Phasenbeziehungen und Natriumionenleitung im quasi-binären System Na2SiF6/Na3AlF6

Phase Relations and Sodium Ion Conductivity within the Quasi-binary System Na₂SiF₆/Na₂AIF₆ . The phase diagram of the Na₂SiF₆/Na₃AlF₆ system has been determined by means of x-ray powder diffraction, thermal analysis and conductivity measurements in the sub-solidus region. Na₃AlF₆ accomodates up to 73 mol.-% Na₂SiF₆ maintaining the crystal structure type. The sodium ion conductivity increases by about five orders of magnitude upon doping Na₃AlF₆ with Na₂SiF₆.     

The lead tetraacetate oxidation of bisacylhydrazones of α-diketones: A scope re-assesment

Oxidation of the title compounds yields, besides the reported isoimides 3 and/or the amides 4 , also the imides 5 . The observed product dichotomy is considered as the result of an intramolecular nucleophilic attack on the aroyl group, of the pressumed zwitterionic intermediate 2 , by O or N present in the ambident N-aroylimine site of 2 . The results of AM1 calculations agree with the product studies and both permit the formulation of a set of rules correlating structure and selectivity.     

Analytical torisionL-tensor formulas for anharmonic force constant transformation

New analytical formulas for the torsionL-tensor are reported, which are used in molecular normal mode analysis calculations for the nonlinear transformation of the force constants from internal coordinates to normal coordinates. The proposed formalism exhibits a relative simplicity as compared to previous reported results. Sample calculations for methanol and hydrazine are presented.     

An infinite family of simply connected flag-transitive tilde geometries

We consider tilde-geometries (orT-geometries), which are geometries belonging to diagrams of the following shape: Here the rightmost edge stands for the famous triple cover of the classical generalized quadrangle related to the group Sp₄(2). The automorphism group of the cover is the nonsplit extension 3·Sp₄(2) – 3 ·S ₆. Five examples of flag-transitiveT-geometries were known. These are rank 3 geometries related to the groupsM ₂₄ (the Mathieu group),He (the Held group) and and 3⁷·Sp₆(2) (a nonsplit extension); a rank 4 geometry related to the Conway groupCo ₁ and a rank 5 geometry related to the Fischer-Griess Monster groupF ₁. In the present paper we construct an infinite family of flag-transitiveT-geometries and prove that all the new geometries are simply connected. The automorphism group of the rankn geometry in the family is a nonsplit extension of a 3-group by the symplectic group Sp_2n (2). The rank of the 3-group is equal to the number of 2-dimensional subspaces in ann-dimensional vector space over GF(2).     

Boundary conditions in quantum field theories

Several interesting and important quantum field theories must contain the coupling constant in the boundary conditions. The theories considered include quantum electrodynamics of spin-1/2 fermions and gauge field theories.     

Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential

We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spinzero particles in any arbitratry spherically symmetric potential, the non-Coulombic effective power-law potential is used as a kernel to produce the spin-averaged bound states of the non-self-conjugate mesons. The analytical formulas are also applicable to the self-conjugate mesons in the equal-mass case. The flavor-independent case is investigated in this work. The calculations are carried out to the third-order correction of the energy series. Results are consistent with those obtained before.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

Electrodialysis of Hydrosols of Ultradispersed Diamonds

The electrical conductivity of hydrosols of ultradispersed diamonds was studied. The electromembrane method for cleaning and concentrating of ultradispersed diamonds in hydrosols was considered. The influence exerted by the concentration of the dispersed phase on the electrical characteristics of the cleaning process was analyzed. A mathematical relation making it possible to evaluate the output characteristics of the process and to determine the geometrical characteristics of the apparatus was proposed.     

Replica Symmetry Breaking in an Axial Model of Quadrupolar Glass

We investigate the replica symmetry breaking (RSB) in a neighborhood of the instability point of the replica-symmetric solution in the axial quadrupolar glass model. We show that the solution with the first-stage RSB is stable against the subsequent RSB. Although there is no reflection symmetry, the first-stage RSB solution continuously bifurcates from the replica-symmetric one. This implies that our model does not belong to either of the two classes into which spin glasses are usually divided.