latter is often neglected in the crystal-field theory). The result agrees with the experimental value. The sign of the g-shift Δg CT due to the contribution of the CT mechanism is opposite to that of Δg CF due to the contribution of the CF mechanism, and the absolute value of Δg CT is about 34% of that of Δg CF . It appears that for transition metal ions in a strong covalent cluster, a reasonable theoretical explanation of the g-shift should take both the CF and CT mechanism into account.

By means of the complete energy matrix diagonalization procedure of 3d 2 /3d 8 ions in trigonal symmetry and using the superposition model, the electron paramagnetic resonance (EPR) parameters for Ni 2+ ions in RbMgF 3 crystals with C 3v and D 3d symmetry are studied. From the investigation, the defect structures of these paramagnetic impurity centers are obtained and the EPR parameters are explained reasonably. - PACS numbers: 76.30.Fc, 61.72.Bb, 71.70.Ch

A previously obtained approximate non-relativistic Helium wave function is improved significantly coming within 0.02% of the “exact” value with 8 terms. The sensitivity of this final result to the parameters in the wave function is examined.