iosr-Jm   Volume-18 ~ Issue-3 ~ May – Jun. 2022

Abstract:This work studies the effects of changes in the initial investments on the dividends of two competing investors in the stock exchange undergoing competition. The ODE 45 numerical scheme was used. The results of our analysis showed that with exceptionally high equal initial investment values of the two investors competing over some specific trading periods, the dividends of the first investor were dominantly higher than that of the second investor. Our results will be useful in the stock exchange investment planning. This has great implication for the socio-economic development of the country..

Key words:Initial Investment, dividends, ODE 45, Competing Investors, trading period, stock exchange, socioeconomic development

[1]. Cajueior, D.O., Tabak, B.M. and Werneck, F.K. (2009). Can we predict crashes? The cases of Brazilian stock market. Physica A. 388, 1603-1609.
[2]. Chiang, S.Y., Wong, G.G., Li, Y. and Yu, H.C. (2003). A dynamics competition analysis on the personal computer shipments in Taiwan using Lotka-Volterra model: IEE Asia Pasific Services Computing Conferences, 3, 1412-1417
[3]. Khamis, S.A., Tchuench, J.M., Lakka,M. and Heilio, M. (2011). Dynamics of fisheries with Pre-Reserve and Harvesting. International Journal of Computer Mathematics, 88(8), 1776-1802
[4]. Khodabin, B. and Shekarabi, F.H. (2016). Numerical solutions of stochastic Lotka-Volterra Equations via operational matrices. Journal of International and Approximation in Scientific Computing, 1, 37-42
[5]. Lakka, S. Michalakelis, C., Varoutas, D. and Martakos, D. (2013). Competitive dynamics in the operating systems market: Modeling and policy implications, Technological Forecasting and Social Change, 8, 88-105.

Abstract: Modeling of bounded outcomes within given intervals is continuously gaining wide applications in various fields as with engineering, economics and health sciences. Major applications have been on the usage of the Beta distribution first introduced by Ospina & Ferrari who used the beta law to define the continuous component of the distribution. This study gives an application of an extension of the Beta distribution incorporating a Bayesian Inference to model the proportion of household expenditure on education in the arid and semi-arid area of Kenya, a case of Isiolo County. The Bayesian Zero/One Inflated Beta Regression model is used in which the household head levels of education, age of household head, household size, household asset value and the distance to an educational facility by a household were evaluated. Data used for the study was secondary data obtained from the......

[1]. S.L.P. Ferrari and R. Ospina, "A general class of zero-or-one inflated beta regression models," Computational Statistics and Data Analysis, vol. 56, no. 6, pp. 1609-1623, 2011.
[2]. Government of Kenya (GoK), Vision 2030 Development Strategy for Northern Kenya and other Arid Lands, Government of Kenya, 2012, https:www.ndma.go.ke.
[3]. Z. Danuta, S. Agnieszka and K.K. Agnieszka, "Application of logistic regression model to assess household financial decisions regarding debt," Procedia Computer Science, Vol. 176, no. 1, pp. 3418-3427, 2020.
[4]. S.P. Danielle, A.G. Terezinha, J. Vanderly, MOG, Aline et al, "Modeling the incidence of citrus canker in leaves of the sweet orange variety," Acta Scientiarum, Vol. 39, no. 1, pp. 1-8, 2017.
[5]. D.R. Bahadar, K.M. Abdul and A. Akhter, "Household energy consumption and its determinants in timor-leste," Asian Development Review, Vol. 34, no. 1, pp. 167-197, 2017

Abstract: Understanding of mathematics is both theoretical and practical that requires adequate instructional materials for effective teaching and learning process. Instructional materials helps pupils to interact with concrete objects or situations directly thereby enhance the pupils understanding of the concepts and the development of positive interest in the subject. Instructional materials are information carriers designed specifically to help fulfill objectives in teaching learning situation. Instructional materials are objects of study that act as stimuli for the learners. Significantly, there may be a link between the use of instructional materials and effective teaching and learning of mathematics in basic education. Against this backdrop, the paper examined the concepts of mathematics and instructional materials......

