Mathematical Journal of Interdisciplinary Sciences
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A Novel approach for optimization in Mathematical calculations using Vedic Mathematics Techniques
Get PDFVedic Mathematics is the name given to the ancient system of mathematics, or to be precise, a unique technique of calculations based on simple rules and principles with which any mathematical problem can be solved – be it arithmetic, algebra, geometry or trigonometry. The system is based on 16 Vedic sutras or aphorisms, which are actually word formulae describing natural ways of solving a whole range of mathematical problems. In this paper, we will be taking a few Vedic sutras. Akadhiken Purven (By one more than the one before), Nikhilam Navtashcharam Dashat (All from 9 and the last from 10) are two of them. NASA has adopted it fully in the realms of advanced robotics. Calculations that can be solved as quick as lightning are a great tool to adopt, but you wouldn’t want to teach it worldwide in the fear that you may churn out a generation of child geniuses that may threaten the intellectual status quo.
The gift that the Hindus gave to the world, thousands of years ago, and that which is currently responsible for global silicon chip technology, was none other than the invention of zero and the use of the decimal point. We call our common numbers “Arabic Numerals” but really they extend back to the Hindu concept of creation and were known as “Bindu” or Unity. All Vedic Maths is based on the understanding of Unity Consciousness which means they utilize processes or Number Bases that correspond to 0, 10, 100, 1000, 10000, etc all of which add to 1. In light of the fact that the Vedas, literally “the illimitable storehouse of All Knowledge” came under 4 headings or categories like the Rig Veda, the Yajur Veda, the Sama Veda, and the Atharva Veda. Thus a Vedic Mathematician was also an astronomer, healer, and poet. It was a total system if you are out in the field and you need to tile a square floor that is, say 108 units square. How do you do it with mental ease? I think only of the excess “8”, saying how much is 108 more than my Base of 100. It is “8”. So we will merely add this “8” to the number in question “108” and tag on the squaring of this excess: 108 Squared = 108 + 8 / 8×8 = 116 / 64 = 11,664.Vedic mathematical methods are derived from ancient systems of computations, Compared to conventional mathematical methods, these are computationally faster and easier to perform. An application of Vedic mathematics can be effectively increased if it can make available to the beginners in various fields of study
Probability Analysis of a Complex System Working in a Sugar Mill with Repair Equipment Failure and Correlated Life Time
Get PDFThe aim of this paper is to present a reliability analysis of a complex (SJP) system in a sugar mill with the assumption that repair equipment may also fail during the repair. This paper considers the analysis of a three-unit system with one big unit and two small identical units of a SJP System in a sugar mill. Failure and Repair times of each unit are assumed to be correlated. Using regenerative point technique various reliability characteristics are obtained which are useful to system designers and industrial managers. Graphical behaviors of MTSF and profit function have also been studied
Monomial Dynamical Systems in # P-complete
Get PDFIn this paper, we study boolean monomial dynamical systems. Colón-Reyes, Jarrah, Laubenbacher, and Sturmfels(2006) studied fixed point structure of boolean monomial dynamical systems of f by associating the dynamical systems of f with its dependency graph χf and Jarrah, Laubenbacher, and Veliz-Cuba(2010) extended it and presented lower and upper bound for the number of cycles of a given length for general boolean monomial dynamics. But, it is even difficult to determine the exact number of fixed points of boolean monomial dynamics. We show that the problem of counting fixed points of a boolean monomial dynamical systems is #P-complete, for which no efficient algorithm is known. This is proved by a 1-1 correspondence between fixed points of f sand antichains of the poset of strongly connected components of χf.
Simultaneous Testing For the Goodness of Fit to Two or More Samples
Get PDFIn this paper we have considered the problem to test for the simultaneous goodness of fit of an absolutely continuous distribution function to many samples. The proposedtest is seen to have many desirable properties
On Inequalities Involving Moments of Discrete Uniform Distributions
Get PDFSome inequalities for the moments of discrete uniform distributions are obtained. The inequalities for the ratio and difference of moments are given. The special cases give the inequalities for the standard power means
Controllability and Observability of Kronecker Product Sylvester System on Time Scales
Get PDFThe main objective in this paper is to present the necessary and sufficient conditions for complete controllability, complete observability associated with kronecker product Sylvester system on time scales.2000 Mathematics Subject Classification: 93B05,93B07,49K15
A Single Server Retrial Queue with Impatient Customers
Get PDFIn the present paper, a single server retrial queue with impatient customers is studied. The primary arrivals and repeating calls follow the Poisson distribution. The service time is exponentially distributed. Explicit time-dependent probabilities of an exact number of arrivals and departures from the orbit are obtained by solving the differential-difference equations recursively. Steady state solution of the number of busy servers is obtained. The numerical results are graphically displayed to illustrate the effect of arrival rate, retrial rate and service rate on different probabilities against time. Some special cases of interest are also deduced