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We examine the asymptotic stability of the zero solution of the first-order linear equation x′(t) = Ax(t) + ∝0tB(t − s) x(s) ds, where B(t) is integrable and does not change sign on [0, ∞). The results are applied to an examination of the stability of equilibrium of some nonlinear population models.
A simple relationship is given between the exact null distribution gm,n(J) of the J-th largest latent root of an m × m Wishart matrix on n degrees of freedom, and the distribution fm,n(J) of the ratio of this root to the trace of the matrix. Explicit expressions for certain fm,n(J) may thus be obtained from previous results for the corresponding gm,n(J).
Two improvements greatly enhancing the rate of phosphotriester oligonucleotide systhesis were developed: 1) the use of hindered primary amines, e.g. t-butyl amine for decyanoethylation of oligonucleotide triester intermediates, 2) a simplified isolation procedure that eliminates the tedious bicarbonate extraction after each condensing reaction.
We consider the problem of existence of solutions Nike Free Run 3.0 Canada for stochastic Navier-Stokes equations. The random elements are the initial value of the solution and forcing terms which may be white noise in time.
The method uses results on multi-valued functions. We also give energy type results and present Cheap Nike Free 5.0 examples.