Abstract:
We deduced the Hubble law
and the age of the Universe, through the introduction of the Inverse Yukawa
Field (IYF), as a non-local additive complement of the Newtonian gravitation
(Modified Newtonian Dynamics). As a result, we connected the dynamics of
astronomical objects at great scale with the Friedmann-Robertson-Walker ΛFRW)
model. From the corresponding formalism, the Hubble law can be expressed as v = (4π[G]/c)r, which was derived by evaluating the
IYF forceat distances much
greater than 50 Mpc, giving a maximum value for the expansion rate of the
universe of H_{0}^{(max) }≈ 86.31 km·s^{-1}Mpc^{-1}, consistent with the
observational data of 392 astronomical objects from NASA/IPAC Extragalactic
Database (NED). This additional field (IYF) provides a simple interpretation of
dark energy as the action of baryonic matter at large scales. Additionally, we
calculated the age of the universe as 11 Gyr, in agreement with recent
measurements of the age of the white dwarfs in the solar neighborhood.

Abstract:
Modified Newtonian Dynamics (MoND) is an empirically modification of Newtonian gravity at largest scales in order to explain rotation curves of galaxies, as an alternative to nonbaryonic dark matter. But MoND theories can hardly connect themselves to the formalism of relativistic cosmology type Friedmann-Robertson-Walker. The present work posits the possibility of building this connection by postulating a Yukawa-like scalar potential, with non gravitational origin. This potential comes from a simple reflection speculate of the well-know potential of Yukawa and it is intended to describe the following physics scenarios: null in very near solar system, slightly attractive in ranges of interstellar distances, very attractive in distance ranges comparable to galaxies cluster, and repulsive to cosmic scales. As a result of introducing this potential into the typical Friedman equations we found that the critical density of matter is consistent with the observed density (without a dark matter assumption), besides this, MoND theory is obtained for interstellar scales and consequently would explain rotation curves. Also it is shown that Yukawa type inverse does not alter the predictions of the Cosmic Microwave Background neither the primordial nucleosinthesys in early universe; and can be useful to explain the large-scale structure formation.

Abstract:
The perception of meaning and signifiers of science and technology. In postmodern society is characterized by the myth of technology, The end of science and belief in a scientific method. A discourse analysis reveals that they are uncritically assumed paradigms. The history and character-istics of the factual sciences reveal the idealistic nature, transitory and transcendental science as intellectual creation. The questioning attitude, criticism, positive of the scientific thinking, should be communicated in postmodern society, rather than the reductionist approach of “scientific method” that leads to the mythical reification of science and technology.

Abstract:
In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.

Abstract:
In this paper, we will see that
some k -Fibonacci sequences
are related to the classical Fibonacci sequence of such way that we can express the terms of a k -Fibonacci sequence in function of some terms of the
classical Fibonacci sequence. And the formulas will
apply to any sequence of a certain set of k' -Fibonacci sequences. Thus we find k -Fibonacci sequences relating to other k -Fibonacci sequences when σ'_{k} is linearly dependent of .

Abstract:
Se postula un modelo cosmológico FRW con A = A(r), como alternativa a la materia oscura no bariónica. Este potencial se construye por reflexión especular del potencial de Yukawa: nulo dentro del sistema solar, poco atractivo en distancias interestelares, muy atractivo a rangos de distancia galácticos y repulsivo en escalas cósmicas. Este modelo es compatible con la densidad crítica observada, y con la teoría Milgrom.

Abstract:
In this paper we will prove that all $k$--Fibonacci sequence contains generalized Fibonacci sequences and we will indicate the form of obtain them.