Experimental study of regions of reversed magnetization in an amorphous layer of Co70Fe5Si10B15

The characteristics of the distribution of magnetization and remagnetization of microsections of the surface in the amorphous alloy Co₇₀Fe₅Si₁₀B₁₅, prepared in the form of thin ribbons, were studied by the magnetooptical method. It was found that the magnetization I on the surface of the amorphous ribbon studied was strongly nonuniform. It was established that heat treatment (HT) of the sample leads to the appearance of regions of reversed magnetization in the surface layer of the ribbon, while thermomagnetic annealing reduces the nonuniformity of I. The conservation of the transverse component in the HT sample in fields where the magnitude of the component of magnetization parallel to the length of the ribbon remains virtually unchanged suggested that a domain structure of the magnetization ripple type, owing to the strong microdispersion of the magnetic anisotropy, is realized in this sample.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 89–94, March, 1988.     

Multivariate cardinal interpolation with radial-basis functions

For a radial-basis function?∶?→? we consider interpolation on an infinite regular lattice , tof∶? ⁿ→?, whereh is the spacing between lattice points and the cardinal function , satisfiesX(j)=δ _oj for allj∈? ⁿ. We prove existence and uniqueness of such cardinal functionsX, and we establish polynomial precision properties ofI _h for a class of radial-basis functions which includes \(\varphi (r) = r^{2q + 1} \) , \(\varphi (r) = r^{2q} \log r,\varphi (r) = \sqrt {r^2 + c^2 } \) , and \(\varphi (r) = 1/\sqrt {r^2 + c^2 } \) whereq∈? ₊. We also deduce convergence orders ofI _hf to sufficiently differentiable functionsf whenh→0.     

Qualitative analysis of finite-gap solutions of the KgΦ equation by the automorphic approach

By the automorphic approach and the use of computer graphics, we carry out a qualitative analysis of finite-gap periodic solutions of the Kg equation. Graphs are constructed for multiphase solutions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 31–41, 1987.     

Addendum to the paper “on a theorem of Miranda”

An existence theorem is proved for closed convex surfaces whose principal radii of curvature regarded as functions of the unit normal vectorn satisfy the equation

Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems

Majorants of the fractal dimension and of the number of determining modes for unbounded sets, invariant with respect to operators of semigroups of classes 1 and 2, are obtained. They are computed for the Navier-Stokes equations (two- and three-dimensional) under the first boundary condition and under periodicity conditions in the spaces and .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 105–129, 1987.     

On immersions ofn-dimensional Lobachevskií space in 2n-dimensional Euclidean space withn principal direction fields

In this article we prove that the principal direction fields are holonomic and use them to introduce curvilinear coordinates on an immersed region in terms of which the linear element of Lobachevskií space is written in the form where The fundamental system of equations is established for an immersion ofn-dimensional Lobachevskií space into 2n-dimensional Euclidean space withn principal direction fields for the functions _i and, and a way of constructing an arbitrary local analytic immersion is shown.Translated from Ukrainskií Geometricheskií Sbornik, No. 28, pp. 3–8, 1985.     

Threshold anomaly in doubletn-d scattering

The behaviour of the doubletn-d scattering phase shift ₂(k) at energies close to the three-particle threshold is studied analytically and numerically. The scattering parameters possess an anomaly associated with the low energy of the singletN-N virtual state. The anomaly manifests itself both as a bend in the energy dependence of the functionk cot(Re ₂) in the range around 0.5 MeV and in the nonstandard behaviour of the break-up cross section near the threshold.     

Phase-space analysis of alternating Δβ couplers

A geometrical method for determining the power transfer between piecewise uniform, alternating , twin-core linear directional couplers is presented. Phase space provides the basis for the method.     

Cubic surfaces in AG(3, q) and projective planes of order q 3

Spread sets of projective planes of order q ³ are represented as sets of q ³ points in A AG(3, q ³). A line through the origin in A can be interpreted as a space A ₀ AG(3, q), and the spread set induces a cubic surface L in A ₀. If the projective plane is a semifield plane of dimension 3 over its kernel, then L has the property that it misses a plane of A ₀. Determining all such surfaces L leads to a complete classification of the semifield planes of order q ³, whose spread sets are division algebras of dimension 3.An alternative proof of a result due to Menichetti, that finite division algebras of dimension 3 are associative or are twisted fields, follows with the classification.     

Properties of nonlinear waves in dissipative-dispersive media with instability

Wave processes in dissipative-dispersive media with instability described by a fourth-order nonlinear evolution equation are considered. Analytic solutions in the form of solitary and cnoidal waves are obtained. The existence of a critical value of the dispersion coefficient beyond which an initial disturbance (in particular, white noise) is transformed into a structure is demonstrated by numerical modeling.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–136, July–August, 1990.