We propose a new criteria to cluster the referent vectors of the self-organizing map. This criteria contains two terms which take into account two di erent errors simultaneously: the square error of the entire clustering and the topological structure given by the Self Organizing Map. A parameter T allows to control the corresponding in uence of these two terms. The eÆciency of this criteria is ...

The objective of this article is to study the oscillation properties of the solutions to the fourth-order linear trinomial delay differential equation y(t) + p(t)y′(t) + q(t)y(τ(t)) = 0. Applying suitable comparison principles, we present new criteria for oscillation. In contrast with the existing results, we establish oscillation of all solutions, and essentially simplify the examination proce...

By means of Riccati transformation technique, we establish some new oscillation criteria for the third-order nonlinear delay dynamic equations x 3 (t) + p(t)x(τ(t)) = 0 on a time scale T unbounded above, here γ > 0 is a quotient of odd positive integers with p real-valued positive rd-continuous function defined on T. Three examples are given to illustrate the main results.

In this paper, by defining a class of functions, we establish some oscillation criteria for the second order nonlinear dynamic equations with forced term x (t) + a(t)f(x(q(t))) = e(t) on a time scale T. Our results unify the oscillation of the second order forced differential equation and the second order forced difference equation. An example is considered to illustrate the main results.

-Some new oscillation criteria for the even order damped functional differential equation (a(t)z(n-1)(t)) ' ÷ p(t)lz(n-1)(Ol#x(n-a)(O ÷ q(t)f(xIaa(t)] . . . . . =Lq.~(t)]) = 0 are established, where ~ _> O. These criteria are an extension of some of the known results. 1. I N T R O D U C T I O N Recently, Grace and Lalli [1] discussed the oscillation of the nth-order functional differential equa...

We investigate the oscillatory behavior of the second order nonlinear dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = 0, the forced dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = e(t) and the forced-perturbed dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = e(t) + p(t)x (t). The obtained results are new and not only extend the known results appeared in the literature, but they also improve and unify the kn...

Duplex scanning has been proposed as a safe alternative to contrast venography for diagnosing deep venous thrombosis, but its accuracy has not been proved. In this prospective, double-blind study of 47 patients, the sensitivity and specificity of duplex scan criteria were determined relative to contrast venography for lower extremity deep venous thrombosis. Criteria considered to show the prese...

Click reactions have provided access to an array of remarkably complex polymer architectures. However, the term "click" is often applied inaccurately to polymer ligation reactions that fail to respect the criteria that typify a true "click" reaction. With the purpose of providing a universal way to benchmark polymer-polymer coupling efficiency at equimolarity and thus evaluate the fulfilment of...

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay x(t) + ψ(x(t− r), x′(t− r), x′′(t− r), x′′′(t− r), x(t− r))x(t) +f(x′′(t− r), x′′′(t− r)) + α3x(t) + α4x(t) + α5x(t) = 0 are obtained by using Lyapunov’s second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null soluti...

The singular nonlinear three-point boundary value problems { −(Lu)(t) = h(t)f (u(t)), 0 < t < 1, βu(0)− γ u′(0) = 0, u(1) = αu(η) are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u′(t))′+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be nonnegative. The associated ...