In this work, we revisit the spectral Petrov-Galerkin method for fractional elliptic equations with general operators. To prove optimal convergence of method, first present ultra-weak formulation and establish its well-posedness. Then, based on such a novel formulation, are able to discrete counterpart obtain in weighted L2-norm. For simple easy implementation also describe fast solver linear s...

We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

Authors: Alan O. Bergland, Ray Tobler, Josefa González, Paul Schmidt, Dmitri Petrov 1. Department of Biology, Stanford University, Stanford, CA 94305-5020 2. Institut für Populationsgenetik, Vetmeduni Vienna, Veterinärplatz 1, Vienna A-1210, Austria 3. Institute of Evolutionary Biology (CSIC-Universitat Pompeu Fabra). Passeig Maritim de la Barceloneta 37-49. 08003 Barcelona, Spain. 4. Departmen...

This article evaluates the integration of data extracted from a French syntactic lexicon, the Lexicon-Grammar (Gross, 1994), into a probabilistic parser. We show that by applying clustering methods on verbs of the French Treebank (Abeillé et al., 2003), we obtain accurate performances on French with a parser based on a Probabilistic Context-Free Grammar (Petrov et al., 2006).

An abstract functional framework is developed for the dual Petrov-Galerkin formulation of the initial-boundary-value problems with a third-order spatial derivative. This framework is then applied to study the wellposedness and decay properties of the KdV equation in a finite interval.

The connection between general moment conditions and the applicability of strong laws of large numbers for a sequence of identically distributed ρ-mixing random variables are obtained. The results obtained generalize the result of Petrov (1996, Statist. Probab. Lett. 26, 377-380) to ρ-mixing sequences and NA sequences.

We answer to a question posed recently in reference [Lovitz B, Petrov F. A generalization of Kruskal's theorem on tensor decomposition. Available at arXiv 2103.15633; 2021], proving the conjectured sufficient minimality and uniqueness condition 3-tensor

We have recently described a novel method of estimating neutral rates and patterns of spontaneous mutation (Petrov et al., 1996). This method takes advantage of the propensity of non-LTR retrotransposable elements to create non-functional, 'dead-on-arrival' copies as a product of transposition. Maximum parsimony analysis is used to separate the evolution of actively transposing lineages of a no...

Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...

Let M be a Lorentzian space-time manifold. If p G 31, let TV(M) denote the tangent space to M at p and let I e Tp (M ) be a null vector. Because of the identification of radiation in General Relativity with null geodesic congruences of curves in M, one is led to study the geometrical properties of the wave surfaces of I. These are the two dimensional subspaces of TP(M), each member of which is ...