Shown an approach to the calculation of anisotropic plates numerically-analytical boundary elements method. The two-dimensional problem is reduced to one-dimensional by variation method Kantorovich-Vlasov. To select a function of the transverse distribution of deflecitons are encouraged to use one of two methods - dynamic or static. Application of numerical and analytical boundary element method allows a single approach to obtain the solution of basic differential equation of bending of anisotropic plate with any boundary conditions and without any restrictions on the nature of the application of the external load. and Obsahuje seznam literatury
In this paper we consider the nonlinear difference equation with several delays (axn+1 + bxn) k − (cxn) k + ∑m i=1 pi(n)x k n−σi = 0 where a, b, c ∈ (0, ∞), k = q/r, q, r are positive odd integers, m, σi are positive integers, {pi(n)}, i = 1, 2, . . . , m, is a real sequence with pi(n) ≥ 0 for all large n, and lim inf n→∞ pi(n) = pi < ∞, i = 1, 2, . . . , m. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all relevant cases. Also non-oscillating terms in the solution were found by studying the same determinant using similar parameter values.