iosr-Jm   Volume-15 ~ Issue-6 ~ Nov – Dec 2019

Abstract: In this paper, association rules, logistic regression model and ARMA model are established for reflecting the internal factors of influencing the Pediatric Pneumonia. It is concluded that age, delivery, feeding style, current address and normal physical condition have significant influence on Pediatric Pneumonia. The prediction results showed that the change trend of the predicted value is basically consistent with that of the actual number.

Keywords: Pediatric Pneumonia, association rules, logistic regression, ARMA model

[1]. Seyed Mohssen Ghafari,Christos Tjortjis. A survey on association rules mining using heuristics[J]. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery,2019,9(4).
[2]. Hanzhu Xing, Effects of haze air exposure on bronchial pneumonia control in children[J]. Primary Medical Forum, 2015,19(33):4630-4631.
[3]. Sijing Yu, Jun Zheng, Using COX regression analysis to explore the influencing factors of pediatric pneumonia[J]. Practical Preventive Medicine, 2001(04):306-307.
[4]. Yan Liu, Ying Wang, Impact of climate factors on pediatric pneumonia[J].Heilongjiang Medicine,2000(03):78-79.
[5]. Guoguang Zhao.Investigation on the clinical characteristics and prognostic factors of children with streptococcal meningitisin different age groups[J].Armed Police Medicine ,2018,29(03):229-232.

Abstract: By using the invariance principle, we are proving Yang Mills theory exists on R4 and Has a Mass Gap Delta > 0 by the formula Pr (A). As we know – Einstein's two postulates –
I. Physical laws are the same in all frames of reference. That is; any event with in apportion of space (a frame) can be specified by three spatial dimensions (east – west, north – south, up – down) and one temporal dimension (time). Also, the laws that apply to us in everyday circumstances (such as Newton's Laws) also apply within each frame of reference. II. The speed of light is constant Energy = mass x the speed of light squared......

Key Words: Yang Mills, R4, Mass Gap Delta, Gauge Group

[1]. Research Paper, Counter Examples to Riemann Hypothesis, Ekta Singh, Director , Nyaysangat Foundation, published in IOSR Journal of Mathematics, e –ISSN: 2278 -5728, p-ISSN 2319 – 765x, Volume 15, Issue 5, Series III (Sep – Oct 2019)
[2]. Clay Mathematics Millenium Problem.
[3]. Research Paper, Updated Examples to Riemann Hypothesis, Author Ekta Singh, Director, Nyaysangat Foundation, published in IOSR Journal of Mathematics
[4]. GOD is logically Exist Author Ekta Singh, Director, Nyaysangat Foundation, published in IOSR Journal of JAC.
[5]. Research Paper, A NEW IDEA ON TIME TRAVEL IS MORE THAN MERE FANTASY, Author Ekta Singh, Director, Nyaysangat Foundation, published in IOSR Journal.

Abstract: Abacus is a method of numerical calculation with abacus as a tool, which is known as the fifth invention. Abacus teaching is not only an exercise of computing skills, but also an all-round improvement of students' quality through the coordinated action of various organs to promote the healthy education of brain. This paper studies the curriculum standard of Korean primary school and the setting of abacus in primary school mathematics, and analyzes the important role of abacus in children's intelligence development and mathematics learning.

Key Words: abacus; interest; teaching aids.

[1]. S Tanaka, C Michimata, T Kaminaga et al． Superior digit memory of abacus experts: an event related functional MRI study. Neuroreport, 2002, 13: 2187－2191.
[2]. T Hanakawa, M Honda, T Okada et al． Neural correlates underlying mental calculation in abacus experts: a functional magnetic resonance imaging study. Neuroimage, 2003, 19: 296－307.
[3]. Jean Piaget. Genetic epistemology. New York:W.W. Norton & Company, 1970.
[4]. Juan Wang. How to explore the potential of students in the teaching of abacus mental arithmetic. Educational theory research. 2019 (01): 48
[5]. Philip S. Cho, Wing Chee So. A feel for numbers: The changing role of gesture in manipulating the mental representation of an abacus among children at different skill levels. Frontiers in Psychology, 2018; 9:1267.

Abstract: This study proposes a three components survival mixture model of Gamma distribution. The performance of the model was investigated using simulated survival data. The data were simulated based on two different sets of mixing proportion arranged in ascending and descending order with three different censoring proportions (10%, 20% and 40%). The Expectation Maximization (EM) Algorithm was used to estimate the maximum likelihood estimates of the model parameters. The hazard functions of each of the censoring proportions were investigated graphically. The parameters of the model were estimated successfully and they were all close the initial values used in generating the data. Three hundred times repetitions of the simulation were run. The mean square error.....

