Limiting-type theorem for conditional distributions of products of independent unimodular 2×2 matrices

We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments.     

Surface functionalization of porous ZrO2-TiO2 membranes using γ-aminopropyltriethoxysilane in palladium electroless deposition

A pre-treatment technique was developed to facilitate the electroless deposition of Pd layers onto ZrO₂-TiO₂ ceramic membrane surfaces in the preparation of novel multi-functional porous membranes. Surface functionalization using an aqueous solution of γ-aminopropyltriethoxysilane (γ-APTES) aided the surface immobilization of the Pd activation particles and the subsequent electroless deposition of metal layers onto the hydroxyl-rich membrane surface. The attractiveness of γ-APTES functionalization, in the electroless deposition of metal layers, was thus demonstrated. Characterization techniques employed in the structural study of the surface-modified membranes included SEM, EDS, dynamic analysis in micro-PIXE, and XRD. Special membrane techniques such as electrokinetic analysis and single-gas permeation measurements were also used in the study of surface modification. These membranes were developed for application in tasks associated with the hydrogen economy.     

Thermodynamics and topology of disordered systems: Statistics of the random knot diagrams on finite lattices

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants, was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro-and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q→∞. It is shown that the highest power of the Kauffman invariant correlates with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The results obtained are compared to the probability distribution of the minimum energy of a Potts system with random ferro-and antiferromagnetic bonds.     

Change in surface states of Ag(111) thin films upon adsorption of a monolayer of PTCDA organic molecules

The change in the electronic structure of silver thin films of different thicknesses with the Ag( 111) orientation due to the interaction with an adsorbed monolayer of ordered organic molecules of 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) has been investigated in terms of density functional theory. It has been shown that one of the two surface states of the pure films transforms into an unocc upied interface state due to the interaction so that all the main features of the initial state are retained. The relation of the resulting state to the unoccupied state experimentally observed in the PTCDA/Ag( 111 ) system by scanning tunneling and two-photon photoemi ssion spectroscopy has been discussed.     

Investigation of the reaction D(<Superscript>4</Superscript>He, γ)<Superscript>6</Superscript>Li at ultralow energies

The cross section of the reaction D(⁴He, γ)⁶Li with titanium and zirconium deuterides as targets is measured for incident ⁴He⁺ ion energies of 30 and 36 keV, respectively. The ion beam is generated by a Hall pulsed plasma accelerator. For the first time, upper limits on the cross section of the reaction D(⁴He, γ)⁶Li at ultralow energies are imposed (at 90% confidence level): σ ≤ 1.2 × 10^?35 cm² for the TiD₂ target and E(⁴He⁺) = 30 keV, and σ ≤ 7 × 10^?36 cm² for the ZrD₂ target and E(⁴He⁺) = 36 keV     

Calculation of the IR Spectrum of Ethyl Chlorophyllide a by the Method of Density Functional

The structure, frequencies of normal vibrations, and the absolute IR intensities of ethyl chlorophyllide a have been calculated by the DFT/B3LYP/6-31G(d) density functional method. The force constants have been scaled by the Pulay method. The force field of ethyl chlorophyllide a has been obtained in independent and dependent natural coordinates. The vibrational IR spectrum of ethyl chlorophyllide a has been modeled. The experimental IR spectrum of chlorophyll a has been interpreted on the basis of the calculation performed.     

Ten-Megawatt Pulsed Gyrotron with a 1-cm Wavelength and a 50% Efficiency

Development of a gyrotron driven by a relativistic electron beam and generating radiation at the wavelength 1 cm with an output power of 10 MW, an efficiency of 50%, and a pulse duration of a few hundreds of nanoseconds is reported.     

Ab initio calculation of the lifetime of quasiparticle excitations in transition metals within the framework of the <Emphasis Type="Italic">GW</Emphasis> approximation

This paper reports on the results of ab initio calculations of the lifetimes τ of quasiparticle excitations in cubic d transition metals (V, Nb, Ta, Mo, W, Rh, Ir) within the GW approximation, which represents the self-energy of quasiparticles by the product of the Green’s function and the dynamically screened Coulomb potential. A comparative analysis of the dependences of the lifetime τ(ω) on the excitation energy ω is performed, and the specific features of the dependences τ(ω) in going from metal to metal within a particular group and along the d periods are revealed. It is found that the dependence τ(ω) on the excitation energy differs from the dependence τ ～ ω^?2 obtained within the free-electron model and is primarily determined by the density of d states localized in the vicinity of the Fermi level and by the electron interaction screened by the d electrons.     

Vibrational spectra of lanthanide endofullerenes with different symmetries of molecular structure

Quantum-chemical calculations of the geometric structure and vibrational spectra of lanthanide endofullerenes have been carried out. The vibrational frequencies of lanthanide atoms depend substantially on the symmetry of the molecular structure of the endofullerene and on the distance between the metal atom and the carbon cage. The infrared spectra of the endofullerenes M@C₆₀ contain vibrations that are forbidden by symmetry for the empty fullerene C₆₀. A change in the vibrational spectra due to the encapsulation of a metal atom in fullerenes with a C₆₀ cage is considerably more pronounced than that of the higher fullerenes. In the vibrational spectra, there are lines not characteristic of C₆₀, which indicates the presence of M@C₆₀ endofullerenes in a mixture with C₆₀ fullerenes.     

When are all group codes of a noncommutative group Abelian (a computational approach)?

Let G be a finite group and F be a field. Any linear code over F that is permutation equivalent to some code defined by an ideal of the group ring FG will be called a G-code. The theory of these ??abstract?? group codes was developed in 2009. A code is called Abelian if it is an A-code for some Abelian group A. Some conditions were given that all G-codes for some group G are Abelian but no examples of non-Abelian group codes were known at that time. We use a computer algebra system GAP to show that all G-codes over any field are Abelian if |G|?<?128 and |G| ? {24, 48, 54, 60, 64, 72, 96, 108, 120}, but for F?=? $ {\mathbb{F}_5} $ and G?=?S₄ there exist non-Abelian G-codes over F. It is also shown that the existence of left non-Abelian group codes for a given group depends in general on the field of coefficients, while for (two-sided) group codes the corresponding question remains open.