In this paper we apply Melnikov method for the Duffing oscillator modified. We change the last term of the Duffing oscillator. We will prove that the critical surface of transition to chaos remains unchanged

In this paper we extend the definition of martingale to a larger class of processes named -martingales, motivated by the study of trading-speculation with stop-loss techniques. We present a convenient “Doob” decomposition for this class of processes. An Itô type stochastic integral is also...

In this paper a few identities connecting the area under a ROC curve with the expected values of sensitivity and specificity are derived. In the second part, an analytic expression for the area is given in the case of normal distributions of test values for the classes discriminated against as...

One important issue in the theory of Ordered Weighted Averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested by O'Hagan, determines a special class of OWA operators having maximal entropy of the OWA weights for a given level of ;...

On généralise le théorème de renouvellement de Feiler au cas d'un Systéme d'équations de renouvellement faisant intervenir des mesures qui ont pour support tout la droite réelle. Pour cela on suit la même démarche que Feller en faisant intervenir de plus la théorie de Perron-Frobenius...

We classify (1+3)-dimensional Schrödinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the electromagnetic vector potentials of the electromagnetic field providing...

In this article we describe the theory of and discuss its application to power series solutions of ordinary and partial differential equations. In particular, we give some new application to a singular perturbation of a regular singular point

Predicted survival probability functions of censored event free survival are improved by bagging survival trees. We suggest a new method to aggregate survival trees in order to obtain better predictions for breast cancer and lymphoma patients.A set of survival trees based on bootstrap samples is...

Let *() denote the order of the largest odd-order group of automorphisms that a compact Riemann surface of genus can admit. In this paper we obtain sharp upper and lower bounds for *(), and exhibit infinite sequences of genera in which the upper bound is attained and infinite sequences in which...

Suppose 0, (0)={σ,|σ|}, and is an odd, analytic function on (0). Suppose that is a point, not zero. For σ a point, let and, with σ∈(0), +1 (,σ)=(σ)−(,σ). Suppose that for σ∈(0)−{0} , ()(0)=0, and for σ a point in the plane, not zero, . Then () is an odd function, analytic on...