Uniform non-amenability of free Burnside groups

The aim of this paper is to show that free Burnside groups of sufficiently large odd exponent are non-amenable in a certain strong sense. More precisely their left regular representations are isolated from the trivial representation uniformly on finite generating sets. It follows that free Burnside groups are of uniform exponential growth. This answers a question of de la Harpe. This work has been partially supported by the NSF grant DMS-0605093 and by the RFBR Grant # 05-01-00892. Received: 25 April 2006     

Fused Fluorinated Bis-β-diketones and Luminescent-Spectral Properties of Their Complexes with Europium

Russian Journal of General Chemistry - Claisen condensation of diacetylated fused aromatic and heteroaromatic compounds (fluorene, dibenzofuran, dibenzothiophene, or carbazole) with...     

Fabrication of composite based on GeSi with Ag nanoparticles using ion implantation

Comparative analysis of the structural and optical properties of composite layers fabricated with the aid of implantation of single-crystalline silicon (c-Si) using Ge⁺ (40 keV/1 × 10¹⁷ ions/cm²) and Ag⁺ (30 keV/1.5 × 10¹⁷ ions/cm²) ions and sequential irradiation using Ge⁺ and Ag⁺ ions is presented. The implantation of the Ge⁺ ions leads to the formation of Ge: Si fine-grain amorphous surface layer with a thickness of 60 nm and a grain size of 20–40 nm. The implantation of c-Si using Ag⁺ ions results in the formation of submicron porous amorphous a-Si structure with a thickness of about 50 nm containing ion-synthesized Ag nanoparticles. The penetration of the Ag⁺ ions in the Ge: Si layer stimulates the formation of pores with Ag nanoparticles with more uniform size distribution. The reflection spectra of the implanted Ag: Si and Ag: GeSi layers exhibit a sharp decrease in the intensity in the UV (220–420 nm) spectral interval relative to the intensity of c-Si by more than 50% owing to the amorphization and structuring of surface. The formation of Ag nanoparticles in the implanted layers gives rise to a selective band of the plasmon resonance at a wavelength of about 820 nm in the optical spectra. Technological methods for fabrication of a composite based on GeSi with Ag nanoparticles are demonstrated in practice.     

Kazhdan Constants of Hyperbolic Groups

Let H be an infinite hyperbolic group with Kazhdan property (T) and let (H,X) denote the Kazhdan constant of H with respect to a generating set X. We prove that inf_X(H,X)=0, where the infimum is taken over all finite generating sets of H. In particular, this gives an answer to a Lubotzky question.     

Solvable groups with polynomial Dehn functions

Given a finitely presented group , finitely generated subgroup of , and a monomorphism , we obtain an upper bound of the Dehn function of the corresponding HNN-extension in terms of the Dehn function of and the distortion of in . Using such a bound, we construct first examples of non-polycyclic solvable groups with polynomial Dehn functions. The constructed groups are metabelian and contain the solvable Baumslag-Solitar groups. In particular, this answers a question posed by Birget, Ol'shanskii, Rips, and Sapir.

     

Elementary Classes of Groups

Let be a class of groups. The elementary class with base is defined as the minimal class of groups containing and closed with respect to taking subgroups, quotient groups, group extensions, and direct limits. Properties of such classes are studied. Some applications to the theory of elementary amenable groups and a relation to the Kurosh--Chernikov classes of generalized solvable groups are considered.     

Electrochemical synthesis of metal nanoparticles using a polymeric mediator,whose reduced form is adsorbed (deposited) on an electrode

Efficient mediated electrosynthesis of nanocomposite Au@р(MVCA⁸⁺-co-St) (~6 nm), in which ultrasmall Au nanoparticles (Au-NP) were bound in nanocapsules of water-soluble nanoparticles of соpolymer р(MVCA⁸⁺-co-St) of tetraviologen calix[4]resorcinol (MVCA⁸⁺) with styrene (St), was accomplished by the reduction of Au^I in aqueous medium. The quanti- tative reduction of Au^I was carried out using the theoretically necessary amount of electricity and was not accompanied by the deposition of metal on the electrode. Radical cations of viologen units MV^?+ of the molecule р(MVCA^4?+-co-St) adsorbed on the electrode and π-dimers MV^?+···MV^?+ of π-polymers [р(MVCA^4?+-co-St)] _n deposited on the electrode act- ed as the reducing agents with respect to Au^I. During electrolysis, the nanoparticles agglo- merated to 37—50 nm. The nanocomposite particles dispersed in ethanol had sizes of 72±16 nm and also contained Au-NP with sizes of 51±8 and 19±3 nm. The catalytic activity of the nanocomposite in the reduction of p-nitrophenol with sodium borohydride was demon- strated. A similar reduction of AgCl nanoparticles (~250 nm) led to the formation of silver nanoparticles with crystallite sizes in the range of 7—11 nm, the process was inefficient, however, even when using 250% of electricity, an incomplete reduction of AgCl was still observed.     

Microscopic Examination of the Silicon Surface Subjected to High-Dose Silver Implantation

Technical Physics - Low-energy (E = 30 keV) Ag+ ions have been implanted into single-crystalline Si wafers (c-Si) with an implantation dose varying from 1.25 × 1015 to 1.5 × 1017 ions...     

Two-step one-pot electrosynthesis and catalytic activity of xCoO–yCo(OH)2-supported silver nanoparticles

Journal of Solid State Electrochemistry - Efficient two-step electrosynthesis of xCoO–yCo(OH)2 (CoOxHy)-supported silver nanoparticles (AgNPs) is carried out in N,N-dimethylformamide (DMF)...     

Molecular Oxygen as Mediator in the Metal Nanoparticles’ Electrosynthesis in <Emphasis Type="Italic">N,N</Emphasis>-Dimethylformamide

Ultra-fine gold (<2 nm), silver (5 ± 2 nm), and palladium (<1–2 nm) nanoparticles stabilized in polyvinylpyrrolidone shell were synthesized in N,N-dimethylformamide, using molecular oxygen dissolved in the electrolyte as mediator, by the reduction of the metals’ ions and complexes at the controlled potential of the oxygen reduction to its radical-anion. Pd-nanoparticles showed high catalytic activity in the reactions of p-nitrophenol reduction and Suzuki cross-coupling. Long-term ageing of spherical Ag-nanoparticles for 60 days in the post- electrolysis solution resulted in their consolidation (up to 17 ± 5 nm; the average size of crystallites 7.5 (3) nm). Upon similar exposure of Au-nanoparticles for 15 days, V-shaped nanoparticles were formed (length 112 ± 53 nm, width 58 ± 22 nm, crystallites 20(2)–31(1) nm); upon the isolation, dispersing into ethanol, and exposure for 48 h, hexagonal nanoparticles (105 ± 29 nm) and polygons (56 ± 25 nm, crystallites 24(2)–51(1) nm; upon dispersing into water and exposure for 8 h, spherical nanoparticles (13 ± 8 nm, crystallites 7(1)–13.4(5) nm). Thus obtained nanoparticles are characterized by methods of cyclic voltammetry, dynamic light scattering, scanning and high resolution transmission electron microscopy, and X-ray powder diffraction.