http://popups.lib.uliege.be/1373-5411/index.php?id=3516 Publications of Auteurs Eufrosina Otlacan fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4636 The continuity is a common concept, often used by people. It is not the case of topology, although behind the phenomenon of continuity always a topology must be understood. In a continuous process, if two possible causes remain close, that is in a certain neighborhood, they will produce close effects. The set of possible causes which lead to a studied effect is organized as a topological space. Researchers can deal with metric spaces, with norms or semi-norms, but it is important to establish the notion of neighborhood, or to define a system of open sets. In the study of dynamic systems with infinite memory a locally convex topology was introduced. The present paper reviewed results obtained when the inputs were continuous and indefinite derivable functions from minus infinite to the present moment, then it pass to the case when the inputs are known only as rows of values. In the last part the informational topology is exposed. Mon, 14 Oct 2024 15:39:14 +0200 Mon, 14 Oct 2024 15:39:22 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4636 http://popups.lib.uliege.be/1373-5411/index.php?id=3964 The antique study of geometric properties of symmetries continued by algebra with the group theory, and then with matrix calculus. The present paper illustrates new trends in the study of symmetry concept and its implication in explanation of the matter structure and of the evolutionary phenomena from nature. It is well known that in 2008 the Nobel Prize in Physics was awarded for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics. As an introduction to the necessity to study symmetryn ot for static states only, but also for dynamic systems, the paper presents the philosophical concept of the symmetry of senses in the profound matter. For the dynamical systems, the definition of the symmetry by anticipation and retardation belong to the author. Certain cases when the symmetrical evolution of two conjugate systems is broken are indicated in a mathematical model. Tue, 01 Oct 2024 16:54:19 +0200 Tue, 01 Oct 2024 16:54:32 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3964 http://popups.lib.uliege.be/1373-5411/index.php?id=3512 The paper contains several results belonging to the theory of systems with infinite memory, using the differential calculus in locally convex spaces. These results are the following: the general constitutive functional can have, as a first approximation, an integral representation; the constitutive functional could be expressed by a double integral, so obtaining a better approximation; the speed of the present state modification is in a linear dependence on the history of the speed by which the inputs were changed, the whole time elapsed till the present moment; the state of the system in a next moment is obtained also by means of some formulae using the derivative of the constitutive functional; the problem of optimal control of the system evolution, formulated for this general functional representation, leads to the equations of the Calculus of Variations. Mon, 23 Sep 2024 14:54:11 +0200 Mon, 23 Sep 2024 14:54:20 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3512