International Journal of Mathematical Research

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Online ISSN: 2306-2223
Print ISSN: 2311-7427
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No. 1

Upgraded Harmony Search Algorithm for Solving Optimal Reactive Power Dispatch Problem

Pages: 42-52
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Upgraded Harmony Search Algorithm for Solving Optimal Reactive Power Dispatch Problem

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DOI: 10.18488/journal.24/2015.4.1/24.1.42.52

Citation: 2

K. Lenin , B. Ravindhranath Reddy , M. Suryakalavathi

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K. Lenin , B. Ravindhranath Reddy , M. Suryakalavathi (2015). Upgraded Harmony Search Algorithm for Solving Optimal Reactive Power Dispatch Problem. International Journal of Mathematical Research, 4(1): 42-52. DOI: 10.18488/journal.24/2015.4.1/24.1.42.52
In this paper, a new-fangled Improved harmony search algorithm (IHS) is projected to solve optimal reactive power dispatch problem. Harmony search (HS) is a derivative-free tangible parameter optimization algorithm. It draws encouragement from the musical improvisation process of searching for a perfect state of harmony. The projected opposition-based HS of the present work employs opposition-based learning for harmony memory initialization and also for generation jumping. The perception of opposite number is employed in IHS to improve the convergence rate of the HS algorithm.   The proposed IHS has been tested on standard IEEE 57 bus test systems and simulation results show clearly the better performance of the proposed algorithm in reducing the real power loss.
Contribution/ Originality
This study uses new estimation methodology-Opposition based Harmony search algorithm to solve the Reactive power dispatch problem. The main aim is to reduce the Real Power loss and also to maintain the voltage profiles within the specified limits.

A Steady MHD Boundary-Layer Flow of Water-Based Nanofluids over a Moving Permeable Flat Plate

Pages: 27-41
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A Steady MHD Boundary-Layer Flow of Water-Based Nanofluids over a Moving Permeable Flat Plate

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DOI: 10.18488/journal.24/2015.4.1/24.1.27.41

Citation: 9

Eshetu Haile , B. Shankar

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  1. A. B. Ahmadreza, "Application of nanofluid for heat transfer enhancement," PID: 2739168, EEE-5425, 2013.
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Eshetu Haile , B. Shankar (2015). A Steady MHD Boundary-Layer Flow of Water-Based Nanofluids over a Moving Permeable Flat Plate. International Journal of Mathematical Research, 4(1): 27-41. DOI: 10.18488/journal.24/2015.4.1/24.1.27.41
A steady boundary-layer flow of water based nanofluids over a moving permeable surface were analyzed. The plate was assumed to move in the same or opposite direction to the free stream. The model describing the flow regime characterizes the Sakiadis and Blasius flow scenarios. The PDEs in the governing equations were transformed into ODEs with the help of similarity transformations. The transformed equations were solved numerically by the shooting method with Runge-Kutta integration scheme. Effects of the governing parameters were thoroughly studied and explicitly explained graphically and in tabular form. Numerical results of the velocity field, temperature distribution, skin friction and Nusselt number were obtained. The results were compared with previous works and they are found in excellent agreement.
Contribution/ Originality
For further applications, new improvements of the models of Motsumi and Makinde [15] were made by including uniform magnetic field and Ohmic effects. Accordingly, the paper briefly explains effects of the various governing parameters on velocity and temperature profiles, skin friction and wall heat transfer rate for both Blasius and Sakiadis flow situations. 

The Importance of Computers with Matlab Software in the Teaching and Learning of Geometry in Space

Pages: 16-26
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The Importance of Computers with Matlab Software in the Teaching and Learning of Geometry in Space

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DOI: 10.18488/journal.24/2015.4.1/24.1.16.26

