iosr-Jm   Volume-16 ~ Issue-5 ~ Sep. – Oct. 2020

Abstract: In this paper an inversion formula for integral transform of I- function of several complex variables has been
established. Certain special cases are also given.

Keywords: I- function, Mellin transform, Mellin-Barnes contour integral.

[1]. Braaksma, B.L.J (1964): Asymptotic expansions and analytic continuations for a class of Barnes integrals, Compositio
Math.15.239-341.
[2]. Erdelyi, (1954): Tables of integral transforms, I, II, Mc, Graw Hill, New York.
[3]. I.S Ansari, F. Yilmaz, M,S.Alouni and O. Kucur: New results on the sum of Gamma random variables with application to the
performance of Wireless communication system over Nakagami-m Fadding Channels, arxiv:1202-2576v4 cs IT, (2012).
[4]. Joshi,N (1986): The generalized complex inversion theorem for integral transforms; Vijnana parishad Anusandan Patrika, Vol-29,
No-2.
[5]. K, Arjun Rathie (1997): A new generalization of generalized hyper geometric functions, Le Mathematiche,, Vol.LII. Fasc.II ,297-
310.

Abstract: In this paper, we develop a solution for pricing a European put option under the assumption that the distribution returns (losses) are Gumbel distributed at maturity. Further, we use the derived solution to check its relevancy with the data of actual market. We compare the Black- Scholes model which is based on assumption that distribution returns follow log-normal distribution with our derived solution which is based on the assumption that returns follow truncated Gumbel distribution numerically and observe some interesting underlying phenomenon.

Keywords: European put, Truncated Gumbel distribution, Fat tail, Black- Scholes model

[1]. Black, F., & Scholes, M. The pricing of options and corporate liabilities. Journal of political economy, 1973, 81(3), 637-654.
[2]. Markose, S., & Alentorn, A. (2005). Option Pricing and the Implied Tail Index with the Generalized Extreme Value (GEV) Distribution 1, 2005, Centre of Computational Finance and Economic Agents (CCFEA).
[3]. Madan, D. and Seneta, E. The Variance Gamma (V.G.) Model for Share Market Returns. Journal of Business, 1990, 63, 511-524. [4]. Geske, R., & Torous, W. Skewness, kurtosis, and black-scholes option mispricing. Statistical Papers, 1991,32(1), 299.
[5]. Cont, R. and Tankov, P. Financial Modelling with Jump Processes. Chapman and Hall/CRC, 2004

Abstract: The Black-Scholes model is widely used to determine price of European type options. The underlying stock prices have taken as normally distributed in Black-Scholes model. But it can be observed that, the underlying price of any option can never reach infinity in reality. So, there is a generalization of the Black-Scholes model by changing the distribution of underlying. We price some selected call options of Stocks listed on NSE by using this modified model and compare their prices with classical Black-Scholes model.

Keywords: Black-Scholes model, normal distribution, truncated distribution, options pricing, NSE.

[1]. Black F., Scholes M. (1973), The pricing of options and corporate liabilities, J. Polit. Econ. 637-654.
[2]. Peiro A. (1999), Skewness in financial returns, J. Banking Finance 23 (6) 847–862.
[3]. Rachev S. T., Menn C., Fabozzi F. J.(2005), Fat-tailed and Skewed Asset Return Distributions:Implications for Risk Management, Portfolio Selection, and Option Pricing, John Wiley & Sons, Vol. 139.
[4]. McDonald J. B., Bookstaber R. M. (1991), Option pricing for generalized distributions, Comm.Statist.Theory Methods 20 (12) 4053–4068.
[5]. Sherrick B. J., Garcia P., Tirupattur V. (1996), Recovering probabilistic information from option markets: Tests of distributional assumptions, J. Futures Mark. 16 (5) 545–560.

Abstract: Let 𝓖 be the set of all 3 X 3 non-singular matrices 𝑎𝑏𝑐𝑑𝑒𝑓𝑔𝑕𝑖 , where a,b,c,d,e,f,g,h,i are integers modulo p. Then 𝓖 is a group under matrix multiplication modulo p, of order 𝑝𝑛−1 𝑝𝑛−𝑝 𝑝𝑛−𝑝2……𝑝𝑛−𝑝𝑛−1. Let G be the subgroup of 𝓖 defined by 𝐺=𝑎𝑏𝑐𝑑𝑒𝑓𝑔𝑕𝑖∈𝓖:𝑎𝑏𝑐𝑑𝑒𝑓𝑔𝑕𝑖=1. Then G is of order 𝑝𝑛−1 𝑝𝑛−𝑝 𝑝𝑛−𝑝2 …… 𝑝𝑛−𝑝𝑛−1 𝑝−1. Let L(G) be the lattice formed by all subgroups G. In this paper, we give the structure of the subgroups of order 16 of L(G) in the case when P=3.

Keywords: Matrix group, subgroups,Lagrange's theorem,Lattice, Atom.

[1]. Bourbaki N. Elements of Mathematics, Algebra I, Chapter 1-3 Springer Verlag Berlin Heidelberg, New York, London Paris Tokio.1974.
[2]. Fraleigh. J.B, A first course in Abstract Algebra, Addison – Wesley,London, 1992.
[3]. Gardiner. C.F, A first course in group theory, Springer-Verlag, Berlin,1997.
[4]. Gratzer. G, General Lattice theory :BirkhauserVeslag, Basel,1998.
[5]. Herstien I.N, Topics in Algebra, John Wiley and sons, New York,1975.

