The Strong Perfect Graph Conjecture, suggested by Claude Berge in 1960, had a major impact on the development of graph theory over the last forty years. It has led to the definitions and study of many new classes of graphs for which the Strong Perfect Graph Conjecture has been verified. Powerful concepts and methods have been developed to prove the Strong Perfect Graph Conjecture for these spec...

To verify fixed-time constraints in grid workflow systems, the consistency and inconsistency conditions have been defined in the conventional work. However, in this paper, we argue that although the conventional consistency condition is reasonable, the conventional inconsistency condition is too rigorous and covers several different situations. These situations which are handled conventionally ...

The Forward Search is a powerful general method for detecting anomalies in structured data, whose diagnostic power has been shown in many statistical contexts. However, despite the wealth of empirical evidence in favour of the method, only few theoretical properties have been established regarding the resulting estimators. We show that the Forward Search estimators are strongly consistent at th...

Abstract: Let {Xn, n=1} be a sequences of i.i.d. random variables with survival function 1 F(x) P[X x] = > . A wavelet linear survival function n F(x) based on X1, X2,..., Xn is introduced as an estimator for n F(x) . We establish that the Lp’-loss (2=r=p′= ∞) of the linear wavelet survival function estimator for a stochastic processes convergence at the rate rs 2 s 1 n (s s 1 /p 1 / p ) ′ − ′+...

We use Lax equations to define a scattering problem on an infinite elbow shaped line of the (x, t) plane. The evolution of scattering coefficients when the elbow is translated in the plane shows how convenient scannings may reconstruct the solution V (x, t) of the nonlinear equation associated to the Lax pair. It also helps us understanding why this can work only if strong consistency condition...

By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and ...

In this article, we present a characterization of basic graphs in terms of forbidden induced subgraphs. This class of graphs was introduced by Conforti, Cornuéjols and Vušković [3], and it plays an essential role in the announced proof of the Strong Perfect Graph Conjecture by Chudnovsky, Robertson, Seymour and Thomas [2]. Then we apply the Reducing Pseudopath Method [13] to characterize the su...

This paper presents a Bayesian nonparametric approach to the estimation of a system and its components’ survival functions arising from observing the failure of a series system or a competing-risks model. A Dirichlet multivariate process is used as a prior for the vector of the components’ random subsurvival function to derive the Bayes estimator of the survival function when the cause of failu...

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(∞) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particula...