Abstract:
We propose a theoretical model of magnetization switching in a ferromagnetic multilayer by both electric current and microwaves. The electric current gives a spin transfer torque on the magnetization, while the microwave induces a precession of the magnetization around the initial state. Based on numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation, it is found that the switching current is reduced by less than a half compared with the switching caused solely by the spin transfer torque when the microwave frequency is in a certain range. We develop a theory of switching from the LLG equation averaged over a constant energy curve. It was found that the switching current should be classified into four regions, depending on the values of the microwave frequency. Based on the analysis, we derive an analytical formula of the optimized frequency minimizing the switching current, which is smaller than the ferromagnetic resonance frequency. We also derive an analytical formula of the minimized switching current. Both the optimized frequency and the minimized switching current decreases with increasing the amplitude of the microwave field. The results will be useful to achieve high thermal stability and low switching current in spin torque system simultaneously.

Abstract:
In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.

Abstract:
This paper consists of three parts. In the first part, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion. In the second part, intrinsic properties of quantum mechanics are shown, which justify the Boltzmann formula to yield a unique entropy in statistical mechanics. These properties clarify three conditions, one of which is necessary and others are sufficient for the validity of Boltzmann formula. In the third part, by combining the above results, we find a reasonable suggestion from the sufficient conditions that the potential of gravitational interaction among microstates of underlying quantum gravity may not diverge to negative infinity (such as Newtonian gravity) but is bounded below at a finite length scale. In addition to that, from the necessary condition, the interaction has to be repulsive within the finite length scale. The length scale should be Planck size. Thus, quantum gravity may become repulsive at Planck length. Also, a relation of these suggestions with action integral of gravity at semi-classical level is given. These suggestions about quantum gravity are universal in the sense that they are independent of any existing model of quantum gravity.

Abstract:
La constitución de 1962 ha insistido literalmente en la paridad entre hombres y mujeres en el ejercicio de los derechos políticos. Este espíritu se ha visto confirmado por las constituciones siguientes (1970, 1972, 1992 y 1996). En un país donde las elecciones revisten una gran importancia, en el cuadro de la lucha por el poder político, este derecho adquiere una extrema importancia en la medida que el género femenino tiene un gran peso, no sólo en términos numéricos. Sin embargo, el derecho de la mujer a la candidatura política permanece incierto. Esgrimir la consigna de la participación política no es suficiente y no altera el marco del discurso, tanto al no haber una conciencia de la participación de la mujer en el juego político como que ésta no es considerada un elemento activo y esencial en toda lucha emprendida por la elite marroquí. Con el concurso de los partidos, será posible familiarizar a la mujer con la práctica política y proporcionarle una experiencia decisiva en este campo.

Abstract:
This paper provides evidence on market making behaviour of FX dealer in the Tunisian FX. It uses a complete data set that includes intra-day trades for the euro and US dollar. The sample period is 1 January 2007 to 31 December 2007. The results are consistent with the findings of the literature that used trades and inventories data. I find evidence that customer order flow has information effect on USD/TND. However, I do not find evidence that customer order flow has information effect on EUR/TND. Moreover, inter-dealer order flow has a positive effect on the market maker price strategy. I also find that the central bank intervention has positive and significant effect on dealer’s behaviour and price formation process. My study also suggests that dealer is risk aversion and his quotes flows the references quotes tendency.

Abstract:
The existing thermodynamics of the cosmological horizon in de-Sitter spacetime is established in the micro-canonical ensemble, while thermodynamics of black hole horizons are established in the canonical ensemble. Generally in the ordinary thermodynamics and statistical mechanics, both of the micro-canonical and canonical ensembles yield the same equation of state for any thermodynamic system. This implies the existence of a formulation of de-Sitter thermodynamics based on the canonical ensemble. This paper reproduces the de-Sitter thermodynamics in the canonical ensemble. The procedure is as follows: We put a spherical wall at the center of de-Sitter spacetime, whose mass is negligible and perfectly reflects the Hawking radiation coming from the cosmological horizon. Then the region enclosed by the wall and horizon settles down to a thermal equilibrium state, for which the Euclidean action is evaluated and the partition function is obtained. The integration constant (subtraction term) of Euclidean action is determined to reproduce the equation of state (e.g. entropy-area law) verified already in the micro-canonical ensemble. Our de-Sitter canonical ensemble is well-defined to preserve the "thermodynamic consistency", which means that the state variables satisfy not only the four laws of thermodynamics but also the appropriate differential relations with thermodynamic functions; e.g. partial derivatives of the free energy give the entropy, pressure, and so on. The special role of cosmological constant in de-Sitter thermodynamics is also revealed.