Abstract: This research paper cracks the secret of Euclid's Fifth Postulate. Paper is based on thought experiment cognitive model of an approximation and cryptography. Locking infinity is great deal of insight, innovation and discovery. The best model finds its difficult answer and cracks the secret of Euclid's Fifth Postulate by 5 best cognitive models which are interdependent

Keywords: G105008, EUCLID'S 5th Postulate, SINGHSISTERS@LEGALSERVICES, IOSR, RESEARCH

[1]. 4th, 5thth chapter of auspicious BHAGAVAD GITA
[2]. Sunder Kaand, Hanuman Chalisa
[3]. CID - Bhootiya Hotel
[4]. Poetess Lawrence Mark Lesser
[5]. The true story of Hilbert‟s Infinite Hotel

Abstract: In this paper, we provide discrete game models controlled by a finite control set for the treatment of a widely spread disease. In this regard, we build available strategies for curing defected people with possible number of treatments, each of which emerges from a discrete model which is controlled by a finite set. More precisely, we assume that the exact spreading time for the disease is not known, namely there are some certain number of infected people at the initial time and the aim is to build a discrete controlled system which would be our treatment model limited initially in such a way that those patients receive their treatments accordingly. Hence, we consider a two-player game as one player determines the total number of infected people which is increasing day by day and the other tries......

Keywords: Kronecker's theorem, two-player games, discrete control model, infectious disease, finite control set.

[1]. Hamidoğlu A., Taghiyev M.H. and Weber G.W., On Construction of Pursuit-Evasion Games in Discrete Control Models, Appl. Comput. Math., (2020) (to appear).
[2]. Agaba, G.O. and Soomiyol M.C., Analysing the Spread of COVID-19 using Delay Epi-demic Model with Awareness, IOSR Journal of Mathematics, 16(3), (2020): pp. 52-59.
[3]. Agaba, G.O., Modelling the spread of COVID-19 with impact of awareness and medical assistance, Mathematical Theory and Modeling, 10(4), (2020): pp. 21-28.
[4]. Hamidoğlu A. and Mahmudov E.N., On Topology of Polynomial Type Sequences with Bounded Integer Coefficients, Filomat, (2020) (to appear).
[5]. Hamidoğlu A. and Mahmudov E.N., On Construction of Sampling Patterns for Preserving Observability/Controllability of Linear Sampled-Data Systems, International Journal of Control, (2020): https://doi.org/10.1080/00207179.2020.1787523.

Abstract: The purpose of this study was to analyze the influence of student motivation and behavior on learning outcomes in economics mathematics. The initial understanding of this problem will greatly support the lecturers as educators in educating prospective teachers well. In addition, education observers can also use the results of this study as a reference material in increasing student motivation and behavior. This is the main attraction for researchers to conduct a deeper study of the influence of student motivation and behavior on learning outcomes in economic mathematics courses. Specific targets to be achieved through this research are to determine the effect of student motivation and behavior on learning outcomes in economic mathematics courses, and to motivate students to the importance of taking this course in order to know the direction and purpose of the material......

Keywords: motivation, behavior, result study

[1]. Adicondro, N. & Purnamasari, A. (2011). Efikasi Diri, Dukungan Sosial Keluarga dan Self Regulated Learning pada Siswa Kelas VIII. Humanitas : Indonesian Psychological Journal. DOI: http://dx.doi.org/10.26555/humanitas.v8i1.448
[2]. Ardhana, W. 1990. "Atribusi terhadap sebab-sebab keberhasilan dan kegagalan serta kaitannya dengan motivasi untuk berpretasi". Pidato Pengukuhan Guru Besar dalam Bidang Psikologi Pendidikan pada Fakultas Ilmu Pendidikan tanggal 04 Januari 1990. Malang: IKIP Malang.
[3]. Arends, R.I. 2007. Learning to teach (7th ed.). New York: McGraw-Hill Co.motivation" towards geography lessons. Archives of Applied Sciences
[4]. Aydin, F., & Coskun, M., 2011. Secondary School Students' "achievement Research, 3 (2) 121-134.

Abstract: The most effective ways to control the transmission of most infectious diseases are vaccination and treatment, while vaccination and treatment helps to reduce the disease burden. In this papera mathematical model is formulated based on the transmission dynamics of Meningitis. The model has a locally asymptotically stable disease-free equilibrium (DFE) whenever, the basic reproduction number (ℛ0) that is a certain epidemiological threshold, is less than unity. Using a Lyapunovfunction and Lasalle Invariance Principle, it is also shown that the DFE of the co-infection model is globally –asymptotically stable (GAS) whenever ℛ0< 1. Numerical simulation indicates that the reduction of the effective contact rate and increase in the treatment rate and vaccination efficacy rate can reduce the disease burden of co-infection.

Keywords: Equilibrium, Local and Global stability.

[1]. Sáez-Llorens X, McCracken GH (June 2003). "Bacterial meningitis in children". Lancet. 361 (9375): 2139–48. doi:10.1016/S0140-6736(03)13693-8. PMID 12826449. S2CID 6226323.
[2]. H. W. Hethcote, "Tree basic epidemiological models," in Applied Mathematical Ecology, S. A. Levin, T. G. Hallam, and L. J. Gross, Eds., vol. 18 of Biomathematics, pp. 119–144, Springer, Berlin, Germany, 1989.
[3]. "Bacterial Meningitis". CDC. 1 April 2014. Archived from the original on 5 March 2016. Retrieved 5 March 2016.[4]. Chandra (2009). Transmission Dynamics of a two sex Model for Herpes Simplex Virus Type-2. Canadian Applied Mathematics Quarterly , Vol-17, Number-2.
[5]. Harrison LH (January 2006). "Prospects for vaccine prevention of meningococcal infection". Clinical Microbiology Reviews. 19 (1): 142–64. doi:10.1128/CMR.19.1.142-164.2006. PMC 1360272. PMID 16418528.

Abstract: The aim of this paper is to be a complement of a previous work published in the fall of 2019. We illustrate the relation between a truncation of theXi function in the variable z = 1-1/s to order 6 where s is the usual complex variable and the partition functionof a ferromagnetic model on a hexagon (6 spin ½ variables) with long range interaction, with a concrete look at the truth of a possible proof of the Riemann Hypothesis. Concerning Statistical Mechanics, we use an important Theorem of the last century on the locus (unit circle in z)of the zeros (z= e-2·β·H is the magnetic field variable). The content of this note illustrate in detail our previousgeneral results concerning the Riemann Hypothesis......

Key words:Classical Spin ½ model, long range interaction,Lee-Yang Theorem, truncation of the Xi function, loci of the zeros first few Li-Keiper coefficients, Riemann WaveBackground, and Riemann Hypothesis.

