Neural activity influences the patterning of synaptic connections and functional organization of developing sensory and motor systems, but the long-term consequences of intense neural activity suchâ€¦ (More)

The basic linear, Volterra integral equation of the first kind with a weakly singular kernel is solved via a Galerkin approximation. It is shown that the approximate solution is a sum with the firstâ€¦ (More)

in terms of the solution to a certain infinite system of ordinary differential equations. The applicability of the resultant representation formula may be varied, but we will show in future work howâ€¦ (More)

Using some basic observations from stability theory, it is shown that theclassical equationy"+a(t)y = Omust have at least one solution y(j) such that lim sup(|_y(/)l + lv'(/)l)>0 as /-Â»-oo. The sameâ€¦ (More)

This article shows that the zero solution to the system x 0 = A(t)x + f(t; x); f(t; 0) = 0 is unstable. To show instability, we impose conditions on the nonlinear part f(t; x) and on the fundamentalâ€¦ (More)