arXiv subjects
Publications and source records attributed to Beatriz Ruiz.
In this paper we review the properties of families of numbers of the form $6n\pm1$, with $n$ integer (in which there are all prime numbers greater than 3 and other compound numbers with particular properties) to later use them in a new sieve that allows the separation of numbers $n$ that generate primes from those that only generate compounds. In principle, this can be used to find the amount of prime numbers up to a given number $h$; this means, $π(h)$.
This paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane-parallel-faces. This approach introduces the time-averaged Poynting vector modulus as field variable. The conceptual implications of this formalism are that the nonequivalence between the time-averaged Poynting vector and the squared-field amplitude modulus is naturally manifested as a consequence of interface effects. Also, two practical implications are considered: first, the exact transmittance is compared with that given by the Beer's Law, employed commonly in experiments. The departure among them can be significative for certain material parameter values. Second, when the exact reflectance is studied for negative permittivity slabs, it is show that the high reflectance can be diminished if a small amount of absorption is present.