iosr-Jm   Volume-17 ~ Issue-6 ~ Nov. – Dec. 2021

Abstract: The aim of this paper is to introduce and analyse a new type of continuity called somewhat Nag s continuity. Its relation to various other somewhat nano continuous functions are established.

Keywords: Nano topology, somewhat nano continuous, somewhat Nag s continuous.

[1]. S.S. Benchalli and P.M. Bansali, "Somewhat b continuous function in topological spaces ," Int. J. Math. Ana 4 (46) (2010), 2287-2296.
[2]. K. Bhuvaneswari and K. Mythili Gnanapriya, "Nano generalized closed sets, "Int. J. Sci. Research Pub 4(5) (2014), 1-3.
[3]. M .Dharani, V.Senthilkumaran and Y.Palaniappan,"On nano s closed sets in topological spaces", Annals of Pure and Applied Mathematics,Submitted
[4]. J. Dontchev, "Contra continuous function and strongly S closed spaces," Int. J. Math and Math. Sci (19) (1996) 303-310.
[5]. M.Ganster and I.L Reily, "Locally closed sets and L.C. Continuous functions," Int.J. Math and Math. Sci (1989) 417-424.

Abstract: in the classical three dimoensional curve theroy,the geometry of a curve essentially characterized by two scalar functions,curvature κ and torsion τ ,[1] which reperesent the rate of change of the tangent vector and the osculating plane respectively.given two continous function of one parmeter, there is space curve for which the two functions are its curvature and torsion ,which represent the rate of change of the tangent vector and the osculating plane ,respectively .Given two continous functions of one parmeter, there is a space curve for which the two functions are its curvature and torsion(parameterized by arc-length). The curve [2]

[1]. Helix to helix packing in proteins Chothia, Cyrus and Levitt, Michael and Richardson, Douglas 1981, Elsevier
[2]. intuitive helix geometry analysis and abstraction Dahl, Anna Caroline E and Chavent, Matthieu and Sansom, Mark SP 2012, Oxford University Press
[3]. Optimisation of variable helix tool geometry for regenerative chatter mitigation,
[4]. Yusoff, Ahmad R and Sims, Neil D, 2011, Elsevier intuitive helix geometry analysis and abstraction, Dahl, Anna Caroline E and Chavent, Matthieu and Sansom, Mark SP, year=2012, publisher=Oxford Uni- versity Press
[5]. Helix geometry in proteins, Barlow, DJ and Thornton, JM, year=1988, publisher=Elsevier

Abstract: The purpose of this paper is to introduce and study a new class of totally continuous function called.......

Keywords:.....

[1]. D.Andrijevic. , "b – open sets", Mat. Vesink, 48, 59 – 64, 1996
[2]. G – Choquet, "Sur les notations de filter et grille", Comptes Rendus Acad. Sci. Paris, 224(1947), 171 – 173
[3]. Dhananjoy Mandal and M. N. Mukherjee, "On a type of generalized closed sets", Bol. Soc. Paran. Mat. 30 1(2012), 67-76
[4]. J. Dontchev and T. Noiri, "Quasi Normal spaces and – closed sets", Acta. Math. Hunger, 89(3) (2000), 211-219
[5]. J. Dontchev and H. Maki, "On – generalized closed sets", Topology Atlass

Abstract: The demand for crude oil and petroleum products in Kenya has been increasing very fast over the past twenty years. This is mainly because this particular commodity is used in many sectors of the country's economy. Ever changing prices affect the exchange rates which also affects industrial production of goods in Kenya. The oil production sector has a crucial impact on the other industries. Any change in the price of petroleum products has a great impact on the prices of other goods produced and even the growth of the economy. This is mainly due to the transport cost involved in transporting the goods. The major aim of this research is to model petroleum products prices in Kenya using Autoregressive.........

