iosr-Jm   Volume-16 ~ Issue-2 ~ mar – apr 2020

Abstract: This study focuses on Monte Carlo estimation of production function with policy relevance. The ordinary least square (OLS) method is used to estimate the unknown parameters. The Monte Carlo simulation methods are used for the data generating process. In tables 1 to 3, the mean square error (MSE) of 1 are 0.007678, 0.001972 and 0.001253 respectively for sample sizes 20, 40 and 80. Our finding showed that the mean square error (MSE) value varies with the sum of the powers of the input variables, the smaller the mean square error the lesser the viability and the better the estimator. In addition, use of parameters estimated to guide policy formulation to producing firms or industries is treated

Keywords: Cobb-Douglas model, Monte Carlo estimation, production function, returns to scale, Capital

[1]. Ashfag, A. and Muhammad, K. (2015) Estimating the Cobb-Douglas Production Function. International Journal of Research in Business Studies and Management, 2(5): 32 – 33.
[2]. Bhatia, H.L. (1994), Public Finance, 18th Edition. New Deihi: Vikas Publishing House PVT Limited.
[3]. Essi, I.D., 2002 "Econometric Models with Mis-specified Error Terms, "Abacus (Journal of the Mathematical Association of Nigeria), Vol 29 (2). 152 – 160.
[4]. Essi, I. D. (2009) Computing Leaf Rectangularity Index under Alternative Error Specifications AMSE Journal of Modeling C Vol. 70 (1), 67 – 79.
[5]. Essi, I.D., (2010) Computing Leaf Rectangularity Index: An Estimation Problem When the Parameter is a Norm of a vector. African Journal of Mathematics and Computer Science Research, 3 (7), 79-82.

Abstract: Present here in are the analytical studies of nutrition transport in articular cartilage. These studies have enabled the researchers to analyzes the lubrication mechanism of joints amount of nutrition being transported to the bone and the structural behavior of articular cartilage. The variation of concentration in the cartilage for variation values of parameters . it has been observed that the concentration of synovial fluid increases when the gap increases between the bone surfaces . again the concentration of articular cartilage decreases when the gap between the bone increases.

Keywords: Cartilage, Nutrition Transport, Synovial fluid , concentration

[1]. Lai, W.M. et al and V. C. Mow (1974) "Some surface characteristics of articular cartilage"
[2]. Mow, C.W. (1968) "The role of lubrication in Biomechanical joints" J.I.;pbr. Technl. 1,320
[3]. Walker P.S., A.unsworth,Downson, J. Sikorski and V.Wright (1970) "Model of an hyaluronic proteincomplex on the surface of articular cartilage." Ann. Rheum. 591-602.
[4]. Mansour, J.M. and V.C.Mow (1977) "On the natural lubrication of Synovial Joints normal and degenerate"
[5]. Yadav A.K. and kumar S (2016) "Synovial fluid flow in reference to animal joints." Indian str. rj. Vol. 6, Issue-12

Abstract: There have been a countless number of methods for computing the value of 𝜋 , with some dating back to the period of Ancient Babylonians. In this paper, the authors investigate a one-dimensional scenario involving two balls and a wall, to enumerate the digits of pi. Several assumptions follow the scenario, one of which pertains to the perfectly elastic nature of collisions involved. Then, the paper proceeds to analyze the movement of the balls by transforming the movement of the balls into a coordinate plane. This was done through the usage of phase diagrams with regards to energy and momentum. The coordinate planes were expressed as vectors to proceed with the mathematical derivation, in which the small angle approximation for arctan(x) was proven through definite integration of inverse trigonometric functions and other graphical elements.

[1]. "A Brief History of Pi (π)." Exploratorium, 14 Mar. 2019, www.exploratorium.edu/pi/history-of-pi.
[2]. Allen, G. Donald. "Pi: A Brief History." Texas A&M University, Texas A&M University, 16 June 2017, www.math.tamu.edu/~dallen/masters/alg_numtheory/pi.pdf.
[3]. Groleau, Rick. "Approximating Pi." PBS, Public Broadcasting Service, 9 Jan. 2003, www.pbs.org/wgbh/nova/physics/approximating-pi.html.
[4]. G. L. L. Comte de Buffon. Sur le jeu de franc-carreau. 1777.
[5]. Illner, Reinhard. "Hidden Circles and the Digits of Pi." Pi in the Sky, University of Victoria, 18 July 2014, www.math.uvic.ca/faculty/rillner/papers/Pi_in_SKY%20copy.

