Excitation of bulk elastic waves at the surfaces of piezoelectric crystals with 422,622 symmetry

The problem of exciting bulk elastic waves at the surface of a piezoelectric with symmetries 422,622 has been solved by a successive approximation method. In the approximation of a fixed electric field, created at the surface of the piezoelectric crystal by a two-electrode transducer, the distributions are found for the shear wave stress and the energy flux density in the far zone. The equivalent circuit parameters for a two-electrode radiator are determined taking account of the dynamic piezoelectric correction obtained in the second approximation. The equivalent circuit parameters and the transducer loss are treated for TeO₂ crystals. A realistic possibility of using surface transducers in the development of acousto-optic modulators in the s.h.f. region is shown. Tomsk State Academy of Control Systems and Radio Electronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 8–15, January, 1997.     

Thermodynamic stability of the structure of a deformed Fe-C solid solution

An analysis is made of the thermodynamic stability of the dislocation structure in polycrystalline samples of Fe-C, deformed under conditions of high rates and hydrostatic pressures, based on experimental and theoretical data concerning the internal energy and on diffractometer measurements of the broadening of x-ray lines. The method of deformation calorimetry was used to determine the internal energy in a wide range of deformations. A theoretical model is proposed for estimating the change in internal energy in deformed alloys. An investigation is made of the dependence of the interdislocation interaction parameter on the deformation rate for different stressed state-schemes and large plastic deformations. It is shown that the relative quantity δU/A is correlated in a wide range of deformations with the relative root-mean-square distortions of the crystal lattice of the deformed solid solution. The mechanisms for the accumulation of energy in deformed solid solutions having a body-centered cubic lattice are considered. Don State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 77–83.     

Hamiltonian approach to the dynamics of Darwinian systems

It is shown that equations describing the dynamics of Darwinian systems (DS) far from the bifurcation points may be expressed in Hamiltonian form. The cases of DS with constant organization and DS with a constant flux through the system are considered. The configurational part of phase space is formed by variables containing information on the structure of the system. Momentum variables may be regarded as specific rates of multiplication. The evolution of DS with constant organization in this phase space is expressed as uniform rectilinear motion. In the case of DS with a constant flux, the motion occurs in some effective constant and uniform field. The meaning of the elements of the Hamiltonian structure is described in terms of theoretical biology. Tomsk State University. Scientific-Research Institute of Biological Systems, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 23–28, July, 1997.     

Surfaces of Constant Mean Curvature Bounded by Two Planar Curves

In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.     

Numerical methods for finding multiple eigenvalues of matrices depending on parameters

Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods. Received December 19, 1994 / Revised version received January 18, 1996     

Student-Invented Numeration Systems: Pattern-Analysis and Mathematical Understanding

Thirteen fifth graders were given an assignment to invent their own numeration systems, following a unit on bases and a look at early events in the history of numbers. The task presented options that required the students to make decisions (such as whether to use a base, which base to use, design of symbols, etc.), and build a rationale for the elements of their system. Analyses of patterns embedded in their invented systems provided an assessment of student understanding of numeration. The progression of more and less complex thinking related to the student's choice of a base other than 10, consistency of logic throughout the system in words and symbols, rationale for change, and perception of real life examples that would change if the system was adopted. The invention task is presented as another way to make connections.