Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.     

Electroreductive polymerization of phenylmethyldichlorosilane in a divided cell using a neutral membrane

Electrochemical formation of poly(phenylmethylsilane) in a divided cell containing a Teflon® neutral membrane was studied. The electrolysis of dichlorosilanes was carried out in a solution containing tetrahydrofuran + hexamethylphosphoramide as the solvent, tetrabutylammonium perchlorate as the support electrolyte and stainless steel as the cathode, with Pt and graphite as the resistant anodes or stainless steel as the sacrificial anode. Polysilanes with a number-average molecular weight in the range from 2,600 to 130,000 g/mol were obtained, depending on the conditions used.     

Interaction of chromophore, 11-<Emphasis Type="Italic">cis</Emphasis>-retinal,with amino acid residues of the visual pigment rhodopsin in the region of protonated Schiff base: A molecular dynamics study

A molecular dynamics study of the dark adapted visual pigment rhodopsin molecule was carried out. The interaction of the chromophore group, 11-cis-retinal, with the nearest amino acid residues in the chromophore center of the molecule, namely, in the region of the protonated Schiff base linkage, was analyzed. Most likely, the interaction of the CH=NH bond with the negatively charged amino acid residue Glu113 cannot be described as a simple electrostatic interaction of two oppositely charged groups. One can propose that not only Glu113 but also Glu181 and Ser186 are involved in stabilization of the protonated Schiff base linkage. Accord-ing to calculations, Glu181 interacts, as the counter-ion, with the Schiff base indirectly via Ser186. The intramolecular mechanisms of protonated Schiff base stabilization in rhodopsin are discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 19–27, January, 2007.     

Geminally activated nitroethenes in reactions with sodium azide. Synthesis of functionalized 1,2,3-triazoles

Reactions of geminally activated alkoxycarbonyl(acetyl, benzoyl, cyano)nitroethenes with sodium azide provided a series of functionally substituted 1,2,3-triazoles. Their structure was characterized by IR, ¹H, and ¹³C–{¹H} NMR spectroscopy.     

Coherence Evolution and Transfer Supplemented by Sender’s Initial-State Restoring

The evolution of quantum coherences comes with a set of conservation laws provided that the Hamiltonian governing this evolution conserves the spin-excitation number. At that, coherences do not intertwist during the evolution. Using the transmission line and the receiver in the initial ground state we can transfer the coherences to the receiver without interaction between them, although the matrix elements contributing to each particular coherence intertwist in the receiver’s state. Therefore we propose a tool based on the unitary transformation at the receiver side to untwist these elements and thus restore (at least partially) the structure of the sender’s initial density matrix. A communication line with two-qubit sender and receiver is considered as an example of implementation of this technique.     

On Effective Conductivity on ℤ d Lattice

We study the effective conductivity _e for a random wire problem on the d-dimensional cubic lattice ^d , d2 in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.     

Dipolar temperature and multiple-quantum NMR dynamics in dipolar ordered-spin systems

We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by dipole-dipole interactions in the case of the dipolar-ordered initial state. We suggest a new method of MQ NMR based on the measurement of the dipolar temperature in the quasi-equilibrium state, which establishes after the time of order ω _loc ⁻¹ (ω_loc is the dipolar local field) after the MQ NMR experiment. Manyspin clusters and correlations are created faster in such an experiment than in usual MQ NMR experiments and can be used for the investigation of the many-spin dynamics of nuclear spins in solids. The text was submitted by the authors in English.     

Duality relation for the Hilbert series of almost symmetric numerical semigroups

We derive the duality relation for the Hilbert series H (d ^m ; z) of the almost symmetric numerical semigroup S (d ^m ) combining it with its dual H (d ^m ; z ⁻¹). We establish the bijection between the multiset of degrees of the syzygy terms and the multiset of the gaps F _j , generators d _i and their linear combinations. We present the relations for the sums of the Betti numbers of even and odd indices separately. We apply the duality relation to the simple case of the almost symmetric semigroups of maximal embedding dimension, and give the necessary and sufficient conditions for the minimal set d ^m to generate such semigroups.     

Kinetics of formation and growth of antiphase domains during second-order phase transitions

The kinetics of the formation and growth of antiphase domains during second-order phase transitions is investigated theoretically in the Ginzburg-Landau model using a statistical approach. It is shown that depending on the initial conditions both uniform and polydomain-type ordering can be realized in thermodynamic equilibrium. It is found that for small initial inhomogeneities the ordering process can be nonmonotonic in its initial stages. It is established that for special initial conditions long-lived ordered structures of a special type arise in the intermediate stages of the ordering process. The characteristic formation time of the domain structure is estimated. Zh. éksp. Teor. Fiz. 113, 228–239 (January 1998)