[1]. Many References of someimportant works on the subject have been given in our previous papers. [2]. Merlini D., Rusconi L. (2018). "Small Ferromagnetic Spin Systems and Polynomial Truncations of the Riemann ξ Function" Chaos and Complexity Letters, vol. 12 issue 2, pp. 101-122.
[3]. MerliniD., SalaM., and SalaN.,"A possible non negative lower bound to the Li-Keiper coefficients",IOSR Journal of Mathematics,Vol.15,Issue 6 (Nov-Dec 2019), p. 1-16.
[4]. Merlini D., Sala M., and Sala N., "The binomial coefficients in the Riemann Wave background.A possible proof of the Riemann Hypothesis", IOSR Journal of Mathematic, Volume 16, Issue 2 Ser. III (Mar. – Apr. 2020), pp. 22-36
[5]. Merlini D., Rusconi L., Sala N., "I numeri naturali come autovalori di un modello di oscillatori classici a bassa temperatura" (Natural numbersaseigenvalues of a model of classicallow-temperature oscillators) , in Bollettino della Società Ticinese delle Scienze Naturali, Vol. 87, n. 1-2, pp. 29 - 32, 1999

Abstract: This paper shows the role of thermodynamics and energy transfer in ecosystem growth and development and also in evolution and speciation. It also proposes a mathematical model consistent with slowed species biodiversity growth. It also shows the non- existence of a Nash Equilibrium in terms of number of species in an ecosystem before an infinity of time. This is a wonderful example of the interdisciplinarity of the sciences and mathematics. Background: All living organisms require energy to live and perform critical processes. Basis the Laws of thermodynamics, this paper proposes and supports the hypothesis that available energy for growth and development in an ecosystem is constantly increasing, slowly, but surely. This amount of energy will increase with the decrease in entropy....

Key Words: Gross primary productivity, Laws of thermodynamics, Nash Equilibrium, Food Chain, Ecosystem.: Gross primary productivity, Laws of thermodynamics, Nash Equilibrium, Food Chain, Ecosystem.

[1]. Spakovszky, P. Z. (n.d.). 5.1 Concept and Statements of the Second Law (Why do we need a second law?). Retrieved from http://web.mit.edu/: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node37.html
[2]. Khan Academy. (n.d.). Niches & competition. Retrieved from https://www.khanacademy.org/: https://www.khanacademy.org/science/biology/ecology/community-ecosystem-ecology/a/niches-competition.

Abstract: The paper investigates the behavior of the ζ-function. For the zeta function, a series representation is used. The problem of determining nontrivial zeros of the zeta function reduces to solving a system of two equations in a field of real numbers. The paper proves that the Riemann hypothesis is a consequence of the invariance of zeros with respect to symmetry transformations. The performed calculations allow us to understand the reasons for
the validity of the Riemann hypothesis.

Key Words: number theory, natural numbers, ζ-function, Riemann hypothesis. Classification code: 33E20..

[1]. Botelho Luiz C.L. An elementary comment on the zeros of the zeta function. Rio de Janeiro. Centro Brazilico de pesquisas fisices,
2008.
[2]. Gangl H. Duble zeta values and modular forms. (Preprint series). Bonn, 2005. Max-Planck Inst. fur Mathematic.
[3]. Gavrilov N.M. On the distribution of roots of Riemann ζ-functions and Dirichlet L-functions / Preprint. Kiev. Institute of
Mathematics, Academy of Sciences of Ukraine, 2001.
[4]. Gradshtein I. S., Ryzhik I. M. Tables of integrals, sums, series and products. Moscow, Publ. house "Nauka", 1962 (in Russian).
[5]. Handbook of mathematical functions. Ed. by M. Abramowitz and I. A. Stegun. Moscow, Publ. house "Nauka", 1979 (in Russian)..

Abstract: The paper gives the simple way of proving Fermat's last theorem. The proof is based on the study of the properties of natural numbers, an analysis of the constraints on the proposed solutions, and uses some general
theorems on the roots of algebraic equations..

Key Words: number theory, natural numbers, Fermat's theorem Classification code: 11D41 – Higher degree equations; Fermat equation; 11D72 – Equation in many variables.

[1]. Romanov V.N. The Method of proof of Fermat's last theorem. IOSR Journal of Mathematics, 2018, V.14, Issue 3, pp.1-5.
[2]. Romanov V.N. Approaches to the proof of Fermat's theorem. St. Petersburg, Publishing house LEMA, 2009 (in Russian).
[3]. Romanov V.N. Investigation of the fundamental problems of number theory. St. Petersburg, Publishing house "Asterion", 2015 (in Russian).
[4]. Waerdan van der B.L. Algebra. Moscow, Publishing house "Nauka", 1976 (in Russian).
[5]. Wiles A. Modular Elliptic Curves and Fermat's Last Theorem // Annals of Mathematics, 1995, Vol. 142, pp. 443-551.

Abstract: The aim of this paper is to introduce and study some weak forms of regular spaces and weak forms of normal spaces , viz. p- regular spaces , p-regular spaces , p-normal spaces and p-normal spaces by using -closed sets , -open sets ,preclosed sets and preopen sets . Also , we studied some related functions like gp-closed functions , gp-continuous functions for preserving these regular spaces and normal spaces . Mathematics Subject Classification (2010) : 54 A 05 , 54 C 08 ; 54 D 15.

Key Words: preopen sets, -closed sets, -open sets, E.D. spaces ,PS-spaces ,gp-closedness , p-continuity, -continuity, -irresoluteness, preirresoluteness.