Abstract: We consider the series with positive summands given in [1]for the first Li-Keiper coefficient λ1. We first carry out a numericalexperiment to characterize the speed at which the above seriescontains (in memory) bigamounts of the zeros on the criticalline.Then we look at the truth of the RH as an extremal possible grow of λ1 by means of all sets of zeros in the critical strip. Later, in the last section,we formulate the linear Equation for the coefficients φnrelated to the Li-Keiper coefficients λn. Then, we conclude with a possible proof of the correctness of the Riemann Wave backgroundand thus of a (possible) proof of the RH.

Key words: The first increment of the Li-Keiper coefficients,nontrivial zeros, Series for the first coefficient λ1, "Maxi-Min"criterion for the Riemann Hypothesis, Binomials coefficients, Partition Function, Free Energy, Riemann wave background,Riemann Hypothesis (RH).

[1]. MatiyasevichYu.V.: "YetAnotherRepresentation for the Reciprocals of the NontrivialZeros of the Riemann Zeta Function", Mat. Zametki, 97:3 (2015).
[2]. VaccaG.: "A new series for the Eulerian constant γ =0.577... ", Quart. J. Pure Appl.Math. 41(1909-1910) (363-366).
[3]. SondowJ.: "New Vacca-TypeRational Series for Euler'sConstant and Its "Alternating" Analogln(4/)", Additive NumberTheory, Springer, NY, 2010, (331-340). ArXiv.Org/abs/math/0508042.
[4]. Odlyzko A.: "Tables of the zeros". Available at: http://www.dtc.umn.edu/~odlyzko/zeta_tables/zeros1
[5]. Merlini D., &Rusconi L., The Quantum Riemann Wave, Chaos and Complexity Letters, 2017, volume 11 issue 2, 219-237.

Abstract: The object in the paper is to introduce the concept of cut point and punctured space in the Topological spaces, like Topological Manifold M of dimension n , Tangent bundle of dimension – 2n , fiber bundle . Let ∪ be subset of M. We defined cut point p ϵ M of order K , if f: ∪  Rn is a differential map of U into Rn and f is represented by n-co-ordinates functions f1 ,………,fn : ∪  R ( f(p)=f1 (p)….. fn (p) for each p ϵ ∪) all of which are differentials . The main object is to define these sequence of function {fn} are differentiable, also inverses. These inverse functions image, forms a open sets ∪i ϵ M forms a cover for M , which remove the cut point on M i.e. M becomes connected Topological Manifold.

Keywords: Cut points and punctured points, sequence of differential functions, cover space.

[1]. Erwin Kreyszig(2007), " Introductory Functional Analysis with Applications" Wiley Classics Library Edition Publication, Singapore.
[2]. H. G. Haloli (2013), "The Structural Relation between the Topological Manifold-I -Connectedness" IOSR Journal of Engineering e-ISSN-2250-3021, p-ISSN-2278-8719 Vol.3, Issue-7,||V2|| pp-43-54.
[3]. H. G. Haloli (2013), "The Topological Property of Topological Manifold-Compactness with Cut Point and
[4]. Punctured Point", International Journal of Scientific and Engineering Researh, Volume-4 Issue -8, ISSN-2229 -5578, pp-1374-1380.
[5]. H. G. Haloli (2013), "Connectedness and Punctured Space in Fiber bundle space ", International journal of Engineering Research and Technology (IJERT), ISSN -2278- 0181,Vol.-2 Issue 6,(pp-2389-2397).

Abstract: This study handles the three-dimensional linear diffusion in a new way. A general solution is given without particular initial conditions. In addition, solutions are obtained for a source-sink as a constant in time
but spatially varying in three dimensions and having an arbitrary time dependence. An auxiliary function for diffusion is given having an interesting relationship with the concentration. It appears that both the time
derivative and the Laplacian of the concentration obey the diffusion equation. An integro-differential equation for diffusion is presented. 1

[1]. Crank, John: Mathematics of Diffusion, Clarendon Press(1979)
[2]. Churchill, Ruel: Operational Mathematics, McGraw-Hill Kogakusha, 3rd edition (1972), Tokyo
[3]. Stenlund, H.: On the Basics of the Non-Linear Diffusion, arXiv:2003.06282v1 [math.GM] 12 Mar 2020.
[4]. Stenlund, H:On Solving the Cauchy Problem with Propagators, arXiv:1411.1402v1[math.AP], 5th November 2014
[5]. Stenlund, H:A Closed-Form Solution to the Arbitrary Order Cauchy Problem with Propagators, arXiv:1411.6890v1 [math.GM]
24th November 2014

Abstract: This study presents a special case for Beal's conjecture by giving the exact analytic expression, as well as a solution suggestion to the general case

This study presents a special case for Beal's conjecture by giving the exact analytic expression, as well as a solution suggestion to the general case