A new approach to constant term identities and Selberg-type integrals

Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.     

Dust-Acoustic Nonlinear Waves in a Nanoparticle Fraction of Ultracold (2K) Multicomponent Dusty Plasma

The nonlinear dust-acoustic instability in the condensed submicron fraction of dust particles in the low-pressure glow discharge at ultra-low temperatures is experimentally and theoretically investigated. The main discharge parameters are estimated on the basisof the dust-acoustic wave analysis. In particular, the temperature and density of ions, as well as the Debye radius, are determined. It is shown that the ion temperature exceeds the temperature of the neutral gas. The drift characteristics of all plasma fractions are estimated. The reasons for the instability excitation are considered.     

Induced Super‐Halogen Behavior of Metal Moieties in Halogen‐Doped Clusters: LinI(‐) and AlnI(‐), n = 13, 1, 2, 3.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.     

Magnetic measurement of transport AC losses in Bi-2223/Ag tapes

Magnetic nature of the losses in superconducting wire carrying AC current implies that it should be possible to determine these losses in a contactless way. Ribbon-like samples are quite favorable for such an experiment, because a notable portion of magnetic flux related to losses ‘escapes' the sample volume and can be detected by an appropriate pick-up coil. In this case, a model describing the AC current penetration into the tape, based, e.g., on the critical state model, allows one to derive the losses from the pick-up coil signal. Because this signal is proportional to the number of coil turns, extension of the accessible range of measured voltages (and losses) can be achieved. We demonstrate the data obtained on a 1 cm long portion of a low-loss multifilamentary tape carrying AC current with frequency 35 Hz. The pick-up coil technique allowed us to reach loss level more than one order below the experimental limit for direct measurements.     

On a theorem of Tate

We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.      

Pyrazolyc 3-hydroxychromones: Regulation of ESIPT reaction by the “flavonol-like” intramolecular hydrogen bonding to carbonyl group oxygen,which dominates over the “alternative” H-bond to heterocyclic nitrogen

Two isomeric pyrazole derivatives of 3-hydroxychromone (3HC) with and without the possibility of the multiple intramolecular hydrogen bonds formation were compared theoretically and experimentally with the aim to find out whether the excited state intramolecular proton transfer (ESIPT) reaction follows the traditional to the most of 3HCs “flavonol-like” direction towards the CO group oxygen or an “alternative” direction towards the heterocyclic nitrogen atom.Quantum-chemical modeling and comparative study of the experimental spectral parameters of the title compounds indicated the preferential realization of “flavonol-like” ESIPT to oxygen channel.The 3HC systems with the “alternative” intramolecular hydrogen bond to nitrogen were characterized as low fluorescent and practically unable to ESIPT with participation of the nitrogen containing heterocyclic unit.     

A new form of symplectically invariant multimode uncertainty relations

We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson–Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail.     

Simultaneous establishing of stationary growth rate and composition of supercritical droplets at isothermal binary condensation in the diffusion-controlled regime

General integral relations expressing the droplet radius and time of the droplet nonstationary growth as nonlinear functions of solution concentration in the droplet have been derived. These relations are valid for a supercritical droplet (i.e., sufficiently large droplet, for which the Laplace pressure effect on the concentration at saturation of vapors is negligible) isothermally growing via stationary diffusion in the mixture of two condensing vapors and an incondensable carrier gas. The initial composition in the droplet may be arbitrary and partial molecular volumes of components are not fixed. Explicit analytical relations have been found for droplet composition and the droplet size as functions of time at small deviations from the stationary concentration in the growing droplet. These relations show that the assumption of the steady droplet growth rate is not valid for non-small deviations from the stationary concentration. Some illustrations of the general nonlinear theory have been done in situation when solution in the droplet can be considered ideal.