[1]. M.E.Abd El-Monsef , S.N.El-Deeb and R.A.Mahamoud, -open sets and -continuous mappings, Bull.Fac.Sci. Assiut Univ. ,
12(1983) ,77-90.
[2]. M.E.Abd El-Monsef , R.A.Mahamoud and E.R. Lashin, -closure and -interior, J.Fac.Ed. Ain Shams Univ., 10(1986),235-245.
[3]. M.E.Abd El-Monsef , A.N.Geaisa and R.A.Mahamoud , -regular spaces,Proc. Math.Phys.Soc.,Egypt,no.60(1985) , 47-52..
[4]. M.E. Abd El-Mosef and A.M.Kozae,On extremally dixconnectedness, ro- equivalence and properties of some maximal topologies,
4th Conf.Oper. Res.Math.Methods,(Alex.Univ.,1988).
[5]. T.Aho and T.Nieminen, Spaces in which preopen sets are semiopen , Ricerche Mat., 43,no.1(1994) , 45-59.

Abstract: This paper discusses the modification of Napoleon's theorem using a nagel point on a triangle, that is, if each side of the outside of the original triangle is built, each is an isosceles triangle with a height twice the height if the triangle is equilateral. The nagel points of the three outer isosceles triangles will form a new triangle corresponding to the original triangle. This means that if the original triangle is isosceles, then the new triangle that is formed is also an isosceles triangle. Then if the original triangle is equilateral, then the new triangle formed is also an equilateral triangle. Furthermore, if the original triangle is random, then the new triangle that is formed is also an arbitrary triangle.

Key Words: Modification, Napoleon's theorem, Nagel's point, trigonometry

[1]. O. Deniz, and K. Murat. Napoleon's Theorem in Regular Polygons, inResearchgate. Istanbul University, Turkey. 2016.
[2]. Mashadi. GeometriEdisiKedua. UR Press.Pekanbaru. 2015.
[3]. Mashadi. GeometriLanjut. UR Press.Pekanbaru. 2015.
[4]. Mashadi.GeometriLanjut II. UR Press Pekanbaru. 2020.
[5]. McCartin B. J. Mysteries of The Equilateral Triangle. Hikari Ltd. Flint. 2010

Abstract: Light follows the curvature of space-time, hence when it passes around a massive object, it is bent. The speed of light depends on the gravitational potential and this bending can be viewed as a
consequence. The gravitational attraction can be viewed as the motion of undisturbed objects in a curved geometry. Background: All the observations demonstrate that the light from stars passing close to the sun is slightly bent,
so that stars appeared slightly out of position. A watcher can see various types of image of a single light source, if the light were deflected around a mass.
Materials and Methods: Manifold refers.....

Key Words: Housdorf space, Minkowskian metric, Gravitational potential, Gravitational field, Geodesic, Metric tensor,None inertial field..

[1]. Narlikar, J. V., General Relativity and Cosmology. Tata Institute of Fundamental Research, Bombay, Balaka (1978).
[2]. Foster, J. and Nightingale, J.D., A short course in General Relativity, Third Edition Springer,Brighton. ISBN-10:0-387-26078-1 (1994).
[3]. Richard, L.F., Differential Geometry and Relativity Theory an Introduction. Marcel Dekker, IN. New York and Basel, ISBN 0-8247-1749-X (1983).
[4]. Stephani, H., Introduction to Special and General Relativity, Third Edition, Cambridge Univ. Press, ISBN 0 521 01069 1, (2004).
[5]. Weinberg, S. Gravitational and Cosmology: Principles and Applications of General Theory of Relativity, Wiley York, (1972).

Abstract: In this paper we discussed the basic definitions of soft set, fuzzy soft set, fuzzy soft topological space, fuzzy soft continuous mapping and the composition of the mapping. Then we studied fuzzy soft separation axioms (𝑇0,𝑇1,𝑇2) with some of the properties.

[1]. Abdulkadir Aygunoglu,Vildan Cetkin, Halis Aygun,An introduction to fuzzy soft topological spaces,43(2),2014,197-208
[2]. Chang, C. L. Fuzzy topolocial space, J. Math. Anal. Appl. 24, 1968,182–190.
[3]. L. A. Zadeh, Fuzzy Sets, Information and Control, 8,1965, 338-353.
[4]. Maji P. K., Biswas R. and Roy A.R., Fuzzy Soft Sets‖, Journal of Fuzzy Mathematics, 9 ( 3),2011, 589- 602.
[5]. Molodtsov, D. Soft set theory-First results, Comput. Math. Appl. 37 (4/5),1999, 19-31.

Abstract: The mean reversion phenomenonis very useful in the financial markets. There are many technical Analysis tools that follow the mean reversion process. These tools are known as Technical Indicators. In this paper, we take the moving average known as Exponential Moving Average (EMA) which follows the mean reversion process and is called mean reverting indicator. To reduce the layback of EMA, we try to combine it with Parabolic Stop and Reversal Indicator (PSAR). In this paper we attempt to construct a Hybrid Strategy of EMA and PSAR. We apply this strategy on stock which is sampled using some important fundamental factors

Key Words: Mean Reversion, Technical Analysis, Fundamental Factors, PSAR, EMA

[1]. Akyıldırım, E., &Soner, H. M. (2014). A brief history of mathematics in finance. Borsa Istanbul Review, 14(1), 57-63.
[2]. Article on Mean Reversion: https://www.investopedia.com/terms/m/meanreversion.asp
[3]. Article on Mean Reversion Trading Strategy: https://decodingmarkets.com/mean-reversion-trading-strategy/ [4]. Praekhaow, P. (2010, August). Determination of trading points using the moving average methods. In International Conference for a Substation Greater Mekong Sub-Region, GMSTEC. [5]. Mitra, S. K. (2011). Usefulness of moving average based trading rules in India. International Journal of Business and Management, 6(7), 199-206.

Abstract: We consider here the sum of the first n natural numbers and their powers. In order to achieve this, we derive their summation in terms of n and with varying values of n, 1 , 2 , 3 , . . .and so on ,we obtain the sum for the first n terms.

[1]. Youse , B.K. (1970)An Introduction to Mathematics, Allyn and Bacon.

Abstract: Background: With rapid technological advancement, mankind's dealings have been greatly affected in many ways, especially in the fields of learning and teaching of mathematics and other scientifically related subjects in schools, not even talking about the occurrences in our homes, offices, market places and other employment fields. To make dealings with all these aspects of life faster and easier, calculators and other forms of calculating machines, example the computer, are used. However, the use of calculator at the basic level in any Ghanaian school is not allowed by law, either for teaching or in any form of examination. The purpose of the study was therefore to investigate whether the use of calculators in the mathematics problem-solving abilities of pupils at the basic level would enhance their learning of mathematics....

