Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.

Three Spaces Problem for Lyapunov Theorem on Vector Measure

It is proved that a Banach space X has the Lyapunov property if its subspace Y and the quotient space X/Y have it.

M-Solid Subvarieties of some Varieties of Commutative Semigroups

∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.

Backlund-Darboux Transformations in Sato's Grassmannian

We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.

An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

Data Extraction from Carte Du Ciel Triple Images

Carte du Ciel (from French, map of the sky) is a part of a 19th century extensive international astronomical project whose goal was to map the entire visible sky. The results of this vast effort were collected in the form of astrographic plates and their paper representatives that are called astrographic maps and are widely distributed among many observatories and astronomical institutes over the world. Our goal is to design methods and algorithms to automatically extract data from digitized Carte du Ciel astrographic maps. This paper examines the image processing and pattern recognition techniques that can be adopted for automatic extraction of astronomical data from stars’ triple expositions that can aid variable stars detection in Carte du Ciel maps.