Keywords: trends, production of instructional materials, mathematics, mathematics teaching, lower basics education, teaching materials

[1]. Achimugu, L. and Onojah, P.K. (2017). Factors hindering effective production and utilization of teacher-made instructional materials in teaching senior secondary Chemistry in Federal Capital Territory, Abuja, Nigeria. International Journal of Scientific Research in Education, 10(2), 352 – 361
[2]. Aminu, D.K. (2005). "Mathematics as a discipline-its usefulness in relation to life", Abacus, 30(1), pp 46 – 50 s
[3]. Brown, H. (2015). Predicting class learning. America Educational Research Journal,7(2), 301 – 320.
[4]. Cronbach, L. (2009). Teaching tool in secondary school. New York: Macmillan Publishing Co. Inc
[5]. Effiong, O.E. and Igiri, C.E. (2015). Impact of instructional materials in teaching and learning of Biology in senior secondary schools in Yakurr Local Government Area. International Letters of Social and Humanistic Sciences

Abstract: In this paper, we introduce the concepts of neutrosophic beta omega locally indiscrete space, neutrosophic weakly hausdorff spaces, neutrosophic ultra hausdorff spaces and analyze the properties of these spaces. Furthermore, we have defined neutrosophic beta omega T0, neutrosophic beta omega T1, neutrosophic beta omega T2 and neutrosophic beta omega normal spaces. We also have studied the concept of neutrosophic almost beta omega continuous mapping.

Keywords: neutrosophic beta omega T0, neutrosophic beta omega T1, neutrosophic beta omega T2, neutrosophic beta omega normal, neutrosophic almost beta omega continuous mapping

[1]. Anitha S, Mohana K, Florentin Smarandache, "On NGSR Closed Sets in Neutrosophic Topological Spaces", Neutrosophic Sets and Systems, Vol. 28, pp.171-178(2019).
[2]. Arokiarani R, Dhavaseelan S, Jafari, Parimala M, "On Some New Notions and Functions in Neutrosophic Topological Spaces", Neutrosophic Sets and Systems, Vol.16, pp.16-19(2017).
[3]. Atkinswestley A, Chandrasekar S, "Neutrosophic Weakly G∗-,Closed Sets". Advances in Mathematics: Scientific Journal, Vol.9, pp.2853-2864(2020).
[4]. Banu Priya V, Chandrasekar S, Suresh M, "Neutrosophic α generalized semi homeomorphisms", Malaya Journal of Mathematik, Vol.8, pp.1824-1829(2020).
[5]. Blessie Rebecca, S, Francina Shalini A, "Neutrosophic Generalized Regular Sets in Neutrosophic Topological Spaces", IJRAR Feb 2019, Vol.6, Issue (2019

Abstract: Collatz conzecture a theorem that can be understood not only Mathematician but a standard one student who does know only some operations like summation , multiplication and divison .But it can't be proved by abstractly many decades .In this paper I'm going to represent this millennium proof with single number theory that can be understood every body And I'm 100% sure it is an unique Proof and the simplest proof like the simplest problem . This proof is less that 1 page !! But it's value is

Keywords:Collatz Conzecture Number theory

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Abstract: In this paper we have discussed the odd sum labeling of grid graph, path union of grid graphs with different size, graph obtained by joining vertex of a grid graph and a complete bipartite graph by a path, step grid graph and the graph obtained by joining step grid graphs of different size by arbitrary paths.

Keywords: Odd sum labeling, odd sum graph, grid graph, step grid graph, path union.

[1]. Rosa A. On certain valuation of the vertices of a graph. Theory of Graphs (Rome, July 1966), Gordon and Beach. N.Y. and Paris. 1967; 349–355.
[2]. Gallian JA. A dynamic survey of graph labeling. The Electronic Journal of Combinatorics. 2021; 24: # DS6.
[3]. Arockiaraj S, Mahalakshmi P. On odd sum graphs. International Journal of Mathematical Combinatorics. 2013; 4: 58–77.
[4]. Arockiaraj S, Mahalakshmi P, Namasivayam P. Odd sum labeling of some subdivision graphs. Kragujevac Journal of Mathematics. 2014; 38(1): 203–222.

Abstract: In this paper we assume that Hardy's inequality on a Skew-symmetric function. In general, it has much better constants. This enables us they depend on the lowest degree of spherical harmonics Skew-symmetric polynomial. We prove the existence of Hardy inequalities on the class of a Skew-symmetric function. In addition, we find some conditions for specific Schrödinger operators in Skew-symmetric functions that do not have nonpositive eigenvalues. Then we discuss some cases of Caffarelli-Kohn-Nirenberg inequalities and apply our results to spectral properties of Schrödinger operators

Keywords: Skew-symmetric function, Holder's inequality, Hardy inequality, Caffarelli-Kohn-Nirenberg inequality..