Keywords: Calculator, Basic school, Experimental group, Control group, Mathematics problem-solving abilities, Covariance, Pre-test, Post-test

[1]. Ackuaku K. An Assessment of Calculator use in three selected Senior Secondary Schools in the Cape Coast Municipality.A Project Work Presented to the Department of Science Education. University of Cape Coast, Ghana. 2002.
[2]. Agyenim-Boateng. The Effect of the Use of Hand-Held Calculators on Attitudes And Computational Skills of Second Year Students of St. Peter‟s Senior Secondary School, Nkwatia-Kwahu. A Dissertation Presented to the Department of Education. University of Cape Coast, Ghana. 1996.
[3]. Campbel P. & Stewart E. Calculators and Childhood Mathematics. NCTM Research Interpretation Project, Macmillan Publishing Company, New York. 1993; 251-268.
[4]. Cockroft W H. Mathematics Count Report on the Committee of Inquiring into the Teaching of Mathematics in Schools. (HMSO).1982.
[5]. Dessart J and Hembree R. Effect of Hand-Held Calculators in Pre-College Mathematics Education: A Mata-Analysis, Journal for Research in Mathematics Education. 1986; 16(2): 87-99.

Abstract: The basic definition of a semi-Montel space is "A locally convex Hausdorff space E is said to be a semi-Montel space if every bounded subset of E is relatively compact". Here, we take the new definition of semi-Montel space as follows : "A locally convex space E is to be semi-Montel space if every bounded subset of E has compact closure". On the basis of the above definition, we give a new characterization to the theory of semi-Montel and Montel space.

[1]. A. Grothendick : Topological vector spaces. Springler Verlag, Berlin, 1964.
[2]. Aharon Atzmon : An operator on a Frechet space with no common invariant subspace with its inverse, Journal of Functional Analysis 55-68-77 (1984).
[3]. A. Mallics : Topological Algebras : Selected Topics [North Holland Mathematics Studies 124 (1986)].
[4]. A. Rodes-Usan : Geometrical Aspects of Banach spaces, London Mathematical Society Lecture Note Series (1989).
[5]. Horvath, J. : Topological vector space and distributions, Addison Wesley, Massachusetts (1966).

Abstract: In this paper......

.....

Abstract: COVID-19 upside-down the globe. It's all affected. How we live and connect, fly and ride. How we work and communicate. Even though the world is locked up, governments, epidemiologists, Educational administrators, businessmen's and families around the world are hoping to reopen schools and businesses safely, how to fly and work safely, how to help the millions are under the crisis who have lost their livelihoods and loved ones. They'll affect people worldwide for years to come. Governments making such decisions must have the best knowledge available. During the crisis, the international statistics organisation continued to collaborate with national statistical agencies and initiatives....

Keywords: Covid-19, Catastrophic,Unprecedented, Diversifying, Enumeration Methodology,United Nations

[1]. CONGRESSIONAL RESEARCH SERVICES. (2020). Global Economic Effects of COVID-19. CONGRESSIONAL RESEARCH SERVICES, 1-112.
[2]. Peterson Ozili and Thankom Arun. (2020). Spillover of COVID-19: impact on the Global Economy. SSRN Electronic Journal, 1-28.
[3]. UNDP. (2020). COVID-19 AND HUMAN DEVELOPMENT: Assessing the Crisis, Envisioning the Recovery. 2020 HUMAN DEVELOPMENT PERSPECTIVES, 1-35.
[4]. UNTCD. (2020). COVID-19 AND TOURSIM: ASSESSING THE ECONOMIC CONSEQUENCES. UNTCD, 1-27.
[5]. Warwick McKibbin and Roshen Fernando. (2020). The Global Macroeconomic Impacts of COVID-19:Seven Scenarios. ‡ Australian National University and Centre of Excellence in Population Ageing Research (CEPAR), 1-43..

Abstract: This study investigates the effects of fluid, wellbore and reservoir characteristics on dimensionless pressure and dimensionless pressure derivatives at late time flow of a horizontal well in a bounded oil reservoir subjected to a single edge and bottom water drive mechanisms. The properties considered in this paper include the dimensionless well length, dimensionless reservoir width and dimensionless pay thickness. The main objective is achieved by using the source and Green's functions together with Newman product method. Spline functions for interpolation in curve fitting was used to plot the graphs aided by MATLAB program. Results show that the dimensionless pressure increases with decrease in dimensionless reservoir width and pay thickness. The dimensionless pressure derivative......

Keywords: Dimensionless Pressure, Bounded Oil Reservoir, Horizontal Well, Edge and Bottom Water Drive, Late Flow Period..

[1]. Wong, D.W., Harrington, A.G, and Cinco-Ley, H., "Application of the Pressure Derivative Function in the Pressure Transient Testing of Fractured Wells", SPE Formation Evaluation, SPE-13056-PA, Vol. 1(05)., pp. 470-480., October 1986.
[2]. Daviau, F., et.al., "Pressure Analysis for Horizontal Wells", SPE 14251, SPE Formation Evaluation, Vol. 5(04), pp. 716–724. https://doi.org/10.2118/14251-PA, December, 1988.
[3]. Bourdet, D., Ayoub, J.A., and Pirard, Y.M., "Use of Pressure Derivative in Well Test Interpretation", SPE Formation Evaluation., Vol. 4(02). pp. 293-302. SPE-12777-PA., https://doi.org/10.2118/12777-PA, June, 1989.
[4]. Onur, M., Yeh, N. and Reynolds, A.C., "New Applications of the Pressure Derivative in Well-Test Analysis", SPE Formation Evaluation., SPE-16810-PA., https://doi.org/10.2118/16810-PA Vol. 4(03). pp. 429 - 437., September 1989
[5]. Jelmert, T.A., "Derivative Type Curves for New Horizontal and Stimulated Wells", SPE-23574-MS.,1991.

