Radio Mean Labeling Of Paths And Its Total Graph

A graph labeling problem is an assignment of labels to the vertices or edges (or both) of a graph G satisfying some mathematical condition. Radio Mean Labeling, a vertex-labeling of graphs with non-negative integers has a significant application in the study of problems related to radio channel assignment. The maximum label used in a radio mean labeling is called its span, and the lowest possible span of a radio mean labeling is called the radio mean number of a graph. In this paper, we obtain the radio mean number of paths and total graph of paths.

Ontologie et mathématiques : Théorie des Ensembles, théorie des Catégories, et théorie des Infinis, dans L'Être et l'événement, Logiques des mondes et L'Immanence des vérités

This paper examines the relationship between philosophy and its conditions. The affirmation “mathematics is ontology”, which I posited thirty years ago, has certain inconveniences. In this article, I present six varying possibilities for ontology. My own philosophical decision was to proclaim that being is a pure multiplicity, without the One and without any specific attribute such as “matter” or “spirit”. This movement of thought brought me to study the mathematical condition of philosophy and to search for a rigorous structuration of my speculative decision within the field of mathematics. However, my initial postulate that “Being is the multiplicity without the One” is not a mathematical but a philosophical statement. This paper concludes with a presentation of the relationship between mathematics and philosophy in Being and Event, Logics of Worlds, and The Immanence of Truths.

The role of a steepness parameter in the exponential stability of a model problem: Numerical aspects

The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed on a 4-dimensional steep symplectic map designed in a way that a parameter smoothly regulates the steepness properties in the model.

A New Theoretical Method and Application to Superconductivity

Bifurcation theory is applied to study the spontaneous symmetry breaking and phase transition. The mathematical condition is derived from physical consideration. Generalized parameter imbedding theory is used to solve the bifurcation equation. Using this method, we have solved the Migdal–Elishaberg's equation.

CONSEQUENCES OF COVARIANCE IN KALUZA–KLEIN THEORY

When the (3+1) Einstein equations with matter are regarded as a subset of the (4+1) Kaluza–Klein equations in apparent vacuum, the recovery of appropriate properties of matter requires in general that the (4+1) metric depend on all the coordinates including the extra one. We display some consequences of (4+1) covariance through the use of exact solutions and coordinate transformations. We conclude that 4-D physics can be regarded as taking place on a hypersurface in 5-D, a mathematical condition which may be set by a physical one on the rest masses of particles.

Spherically Symmetric Charged Dust Distribution in General Relativity. I. General Solution

The Einstein-Maxwell field equations characterizing a spherically symmetric charged dust distnbution are solved exactly without imposing any mathematical condition on them. The solution is expressed in terms of two arbitrary variables and these can be chosen to correspond to an arbitrary ratio of charge density to mass density, thus allowing the possibility of understanding the interior of the horizon in a more precise manner.