[1]. L. Caffarelli, R. Kohn, and L. Nirenberg, "First order interpolation inequalities with weights", Compositio Math., 53:3 (1984), 259–275.
[2]. Yu. V. Egorov and V. A. Kondrat_ev, On Spectral Theory of Elliptic Operators, Operator Theory: Advances and Applications, no. 89, Birkh¨auser, Basel, 1996.
[3]. A. Laptev and T. Weidl, "Hardy Inequalities for Magnetic Dirichlet Forms", Operator Theory: Advances and Applications, no. 108, Birkh¨auser, Basel, 1999, pp. 299–305.
[4]. M. Sh. Birman, "On the spectrum of singular boundary-value problems", Mat. Sb., 55(97):2 (1961), 125–174; English transl.: Amer. Math. Soc. Trans., 53 (1966), 23–80.
[5]. A. A. Balinsky, W. D. Evans, and R. T. Lewis, "On the number of negative eigenvalues of Schr¨odinger operators with an Aharonov–Bohm magnetic field", Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci., 457:2014 (2001), 2481–2489.

Abstract: The main aim of the present study is to optimize the availability and profit of cement manufacturing plant using genetic algorithm and particle swarm optimization. For this purpose, a mathematical model has been developed using Markovian birth-death process. The differential-difference equation has been optimized by GA and PSO. In cement manufacturing plant various subsystems arranged in series structure. Sufficient repair facility always available with plant. All time dependent random variables are statistically independent and exponentially distributed. The repairs are perfect. Numerical and graphical results have been obtained to highlight the importance of the study.

Keywords: Cement Manufacturing Plant, Genetic Algorithm, Particle Swarm Optimization, Availability

[1]. Saini M and Kumar A (2019) Performance analysis of evaporation system in sugar industry using RAMD analysis. J Braz Soc Mech Sci Eng 41:4
[2]. Kumar, A.Goyal, D., Saini, M., Joshi. H. (2019). Reliability, maintainability and sensitivity analysis of physical processing unit of sewage treatment plant. SN Appl. Sci. 1: 1507. https://doi.org/10.1007/s42452-019-1544-7
[3]. Kumar A, Saini M (2018) Fuzzy availability analysis of a marine power plant. Materials Today: Proceedings. 5 (11P3): 25195-25202.
[4]. Dahiya O, Kumar A, Saini M (2019) Mathematical modeling and performance evaluation of A-Pan crystallization system in a sugar industry. SN Applied Sciences, https://doi.org/10.1007/s42452-019-0348-0
[5]. Gupta, N., Saini, M. & Kumar, A. Operational availability analysis of generators in steam turbine power plants. SN Appl. Sci. 2, 779 (2020). https://doi.org/10.1007/s42452-020-2520-y

Abstract: We use reverse geometry to determine a geometric magnitude what allows us to show how the square that circumscribe the given circle determine the square whose area is equal to that of the given circle.

Keywords: Pi, area, circle square

[1]. F. Lindemann, Über die Zahl , Mathematiche Annalen 20, 213-225, 1882.
[2]. Rd Sarva Jagannadha Reddy, New Methods of computing value (Siva methods), IOSR Journal of Mathematics (IOSR-JM), e-ISSN: 2278-3008, p- ISSN, 2319-7676. Vol. 10, Issue 1 ver IV (feb 2014), pp48-49. www.iosrjournals.org
[3]. Durga Methods of squaring a circle
IOSR Journal of Mathematics (IOSR-JM), e-ISSN: 2278-5728, p- ISSN, 2319-765. Vol. 10, Issue 1 ver IV (feb 2014), pp14-15. www.iosrjournals.org
[4]. Alcantara Montes S. and Gonzalez Sanchez A., A remark on squaring the circle, IOSR Journal of Mathematics (IOSR-JM), e-ISSN: 2278-5728, p- ISSN, 2319-765. Vol. 17, Issue 5 ver II (Sep-Oct 2021), pp22-24. www.iosrjournals.org
[5]. S. Ramanujan, Squaring the circle, Journal of the Indian Mathematical Society, V, 1913, 132.