Abstract: In this study, by using the conformal structure in Euclidean space, the conformal structures in spherical space and the equality of the internal angles and vertex points of conformal triangles in spherical space are given.
Especially in these special conformal triangles, the conformal spherical equilateral triangle and the conformal spherical isosceles triangle, the internal angles and vertices are shown..

Keywords: Conformal spherical triangle, Conformal spherical isosceles triangle, Conformal spherical equilateral triangle..

[1]. Asmus, I., Duality Between Hyperbolic and de-Sitter Geometry, Cornell University, New York, (2008) 1-32.
[2]. O'neil, B., Semi-Riemannian Geometry, AcademicPress., London, (1983) 46-49, 54-57, 108-114, 143-144.
[3]. Suarez-Peiro, E., A SchlafliDifferential Formula for Implices in Semi-Riemannian Hyperquadrics, Gauss Bonnet Formulas forSimplices in the de Sitter Sphere and the Dual Volume of a Hyperbolic Simplex, Pasicif Journal of Mathematics, 194(1) (2000) 229.
[4]. Karlığa, B., Edgematrix of hyperbolic simplices, Geom. Dedicata, 109 (2004) 1–6.
[5]. Karlığa, B., Yakut, A.T., Vertexangles of a simplex in hyperbolic space n H , Geom. Dedicata, 120 (2006) 49-58

Abstract: The present piece of work has been devoted to human circulatory system. The structure and function of pulmonary capillary has been discussed so as to develop a mathematical model in tensorial form. The resulting governing equations have been transformed in to cylindrical polar form taking in view the shape of capillaries. The relationship between blood pressure drop and hematocrit has been derived to interpret a clinical data into graphical approach...

Keywords: Pulmonary blood flow, Hematocrit, Blood pressure drop, Lung cancer

[1]. Berkow, Robert, ed. Merck Manual of Medical Information. Whitehouse Station, NJ: Merck Research Laboratories, 1997
[2]. Bessonov N., A., sequeira S. Simakov, Yu.,Vassilevskii V. Volpert; Mthods of blood flow modeling, math. model. nat.
phenom. 2016, Vol. 11, No. 1, pp. 1-25.
[3]. Fung Y.C.; Structure and Stress-Strain Relationship of Soft Tissues, AMER. Zool.,1984, Vol. 24.
[4]. Glenn Elert 2010. "Viscosity, the physics hypertext book".

Abstract: Asymptotic approximations are derived for integrals that depends on a Matrix. A matrix version analogous to Watson's lemma for scalar functions are obtained.

Keywords: Special functions; Asymptotics; Asymptotic Approximations; Asymptotic Expansions; Matrix; Gamma function of Matrices; Jordan Canonical For Watson's lemma. AMS Subject Classification: 33C05 , 33C15, 34A05, 15A60, 41A30,41A60.

[1]. Batahan R. S. Generalized Form Of Hermite Matrix Polynomials Via the Hypergeometric Matrix Function, Batahan Advances In Linear Algbra And Matrix Theory, (2014) ,4,134-141.
[2]. Carl M. Bender and Steeven A. Orszag Advanced Mathematical Methods for Scientists and Engineers (Asymptotic Methods and Perturbation Theory ) Springer- Verlag New York,Inc,(1999).
[3]. Defez E. and J´odar, L. Some Applications of the Hermite Matrix Polynomials Series Expansions, Journal Of Computational Applied Mathematics 99, 105-117, (1998).
[4]. Defez E. , and J´odar L. Chebyshev Matrix Polynomials And Second Order Matrix Differential Equation. Utilitas Mathematica, (2002). 61. 107-123.

Abstract: We establish a number of properties of the dyadic rational numbers associated with surreal number theory. In particular, we show that a two parameter function of dyadic rationals can give all the trees of n-days in surreal number formalism.

......

Abstract: A generalization of beta distribution is theDirichlet distribution.It is commonly used in various fields, such asthe categorical response modeling and prior distribution in Bayesian statistics. The distribution of Dirichlet belongs to the conjugate family and to multinomial and categorical distributions prior to it. In this case, the previous model of the adverse effect of ArtesunateAmodiaquine in Nigeria was adapted as the Dirichlet distribution. The reactions are divided into three: the neurologicaleffect, musculoskeletal effect and the and the dietary effect.Through the MCMC Gibbs Sampling techniques, we determine the posterior density.The posterior estimate for neurological adverse incidents encountered is close to 28.8 percent, 43.5 percent for the Musculoskeletal and 27.7 percent for the Dietary effect, from the findings using symmetric Dirichletprior. Using the previous distribution of the Non-Symmetric Dirichlet, the neurological adverse effectsencountered by the patients taking malarial medication is 24.9 percent, for the Musculoskeletal effect about 40.3 percent of the patients were observed and 34.8 percent is for the Dietary effect.

Keywords: Bayesian Modelling,Dirichlet Prior, MCMC, Gibbs Sampling

[1]. Anthony O'Hagan. (1994). Advanced Theory of Statistics Bayesian Inference, 1st Edition
[2]. Antti Penttinen and Robert Piche'. (2010). Bayesian Method, University of Jyvaskyla, MT51706, 78pp
[3]. Bassi PU, Osakwe AI, Isah A, Suku C, Kalat M, Jalo I, Wammanda RD, Ugochukwu C, Adesina O, Nyong AA, Osungwu F, Pal S, Nwoasu SC, Walllberg M, Coulter D. Safety of Artemisinin-Based Combination Therapies in Nigeria: A Cohort Event Monitoring Study. Drug Saf. (36): 747-756
[4]. Cogdon. P (2003). Applied Bayesian Modelling. London, John Wiley and Sons, Ltd. 465pp.
[5]. D Nicholas Bateman. (2003). Clinical Pharmacology Medicine on CD-ROM, Medicine Publishers. 50pp.

