iosr-Jm   Volume-15 ~ Issue-5 ~ Sep-Oct 2019

Abstract: Al-Gonah and Mohammed (A New Extension of Extended Gamma and Beta Functions and their Properties, Journal of Scientific and Engineering Research 5(9), 2018, 257-270) introduced a new extension of Gamma and Beta functions. In this note, we will show that a problem has been encountered regarding the Gamma function integral representations. We also studied certain results of the Gamma and Beta functions such as beta distribution, new defined Gauss and Confluent hypergeometric functions with their properties.

Key Word:Classical Gauss and Confluent Hypergeometric functions, Generating function, Mittag-Leffler function

[1]. Al-Gonah, A.A. & Mohammed, W.K. (2018). A New Extension of Extended Gamma and Beta Functions and their Properties.. Journal of Scientific and Engineering Research, 5(9): 257-270
[2]. Chaudhry, M.A., Qadir, A., Rafique, M. and Zubair, S.M.(1997). Extension of Euler's beta function. J. Comput. Appl. Math. 78, 19-32
[3]. Chaudhry, M.A., Qadir, A., Srivastava, S.M. and Paris, R.B. (2004). Extended hypergeometric and confluent hypergeometric functions. J. Comput. Appl. Math. 78, 19-32
[4]. Podlubny, I.(1999). Fractional Differential Equations, Mathematics in Sciences and Engineering, 198, Academic Press, California.
[5]. Shadab, M., Jabee, S., and Coi, J. (2018). An extended Bête function and its Applications. Far East Journal of Mathematical Sciences, 103(1), 235-251, http://dx.doi.org/10.17654/MS103010235

Abstract: The aim of this research work is to study the extension of the extended beta function............................

Key Word:Classical Gamma and Beta functions, Extended Gamma and Beta functions, Exponential function, Modified Bessel function.

[1]. A.A. Al-Gonah and W.K. Mohammed, A New Extension of Extended Gamma and Beta Functions and their Properties. Journal of Scientific and Engineering Research, 5, 9 (2018), 257-270.
[2]. A.A. Atash, S.S. Barahmah and M.A. Kulin, On a New Extensions of Extende Gamma and Beta Functions. International Journal of Statistics and Applied Mathematics, 3, 6 (2018), 14-18.
[3]. A. Gaswani, S. Jain, P. Agarwal and S. Aracis, A Note on the New Extended Beta and Gauss Hypergeomentric Functions. Applied Mathematics and Information Sciences, 12, 1 (2018), 139-144, http://dx.doi/10.1857/amis/120113.

Abstract: I. As of august 1, 2002, 100 billion zeros have been shown to satisfy RH. Besides the actual number of zeros, also of interest is their height up the critical line, and the accuracy (number of decimal places) in their value.
II. There is a formula for the number N(T) of zeroes up to a given height T: namely, it is approximately (T/2pi) log (T/2pi)- T/2pi.
III. The harmonic series adds up to infinity, mean given any number "s‟, no matter how large, the sum of the harmonic series eventually exceeds s. No "infinity". The whole of the analysis was rewritten in this kind of language in the middle third of the nineteenth century. Any statement that cannot be so rewritten is not allowed in modern mathematics. You can consider the relation as mapping by their domain and range. Is each relation a function? The answer is not function.
IV. If an element in the first set (domain) is associated with more than one element in the second set (range) then the relation is not a function, definite set gone by in time and no longer existing.
V. A trick of bell curved graph of the normal distribution shows the approximation to the prime distribution.

Key Word: RH, Riemann Hypothesis, NYAYSANGAT FOUNDATION

[1]. CNO"7", CN5O7 –A patented formulas based on Riemann Hypothesis. Author – Ekta Singh, Director, NYAYSANGAT FOUNDATION. Published by Amazon.
[2]. Research Paper – Proof of the Yang Mills Theory Exists on R4 and has a mass gap delta > 0, author – Ekta Singh, Director, NYAYSANGAT FOUNDATION, published in International Journal of Professional Studies, IJPS, 2019, Volume No. 7, Jan – Jun. eISSN – 2455-6270; p-ISSN: 2455-7455.
[3]. Research Paper – A New Proposed Elementary Proof that 7 is Pi Exact Value, author Ekta Singh, Director – NYAYSANGAT FOUNDATION. MIJ 2019, VOL. No. 5, Jan – Dec. eISSN 2954 – 924X; p-ISSN: 2454-8103
[4]. GOD is logically exist in words – 2019, published by International Research Publications, New Delhi.
[5]. I am thankful to EXL organization for the fruitful trainings. Trainings are very helpful to solve the equations.

Abstract: In this paper we have presented a PDE mathematical model. The population density depends on special location and time.In the equation, the first and the third terms deal with local behavior, whereas the second deals with horizontal redistribution. The population growth term follows critical depensation growth manner. The growth below its critical mass quantity is negative which shows biologically mate is rare so that population growth declines. The critical points origin and the carrying capacity are stable whereasthe critical mass quantity is unstable. To solidify the analytical results, numerical simulations are provided for hypothetical set of parametricvalues.

Key Word: Critical depensation growth function, Diffusion, Population harvesting, Equilibrium solution, Stability analysis, Wave solution.