Lupu Costica

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  1. C.-V. Muraru, Matlab - guide study. Bacau: Publisher Edusoft, 2006.
  2. C. Lupu, "The contribution of the new technologies to learning mathematics," Procedia - Social and Behavioral Sciences, vol. 128, pp. 240-245, 2014.
  3. C. Lupu, "The efficiency of computer use geometric, representation and problem solving of the concurrence," International Journal of Innovation in Science and Mathematics, ISSN (Online), vol. 2, pp. 2347–9051, 2014.
  4. V. Postolic?, E. Nechita, and C. Lupu, "The Romanian mathematics and informatics education," British Journal of Education, Society & Behavioural Science, vol. 4, pp. 226-240, 2014.
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Lupu Costica (2015). The Importance of Computers with Matlab Software in the Teaching and Learning of Geometry in Space. International Journal of Mathematical Research, 4(1): 16-26. DOI: 10.18488/journal.24/2015.4.1/24.1.16.26
The aim of this study is to evaluate the efficiency of using computers with MATLAB software in the teaching-learning of Geometry in middle-school, by the students from the specialization of Mathematics, “Vasile Alecsandri” University of Bacau. During the pedagogical practice stage, the students in the 3rd year, although better trained in Mathematics than the students from other departments,  face various problems related to their practical skills in using the computer in teaching, as well as to their lack of teaching experience.
The research was conducted at the National Pedagogical College “Ştefan cel Mare” from Bacau and consisted in assisting and observing 28 lessons of Mathematics and 28 lessons of Information and Communication Technologies, involving a group of 200 students from grades 1-4, 180 middle-school students and 40 teachers of various specializations. 
The applied tests and questionnaires have shown the efficacy of using the computer in building active thought and competences in the graphical representation of geometrical figures and shapes, as well as in solving problems of plane collinearity. In relation to these problems, we are looking for a solution to comprise the best teaching-learning strategies using the calculus technique. 
With nearly 5000 functions, the MATLAB software menu provides techniques for acquiring knowledge in an electronic format, calculus techniques, explanatory mathematical texts, graphs, sounds and diagrams, e-learning solutions, including online testing and evaluation, as well as web-based learning tools designed for Mathematics (www.maplesoft.com).

Contribution/ Originality
This study contributes in the existing literature mathematics teaching. This study uses new estimation the statistical methodology. This study originates new formula for solving the problems. This study is one of very few studies which have investigated the importance MATLAB.  The paper contributes the first logical analysis to optimize teaching activity. 
The paper’s primary contribution is finding that modern methods. This study contains original modern documents.

Alternative Way of Statistical Data Analysis: L-Moments and Tl-Moments of Probability Distribution

Pages: 1-15
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Alternative Way of Statistical Data Analysis: L-Moments and Tl-Moments of Probability Distribution

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DOI: 10.18488/journal.24/2015.4.1/24.1.1.15

Citation: 2

Diana Bilkova

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  1. J. R. M. Hosking, "L-moments: Analysis and estimation of distributions using linear combinations of order statistics," Journal of the Royal Statistical Society (Series B), vol. 52, pp. 105–124, 1990.
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  3. K. Adamowski, "Regional analysis of annual maximum and partial duration flood data by nonparametric and l-moment methods," Journal of Hydrology, vol. 229, pp. 219–231, 2000.
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Diana Bilkova (2015). Alternative Way of Statistical Data Analysis: L-Moments and Tl-Moments of Probability Distribution. International Journal of Mathematical Research, 4(1): 1-15. DOI: 10.18488/journal.24/2015.4.1/24.1.1.15
This paper deals with an alternative method to characterize some probability distribution, i.e. L-moments and TL-moments. Moments and cumulants were commonly used for this purpose before. Moment method of parameter estimation is indeed very simple, but it is very inaccurate, especially if there are the moments of the third or higher order. These problems mainly occur in the case of small samples. Maximum likelihood method has been considered as the most accurate method of parameter estimation for a long time. Using the method of L-momednts gives more accurate results than using the maximum likelihood method in many cases when estimating parameters of probability distribution. The method of TL-moments brings still more accurate results than the method of L-moments. This paper deals with these three methods of parameter estimation and with the comparison of their accuracy. Three-parametric lognormal curves constitute basic probability distribution. They were used as the model distribution of income in the Czech Repubublic in 1992, 1996, 2002 and 2004−2007.
Contribution/ Originality
This study contributes in the existing literature and it develops the theory of estimation of parameters of continuous probability distributions in the case of large economic data sets. This study originates some new formulas, proofs and derivations, which were not published at all. This study is one of very few studies which have investigated the use of the method of TL-moments on economic data.