This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with the L-topological system and L-topological space are established.

In this paper first we define the morphism between geometric spaces in two different types. We construct two categories of U-GESP and L-GESP from geometric spaces then investigate some properties of the two categories, for instance U-GESP is topological. The relation between hypergroups and geometric spaces is studied. By constructing the category SNS-Hv of Hv-groups we answer the question that which construction of hyperstructures on the category of sets has free object in the sense of universal property. At the end we define the category of geometric Hypergroups and we study its relation with the category of hypergroup.

In this paper, we study a three-parameter bivariate distribution obtained by taking Geometric minimum of Rayleigh distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.

This article comprises three parts. The first section deals with the evaluation of geometry & its relation to the parallelism among the main three fold worlds [intellectual world, absolute imagination world, & material world]. In this section, we considered Pythagoreans, Plato, Ibn Sina, Ekhvan alsafa, Abu Reyhan Biruni and Rene Guene view points about the symbolic position of geometry & its relation to the spiritual insights. In the thoughts of these figures, geometry describes the super natural realm & cosmic lives of the heavens by a philosophic language & by offering interior insights leads the soul to the real existence. In Ekhvan alsafa's view points, geometry splits into two Categories of sensible & rational & both are considered as a new way in recognition of the wisdom essence & the nature of the soul. The second section deals with geometric position of the existence system in creating the order & unity of the world components. In this section the cosmic orderlines & parallelism of the symbolic appearance of god's justice in proportion to the inner merit &, in other words, the worth of every thing are explained. Third section is allocated to the relationship between geometry & monotheism insights & also some meanings of geometric symbols. The presence of geometric structure in the abstract styles of geometric ornaments, Islamic, Khatayi or architectural forms & volumes is adopted from the holy principle of monotheism. The essence of monotheism in the field of visual imagination is manifested in the geometric crystallized forms & by itself forms the essence of the Islamic art. At the end of this section we deal with the meanings of the main geometric symbols: point, triangle, circle & square in the obtained view points.

In this paper، with respect to the advantages of geometric phase in quantum computation، we calculate the geometric phase of the optomechanical systems. This research can be considered as an important step toward using the optomechanical systems in quantum computation with utilizing its geometric phase.