Abstract: The well-known single parameter Geometric Distribution arising in the context of Bernoulli Trials has the negative exponential pattern for the underlying probability distribution and is generally considered suitable for individual non-life insurance policies. Portfolios covering a large number of policies pertaining to individual portfolios are likely to require different patterns for the number of claims. In the following Sections, we suggest a Multi-parametric Discrete Probability Distribution holding potential for Exponential, Negative Exponential, Double Exponential, Uniform, Peaked, and U-shaped patterns. While Modular Expressions are suggested for the end-user for the VGD, Explicit Expressions are obtained for the Characterizers' - Mean, Variance, and Median of the Simple Variants.

Keywords: Non-Life Insurance Portfolio. Probability Distribution of the Number of Claims. VGD- Versatile Geometric Distribution. Simple Variants of VGD. Contextual Characteristics of VGD and its Variants

[1]. Y. P. Sabharwal and S. Pal, "Equispaced Discrete Finite Range Geometric Distribution," The Actuary, 2000.
[2]. W. Feller, Introduction to the Theory of Probability and its Applications, Volume 1, 3 ed., New York: Wiley Series in Probability and Statistics, 1968

Abstract: The concept of mathematics laboratory has become very popular in recent years. This study investigated the effect of Mathematics Laboratory on the perception of mathematics and how this affects female students performance in the subject. A total of 150 SSS1 students were involved in the study. Results of this study were analyzed using the mean, standard deviation and analysis of co- variance (ANCOVA). The findings revealed that the use of mathematics laboratory positively altered the perception of SSS1 female students to mathematics. The results also revealed that there is a significant difference in the performance of female student to mathematics taught with mathematics laboratory. This study recommends the following; That every school should have a mathematics laboratory at its grass root (i. e Kindergarten, Nursery, Primary), secondary to tertiary levels; the mathematics laboratory should be introduced in mathematics curriculum by NERDC and NABTEB; Mathematics students teachers should be tutored.......

Keywords: (Science, Technology and Mathematics) STM,

[1]. Ahiven, R. (1970). Women and Work: Social attitudes and Women's careers. Impact on Science and Society. Xx (i) 73-81.
[2]. Obodo G.C. (2004). "Principles and Practice of Mathematics Education in Nigeria Floxtoine press, Enugu.
[3]. Okereke S.C. (2006). Effects of prior knowledge of Implications of Mathematical tasks/concepts to career types and gender students' achievements. In G.A. Badmus and C.O. Ocho (Eds.).Science Mathematics and Technology Education in Nigeria Lagos. Eves lead press.
[4]. Okigbo C.E. and Osuafor M.A. (2008). Effects of using Mathematics Laboratory in teaching mathematics on the achievement of mathematics students. Educational research and review vol.3 (8). Pp257- 261. http//ww.academicjournals.org/eRR.
[5]. Srinivasa N. (1978): A laboratory for teaching Mathematics: JSTAN 9(1):22-24.

Abstract:An analysis is made on the three dimensional free convection and mass transfer flow through a vertical channel in the presence of radiation in slip flow regime. The solutions have been obtained using perturbation technique. It is seen that the primary velocity decreases with increase in Schmidt number, slip parameter and radiation parameter for cooling of the plate . It is found that the primary velocity increases with increase in Reynolds number but for higher Reynolds number it decreases. The primary velocity also increases
with increase in mass Grashoff number. The temperature distribution decreases with the increase of both radiation parameter and Reynolds number. The Concentration field also decreases with the increase of both Schmidt number as well as Reynolds number..

Keywords: Three-dimensional, injection, periodic suction, mass transfer, transpiration, free convection

[1]. Takhar H S., Gorla R S R, Soundalgekar V.M.(1996). Radiation effects on MHD free convection flow of a radiating gas past a semi-infinite vertical plate . Int J Numer Math Heat Fluid Flow, 6(2), 77-83.
[2]. Guria M, Ghara N and Jana R.N.(2010). Radiation effect on three dimensional vertical channel flow. International Journal of Applied Mechanics and Engineering, 15(4), 1065-1081.
[3]. Guria, M, Ghara, N, Jana, R.N.(2011). Radiation effect on three dimensional MHD flow past a vertical porous plate. Journal of Physical Sciences. 15, 161-170.
[4]. Ahmed S.(2008). Free and forced convective three-dimensional flow with heat and mass transfer. International Journal of Pure and Applied Mechanics, 5(1), 26-38.
[5]. Ahmed S, Liu, IC.(2010). Mixed convective transient three dimensional heat and mass transfer flow with transversely periodic suction velocity. International Journal of Applied Mathematics and Mechanics, 6(1), 58-73.