Kinetics of changes in the modulation period and in dispersion hardening in Cu-Ti-Me alloys

An investigation was made of the kinetics of changes in the flow stress _0.1, modulation period , and electrical resistivity in the course of ageing of Cu-Ti, Cu-Ti-Al, Cu-Ti-Zn, and Cu-Ti-Ga alloys. There were no dispersion hardening effects during the early stages of the precipitation, corresponding to the = const condition. An increase in _0.1. was observed during the stage of coagulation of the secondary phases. The increase in the flow stress was described using a theory of hardening by coherent particles of the new phase but it did not agree with the theory of hardening of alloys exhibiting spinodal precipitation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 81–87, May, 1980.     

Ferromagnetic resonance in media with an inhomogeneous saturation magnetization

The method of transition probabilities is used to calculate the line width of ferromagnetic resonance in a medium with an inhomogeneous saturation magnetization. It is shown that in addition to linear (with respect to the Fourier components of the function describing inhomogeneities) terms, the perturbation Hamiltonian must include also quadratic terms. The frequency dependence of the contribution of the porosity to H is fundamentally different from the frequency dependence of the magnetic anisotropy contribution. This anisotropy contribution H_a() decreases on increase in the frequency and has a maximum at = (2/3)_M, whereas the porosity contribution H_p increases on increase in the frequency and vanishes at = (2/3)_M.deceasedTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp.48–52, December, 1980.     

Dispersion of the permittivity of high-resistance semiconductors

We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length L_s of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time _M and the times of carrier capture: _c and ejection _e by an impurity center. For _cetm and (/L_s) _e/_c1 the dispersion of and is the same as for thick plates (/L_s1). For _{c m e} and (/L_s)_e/_c1 the () curve has a characteristic kink in the region 1/_e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.     

Mass-spectrometric investigation of the photoionization of diphenylmercury

Theoretical and Experimental Chemistry -     

Ein asymptotischer Ausdruck für eine zahlentheoretische Funktion

Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function ged (s, n) and of a generalisation of it are derived.     

LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II

This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain L^P-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.     

Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.     

Striktionseigenschaften von Regelscharen imE n

Let ={e(u)|uI} be a one-parameter family of straight lines forming a ruledC ^r-2-surface E ⁿ (n2,r1) without singular generatorse(u) (uI). As a synopsis, a generalization and an improvement of various results already known about the strictional properties of ruled surfaces E ⁿ (especially in the casen=3) the author demonstrates a uniform geometrical way of defining and uniquely obtaining thestriction point S(u) and theparameter of distribution d(u) of a generatore(u) under the minimal assumptions thate(u)E ⁿ (n2) be noncylindrical andr1. Other methods of obtainingS(u) andd(u) are discussed in comparison, and special strictional properties ofskew ruled surfaces E ⁿ are proved.

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Herrn Prof. Dr. H. R. Müller zum 65. Geburtstag     

A variational proof of the Gauss-Bonnet formula

The classical Gauss-Bonnet formula has the form I(g_ij)=2, where I(g_ij) represents a sum of three terms each of which depends on the metric tensor g_ij. It is shown that the first variation I of I(g_ij) with respect to the metric g_ij vanishes and that for the Euclidean metric _ij we have I(_ij)=2. From this the formula I(g_ij)=2 follows. In the process, explicit expressions are obtained for the first variation of each of the three terms which comprise I(g_ij). Furthermore, a general expression for the first variation of a multiple integral whose integrand is a scalar density depending on the metric tensor g_ij and its derivatives up to the second order is obtained with the aid of results of Rund [1].     

Mean value estimates in lattice point theory

LetQ(u) be a positive definite quadratic form inr2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0b _j <1, forx>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)x, letV(x) be the volume of this ellipsoid andP(x)=A(x)–V(x). Let . By introduction of a parameter we shall show how the treatment of estimates onP(x) and onM(x) can be unified.