iosr-Jm   Volume-12 ~ Issue-6 ~ Nov-Dec 2016

Abstract: In the background of pointfree topology, if L is a locale, the Vietoris locale V (L) corresponding to L has been constructed using the spectrum of L. If L is a spatial, subfit locale, then V (L) is also a subfit locale. Also if L is second countable locale, then V(L) is second countable and hence seperable.

Keywords: Vietoris locale, second countable, Subfit, Seperable.

[1]. Jorge Picardo, Ales Pultr ,Frames and Locales –Topology without points(springer Basel AG 2012)
[2]. Peter.T.Johnstone, Stone Spaces(Cambridge University Press,1982)
[3]. Steven Vickers, Topology via logic(Cambridge Tracts in Theoretical Computer Science, Cambridge University Press1989)
Journal Papers
[4]. B.Banaschewski,C.J.Mulvey,Stone cech Compacti_cation of locales-II,Journal of pure and applied Algebra 33(1984) 107-122,North Holland
[5]. J.Isbell,First steps in descriptive theory of locales,Trans.Am.Math.Soc.327(1991)353371..

Abstract: It is believed that pi (π) is a transcendental number. In author's opinion, it is not the fact. The paper aims at showing that pi (π) is an algebraic number with exact value 17-8√3. The derivation of this value is supported by several geometrical constructions, arithmetic calculations and use of some simple algebraic formulae.

[1]. Exact area of equilateral triangle formula = (√3 † 4) × side², Area of circumscribed hexagon = (2√3) r², Area of circumscribed dodecagon = 12(2 - √3) r²
[2]. Basic Algebra & Geometry concept, History of pi (π) Complete thesis of my research titled as ""Exact value of pi ‟‟ has being published in following journals:
[3]. IOSR(international organization scientific research) journal of mathematics in May-June 2012.
[4]. IJERA (international journal of Engineering research and applications) in July-August 2013.

Abstract: The design of a modern movie theatre is very complicated and it should be done very methodically keeping in mind the innumerable number of details that it should be attended to. A certain degree of price discrimination can be seen at movie theatres. There is a different and varied price not only for when but also for where one sits in a movie theatre. This is to say that one is charged more for the same movie and the same experience based on from where he or she sits. As by norm, the seats in front are charged lesser than the seats at the back. The comfort of viewing, i.e. physical comfort is the best at the back, and worst in the front, but the last few 'expensive' rows may not be the most 'ideal' place to watch the movie from. In this paper includes the design of an ideal movie theatre such that one can have the best possible angle of vision using STAADD PRO ANALYSIS and LSM

Keywords: Movie theatre, Beams, Purlins , Footing, STAADD PRO ANALYSIS , LSM.

[1]. NATIONAL BUILDING CODE
[2]. IS 800-1984, code of practise for general construction in steel.
[3]. IS 456-2000, code of practise for plain & reinforced concrete.
[4]. "Theory of structures" by S.Ramamrutham.
[5]. "Strength of materials & Theory of structures" by B C Punmia.

Abstract: The existence and uniqueness solution of a nonlinear partial differential equation (NPDE)of fractional order are discussed and proved in a Banach space ℋ due to Picard's method depending on the properties we expect a solution to possess. Moreover, some properties concerning the stability of solutions are obtained.A systemof nonlinear Volterra integral equations of the second kind (SNVIEs) is obtained. The modified Toeplitz matrix method (MTMM) is used, as a numerical method, to obtain a nonlinear systemof algebraic equations (NAS). Also, many important theorems related to the existence and uniqueness solution of the algebraic system are derived. Finally,numerical results are obtained and the error is calculated.

Keywords: nonlinear partial differential equation of fractional order,semigroup, system of nonlinear Volterra
integral equations of the second kind,modified Toeplitz matrix method, nonlinear algebraic system

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Vol.68, Springer-Verlag, New York,1986.
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14(2002), 433-440 .
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