Specific heat and frequency shifts for the translational modes in ammonia solid I close to phase transition

The specific heat C(p) is correlated to the frequency shifts (1/nu)( partial differentialnu/ partial differentialT)(p) in ammonia solid I close to the melting point. Our calculated Raman frequencies for the translational modes of nu(T) (100 cm(-1)) and nu(T) (130 cm(-1)), are used for this correlation for the pressures of 0, 1.93 and 3.07 kbar in this crystalline system. We obtain that the specific heat varied linearly with the frequency shifts for those pressures studied and values of the slope dP(m)/dT were extracted. The observed behaviour of the ammonia solid I near the melting point is explained on the basis of our spectroscopic modification of the first Pippard relation.     

A diastereoselective intermolecular heck reaction of 1,3-dioxepins

A highly diastereoselective intermolecular Heck reaction of 1,3-dioxepins is reported. Substitution at both the 2- and 4-positions of the dioxepin directs the Pd coordination and subsequent olefin insertion to provide the trans-disubstituted adduct in good yield and high diastereoselectivity. Chemoselective Heck reaction occurs at the dioxepin alkene in the presence of other olefinic functional groups. A labeling study has been conducted which suggests that the reaction is under kinetic control.     

Approximate Symmetries and Conservation Laws with Applications

The relationship between the approximateLie-Backlund symmetries and the approximate conservedforms of a perturbed equation is studied. It is shownthat a hierarchy of identities exists by which thecomponents of the approximate conserved vector or theassociated approximate Lie-Backlund symmetries aredetermined by recursive formulas. The results areapplied to certain classes of linear and nonlinear waveequations as well as a perturbed Korteweg-de Vriesequation. We construct approximate conservation laws forthese equations without regard to aLagrangian.     

Evaluation of the Potential Release Tendency of Metals and Metalloids from the Estuarine Sediments: Case Study of Raša Bay

Assessing the environmental quality of coastal systems is important not only for the management and protection of such areas, but also for improving the quality of water resources. Since sediment itself can often be a source of certain toxic elements, in addition to information on the distribution of metals in the water column and in the sediment itself, it is useful to determine the bioavailable forms of individual elements, particularly toxic ones. In this study, water and sediment geochemical data were supplemented with oxyanion mobility in sediments estimated by diffusion gradients in thin film (DGTs). The data obtained indicate that the chemical composition of the water in the Raša River estuary primarily reflects the high input of suspended sediment from the catchment, the mixing of freshwater and seawater, and to a lesser extent the effects of anthropogenic activities. Although sediment composition is primarily determined by geological and hydrodynamic conditions in the catchment, it also indicates moderate enrichment in Co, Cr, Mo and Ni. In contrast, the distribution of oxyanions in sediment pore water indicates the influence of sediment as a source of some elements in the bottom water; e.g., sediment contributes to 40% of the arsenic bottom water budget. The obtained depth profiles of the oxyanion distribution in the sediment pore water indicate an early onset of suboxic to anoxic conditions in Raša Bay, which is prone to rapid sedimentation. All this demonstrates the need to consider the bioavailable forms of elements when assessing environmental quality, as the lack of such information can lead to an incomplete assessment, especially in dynamic coastal systems such as estuaries.     

A (2+1)-dimensional KdV equation and mKdV equation: Symmetries,group invariant solutions and conservation laws

In this paper, we analyse the (2+1)-dimensional KdV and mKdV equations. Firtly, on the basis of the extended Lax pair, we derive these equations. Thereafter, the symmetry generators are determined followed by the application of the mCK method. Finally, conservation laws (including higher order) are studied.     

Invariance Analysis and Variational Conservation Laws for the Wave Equation on Some Manifolds

In this paper we discuss symmetries of a nonlinear wave equation that arises as a consequence of some Riemannian metrics of signature −2. The objective of this study is to show how geometry can be responsible in giving rise to a nonlinear inhomogeneous wave equation rather than assuming nonlinearities in the wave equation from physical considerations. We find Lie point symmetries of the corresponding wave equations and give their solutions in two cases. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined.     

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the Low Rank Perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation with a standard assumption that force field does not change under isotopic substitutions. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at ρ atomic sites is considered. In the LRP approach vibrational frequencies ω _k and normal modes of the isotopomer B are expressed in terms of the vibrational frequencies ν _i and normal modes of the parent molecule A. In those relations complete specification of the normal modes is not required. Only amplitudes at sites τ affected by the isotopic substitutions and in the coordinate direction s (s = x, y, z) are needed. Out-of-plane vibrations of the (H,D)-benzene isotopomers are considered. Standard error of the LRP frequencies with respect to the DFT frequencies is on average . This error is due to the uncertainty of the input data (± 0.5 cm⁻¹) and in the absence of those uncertainties and in the harmonic approximation it should disappear. In comparing with experiment, one finds that LRP frequencies reproduces experimental frequencies of (H,D)-benzene isotopomers better () than scaled DFT frequencies () which are designed to minimize (by frequency scaling technique) this error. In addition, LRP is conceptually and numerically simple and it also provides a new insight in the vibrational isotope effect in the harmonic approximation.