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[5]. Kolad M.Owolabi, Pattern Formation in the Diffusive Fisher Equation, Advanced Modeling and optimization(AMO),Vol 16,Number 3, 2014,ISSN: 1841-4311(2014) pp. 113{126.http://dx.doi.org/10.4236/ojmsi.2014.24013

Abstract: In cosmology, one is supposed to derive the properties of early universe by solving FRW metric. According to the FRW model, the universe has a space-time singularity at a finite time in the past. This space time singularity is called the big-bang. Though the big-bang singularity can not describe what the conditions were at the very beginning of the universe, it can help scientists describe the earliest moments after the start of the expansion. In this paper an attempt has been made to describe the relation of radius and density with time of early universe and present universe by calculating different values of christoffels symbols, Ricci tensor , Ricci scalar and Einestein's equation for the flat space.

Key Word: FRW model, Christoffel symbol, Ricci tensor, Ricci scalar, Energy momentum tensor, Einestein equation, Decleration parameter..

[1]. J.V.Narliker, " Introduction to Cosmology", Cambridge University press 2002.
[2]. H.P. Robertson-Walker 1935. "Kinematics and World Structure AD.J.82.248
[3]. Jamal Nazrul Islam. "An Introduction to Mathematical Cosmologies", Cambridge University Press (1992-2002).

Abstract:Our aim in this paper is to study some lattice theoretic properties of factorizable substructures of a product group which will play an important role in the representation of soft substructures of a soft group by certain crisp subgroups. In fact, for any soft group over a group, we construct a crisp group in such way that the complete lattice of all soft substructures of the former is complete epimorphic to a complete lattice of certain crisp substructures of the later.

Key Word: Associated product group for a soft group, (Extended) Soft (normal) subgroup, Factorizable (normal) subgroup, (Product) Group

[1]. Acar U, Koyuncu F, Tanay B Soft sets and soft rings. Comput Math Appl 59, 2010,3458-3463
[2]. Aktas H, Cagman N, Soft sets and soft groups. Inf Sci 177(13), 2007, 2726-2735
[3]. Ali M.I., Feng F., Liu X.Y. Min W.K. Shabir M, On some new operations in soft set theory. Comput Math Appl 57(9), 2009, 1547-1553
[4]. M.I. Ali, M. Shabir, Comments on De Morgan's law in fuzzy soft sets, Jornal of Fuzzy Mathematics, Vol.18, 2010, pp.679-686.
[5]. M.I. Ali, M. Shabir and K.P. Shum, On Soft Ideals over Semigroups. Article in Southeast Asian Bulletin of Mathematics 34,2010, 595610.

Abstract: The paper tested the null hypothesis that there is no statistically significant correlation between rainfall and temperature for 68 years (1949 – 2017) of data. The analyses involved bivariate correlation and linear regression. Annual rainfall range was 1277 mm – 3390 mm, maximum temperature was 32.2 °C – 43.6 °C and minimum temperature was 27.8 °C -5 °C. The highest mean maximum temperature was 34.50 °C and lowest mean maximum temperature was 32.00 °C. The lowest mean minimum temperature occurred in 1973 (13 °C) and the highest was recorded in 1965 (27.50 °C) where highest mean rainfall was recorded in 1960 (273 mm) and lowest in 1963 (100 mm)........

Key Word: Keywords: Barisal District; Rainfall; Maximum Temperature; Minimum Temperature; Correlation Analysis

[1]. World Bank. Bangladesh: Climate Change and Sustainable Development Report No. 21104 RD.World Bank Office, Dhaka. South Asia Rural Development Team. 2000
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[4]. Ahmed, A.U. and M.A. "Development of Climate Change Scenarios with General Circulation. 1999.
[5]. IPCC, Climate Change 2007: Impacts, Adaptation and Vulnerability, WMO, Geneva, 2007; pp. 1-23.

Abstract: This paper analyses monthly maximum and minimum temperatures from the Cox's Bazar and Teknaf area situated in the eastern coast of Bay of Bengal and south-eastern side of Bangladesh. Maximum and minimum temperature data obtained from Bangladesh Meteorological Department (BMD) in Bangladesh for a period of 69 years from 1948-2017 at Cox's Bazar station and data from 1977-2017 at Teknaf station, was investigated for the time series analysis and forecasting. Here ARIMA (Auto Regressive Integrated Moving Average) models have been set-up and used to carry out long-term predictions (9 years) of monthly maximum and minimum temperatures in the Cox's Bazar and Teknaf area of Bangladesh. The Box-Jenkins methodology, stationary, ARIMA models for the....

Key Word: ARIMA Models, Time Series Analysis, Minimum Temperatures, Maximum Temperature, Forecast¸ Cox's Bazar.

[1] E.S. Chung, K. Park and K.S. Lee, The relative impacts of climate change and urbanization on the hydrological response of a Korean urban watershed. Hydrological Processes, vol. 25, pp.544-560, 2011.
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[3] S.A. Shamsnia, N. Shahidi, A. Liaghat, A. Sarraf and S.F. Vahdat, Modeling Of Weather Parameters (Temperature, Rainfall And Humidity) Using Stochastic Methods. Internat. Conference on Environment and Industrial Innovation, IPCBEE, Singapore, pp. 282-285, 2011
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