Key words: Modeling, Forecasting, Stationarity, ARIMA and VAR models

[1]. Kotut C, Menjo K, Jepkwony J. An Econometric Approach to the Economic Impact ofPetroleum oil prices Fluctuation in Kenya. Journal of Economics and SustainableDevelopment 2012; 3:7.
[2]. Nyongesa D, Wagala A. Non- Linear Time Series Modeling of the Diesel Prices in Kenya. International Journal of Academic Research in Economics and Management Sciences. 2016.
[3]. Mecheo J and Omiti, J., Petroleum markets structure and pricing following irregulation. Institute of Policy Analysis and Research. 2003.
[4]. Munyua JN, Ragui M. Drivers of Instability in prices of petroleum products in Kenya. Prime Journal of Business Administration and Management (BAM), 2013; 3(3): 919-926.
[5]. Al hassan A and Klishi A.Analyzing Oil Price-Macroeconomic Volatility in Nigeria. Journal of Applied Statistics 2016; 7(1)

Abstract: This paper attempts to study the performance of an infinitely short rough journal bearing. The study has been extracted using the Christenson and Tonder model. The corresponding Reynolds equation has been used to calculate the pressure distribution, which is important for constructing the load-carrying capacity equation. A graphical representation is made to display the calculated value of dimensionless pressure and dimensionless load-carrying capacity. It can be underlined that the standard deviation significantly affects the performance characteristics.

Keywords: Journal Bearing, Longitudinal surface roughness, Reynolds equation, Pressure, Load carrying capacity.

[1]. Kuzma, D. C. (1963). The magnetohydrodynamic journal bearing, Transaction of the ASME, pp. 424–428.
[2]. Lin, J. R. (1998). Squeeze film characteristics of finite journal bearings: couple stress fluid model, Tribology International, vol. 31, no. 4, pp. 201–207.
[3]. Nada, G. S. and Osman, T. A. (2007). Static performance of finite hydrodynamic journal bearings lubricated by magnetic fluids with couple stresses, Tribology Letters, vol. 27, no. 3, pp. 261– 268.
[4]. Montazeri, H. (2008). Numerical analysis of hydrodynamic journal bearings lubricated with ferrofluid. Journal of Engineering Tribology 222, 51-60.
[5]. Patel, N. S., Vakharia, D. P. and Deheri, G. M., (2012). A study on the performance of a magnetic-fluid-based hydrodynamic short journal bearing, ISRN Mechanical Engineering, vol. 2012, Article ID 603460, 7 pages

Abstract:This particular method is for finding the fastest way to calculate the sum of powers of natural numbers by integration method.

Keywords: integration, powers of natural numbers, integration, coefficients, algebraic method

[1]. Elementary number theory (Seventh edition) by David M. Burton (1976)
[2]. NCERT Mathematics Textbook (12th standard 2014)
[3]. Calculus by Edwin Herman and Gilbert Strang

Abstract: This article focuses on the development of a mathematical model describing an inventory system with time dependent three-parameter Weibull deterioration, and witha Ramp-type demand rate, which is a quadratic function of time in the beginning of a cycle, and subsequently becomes linear over time. The model incorporates shortages which are partially backlogged.We derived the optimal inventory policy for the model and established the necessary and sufficient conditions for the optimal policy. The objective of the model is to minimize the total inventory costs. For the numerical solution of the model, MathCAD14 numerical software was employed. We obtained satisfactory results. We then proceeded to performed sensitivity analysis of our model. The sensitivity analysis showed that the optimal solution of the model is affected by slight changes or errors in its input parameter values.

Keywords: Inventory System, Price-Ramp, Dependent Demand and Deterioration Function

[1]. Chakrabarti, T., Giri, B.C., Chaudhuri, K.S. (1998). An EOQ model for items with Weibull distribution deterioration, shortages and
trended demand. An extension of Philip's model. Computer and Operations Research, 25 (7/8), 649-657.
[2]. ChukwuW.I.E(2002) Inventory Control with inverse Gaussian demand and gamma lead time Uniswa Research Journal Vol 16, pp 84-88.
[3]. Chung C. S., Flynn J., Zhu J. (2009). "The newsvendor problem with an in-season price adjustment," European Journal of Operational Research, vol. 198, no. 1, pp. 148–156.
[4]. Covert, R.P., Philip, G.C. (1973): An EOQ model for items with Weibull distribution deterioration. AIIE Trans. 5, 323–326.
[5]. Datta, T.K., Pal, A.K. (1988): Order level inventory system with power demand pattern for items with variable rate of deterioration. Ind. J. Pure Appl. Math. 19(11), 1043–1053.