Of dipole antennas in a magnetized plasma in the resonance frequency band

We consider characteristics of slow quasielectrostatic waves excited in the resonance frequency band by a source whose dimensions are much less than the wavelength of the electromagnetic wave. We primarily focus on the analysis of the radiation of a harmonic wave in pulsed mode by a dipole source. Firstly, we study the influence of electromagnetic, dispersive, and collisional corrections in the dispersion relation on the field shape. Secondly, we analyze the field structure near the resonance cone. In particular, the effects of the group delay and anomalous spreading of the wave are considered. The developed theory is used to interpret the “OEDIPUS-C” experiment. For example, a delay of 10⁻⁴ s and a significant (severalfold) spreading of the pulse were observed at a distance of about ten wavelengths. Finally, some aspects of the inverse problem of electrodynamics are examined. Namely, the role of the smoothness of the antenna charge distribution in the field structure formation is shown and a class of smooth charge distributions creating a given field structure is found.     

Basis of invariants for multiferroic

A method for constructing a basis of invariants with the simultaneous selection of independent and linear bases is described. The partition proposed makes it possible to unambiguously find all invariants in a specified power. The basis of invariants is constructed and a linear basis is found for two three-component order parameters of a multiferroic: polarization and magnetic moment.     

On the decay rate of (p, A)-lacunary series

A power series with radius of convergence equal 1 is called a (p,A)-lacunary one if n_k ≥ Ak^p, A > 0, 1 < p < ∞. It is proved that if 1 < p < 2 and f(x) is a (p,A)-lacunary series that satisfies the condition

Classification of Lie algebras of specific type in complexified Clifford algebras

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These 16 Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present 16 Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups.     

Finite Rank Bergman–Toeplitz and Bargmann–Toeplitz Operators in Many Dimensions

The recent theorem by D. Luecking that finite rank Toeplitz–Bergman operators must be generated by a measure consisting of finitely many point masses is carried over to the higher-dimensional case.     

The nevanlinna factorization in certain classes of analytic functions

It is announced that in the classes H _n ^p , 0 pz+, 0 <l/.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 205–207, 1983.     

Changes in depth profiles of oxygen and copper in Y-Ba-Cu-O film under annealing

Changes in element depth profiles in a YBaCuO superconducting film on a SrTiO₃ substrate due to one year aging and annealing were investigated by the ion backscattering technique. Crystal perfection of the film was checked by the X-ray rocking curve method. It was found that the film was polycrystalline, with the preferred orientation of thec axis along the normal to the substrate surface with an angle dispersion of 2 °, and that the in-planea andb axes were randomly orientated. The aging experiments have shown that the oxygen content in the surface region increases with the time constant = 20 days. Annealing in a vacuum at 100 °C restores the initial oxygen content. After 2 hours of annealing in an oxygen atmosphere at 400 °C, an unexpectedly strong change in oxygen and copper depth profiles is observed. Since a strong correlation exists between the profile changes, a hypothesis has been advanced about the relationship between oxygen and copper transport in the process of annealing. Taking into account the polycrystalline structure of the film, one can conclude that intergrain diffusion dominates in the oxygen and copper transport.     

Projector operators for the no-core shell model

Projection operators for the use within the ab initio no-core shell model are suggested. The text was submitted by the author in English.     

The method of noncommutative integration for linear differential equations. Functional algebras and noncommutative dimensional reduction

The method of noncommutative integration for linear partial differential equations [1] is extended to the case of the so-called functional algebras for which the commutators of their generators are nonlinear functions of the same generators. The linear functions correspond to Lie algebras, whereas the quadratics are associated with the so-called quadratic algebras having wide applications in quantum field theory. A nontrivial example of integration of the Klein-Gordon equation in a curved space not allowing separation of variables is considered. A classification of four- and five-dimensional quadratic algebras is performed.A method of dimensional reduction for noncommutatively integrable many-dimensional partial differential equations is suggested. Generally, the reduced equation has a complicated functional symmetry algebra. The method permits integration of the reduced equation without the use of the explicit form of its functional algebra.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 3–15, January, 1996.