Keywords: Gamma; Proportion; Survival function; Mixture model; Expectation maximization

[1]. Ibrahim, J. G., Chen, M. H., Sinha, D., Bayesian survival analysis. New York: Springer-verlag.ISBN 0-387-95277-2.
Jiang, S., Kececioglu, D., 1992a, Graphical representation of two mixed-Weibull distributions. IEEE Transaction on Reliability, vol. 41, 2001, 241-247, 2001. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=257789 10.1109/24.257789
[2]. Kalbfleisch J. D., Prentice R. L., The statistical analysis of failure time data (2nd ed.). John Wiley & Sons, Inc. Hoboken, New Jersey. 2002, ISBN 0-471-36357-X.
[3]. Lawless J. F., Statistical models and methods of lifetime data, (2dn ed.). John Wiley and Sons, Inc. Hoboken, New Jersey. 2003, ISBN 0-471-37215-.
[4]. Lee, E. T., Wang, J. W., Statistical methods for survival time data analysis (3rd ed.). John Wiley & son. New Jersey.,2003, ISBN 0-471-36997-7.
[5]. Jiang, S., Kececioglu, D., Graphical representation of two mixed-Weibull distributions. IEEE Transaction on Reliability, vol. 41, 1992, 241-247. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=257789 10.1109/24.257789

Abstract: The concept of fuzzy chromatic polynomial 𝑃𝛼𝑓 𝐺,𝑘 of a fuzzy graph 𝐺 based on 𝛼-cuts of 𝐺 was introduced by Mamo and Srinivasa Rao. The authors studied the concept on a fuzzy graph whose vertex set is crisp and fuzzy. In this paper, we present some properties of fuzzy chromatic polynomials of fuzzy graphs by relating to their coefficients and chromatic roots. Related results are proved.

Keywords: Fuzzy graph; Fuzzy chromatic polynomials; Coefficients; Chromatic roots

[1]. G.D. Birkhoff, "A determinant formula for the number of ways of coloring a map," Annals of Mathematics, 1912, 14: 42-46.
[2]. H. Whitney, "The colouring of graphs," Annals of Mathematics, 1932, 33: 688-718.
[3]. R.C. Read, " An introduction to chromatic polynomials," Journal of Combinatorial Theory, 1968, 4: 52-71.
[4]. C.H. Meredith, "Coefficients of Chromatic Polynomials," Journal of Combinatorial Theory (B), 1972, 13: 14-17.
[5]. E. J. Farrell, "On chromatic coefficients," Discrete Mathematics, 1980, 29: 257-264.

Abstract: In this paper, the steady flow between two parallel plates and a laminar flow between two parallel walls has been studied. This paper also includes how the Navier stoke's equation is compulsory for steady flow and oil flow between two parallel plates, one of which is at rest and other moves with a certain velocity. The case study for plane Couette flow, plane Poiseuille flow and generalized plane Couette flow have been discussed with different plate conditions when (i) Lower plate is stationary while the upper is moving with uniform velocity U, parallel to x-axis in case of Couette flow. (ii) When both the walls are at rest in the case of plane Poiseuille flow and (iii) In generalized plane Couette flow case 𝑑𝑝𝑑𝑥=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, the lower plate is at rest while the upper is in motion with velocity U.

Keywords: Fluid flow Reynolds number, plates, Couette flow, Poiseuille flow, walls etc.

[1]. Berman A.S. Laminar flow in channels with porous walls. Journal of Applied Physics, 1953, v. 24, 1232
[2]. Sellars J.R. Laminar flow in channels with porous walls at high suction Reynold number. Journal of Applied Physics, 1955, v. 26, 489
[3]. Yuan S.W. Further Investigation of Laminar Flow in Channels with Porous Walls. Journal of Applied Physics, 1956, v. 27(3), 267–269.
[4]. Choi JJ, Rusak Z, Tichy JA. Maxwell fluid suction flow in a channel. J Non-Newton Fluid Mech 1999;85:165–87.
[5]. Rosenhead L. Laminar boundary layers. Oxford: Clerendon Press; 1963.

