ADVANCE OF SMARANDACHE APPROACH TO SOLVING SYSTEMS OF DIOPHANTlNE EQUATIONS

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and analytical formulae, which may be used for fmding numerical solutions of some combinatorial and number-theoretic problems

Design and economic analysis of solar home system for urban areas of Mogadishu using homer software

In this century of enhanced progress by various spaces, some African states are still challenging lack of energy due to scarcity in some places. The most used energy (generation of electricity) is hydropower because heat and fuel are still on some scale. This problem comes about in less efficiency and financial decay of some nations such as Somalia which is among the country at very high speed in progress, the grid lines from distant places are stack and they are rare matched to the required of power in all areas of the nation, especially in remote or urban areas where each household needs electricity utilization instead of utilizing local, conventional and lighting at domestic. This issue can be illuminated utilizing other elective sources of renewable energy for provincial electrification such as Photovoltaic systems. Hence, this project basically focuses on the design of SHS that incorporate financial assessment and utilize of an individual SHS of 200W, so that the satisfaction of the people and the targets of the country can be effectively achieved. Under this project, the dedicated on the investigation of power utilization based on single house household family SHS has been taking a case study of one village in Mogadishu Somalia named Heliwaa placed in Benaadir region. The survey was conducted by assessing the average major load conditions for consecutive hours per day based on photovoltaic capacity. The purpose of this study was achieved the optimal size of the photovoltaic panel and the battery capacity that can be used to power the home. Ultimately, designed project and cost will be compared to other private sector electricity cost, it means which one is more reliable and economically for electricity generation. Therefore according to, the findings the cost of energy is 2.614 in $/KWh which is lower than the private sector. This was considered optimum solution. In this project the design and simulation tasks was achieved through the assistance of HOMER software. The electrification and economics information on combination of photovoltaic systems, in the form of SHS and other renewable energy like stand-alone systems, to provide a reliable and economic system

On Superalgebras of Matrices with Symmetry Properties

It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for square matrices give rise to similar superalgebra structures, pointing to novel symmetry types in their complementary parts. In particular, this provides a unifying framework for the composite `most perfect square' symmetry and the related class of `reversible squares'; moreover, the semi-magic square algebra is identified as part of a 2-gradation of the general square matrix algebra. We derive explicit representation formulae for matrices of all symmetry types considered, which can be used to construct all such matrices.Comment: 25 page