Abstract: In the production process of all kinds of electronic products such as integrated circuit board, the temperature setting of each temperature zone of the reflow furnace and the setting of the passing speed of the
conveyor belt are very important to the quality of the electronic components heated in the reflow furnace.The temperature change ofWelding area is analyzed and studied by mathematical method in order to reveal the law
of temperature change of Welding area and provide theoretical basis for the study of optimal furnace temperature curve.In this paper, the mathematical model is established by the heat conduction equation, and the
temperature change of the welding area is analyzed, so as to obtain the optimal temperature setting of each temperature zone and the furnace passing speed of the conveyor belt under certain conditions.

Keywords: heat conduction equation，partial differential equation,nonlinear programming

[1]. Feng Zhigang, Yu Dingwen, Zhu Yunhe. Effect of reflow parameters on temperature curve [J]. Electronic technology,2004,25(6):243-246,251.
[2]. Cai Haitao, Li Wei, Wang Hao. Study on temperature curve control of reflow soldering [J]. Microprocessor,2008,29(5)：24-26.
[3]. Zhuo Jinwu. Application of MATLAB in mathematical modeling [M]. Beijing University of Aeronautics and Astronautics Press, 2014
[4]. Jiang Qiyuan, Xie Jinxing, ye Jun, mathematical model (Fourth Edition), Beijing: Higher Education Press, 2011.1.

Abstract: In this paper,using A.Rosenfeld [1] definition of fuzzy group,we have tried to establish some independent proof of fuzzy group homomorphism and anti fuzzy group homomorphism

Keywords: Fuzzy subgroup,Fuzzy point,anti fuzzy subgroup.

[1]. A.Rosenfeld.: Fuzzy group. J.Math.Anal.Appl.35,512-517 (1971).
[2]. S.Sebastian and S.Babunder. Fuzzy groups and group homomor phism.Fuzzy sets and systems.8,397-4'1 (1996).
[3]. S. Abou-zaid, On fuzzy subgroup, Fuzzy sets and systems,55. 1993, pp. 237–24'.
[4]. N.Ajmal and A.S.Prajapati,Fuzzy cosets and fuzzy normal subgroup, Inform.Sci, 64 (1992) 17-25.
[5]. R.Biswas,Fuzzy subgroup and anti fuzzy subgroup.Fuzzy sets and systems.35,121-124 (199').

Abstract: In Mathematics, the wreath product of groups is a specialized product of two groups, based on a semi direct product. Factorization of wreath product seems to be nice source of examples, it may be interesting to investigate their nature in a systematic way and also its basic properties connected with the properties of factorization of each constituent.

Key Words: Wreath Product, Factorization, Constituent, Zappa-Szip product, Exact

[1]. Achaku, D. T and Abam A. O, (2016). Properties of Permutation Groups using Wreath Product. International Journal of Mathematical Research, 5(1): 58-62
[2]. Alice, M. (2007). Distinguishing sets under Group Actions, The wreath product Action. Paper on Algebra1-10.
[3]. Apine E. (2015). On Application of Transitive permutation Groups to wreath product. Mathematical theoryand modelling 5(1):2224-5804.
[4]. Audu, M. S. (2001). Wreath Product of Permutation Group. A research Oriented Course in Arithmetic of Elliptic Curves, Groups and Loops, Lecture Notes Series, National Mathematical Centre, Abuja.
[5]. Beata B. and Vitality S, (2014). On a factorization of an iterated Wreath Product of Permutation Groups. Journal of Algebra and Discrete Mathematics,18(1): 14-26.

Abstract: In this paper we introduce a relationship between curve evolution and the soliton equations in Minkowski 3- space in case of space-like curve with space-like principal normal.
MSC: 53A05, 53A17.

Key Word: Moving space curve; Minkowski 3-space; Soliton equations

[1]. Ablowitz M.J. and Segur H.; Solitons and the inverse scattering transformation, SIAM, Philadelphia, 1981.
[2]. Ablowitz, M.J., Kaup, D.J., Newell, A.C. and Segur, H.; The inverse scattering transform-Fourier analysis for nonlinear problem ,
Stud. Appl. Math. 53, (1974), 249-315.
[3]. Balakrishnan, R. and Murugesh, S.; Kinematics of the three moving space curves assoiated with the NLS equation , Theor. Math.
Phys. 133, (2002), 1609-1618.
[4]. Bishop, R.L.; There is more than one way to frame a curve , Amer, Math, Monthly 82, (1975), 246-251.
[5]. ] chern, S.S. and Tenenblat, K.; Pseudospherical surfaces and evolution equations , Stud. Appl. Math. 74, (1986), 55-83.
[6]. Ding, Q.; A note on the NLS equation and the Schrödinger flow of maps , Phys. Lett. A 248, (1998), 49-56.

Abstract: Background: In general, a lot of discussion on the line for discussing the angle bisector, in this paper will discuss about the angle trisector (a line that divides an angle into three equal parts). The discussed is about the side lengths of the angular trisector and the ratio of the area of the corner trisector formed from each corner of the triangle. The proof is done using a very simple method, namely by using the concept of the height line on the triangle and the trigonometric ratio of the triangle.

Keywords: Angle trisector, The side length of the trisector,Comparison of the area of the trisector triangle.

[1]. Amarasinghe, G.W. I. S. On the standard lengths of angle bisector and the angle theorem, Global Journal Of Advanced Research on Clasical and Modern Geometries. 2012:15-27.
[2]. Barutu, F. A. Mashadi, dan S. Gemawati.Pengembanganteorema Morley padasegiempat, Global Journal of Advanced Research on Classical and Modern Geometries.2012;15-27.
[3]. Conway, J. On Morley's Trisector Theorem, The Mathematical Inteligencer, 36 (2014), 3.
[4]. Donolato, C. A Verctor-based proof of Morley trisektor theorem.Forum Geometricorum.2013;(13): 233-235.
[5]. Husna, R, Mashadidan S. Gemawati., Morley's theorem outer trisektor on triangle and isosceles trapezoid. . Internasional Journal of Current Advancesd Research. 2019;18(5):18778-18780

Abstract: An appropriate constructive planning is the most important key to a success of production system. This paper is to describe problems in production planning using the combination of forecasting methods and linear goal programming for decision making. Both methods are used to predict sales of bakery products and to determine the best and most efficient product combinations to achieve multi goals. Forecasting methods implemented are the single exponential smoothing, double exponential smoothing, and triple exponential smoothing. Then the three methods are compared in order to choose the best forecasting method by selecting the method having the smallest MSE value. Furthermore,the best.....

