Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page

Estimation of hormone residuals (B-Estradiole) in rainbow trout

Residual level of 17- Beta Stradiol and progesterone hormones in rainbow trout fish plasma were measured during different period using RIA method. Blood sampling from abdominal aorta were taken from 70 individual of female fishes (100±11 g) which had been exposed to hormone at 0.5, 1,2,4,8,12,24 and 168 h (7 groups) compared with control group which was not exposed to this hormone. Results showed that plasma hormones measurement in different fish groups after exposing had significant differences (P<0.01) and the highest and lowest 17-Beta Stradiol hormone residue were observed in fishes that exposed 0.5h and 168h to hormone respectively (121±9 ng. ml^-1 and 3±0.9 ng. ml^-1) but there is no any differences between fishes exposed 168h to hormone and control group. Also the highest progesterone hormone level were measured in fishes 0.5 an 1h exposed and the lowest one was in fishes 168 h exposed. The range of progesterone hormone were between 0.3 to 1.1 ng .ml^-1 and significant increasing of this hormone levels were obtained in fishes exposed to hormone 4 to 24h (P<0.01). As consequence these hormone can not residue in fishes for a long time and maximum after one week the levels back to the normal

Full-dimensional, high-level ab initio potential energy surfaces for H2(H2O) and H2(H2O)2 with application to hydrogen clathrate hydrates

New, full-dimensional potential energy surfaces (PESs), obtained using precise least-squares fitting of high-level electronic energy databases, are reported for intrinsic H2(H2O) two-body and H2(H2O)2 three-body potentials. The database for H2(H2O) consists of approximately 44000 energies at the coupled cluster singles and doubles plus perturbative triples (CCSD(T))-F12a/haQZ (aug-cc-pVQZ for O and cc-pVQZ for H) level of theory, while the database for the three-body interaction consists of more than 36000 energies at the CCSD(T)-F12a/haTZ (aug-cc-pVTZ for O, cc-pVTZ for H) level of theory. Two precise potentials are based on the invariant-polynomial technique and are compared to computationally faster ones obtained via "purified" symmetrization. All fits use reduced permutational symmetry appropriate for these non-covalent interactions. These intrinsic potentials are employed together with existing ones for H2, H2O, and (H2O)2, to obtain full PESs for H2(H2O) and H2(H2O)2. Properties of these full PESs are presented, including a diffusion Monte Carlo calculation of the zero-point energy and wavefunction, and dissociation energy of the H2(H2O) dimer. These PESs together with an existing one for water clusters are used in a many-body representation of the PES of hydrogen clathrate hydrates, illustrated for H2H2O)20. An analysis of this hydrate is presented, including the electronic dissociation energy to remove H2 from the calculated equilibrium structure