Abstract:
When a black hole evaporates, there arises a net energy flow from black hole into its outside environment (heat bath). The existence of energy flow means that the thermodynamic state of the whole system, which consists of the black hole and the heat bath, is in a nonequilibrium state. Therefore, in order to study the detail of evaporation process, the nonequilibrium effects of the energy flow should be taken into account. Using the nonequilibrium thermodynamics which has been formulated recently, this paper shows the following: (1) Time scale of black hole evaporation in a heat bath becomes shorter than that of the evaporation in an empty space (a situation without heat bath), because a nonequilibrium effect of temperature difference between the black hole and heat bath appears as a strong energy extraction from the black hole by the heat bath. (2) Consequently a huge energy burst (stronger than that of the evaporation in an empty space) arises at the end of semi-classical stage of evaporation. (3) It is suggested that a remnant of Planck size remains after the quantum stage of evaporation in order to guarantee the increase of total entropy of the whole system.

Abstract:
In general, when a black hole evaporates, there arises a net energy flow from black hole into its outside environment due to Hawking radiation and energy accretion onto black hole. The existence of energy flow means that the thermodynamic state of the whole system, which consists of a black hole and its environment, is in a nonequilibrium state. To know the detail of evaporation process, the nonequilibrium effects of energy flow should be taken into account. The nonequilibrium nature of black hole evaporation is a challenging topic including issues of not only black hole physics but also nonequilibrium physics. Using the nonequilibrium thermodynamics which has been formulated recently, this report shows: (1) the self-gravitational effect of black hole which appears as its negative heat capacity guarantees the validity of generalized 2nd law without entropy production inside the outside environment, (2) the nonequilibrium effect of energy flow tends to shorten the evaporation time (life time) of black hole, and consequently specific nonequilibrium phenomena are suggested. Finally a future direction of this study is commented.

Abstract:
When a black hole evaporates, there arises a net energy flow from the black hole into its outside environment due to the Hawking radiation and the energy accretion onto black hole. Exactly speaking, due to the net energy flow, the black hole evaporation is a nonequilibrium process. To study details of evaporation process, nonequilibrium effects of the net energy flow should be taken into account. In this article we simplify the situation so that the Hawking radiation consists of non-self-interacting massless matter fields and also the energy accretion onto the black hole consists of the same fields. Then we find that the nonequilibrium nature of black hole evaporation is described by a nonequilibrium state of that field, and we formulate nonequilibrium thermodynamics of non-self-interacting massless fields. By applying it to black hole evaporation, followings are shown: (1) Nonequilibrium effects of the energy flow tends to accelerate the black hole evaporation, and, consequently, a specific nonequilibrium phenomenon of semi-classical black hole evaporation is suggested. Furthermore a suggestion about the end state of quantum size black hole evaporation is proposed in the context of information loss paradox. (2) Negative heat capacity of black hole is the physical essence of the generalized second law of black hole thermodynamics, and self-entropy production inside the matter around black hole is not necessary to ensure the generalized second law. Furthermore a lower bound for total entropy at the end of black hole evaporation is given. A relation of the lower bound with the so-called covariant entropy bound conjecture is interesting but left as an open issue.

Abstract:
It may be a common understanding at present that, once event horizons are in thermal equilibrium, the entropy-area law holds inevitably. However, no rigorous verification is given to such a very strong universality of the law in multi-horizon spacetimes. In this article, based on thermodynamically consistent and rigorous discussion, we investigate thermodynamics of Schwarzschild-deSitter spacetime in which the temperatures of two horizons are different. We recognize that three independent state variables exist in thermodynamics of the horizons. One of the three variables represents the effect of "external gravity" acting on one horizon due to another one. Then we find that thermodynamic formalism with three independent variables suggests the breakdown of entropy-area law, and clarifies the necessary and sufficient condition for the entropy-area law. As a by-product, the special role of cosmological constant in thermodynamics of horizons is also revealed.