Abstract:
A study was performed to investigate the effect of some selected sintering additives on the densification and microstructure of fluorapatite (FAp, Ca_{10}(PO_{4})_{6}F_{2}). The sintering aids, used for improving the material densification at lower than 1080℃ temperature, were classified according to their cations as alkaline such as Li_{2}CO_{3}, NaF, Na_{2}CO_{3}, Na_{3}PO_{4}, KCl, K_{2}CO_{3}, and alkaline-earth such as CaF_{2}, CaCl_{2} and MgCl_{2}. Amounts of 0.1; 1 and 3 wt% were vigorously homogenized with FAp powders then the solid mixture was pressurelessly sintered under argon flow with 10℃ .？min^{-1} heating and cooling speed. The density of each sintered material was determined by calculation of the pellet dimension and weight, the crystalline phases were identified using X-ray diffraction (XRD) and the phase morphology was examined by scanning electron microscopy (SEM). The dependence of densification and microstructure on sintering temperature range 900℃ - 1000℃ and amount of sintering aids was studied. It was found that all sintering additives were able to ameliorate the sintrability of the material at temperatures 900℃ and 1000℃. Maximums of about 96% were reached with adequate amounts and sintering temperatures. An exception was found with KCl which had no effect on the density. The microstructures of sintered specimens strictly follow the densification ratios and the sintering mechanism depended on the melting point of the additive.

Abstract:
In this paper, we present a new cosmological model using fractal manifold. We prove that a space defined by this kind of manifold is an expanding space. This model provides us with consistent arguments pertaining to the relationship between variation of geometry and movement of matter. This study leads to the existence of new fundamental principles. A clear picture is then portrayed about the expansion of the universe represented by fractal manifold.

Abstract:
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A fluctuant manifold has been built with an appearance of a new structure on it at every scale, and we embedded into it an internal structure to transform its fluctuant geometry to a new fixed geometry. This approach leads us to what we call fractal manifold. The elements of this kind of manifold appear locally as tiny double strings, with an appearance of new structure at every step of approximation. We have obtained a variable dimensional space which is locally neither a continuum nor a discrete, but a mixture of both. Space acquires a variable geometry, it becomes explicitly dependent on the approximation process, and the geometry on it assumed to be characterized not only by curvature, but also by the appearance of new structure at every step of approximation.

Abstract:
In this paper, we present a new formulation of Lorentz transformations using a metric that quantifies the space expansion. As a consequence, we sort out that the limiting velocity of moving bodies is decreasing together with the space expansion. A new adjustment of relativistic laws is added to incorporate the non static nature of space-time. The conservation of the physical laws at each step of the quantified expansion allows the obtaining of new formalisms for the physical laws, in particular when an object starts moving under any force, its total energy, momentum and mass are directly affected by the expansion of the space. An example of inelastic collision is studied and several conclusions derived, specially the example of fission of atoms leads to clear correlation between liberated energy and universe expansion, it turns out that the liberated energy is increasing together with the universe expansion.

Abstract:
In this paper, a geometrical interpretation of light diffraction is given using an infinity of fluctuating geodesics that represent paths of least time in an homogeneous space. Without using the wave theory, we provide a geometrical explanation of the deviation of light's overall direction from rectilinear when light encounters edges, apertures and screens, which reconciles light particle-like nature with the interference phenomena.

Abstract:
In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an uncertainty in the simultaneous determination of values of its physical properties. The uncertainty in the simultaneous knowledge of the position deviation and the average rate of change of this deviation is found to be governed by a relation equivalent to the one discovered by Heisenberg in 1925. Conversely, we prove that any physical system with a continuous position function that is subject to an uncertainty relation must have a nowhere differentiable position function, which makes the set of continuous and nowhere differentiable functions a candidate for the quantum world.

Abstract:
In this paper we construct an illustration of a space that expands via discrete expansion of its basic elements. We prove that in such an expanding space-time, the geodesics are curved and more precisely they fluctuate on the boundaries of the expanding basic elements. This induces a variable curvature of the space as well as a variable topology. The identification of the light geodesics in this expanding space-time leads to determine matter location; we prove that the variation of the space-time curvature is responsible for matter distribution at large scale and makes the geometry of the expanding space-time invisible.

Abstract:
The solids are widely used in the refining industry. They are involved in most processes of heterogeneous catalysis that has greatly revolutionized the refining processes during the half past century. It has contributed to the rapid development of processes such as: catalytic cracking, catalytic reforming and isomerization. As we know, the heterogeneous catalysis or contact catalysis aims to carry out a transformation of gaseous or liquid reactants by using a solid catalyst. The chemical processing occurs at the interface solid-fluid due to the absorption of reactants in the solid surface; this adsorption involves specific sites that are capable of contracting with the reactants of chemical bonds more or less strong. The adsorbed and formed sorts lead to the desired reaction if the catalyst is well selected, which is Sabatier principle. Thus, the establishment of superficial atoms and ions plays an important role. As a whole, the industrial solid catalyst are the heart of refining process and determine their future as well. More and more, the catalytic processes develop at the expense of thermal processes, and the discovery of new catalysts determines the development of new processes.

Abstract:
Group key security protocols play an important role in today’s communication systems. Their verification, however, remains a great challenge because of the dynamic characteristics of group key construction and distribution protocols. Security properties that are well defined in normal two-party protocols have different meanings and different interpretations in group key distribution protocols, specifically, secrecy properties, such as group secrecy, forward secrecy, backward secrecy, and key independence. In this paper, we present a method to verify forward secrecy properties for group-oriented protocols. The method is based on a correct semantical link between group key protocols and event-B models and also uses the refinement process in the B method to model and verify group and forward secrecy. We use an event-B first-order theorem proving system to provide invariant checking for these secrecy properties. We illustrate our approach on the Tree based Group Diffie-Hellman protocol as case study.

Abstract:
This paper is devoted to the computation of the spectrum of the finite Laplace transform (FLT) and its applications. For this purpose, we give two different practical methods. The first one uses a discretization of the FLT. The second one is based on the Gaussian quadrature method. The spectrum of the FLT is then used to invert the Laplace transform of time limited functions as well as the Laplace transform of essentially time limited functions. Several numerical results are given to illustrate the results of this work.