Stäckel electrovacuum spaces with isotropic complete sets. Integration of field equations for the metric generalizing a space of type (1.1)

A system of Einstein-Maxwell equations is integrated for the metric that generalizes the metric of a space with full set of type (1.1). This is necessary for carrying out the classification of the corresponding Stäckel electrovacuum spaces. An algebraic classification of the solutions obtained is carried out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 17–20, December, 1987.     

Stackel spaces of an electrovacuum with isotropic complete sets. Formulation of problem and basic relations

We consider the problem of the classification of the Stackel spaces of the electrovacuum with isotropic complete sets. The metrics of the spaces are represented in a form that is convenient for their investigation. We obtain necessary relations for the construction of the field equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 17–21, May, 1987.     

Stäckel spaces in electrovacuum,permitting complete separation of variables in the diagonalized dirac equation. Type (1.1)

Institute of High-Current Electronics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 31–34, June, 1992.     

Stueckel spaces of the electrovacuum with two-parameter Abelian group of motions. Formulation of the problem and sets of the type (2.1)

The problem of finding all spaces of the electrovacuum with the additional condition that thh variables in the Hamilton-Jacobi equation be completely separable is formulated. All spaces admitting separation of variables of the type (2.1) are found.     

Stäckel electrovacuum spaces of type (2.1)

Classification of Stäckel electrovacuum spaces of type (2.1) is carried out. All metrics and potentials associated with the given type of spaces are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–56, February, 1989.     

Representation of complete ortholattices by sets with orthogonality

We consider an algebraic closure operator induced by orthogonality on an arbitrary set and we investigate some problems with regard to the orthomodular law for a complete lattice of closed subsets.     

Separation of variables in the wave equation. Sets of the type (1.1) and the algebra SU(1.2)

It is shown that for the wave equation in Minkowski space all complete sets of symmetry operators that contain one istropic operator reduce to sets in which the isotropic operator has the form /x⁰+/x³.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 102–105, February, 1991.     

Informationally complete sets of physical quantities

The notion of informational completeness is formulated within the convex state (or operational) approach to statistical physical theories and employed to introduce a type of statistical metrics. Further, a criterion for a set of physical quantities to be informationally complete is proven. Some applications of this result are given within the algebraic and Hilbert space formulations of quantum theory.     

On complete sets of polarization observables

A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent T-matrix elements of a reaction of the type a + b → c + d + … As an illustrative example, this criterion is applied to the longitudinal observables of deuteron electrodisintegration.     

Decomposition of (Co)isotropic Relations

We identify 13 isomorphism classes of indecomposable coisotropic relations between Poisson vector spaces and show that every coisotropic relation between finite-dimensional Poisson vector spaces may be decomposed as a direct sum of multiples of these indecomposables. We also find a list of 13 invariants, each of which is the dimension of a space constructed from the relation, such that the 13-vector of multiplicities and the 13-vector of invariants are related by an invertible matrix over \({\mathbb{Z}}\). It turns out to be simpler to do the analysis above for isotropic relations between presymplectic vector spaces. The coisotropic/Poisson case then follows by a simple duality argument.     

A complete classification of Stäckel spaces of type (2.1) in the Brans-Dicke theory

In the paper the complete classification of vacuum stäckel spaces of type (2.1) in the Brans-Dicke theory is completed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 93–96, February, 1992.     

Special Stâckel spaces of the electrovacuum

The investigation of the problem of classifying the spaces of the electrovacuum that admit a complete separation of variables in the Hamilton-Jacobi equation for a charged test particle is completed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 20–22, August, 1984.     

Conductive property of Zr_(0.1)Fe_(0.9)V_(1.1)Mo_(0.9)O_7 with low thermal expansion

Low thermal expansion materials are mostly ceramics with low conductive property, which limits their applications in electronic devices. The poor conductive property of ceramic ZrV_2 O_7 could be improved by bi-substitution of Fe and Mo for Zr and V, accompanied with low thermal expansion. Zr_(0.1) Fe_(0.9) V_(1.1 )Mo_(0.9 )O_7 has electrical conductivity of 8.2× 10~(-5) S/cm and 9.41× 10~(-4) S/cm at 291 K and 623 K, respectively. From 291 K to 413 K, thermal excitation leads to the increase of carrier concentration, which causes the rapid decrease of resistance. At 413–533 K, the conductivity is unchanged due to high scattering probability and a slowing increase of carrier concentration. The conductivity rapidly increases again from533 K to 623 K due to the intrinsic thermal excitation. The thermal expansion coefficient of Zr_(0.1) Fe_(0.9) V_(1.1 )Mo_(0.9 )O_7 is as low as 0.72× 10~(-6 )K~(-1) at 140–700 K from the dilatometer measurement. These properties suggest that Zr_(0.1) Fe_(0.9) V_(1.1 )Mo_(0.9 )O_7 has attractive application in electronic components.     

On the elasticity of transverse isotropic soft tissues (L)

Quantitative elastography techniques have recently been developed to estimate the shear modulus μ of soft tissues in vivo. In the case of isotropic and quasi-incompressible media, the Young's modulus E is close to 3 μ, which is not true in transverse anisotropic tissues such as muscles. In this letter, the transverse isotropic model established for hexagonal crystals is revisited in the case of soft solids. Relationships between elastic constants and Young's moduli are derived and validated on experimental data found in the literature. It is shown that 3 μ(⊥) ≤ E(⊥) ≤ 4 μ(⊥) and that E(//) cannot only be determined from the measurements of μ(//) and μ(⊥).     

Photoproduction of πΔ(1236) from protons below 1.1 GeV

A model for the annihilation of electron-positron pairs into hadrons for q² = s > 4 GeV² and up to the highest measured energies is developed. The main ingredients are point-like couplings between three resonances and photons and the high level of opening thresholds that follows from an effective Lagrangian formalism. The model gives an almost constant annihilation cross section, soft pions everywhere and at all energies, high multiplicities and a large absolute cross section. The details of all exclusive channels are also predicted. Other consequences of this point of view concern the discovery of hitherto ignored couplings in low-energy photon initiated reactions. We argue that the energy regime explored by SPEAR is not the asymptopia and we discuss possible further constancy of the cross section in a range of s.     

Spectral reflectance of the one-dimensional organic metals (perylene)2(PF6)1.1 × 0.8CH2Cl2 and (perylene)2(AsF6)1.1 × 0.7CH2Cl2

We report on the optical reflectance of (perylene)₂(PF₆)_1.1 × 0.8CH₂Cl₂ and (perylene)₂(AsF₆)_1.1 × 0.7CH₂Cl₂ single crystals in the energy range from 0.25 to 4 eV. For light polarized perpendicular to the molecular stacks the crystals exhibit the optical behaviour of an insulating molecular crystals, whereas for light polarized parallel to the stacks a pronounced plasma edge at $\text{h}\text{?}\text{ω = 0.9}\text{eV}$ is observed. The experimental data were analyzed by a Lorentz-Drude model in order to determine the electrical conductivity, the carrier concentration, the effective mass, the collision time, the band width, and the Fermi vector of the crystals.