M. Sivasubramanian ¹

Affiliations
1 Department of Mathematics, Dr.Mahalingam College of Engg. & Technology, Pollachi, Tamil Nadu 642003, IN

Abstract

It has been established that it is impossible to deduce Euclid V from Euclid I, II, III, and IV. The investigations devoted to the parallel postulate gave rise to a number of equivalent propositions to this problem. Also, while attempting to prove this statement as a special theorem Gauss, Bolyai and Lobachevsky independently found a consistent model of first non-Euclidean geometry namely hyperbolic geometry. Gauss's student Riemann developed another branch of non-Euclidean geometry which is known as Riemannian geometry. The formulae of Lobachevskyian geometry widely used tot sty the properties of atomic objects in quantum physics. Einstein's general theory of relativity is nothing but beautiful application of Riemannian geometry. Einstein derived these field equations by analyzing geometry of space-time. In this study the author re-visited the parallel postulate and by protecting himself under Saccheri's umbrella found a consistent geometric result which challenged the previous contributions in this field.

Keywords

Euclid, Elements, Postulates, Non-euclidean Geometries Physical Applications

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M. Sivasubramanian ¹

Affiliations
1 Dept. of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi, Tamilnadu– 642 003, IN

Abstract

The famous unsolved classical problem such as trisection of a general angle, doubling the cube, squaring the circle, to draw a regular septagon and to prove the parallel postulate of Euclidean geometry as a theorem are forgotten by the research community. These problems were shown mathematically and logically impossible to solve. In this work the author made a brief survey and attempted to establish the fifth Euclidean postulate.

Keywords

Algebra, Geometry

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B. Kavya Santhoshi ¹, K. Mohana Sundaram ¹, M. Sivasubramanian ¹, S. Akila ¹

Affiliations
1 Department of Electrical and Electronics Engineering, Vel Tech Multi Tech, Chennai - 600062, Tamil Nadu, IN

Abstract

Background/Objectives: Multi Port Converters (MPCs) have gained importance in renewable power generation recently. MPCs can interface and control many power terminals and are generally economical with high power density, efficiency, and compact structure. Bidirectional MPC is proposed in this paper to facilitate power flow between load and source in a two way channel. Methods/Statistical Analysis: The proposed model is simulated using MATLAB software. The results confirm that the overall efficiency of the system is increased and the power flow is bidirectional with reduced losses. Findings: In the present existing topology, Bidirectional flow of energy is a challenging study in case of MPCs. Power losses will be high due to the use of Diode Bridge. The main motive of this paper lies in proposing a systematic method for deriving MPC topologies from non-isolated BDCs and FBCs. The derived MPCs use four port converters with both buck and boost topologies. Due to the usage of full bridge converter, bidirectional power flow is achieved unlike the traditional method. Application/Improvements: The proposed system is capable of being used for the applications of renewable power system, namely, PV-supplied aerospace power systems, fuel cell, battery systems, hybrid energy storage systems, and thermoelectric systems with energy backup. It has reduced power loss and facilitates two way power flow.

Keywords

Bidirectional, MPC, Multiport, Renewable Power Generation

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