International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 16 No. 2or Keyword in Title:
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Table of Content for Vol. 16 No. 2, 2018

Bayesian Analysis of Average Age Prevalence of Hypertensive Patients in South Western Part of Nigeria
Olawale Basheer Akanbi
 PP. 76 - 86
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ABSTRACT: Hypertension is a non-communicable disease which is mostly related to age distribution and is rampant in Nigeria. One is likely to develop high blood pressure as long he is getting older. This paper was aimed to determine the average age that one is likely to develop hypertension in Ibadan North Local Government (IBLG). Bayesian Inference was used to analysis this problem. Both uniform and Normal priors were used for the probability update. The month that had the highest number of cases was January and the minimum was recorded in November. It was also observed that 862 (73.4%) of hypertensive patients in the IBLG were female while 312 (26.6%) of them were male. Age group with the highest case was between (52 and 61) years (29.1%) while only one person (0.1%) fell in the age group of 92years and above. The classical estimate, the posterior means for uniform and conjugate priors were (53.5, 53.4 & 53.7) years respectively. The 95% credible interval for the age using conjugate prior was [47.23, 60.17]. It was recommended that an informative normal prior and normal likelihood should be considered for analysing average age prevalence of hypertensive patients in IBLG.

Modified Ratio Estimators Using Coefficient of Skewness of Auxiliary Attribute
Tolga Zaman
 PP. 87 - 95
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ABSTRACT: This paper proposes some ratio estimators for population mean using known skewness coefficient of auxiliary attribute. Theoretically, it is obtained mean square error (MSE) equations for all proposed estimators. The efficiency between the suggested estimators and some known estimators is compared. The theoretical findings are also supported by a numerical examples using original data sets.

Compartmental Model to Study Calcium Distribution in Oocytes
Parvaiz Ahmad Naik
 PP. 96 - 105
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ABSTRACT: Ca2+ plays an important role in the cellular processes. It is important to master the ability to develop model. Modelling of dynamic systems plays a very important role in applied sciences. Compartment models are among the most important tools used for analysing dynamical systems. Ca2+ is considered as second messenger in communication process. Ca2+ distribution in oocytes helps in oocyte maturation. Considering the importance of the Ca2+, in the present paper an attempt has been made to develop a mathematical model to study the effect of various parameters on Ca2+ distribution in oocytes during the fertilization process. The main objective of the paper is to study the effect of buffers, Ca2+ channels and Ca2+ pumps on the intracellular Ca2+ concentration distribution in the oocyte cell.

Solution of System of Viscous Burgers’ Equation via Collocation Method
Hamad Mohammed Salih, Luma Naji ohammed Tawfiq, Zainor Ridzuan Yahya
 PP. 106 - 123
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ABSTRACT: This paper presents a new approach to solve one dimensional system viscous Burgers’ equation with boundary conditions Dirichlet type using collocation method based on cubic trigonometric B-spline. The usual finite difference scheme is applied to discretize the time derivative. Cubic Trigonometric B-spline basis functions are used as an interpolating function in the space dimension. Two test problems are presented to confirm the accuracy and efficiency of the new scheme and to show the performance of trigonometric basis functions. The numerical results are found to be in good agreement with known exact solutions and also with earlier studies.

Application of the Method of Lines to Parabolic Nonhomogeneous Initial Condition
Rajesh Kumar Shukla and Dinesh Kumar
 PP. 124 - 134
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ABSTRACT: In this paper we study a parabolic problem with nonhomogeneous initial condition. We apply the method of lines popularly known as the Rothe method to establish the existence and uniqueness of weak solution.

Effect of Crude Oil Spot Prices: A Markov Switching Intercept and Heteroscedasticity Approach
Ayoola, F.J. and Olanrewaju, R.O
 PP. 135 - 147
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ABSTRACT: In this work, we examine the switching of market value of Nigeria crude spot oil classification prices of West Texas Intermediate (WTI), Bonny Light (BL), Brent (BR) and Market Average (MA) via Markov Switching Intercept and Heteroscedasticity (MSIH) as their returns significantly contribute to the financial market and Nigeria economy. The result showed that MSIH (2)-AR (1) was the ideal explanation for the volatility spillover of two Markov switching at lag-one on the All Share Index between years 2001 to 2016. A higher transition probability of (0.3768) was estimated in the second regime, this indicated a fluctuating financial market activities (ASI) via the non-stable returns benchmarks of exchange trade while a lower transition probability of (0.0763) in the first regime compared with a lower transition probability of (0.0763) in the first regime with a more stable returns from benchmarks of exchange trade of the crude oil.

Extensive Quantum Theory with Different Quantum Constants, and Its Applications
Yi-Fang Chang
 PP. 148 - 164
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ABSTRACT: First, according to Feynman’s idea and based on a new form of the Titius-Bode law, we can develop a similar theory with the Bohr atom model, and obtain the quantum constants of the solar system and corresponding Schrödinger equation. Some exoplanets and ten satellite galaxies of Galaxy, etc. agree with the same form. Next, we propose the extensive quantum theory and its three laws: 1. Extensive quantum is its element in any system. 2. Its theory has similar quantum formulations with different quantum constants H. 3. Evolutions of systems may be continuous, but stable states are quantized. Its mathematical base is fractal. Using the geometric average method, three different values of the quantum constants of man, cell and macromolecule may be derived for biological, chemical and physical discrete systems with different scales. Third, we researched superconductivity, superfluidity, Bose-Einstein condensation (BEC), and various macroscopic quantum phenomena by this theory. Fourth, we search the extensive quantum biology and its application in DNA. Fifth, extensive quantum theory and macro-microscopic fractals are discussed. Finally, we research the extensive quantum theory in social sciences, in which the social entangled states and exclusion is discussed. This theory agrees with symmetry and its violation as first principle of physics.