TURAN'S EXTREMAL PROBLEM FOR POSITIVE DEFINITE FUNCTIONS ON GROUPS

We study the following question: given an open set , symmetricabout 0, and a continuous, integrable, positive definite functionf, supported in and with f(0) = 1, how large can f be? Thisproblem has been studied so far mostly for convex domains inEuclidean space. In this paper we study the question in arbitrarylocally compact abelian groups and for more general domains.Our emphasis is on finite groups as well as Euclidean spacesand ^d. We exhibit upper bounds for f assuming geometric propertiesof of two types: (a) packing properties of and (b) spectralproperties of . Several examples and applications of the maintheorems are shown. In particular, we recover and extend severalknown results concerning convex domains in Euclidean space.Also, we investigate the question of estimating f over possiblydispersed sets solely in dependence of the given measure m :=||of . In this respect we show that in and the integral is maximalfor intervals.     

Periodicity of the Spectrum of a Finite Union of Intervals

A set Ω, of Lebesgue measure 1, in the real line is called spectral if there is a set Λ of real numbers such that the exponential functions e _λ (x)=exp (2πiλx), λ∈Λ, form a complete orthonormal system on L ²(Ω). Such a set Λ is called a spectrum of Ω. In this note we present a simplified proof of the fact that any spectrum Λ of a set Ω which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.     

Universal mechanism of dissipation in Fermi superfluids at ultralow temperatures

We show that the vortex dynamics in Fermi superfluids at ultralow temperatures is governed by the local heating of the vortex cores creating the heat flux carried by nonequilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of ^{3}He-B, the temperature of the vortex cores is estimated to be of the order 0.2 T(c). The dispersion of Kelvin waves is derived, and the heat flow generated by Kelvin cascade is shown to have a value close to that experimentally observed.     

Reactions on polymers with amine groups. III. Description of the addition reaction of pyridine and imidazole compounds with α,β-unsaturated monocarboxylic acids

A detailed study of the synthesis of betaine products that result from addition reactions of poly (4-vinylpyridine) and poly (N-vinylimidazole) as well as of their model compounds, with α,β-unsaturated monocarboxylic acids is presented. A reaction mechanism based on experimental observations and proved by kinetic analysis is proposed. It consists of two reactions: the addition, which involves two molecules of acid and leads to X⁺B⁻-like structures, where the cation X⁺ results from the addition of the amino nitrogen to the double bond of acid and B⁻ is the carboxyl anion, and an equilibrium reaction between X⁺B⁻ and the betaine structure X^±. The latter occurs only in protic solvents and is coupled with the addition reaction. The process was especially investigated in methanol, because this solvent allows determination of the kinetic parameters. Some values of the addition rate constants are given. The study is based on ¹H-NMR measurements and observations. © 1996 John Wiley & Sons, Inc.     

Hydro­gen bonding in calcium–tri­fluoro­methane­sulfonate–1,3‐di‐4‐pyridyl­urea–methanol (1/2/2/4)

The structure of the supramolecular complex calcium–tri­fluoro­methane­sulfonate–1,3‐di‐4‐pyridyl­urea–methanol (1/2/2/4), Ca²⁺·2CF₃SO₃⁻·2C₁₁H₁₀N₄O·4CH₄O, is presented. The Ca²⁺ ion lies on an inversion centre and is octahedrally coordinated by four methanol mol­ecules and two tri­fluoro­methane­sulfonate counter‐ions. The molecular packing is dominated by hydrogen‐bonded sheets in the (110) plane which contain R(32) rings; in these rings, significant π–π interactions are observed between inversion‐related 1,3‐di‐4‐pyridyl­urea mol­ecules.     

CuI and CuII salts of group VIA elements as catalysts for living radical polymerization initiated with sulfonyl chlorides

The living radical polymerization of methyl methacrylate initiated from sulfonyl chlorides and catalyzed by the new catalytic systems Cu₂Y/Bpy and CuY/Bpy, where Y is O, S, Se, or Te and Bpy is 2,2′‐bipyridine, is described. An induction time was observed in all polymerization experiments. The values of the experimental rate constants of polymerization (k_p ^exp) increased whereas the corresponding induction times decreased in the order Y = O < S < Se < Te. For the entire series of catalysts, k_p ^exp for CuY was less than k_p ^exp for Cu₂Y. A mechanistic interpretation that involves the in situ generation of the CuCl/CuCl₂ pair, starting from Cu₂Y or CuY, is provided. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3839–3843, 2000     

Anyon Quantum Transport and Noise Away from Equilibrium

The quantum transport of anyons in one space dimension is investigated. After establishing some universal features of non-equilibrium systems in contact with two heat reservoirs in a generalized Gibbs state, the abelian anyon solution of the Tomonaga–Luttinger model possessing axial-vector duality is focused upon. In this context a non-equilibrium representation of the physical observables is constructed, which is the basic tool for a systematic study of the anyon particle and heat transport. The associated Lorenz number is determined and the deviation from the standard Wiedemann–Franz law induced by the interaction and the anyon statistics is explicitly described. The quantum fluctuations generated by the electric and helical currents are investigated and the dependence of the relative noise power on the statistical parameter is established.     

Bis-Alkylureido Imidazole Artificial Water Channels

Nature creates aquaporins to effectively transport water, rejecting all ions including protons. Aquaporins (AQPs) has brought inspiration for the development of Artificial Water Channels (AWCs). Imidazole-quartet (I-quartet) was the first AWC that enabled to self-assemble a tubular backbone for rapid water and proton permeation with total ion rejection. Here, we report the discovery of bis-alkylureido imidazole compounds, which outperform the I-quartets by exhibiting ≈3 times higher net and single channel permeabilities (10⁷ H₂O/s/channel) and a ≈2–3 times lower proton conductance. The higher water conductance regime is associated to the high partition of more hydrophobic bis-alkylureido channels in the membrane and to their pore sizes, experiencing larger fluctuations, leading to an increase in the number of water molecules in the channel, with decreasing H-bonding connectivity. This new class of AWCs will open new pathways toward scalable membranes with enhanced water transport performances.