Showing papers by "Voronezh State University published in 1977"

Canonical formalism and relativistic invariance of the Grossman-Peres classical electron model

Abstract: The Grossman — Peres classical electron model is not explicitly a relativistic invariant. The relativistic invariance of the Grossman — Peres model is proved in this paper by the direct construction of Poincare-group generators from integrals of the motion of the model under consideration. The generators found afford the possibility of obtaining also an expression for the 4-vector of coordinate-time.

Some estimates of differentiable functions

Abstract: Suppose thatx(t) ∈ C [a,b (n)] and has n zeros at the pointsa and b. It is shown that if x(n)(t) preserves sign on [a, b], then $$\left| {x\left( t \right)} \right| \geqslant \frac{{p_0 }}{{n - 1}}\mathop {\left[ {\mathop {\sup }\limits_{\tau \in \left( {a, b} \right)} \frac{{\left| {x\left( \tau \right)} \right|}}{{\left( {\tau - a} \right)^{p - 1} \left( {b - \tau } \right)^{q - 1} }}} \right]}\limits_{\left( {a< t< b} \right),} \left( {t - a} \right)^p \left( {b - t} \right)^q $$ where p and q are the multiplicities of the zeros of x(t) ata and b, respectively, and po=min{p,q}. Two-sided estimates of the Green's function for a two-point interpolation problem for the operator Lx ≡ x(n) are established in the proof. As an application, new conditions for the solvability of de la Vallee Poussin's two-point boundary problems are obtained.

Propagation of heat with a variable relaxation period

Abstract: We present an exact solution of the hyperbolic heat-conduction equation for a variable velocity of heat transport.

Degenerate differential operators in weighted Hölder spaces

Abstract: A differential operator ℒ, arising from the differential expression $$lv(t) \equiv ( - 1)^r v^{[n]} (t) + \sum olimits_{k = 0}^{n - 1} {p_k } (t)v^{[k]} (t) + Av(t),0 \leqslant t \leqslant 1,$$ , and system of boundary value conditions $$P_v [v] = \sum olimits_{k = 0}^{n_v } {\alpha _{vk} } r^{[k]} (1) = 0.v - 1, \ldots ,\mu ,0 \leqslant \mu< n$$ is considered in a Banach space E. Herev[k](t)=(a(t) d/dt)k v(t)a(t) being continuous fort⩾0, α(t) >0 for t > 0 and\(\int_0^1 {\frac{{dz}}{{a(z)}} = + \infty ;}\) the operator A is strongly positive in E. The estimates , are obtained for ℒ: n even, λ varying over a half plane.