The duality theorem for locally compact Abelian <Emphasis Type="Italic">n</Emphasis>-groups

We obtain a generalization of the Pontryagin-Van Campen theorem to the case of locally compact topological n-groups. We also consider the convolutions of measures and the Fourier transform on locally compact topological n-groups.     

Miura opers and critical points of master functions

Critical points of a master function associated to a simple Lie algebra come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms of critical points composing the population. Supported in part by NSF grant DMS-0140460 Supported in part by NSF grant DMS-0244579     

Specific features of the magnetic field-induced orientational transition in EuMnO<Subscript>3</Subscript>

It is found that the spin-flop transition in EuMnO₃ manganite induced by a magnetic field H parallel to the b axis is accompanied not only by a magnetization jump and magnetostriction anomalies but also by the appearance of electric polarization in the vicinity of the transition field H_cr ～ 200 kOe. This phenomenon can be associated with the occurrence of magnetically inhomogeneous (modulated) states in the vicinity of H_cr. In these states, the system loses the center of symmetry, which allows for the appearance of the polarization. The formation of such states in a magnetic field is caused by the general tendency of the occurrence of magnetically inhomogeneous (incommensurate) structures in the RMnO₃ series due to the frustration of exchange interactions with decreasing ionic radius of the rare-earth ion R starting with R = Eu.     

Inclusive study of neutrino and antineutrino interactions with nuclei at energiesE_v^{( - )} \leqq 30 GeV

Neutrino and antineutrino charged current reactions are studied inclusively at energies below 30 GeV using the freon filled bubble chamber SKAT at the Serpukhov accelerator. Data are given for the nucleon structure functions and the differential spectradσ/dy. The results are compared with predictions of the Quark-Parton Model and Quantum Chromodynamics.     

Kinetics of enzymatic reactions in the production of fish protein hydrolysates

The kinetic laws of enzyme hydrolysis of waste products (heads, fins, bones, and muscle tissue) of the Atlantic cod Gadus morhua have been investigated. An enzyme specimen hepatopancreatine was used for the hydrolysis reaction (proteolysis). A kinetic model describing the mechanism of enzyme hydrolysis of fish proteins as a second-order reaction was developed. The proteolysis model was based on the existence of easily hydrolysed and hydrolysis-resistant protein fractions. Autolysis of the enzyme was also taken into consideration. In the context of the developed kinetic model, the second-order rate constants of the intermediate stages of proteolysis were calculated.     

Quasielastic neutrino and antineutrino scattering total cross-sections,axial-vector form-factor

Experimental results on the study of quasielastic reactionsv _μ n→μ ^? p and \(\bar v_u p \to \mu ^ + n\) in the energy range 3–30 GeV are presented in this paper. Spark chamber detector with Al filters has been exposed to the wide-band neutrino and antineutrino beams at Serpukhov. Neutrino and antineutrino data have been used to reconstruct the behaviour of axial-vector form-factorF _A (Q ²). We measured the total cross-sections as a function of energy. The parameterM _A =(1.00±0.04) GeV/c² has been determined under the assumption of the dipole parametrization and CVC hypothesis. Upper limit for the second class currents was estimated.     

Resonant Hybrid Metal–Dielectric Nanostructures for Local Color Generation

JETP Letters - Here, we experimentally and theoretically demonstrate a laser-induced change in local color based on the reshaping of gold–silicon asymmetric nanostructures. The evolution of...     

Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution

An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (8 and 1) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.