Keywords: Forecasting, Exponential Smoothing, Linear Goal Programming

[1]. O.S. Balogun, E.T. Jolayemi, T.J. Akingbade, and H.G. Muazu, Use of linear programming for optimal production in a production line in Coca-cola bottling company, Ilorin, International Journal of Engineering Research and Applications, 2 (2012), 2004-2007.
[2]. N. de P.Barbosa, E.da S.Christo, and K. A. Costa, Demand forecasting for production planning in a food company, ARPN Journal of Engineering and Applied Sciences, 10 (2015), 7137-7141.
[3]. N. Hassan and Z. Ayop, A goal programming approach for food productdistribution of small and medium enterprises, Advances in EnvironmentalBiology, 6 (2012), 510-513.
[4]. J. P. Ignizio, Introduction to Linear Goal Programming, Sage Publications, NewburyPark, 1985.
[5]. D. Kumar and K. Sridhar, Multi objectives operations decision by usinggoal programming for a small scale enterprise, International Journal ofResearch in Engineering and Technology, 4 (2016), 7-12.

Abstract: This paper discusses the Economic Ordering Quantity (EOQ) for multi-item deterministic inventory. Deterioration happens to each item when the constraints of shortage capacity are active. Then, Lagrange method is used to determine the EOQ of this case. The main purpose of this model is to determine the time cycle with and without backorder, as well as the amount of optimal shortage so as to minimize the total inventory cost. It is show that the developed model has the effective time cycle with minimum cost..

Keywords: EOQ; deteriorating item; multi-item; shortage; Lagrange method.

[1] Bakker M, Riezebos J and TeunterRH. Review of inventory systems with deterioration since 2001, European Journal of Operational Research. 2012; 221: 275-284.
[2] Cheng TCE. An economic order quantity model with demand-dependent unit cost. European Journal of Operational Research. (1989); 40: 252-256.
[3] Covert RB and Philip GS. An EOQ model with Weibull distribution deterioration. AIIE Transactions. 1973; 5: 323 - 326.
[4] Dave U and PatelLK. (T,Si) policy inventory model for deteriorating items with time promotional demand. Journal of the Operational Research Society. 1981; 32: 137-142.
[5] Ghafour KM, Ramli R, and Zaibidi NZ. Development of multi-items EOQ when the constraints of investment and shortage capacity are active.AIP Conference Proceedings. 2015; 1691: 030005

Abstract: The cooling systems of automobiles influence the design of the frontal part of a car, the fuel consumption and the performance of its engine. In this study, Ethylene-Glycol based nanofluids with copper and Alumina as the nanoparticles are considered as coolants. The steady viscous flow of the electrically conducting liquids is considered to be along a heated vertical plate which imitates the flow of a coolant in a car radiator. The transformed boundary layer equations are non-dimensionalized using appropriate similarity variables and solved using the fourth order Runge-Kutta method coupled with a shooting technique. The influence of pertinent parameters on velocity profile, temperature profile, concentration profile, skin friction and Nusselt number are investigated and the results analyzed graphically using MATLAB.The results obtained were in good agreement with the actual flow dynamics.Al2O3-Ethylene glycol based nanofluid had the highest skin friction while Cu-Ethylene glycol based nanofluid had higher heat and mass transfer rates.

Key Word: MHD; Dissipative; Nanofluid; similarity variable

[1] O. D. Makinde and P. O. Olanrewaju, "Buoyancy Effects on Thermal Boundary Layer Over a Vertical Plate With a Convective Surface Boundary Condition," vol. 132, no. April, pp. 1–4, 2010, doi: 10.1115/1.4001386. [2] S. Desale and V. H. Pradhan, "Numerical Solution of Boundary Layer Flow Equation with Viscous Dissipation Effect Along a Flat Plate with Variable Temperature," Procedia Eng., vol. 127, pp. 846–853, 2015, doi: 10.1016/j.proeng.2015.11.421. [3] B. K. Jha, M. O. Oni, and B. Aina, "Steady fully developed mixed convection flow in a vertical micro-concentric-annulus with heat generating/absorbing fluid: An exact solution," Ain Shams Eng. J., vol. 9, no. 4, pp. 1289–1301, 2018, doi: 10.1016/j.asej.2016.08.005. [4] K. B. Lakshmi, G. S. S. Raju, P. M. Kishore, and N. V. R. V. P. Rao, "The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Diffusion Flow Past A Surface," vol. 5, no. 4, pp. 17–28, 2013. [5] B. Amami, H. Dhahri, and A. Mhimid, "Viscous dissipation effects on heat transfer, energy storage, and entropy generation for fluid flow in a porous channel submitted to a uniform magnetic field," no. February 2016, 2014, doi: 10.1615/JPorMedia.v17.i10.10.

Abstract: We say that a regular graph G of order n and degree r ≥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers τ and θ such that |Si ∩ Sj | = τ for any two adjacent vertices i and j and |Si ∩ Sj | = θ for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Using a method for constructing the magic and semi-magic squares of order 2k + 1, we have created two infinite classes of strongly regular graphs (i) strongly regular graph of order n = (2k + 1)2 and degree r = 8k with τ = 2k + 5 and θ = 12 and (ii) strongly regular graph of order n = (2k + 1)2 and degree r = 6k with τ = 2k + 1 and θ = 6 for

..............

Abstract: .....

[1]. Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Uni¨. Mariae CurieSklodowska Sect. A
[2]. J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Aci. Fenn. Ser. A I Math.
[3]. P. L. Duren, A survey of harmonic mappings in the plane, Texas Tech. Uni¨. Math. Ser. 18 Ž . 1992
[4]. T. Sheil-Small, Constants for planar harmonic mappings, J. London Math. Soc.
[5]. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51.