Abstract: As the desire to attend graduate school grows, educators need to ensure students are well prepared for the rigors of a graduate program. To help ensure student readiness, academic institutions impose prerequisites to help foster academic success. However, requiring an excessive number of prerequisites could lead to unnecessary prolongation of time and money needed to graduate. In non-STEM programs, it's not uncommon for a graduate statistics course to have a mix of students who have and have not completed an undergraduate statistics course. This variability in students' previous coursework can make teaching and learning difficult.The purpose of the present study was to investigate the influence of an undergraduate statistics course on graduate course success in a sample of non-STEM graduate students. Fifty-three graduate students from a public university in the southeastern.....

Keywords: Mathematics curriculum; non-STEM mathematics curriculum; Academic performance, undergraduate statistics, graduate statistics

[1]. Abou-Sayf, F.K. (2008). Does the elimination of prerequisites affect enrollment and success? Community College Review, 36(1), 47-62.
[2]. Ajayi, K.O., Lawani, A.O.,& Adeyanju, H.I. (2011). Effects of Students' Attitude and Self-Concept on Achievement in Senior Secondary School Mathematics in Ogun State, Nigeria. Journal of research in national development, 9(2), 202-211.
[3]. Arismendi-Pardi, E. (1997). Comparison of the Final Grades of Students in Calculus for Business, Management, and Social Sciences with and without a Prior College Algebra Course. (Doctoral dissertation). Retrieved from https://files.eric.ed.gov/fulltext/ED405924.pdf.
[4]. Aron, A., Coups, E.,&Aron, E.N. (2012).Statistics for Psychology (6th ed.). Upper Saddle River, NJ: Pearson.
[5]. Ashcraft, M.H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185

Abstract: This work presents two computational semi-analytic methods for solving a class of two dimensional partial-intgro differential equations of fractional order.The fractional order derivative is described in Caputo sense. First, existence of a unique solution under certain condition is proved.Then,the ADM and HAM are employed to derive a general solution for the mentioned problem and the convergence analysis of the proposed methods is investigated.Finally, some examples are included for demonstrated the efficiency of the proposed methods..

Keywords: Caputo fractional order derivative, partial Integro-differential equations, Homotopy Analysis, Adomian decomposition Method.

[1]. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, "Theory and Applications of Fractional Differential Equations", Elsevier, (2006).
[2]. F. Hecht, T. Jangveladze, Z. Kiguradze and O. Pironneau, "Finite Difference Scheme for One System of Nonlinear Partial Integro-Differential Equations", Applied Mathematics and Computation, 328, 287-300, (2018).
[3]. K. Kumar, R. K. Pandey and S. Sharma, "Comparative study of Three Numerical Schemes for Fractional Integro-Differential Equations", Journal of Computational and Applied Mathematics, Accepted (2016).
[4]. Mohammed. OH., "A Direct Method for Solving Fractional Order Variational Problems by Hat Basis Functions", Ain Shams Eng. J. http://dx.doi.org/10.1016/j.asej.2016.11.006. (2016).
[5]. Podlunny I., "Fractional Differential Equations", Academic Press, (1999).

Abstract: This study investigates the fluid flow and transport in a vertical channel with an exponentially decaying suction and mobile wall. The governing equations are derived based on the assumptions of incompressible flow with buoyancy forces and viscous dissipation. A finite-difference scheme is formulated and implemented. The numerical results are presented graphically. The results show that the increase in Brinkman number, Suction Parameter and Prandtl number increase the temperature distribution, while the increase in Thermal Grashof number, Mass Grashof number and Suction parameter increase the flow velocity..

Keywords: Finite difference scheme, Heat and Mass Transport, Couette flow, Unsteady Suction and Mobile wall, Viscous Dissipation

[1]. Ammhalhel, G., & Furmanski, P. (1997). Problems of Modeling Flow and Heat in Porous Media. Journal of power Technologies, 85, 55-88.
[2]. Amos, E., Amadi, C.P., Nwaigwe, C. (2019). Free Convection Boundary Layer Flow of a Rotating MHD Fluid Past a Vertical Porous Plate with Thermal Radiation. International Journal of Applied Science and Mathematical Theory, 2(5), 1-12.
[3]. Attia, H.A., Abbas, W., Abdeen, M.A, & Saod, A.A. (2015). Heat Transfer Between two Parallel Porous Plates for Couette Flow under Pressure Gradient and Hall Current. Sadhana, 40(1), 183-197.
[4]. Chein, K.Y. (1982). Predictions of Channel and Boundary-Layer Flow with a Low-Reynolds-Number Turbulence Model. AIAA Journal, 20(1), 33-38.
[5]. Da Silva, A.K., & Bejan, A. (2005). Constructal Multi- Scale Structure for Maximal Heat Transfer Density in Natural Convention. International Journal of Heat and Fluid Flow, 26(1), 34-44.