Dans ce travail, nous considérons un opérateur différentiel simple ainsi que des perturbations. Alors que le spectre de l’opérateur non-perturbé est confiné à une droite à l’intérieur du pseudospectre, nous montrons pour les opérateurs perturbés que les valeurs propres se distribuent à l’intérieur du pseudospectre d’après une loi de Weyl.
We study a discrete model of the Yang-Mills equations on a combinatorial analog of . Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.
General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. Such inequalities involve various quantities which characterize...
Summary: It is proven that the Poisson algebra of a locally conformal symplectic manifold is integrable by making use of a convenient setting in global analysis. It is also observed that, contrary to the symplectic case, a unified approach to the compact and non-compact case is possible.
Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given.
The method of brackets is a collection of heuristic rules, some of which have being made rigorous, that provide a flexible, direct method for the evaluation of definite integrals. The present work uses this method to establish classical formulas due to Frullani which provide values of a specific family of integrals. Some generalizations are established.