Marika Ivanova | Searcharxiv

arXiv2023

Strong bounds and exact solutions to the minimum broadcast time problem

Given a graph and a subset of its nodes, referred to as source nodes, the minimum broadcast problem asks for the minimum number of steps in which a signal can be transmitted from the sources to all other nodes in the graph. In each step, the sources and the nodes that already have received the signal can forward it to at most one of their neighbour nodes. The problem has previously been proved to be NP-hard. In the current work, we develop a compact integer programming model for the problem. We also devise procedures for computing lower bounds on the minimum number of steps required, along with methods for constructing near-optimal solutions. Computational experiments demonstrate that in a wide range of instances, in particular instances with sufficiently dense graphs, the lower and upper bounds under study collapse. In instances where this is not the case, the integer programming model proves strong capabilities in closing the remaining gap, and proves to be considerably more efficient than previously studied models.

math.OC↗

arXiv2018

Identification and acceptation of macroscopic magnetism energy levels results in better understanding of the linkages between the traditional theory with quantum electrodynamics and revelation of the limited validity of the Faraday's Law

In this article, we present the result of the research, which was directed to gaining electromotive voltage in a theoretically pure way. We designed and built a brushless generator that simulates a homogenised magnetic field and should theoretically be usable without semiconductors and electronic components. The generator is equipped with superconductive shielding, which ensures the disruption of the theoretical balance of electromotive voltage generation. In the Faraday homopolar generator, the imbalance of the electromotive voltage is secured by fixing the disk to the reference set of rotating magnets. However, the solution of the technical problem initiated a theoretical problem. The result of the experiment suggests that the current concept of electrodynamics, based on magnetic flux using relativistic principles, is Euclidean, idealised. If we continue to persist in the unconditional correctness of Maxwell's concept, we would have to admit that the inhomogeneous field can be screened out of the perspective of any external reference system, but that for a homogeneous magnetic field such a reference system would not exist. A good explanation of the inconsistency with theoretical expectations gives us the introduction of energy levels of the magnetic field, which are measurable and are probably a macroscopic manifestation of the summation of levels from elementary particle environments. Part of this article is an analysis which shows that current electrodynamics use a simplified view of the vector of induction. We show that the induction is a special case of a more general, topological evaluation of the properties of the set of magnetic field vectors. This unavoidably leads to a narrowing of Faraday's Law, which improves the experimental prediction and paradoxically reveals considerable technical potential. Both concepts can coexist in practice, with a wide range of value matches.

physics.class-ph↗