A relative interpolation theorem for infinitary universal Horn logic and its applications

In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case, a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without equality from those with equality. From the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general propositional logic.     

Band structure and model of the paraelectric structure of the Sn2P2S6 crystal

Since a variety of choices exist in the literature for the symbol of the space group of crystals of the type Sn₂P₂S₆, hindering the use of a group-theoretic analysis to determine the properties of the band spectrum and phonon spectrum, identified this symbol is identified with the known coordinates of the atoms of the given crystals. It is shown that the different arrangements P2₁/c and P2₁/n lead to permutations of the points in the Brillouin zone and correspondingly to a change in the irreducible representations. Calculating the spectra of Sn₂P₂S₆ and Sn₂P₂Se₆ by the method of pseudopotentials fitted to the width of the bandgap confirms the double degeneracy at the X, Y, Z points of the Brillouin zone, which was not expected for the X point in the arrangement P2₁/c. We have detected the previously predicted minimal band complexes in the band spectrum, which are the same as for In₄Se₃ of the group D _2h ¹² . Fiz. Tverd. Tela (St. Petersburg) 39, 1219–1222 (July 1997)     

Multi-walled carbon nanotubes-ferroelectric liquid crystal nanocomposites: effect of cell thickness and dopant concentration on electro-optic and dielectric behaviour

Nanocomposites comprise functionalised multi-walled carbon nanotubes (0.00 wt%, 0.05 wt% and 0.07 wt%) and ferroelectric liquid crystals (FLCs) have been studied in the 5-μm- and 12-μm-thickness cells. Effect of anchoring energy and dopant concentration on the mesomorphic, electro-optic and dielectric behaviour of FLC has been explored. Fast switching time and increase in permittivity of non-doped FLCs and resulting nanocomposites as a function of increased cell thickness (from 5 to 12 μm) can be attributed to the change in the anchoring energy and direct current (DC) conductivity of the non-doped and doped systems. π–π stacking between carbon nanotubes and FLC layers give rise to the spontaneous polarisation of nanocomposites. Effect of cell thickness and anchoring energy on bistability are also discussed.     

Quasi-degenerate rayleigh-schrödinger perturbation theory with hermitean model hamiltonian

A method for the construction of the hermitean model hamiltonian in the framework of the quasi-degenerate Rayleigh-Schrödinger perturbation theory is suggested. The approach of a model hamiltonian is based on the assumption that if it is diagonalized in a chosen finite-dimensional model space it will yield eigenvalues of the original hamiltonian in the entire Hilbert space. For a unitary operator transforming the unperturbed state vectors onto the perturbed state vectors, and a model-interaction operator, the perturbation-expansion formulae are developed.     

Thermodecomposition ofo-benzoquinone complexes of transition metals

Thermodecomposition of 3,5- and 3,6-di-tert-butyl-o-benzoquinone complexes of Cu, Fe, Co, Cr, Mo, and W has been investigated in the solid phase by the thermogravimetric method. The relative stability of a series of complexes has been determined from the temperatures at which their decomposition begins. Detachment of a neutral electron-donor ligand takes place in the first stage. Detachment of ano-quinone ligand and decomposition of theo-benzoquinone formed occur in the next stage. Thermodecomposition of Fe, Co, Cr, Mo, and W complexes gives oxides or carbides, while copper complexes decompose to pure metal.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 327–329, February, 1994.     

The dynamic “level shift” method for improving the convergence of the SCF procedure

This article is concerned with the improvement of convergence of the iterative procedure for solving the Hartree–Fock–Roothaan equations by the dynamic “level shift” method.     

Solvothermal Synthesis and Crystal Structures of Alkali Molybdates

Within the frame of systematic morphological studies concerning the solvothermal formation of nanoscale and microscale molybdenum oxides from the interaction of a molybdenum‐based precursor such as MoO₃⋅2 H₂O with ionic additives such as alkali and earth alkali halides, we studied – with the aim to elaborate preparative guidelines – the influence of the precursor structure and the alkali halide upon the crystal structure of the emerging alkali polymolybdates in terms of solvothermal fields and high‐throughput solvothermal techniques. The discussion of the resulting crystal structures revealed a structure‐directing potential of the alkali cations that was explored for the synthesis of new mixed alkali polymolybdates.