Abstract:
The set S_{F}(x_{0};T) of states y reachable from a given state x_{0} at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x_{0} at T in reverse time of the target {x_{0}} while remaining in K. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted; for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example.

Abstract:
The financial equilibrium of pension funds relies on the appropriate computation of retirement benefits, taking account of future payments and discount rates. Short-term errors in the commitment for retirement benefits, ill-suited investment in the stock market, or improper mixture with pay-as-you-go payments have long-term consequences and may lead the pension fund to insolvency. The differential equation governing the current assets shows the respective weights associated with the error on the interest rate, the error on the extra bonus, and the error made in forecasting mortality. These weights are estimated through simulations. A short follow-up is sufficient to estimate the three errors. A threshold for the extra interest rate to be earned on the financial market is given to counter-balance the extra bonus when mortality is forecast correctly.

Abstract:
the transition of contraception use in colombia was an important moment when health and fertility were tightly associated with social behavior. multi-level multi-process (duration and method choice) life history analysis of contraceptive use allows the identification of determinants. individual trajectories show many successive spells of adopting or ceasing contraception. younger women displayed discontinuous behavior with a large proportion of total fertility (which itself has been decreasing since the mid-1960's) concentrated in the earliest ages. after the pioneer generation of 1935-40, the generations of 195559 and 1960-69 mastered contraception, the generation 1970-79 used contraception for spacing. contraception was strongly associated with material life condition, with education taking a secondary role. son (or girl) preference appeared to be absent. contraceptive methods were examined for their influence on intermittent behavior as a particular method might be used for only a short period. the pill and male condoms were the preferred method of adopters; users of male condoms were the less likely to cease, users of traditional methods the most likely to cease. the model highlights the trade-off between the desire to comply to the traditional social norm of a large family and the desire to adopt a modern way of life corresponding to a smaller family.

The introduction of an exponential or power law gradient
in the interstellar medium (ISM) allows to produce an asymmetric
evolution of the supernova remnant (SNR) when the framework of the thin layer
approximation is adopted. Unfortunately both the exponential and power law
gradients for the ISM do not have a well defined physical meaning. The physics
conversely is well represented by an isothermal self-gravitating disk of
particles whose velocity is everywhere Maxwellian. We derived a law of motion
in the framework of the thin layer approximation with a control parameter of
the swept mass. The photon’s losses, which are often neglected in the thin layer
approximation, are modeled trough velocity dependence. The developed framework
is applied to SNR 1987A and the three observed rings are simulated.

Abstract:
A first new luminosity function of galaxies can be built starting from a left truncated beta probability density function, which is characterized by four parameters. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A second new galaxy luminosity function is built starting from a left truncated beta probability for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is six because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The two new galaxy luminosity functions with finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results produce a “better fit” than the Schechter luminosity function in two of the five bands considered. A modified Schechter luminosity function with four parameters has been also analyzed.

Abstract:
We argued that the standard field scalar potential couldn’t be widely used for getting the adequate galaxies’ curve lines and determining the profiles of dark matter their halo. For discovering the global properties of scalar fields that can describe the observable characteristics of dark matter on the cosmological space and time scales, we propose the simplest form of central symmetric potential celestial-mechanical type, i.e. U(φ) = –μ/φ. It was shown that this potential allows get rather satisfactorily dark matter profiles and rotational curves lines for dwarf galaxies. The good agreement with some previous results, based on the N-body simulation method, was pointed out. A new possibility of dwarf galaxies’ masses estimation was given, also.

Abstract:
We study the classical dynamics of binary stars when there is an interchange of mass between them. Assuming that one of
the stars is more massive than others, the dynamics of the lighter one is analyzed as a function of its time
depending mass variation. Within our approximations and models for mass
transference, we obtain a general result which establishes that if the lightest
star looses mass, its period increases. If the lightest star wins mass, its period decreases.

Abstract:
We present a method for determining the motion of an electron in a hydrogen atom, which starts from a field Lagrangean foundation for non-conservative systems that can exhibit chaotic behavior. As a consequence, the problem of the formation of the atom becomes the problem of finding the possible stable orbital attractors and the associated transition paths through which the electron mechanical energy varies continuously until a stable energy state is reached.

Abstract:
Biochemical, immunological and epidemiological evidence increasingly support the suggestion that there is a causal relationship between gluten/gliadin and schizophrenia as originally proposed by F. C. Dohan. Furthermore the necessary physiological mechanisms exist to explain a mechanism involving bioactive peptides from these proteins, and these show that this mechanism is possible and probable in at least in a substantial subgroup of schizophrenic patients. Evidence shows a fairly strong genetic disposition, and it must be recognised that any genetic mechanism must implicate altered chemistry and function of proteins. Evidence supports the likelihood that dietary intervention is beneficial for some, and this demands further investigation. A similar conclusion may apply to autism spectrum conditions.

Abstract:
We study the phenomenon of decoherence during the operation of one qubit transformation, controlled-not (CNOT) and controlled-controlled-not (C^{2}NOT) quantum gates in a quantum computer model formed by a linear chain of three nuclear spins system. We make this study with different type of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of . We also study the behavior of the purity parameter for these gates and different environments and found linear or quadratic decays of this parameter depending on the type of environments.