Localization of compact invariant sets allows understanding the long-time behavior of a chaotic system. In this paper we apply the solution of the conditional extremum problem to the study of a model of a permanent magnet synchronous motor. The localization set is given by a one-parameter set of ellipsoids, crossed by an elliptical paraboloid and a cylinder. This improves the initial ellipsoida...

The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive new representations for the total production rate as two-fold integrals, both for circular laser polarization and for the general case of elliptic polarization, which has not been treated before. Our approach allows us to obtain by analyt...

I . I n t r o d u c t i o n A q u e s t i o n a n s w e r i n g sys tem is a compos i te of subsys tems o f l anguage a n a l y s i s , i n f e r e n c e and l anguage g e n e r a t i o n . I n t h e i n f e r e n c e sys tem, a u s e f u l and f l e x i b l e s t r u c t u r e i s needed f o r t h e r e p r e s e n t a t i o n o f know ledge . There a re two ways o f r e p r e s e n t i n g kn...

We theoretically explore a scheme for generation of bright circularly and elliptically polarized high-order harmonics by bursts of linearly polarized pulses with a rotating polarization axis. Circularly polarized harmonics are formed if the bursts are comprised of N pulses that uphold an N-fold rotational symmetry, for N > 2. Rotating the polarization axes of the comprising pulses can generate ...

We study positivity cases, estimates and asymptotic expansions of condenser p-capacities of points and segments in a given bounded domain, having in mind application fields, such as imaging, requiring detection and quantification of zero measure sets. We first establish estimates of capacities when the internal part of the condenser has a non-empty interior. The study of the point and its appro...

A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD o...

It is a fact of experience from the study of higher type computability that a wide range of approaches to defining a class of (hereditarily) total functionals over N leads in practice to a relatively small handful of distinct type structures. Among these are the type structure C of Kleene-Kreisel continuous functionals, its effective substructure C, and the type structure HEO of the hereditaril...

In this computational study the buckling analysis of symmetrically laminated elliptical and super-elliptical thin plates was carried out. The were considered as clamped or simply supported at boundary. minimum load determined using Rayleigh-Ritz method Galerkin Method based on Classical Laminated Plate Theory (CLPT). influence solution methods, shape functions, boundary conditions, power, lamin...

The four largest well-preserved impact basins in the solar system, Borealis, Hellas, and Utopia on Mars, and South Pole–Aitken on the Moon, are all signifi cantly elongated, with aspect ratios >1.2. This population stands in contrast to experimental studies of impact cratering that predict <1% of craters should be elliptical, and the observation that ~5% of the small crater population on the te...