In this paper, we study the advanced differential equations r(t) x (t) α–1 x (t) + n i=1 p i (t) x(t + τ i (t)) α–1 x(t + τ i (t)) = 0 and r(t)(y(t) – P(t)y(t – τ)) + n i=1 p i (t)f (y(t + σ)) = 0. By using the generalized Riccati transformation and the Schauder-Tyichonoff theorem, we establish the conditions for the existence of positive solutions of the above equations.

We present a novel ensemble of logistic linear regressors that combines the robustness of online Bayesian learning with the flexibility of ensembles. The ensemble of classifiers are built on top of a Randomly Varying Coefficient model designed for online regression with the fusion of classifiers done at the level of regression before converting it into a class label using a logistic link functi...

In this paper, new finite numbers of conditions which are equivalent to the so-called generalized invariant subspaces whoes definitions have infinitely many conditions are studied.

– It is shown that if u is a solution of the initial value problem for the generalized Korteweg–de Vries equation such that there exists b ∈ R with suppu(·, tj ) ⊆ (b,∞) (or (−∞, b)), for j = 1,2 (t1 = t2), then u≡ 0.  2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: Primary 35Q53; secondary 35G25; 35D99

We show that student learning can be accurately modeled using a mixture of learning curves, each of which specifies error probability as a function of time. This approach generalizes Knowledge Tracing [7], which can be viewed as a mixture model in which the learning curves are step functions. We show that this generality yields order-of-magnitude improvements in prediction accuracy on real data...