Cap representations of G2 and the spin L-function of PGSp6

We give a construction of a family of CAP representations of the exceptional group G ₂, whose existence is predicted by Arthur’s conjecture. These are constructed by lifting certain cuspidal representations of PGS _p6. To show that the lifting is non-zero, we establish a Rankin-Selberg integral for the degree 8 Spin L-function of these cuspidal representations of PGS _p6.     

Parabolic problems with the Preisach hysteresis operator in boundary conditions

Parabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose right-hand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocontrol processes in chemical reactors, climate-control systems, biological cells, etc. For the Preisach operator with and without time delay, solvability, periodicity of solutions, and global B-attractors are studied.     

Active polarized target: Measurement of proton spin polarizabilities

The static (electric and magnetic) polarizabilities of the proton are known from measurements of low-energy Compton scattering of real photons. However, no experimental data are so far available about its spin polarizabilities, which describe the response of the proton spin to a varying electromagnetic field. These fundamental structure constants can be obtained in the most model-independent way from measurements of double-polarized Compton scattering at energies below the pion threshold using a polarized photon beam and a polarized proton target. An active polarized target based on polystyrene doped with a scintillator allows recoil protons to be detected directly in the target material, background from the coherent Compton effect on heavier nuclei (¹²C etc.) to be eliminated and precise data on spin polarizabilities to be obtained.     

Subproduct systems over N×N

We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces ${\{X(m,n)\}}_{m,n=0}^{\infty }$ equipped with a multiplication given by coisometries from $X(i,j)?X(k,l)$ to $X(i+k,j+l)$. We find that the character space of the norm-closed algebra generated by left multiplication operators (the tensor algebra) is homeomorphic to a complex homogeneous affine algebraic variety intersected with a unit ball. Certain conditions are isolated under which subproduct systems whose tensor algebras are isomorphic must be isomorphic themselves. In the absence of these conditions, we show that two numerical invariants must agree on such subproduct systems. Additionally, we classify the subproduct systems over $\mathbb{N}\times \mathbb{N}$ by means of ideals in algebras of non-commutative polynomials.     

On the temperature dependence of ballistic Coulomb drag in nanowires

We have investigated within Fermi liquid theory the dependence of Coulomb drag current in a passive quantum wire on the applied voltage V across an active wire and on the temperature T for any values of eV/k(B)T. We assume that the bottoms of the 1D minibands in both wires almost coincide with the Fermi level. We conclude that: (1) within a certain temperature interval the drag current can be a descending function of the temperature T; (2) the experimentally observed temperature dependence T(-0.77) of the drag current can be interpreted within the framework of Fermi liquid theory; (3) at relatively high applied voltages the drag current saturates as a function of the applied voltage; and (4) the screening of the electron potential by metallic gate electrodes can be of importance.     

On the possibility of accelerating α decay: To the problem of disposing of radioactive nuclear waste

A number of experimental tests of the recent information on the possibility of accelerating α decay by implanting α-emitting isotopes into metals with their further cooling to a low temperature were performed using the nuclear orientation technique. The measurement data on half-lives for ²⁵³Es in Fe at 4 K and 50 mK, ²²⁴Rn, ²²⁵Ra, and ²²⁷Ac in Fe at temperatures down to 25 mK, and ²²¹Fr in nonmetal (Si) and metal (Au) at 4 K and ∼20 mK are reviewed. In all cases, no change in half-life was found within an accuracy of 1%.     

A cold-curing adhesive for the construction industry

An epoxy adhesive of cold curing is developed. Its processing characteristics are studied. The properties of the cured adhesive and polymeric composite materials (PCMs) based thereon are examined. It is shown that PCM data have a reinforcing impact on concrete under different climatic effects.     

Structural analysis of composite metal-insulator materials by small-angle x-ray scattering

A small-angle x-ray scattering study of the structure of Cu: SiO₂ composite films obtained by magnetron cosputtering is reported. The experimental spectra are analyzed by direct numerical simulation of scattering from a polydisperse system of spherical particles with a high volume concentration. The calculated scattering spectra were found to fit well to the experiment if a log-normal particle distribution in size is assumed, and the parameters of this distribution were determined.     

Sorption Properties of Phosphorylated Indoles

Sorption properties of 1- and 3-substituted indoles containing a P(III) atom were estimated by gas chromatography. The sorption properties were shown to depend on the nature of substituents on the phosphorus atom.