iosr-Jm   Volume-12 ~ Issue-2 ~ Mar-Apr 2016

Abstract: Step 1: Find the value of a∙c.Step 2: Find the divisors of the value of a∙c, where not required all divisors of the value of a∙c, if you feel find all divisors, then you can find.Step 3: Choose two numbers from divisors of the value of a∙c of which multiplication should be equal to the value of a∙c, and sum or difference should be equal to the value of b. Step 4: Change the sign of both chosen numbers. Step 5: Divide the both numbers by the value of a.

Keywords: Divisors and coefficents

[1]. Mathematics Textbook for class 10th of National Council of Educational Research and Training.
Chapters in books
[2]. Quadratic Equation

Abstract: In this paper, the well known duplication formula for the cosine is used as a veritable tool to analyse the chaotic behaviour of two classical non- linear maps. The results are then extended to certain polynomial functions of higher dimensions which are related to the Chebyshev polynomials as well as to certain rational functions closely related to the duplication formulas of the circular and Jacobian elliptic functions..

Key words: Absorbing States, Absorbing Markov Chain, Transition Rates, Dropout Rates, Completion Rates, Fundamental Matrix

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Abstract:The aim of this paper is to develop a fractional order implicit finite difference scheme for two-dimensional space-time fractional diffusion equation. We also prove that the scheme is unconditionally stable and convergent. As an application of this scheme numerical solution for two-dimensional space-time fractional diffusion equation is obtained with the help of Mathematica software.
Keywords: Finite difference scheme, Space-Time fractional diffusion equation, Mathematica.

[1]. A. P. Bhadane, K. C. Takale, Basic Developments of Fractional Calculus and its Applications, Bulletin of Marathwada Mathematical Society, Vol. 12, No. 2, p. 1-17 (2011).
[2]. J. Chen, F.Liu, Stability and Convergence of an Implicit Difference Approximation for space Riesz fractional reaction-dispersion equation,(2007).
[3]. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore (2000).
[4]. Junichi Nakagawa, Kenichi Sakamoto and Masahiro Yamamoto, Overview to Mathematical Analysis for Fractional Diffusion Equations New Mathematical Aspects Motivated by Industrial Colladoration, Journal of Math-for-Industry, Vol.2 (2010A-10), pp.99-108.

Abstract:This paper gives a transformation formula for composite Appell's hypergeometric functions of two complex variables which satisfy an integer Pfaffian system. These functional equations for  1, c 1 are established.
Keywords: arithmetic–geometric mean, hypergeometric function- - Pfaffian system -composite.

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Abstract:This paper study initial value problem for a class of hyperbolic equation with variable coefficients.Similar to finding D' Lambert formulaofstring vibrating equation, we decompose the hyperbolic differential operator first, and then reduce thesolution of hyperbolic equation to the solution of characteristic lines.
Keywords:Hyperbolic equation with variable coefficients, Initial value problem, Characteristic line, D' Lambert formula

[1]. LishangJiang,Yazhe Chen, XiyuanLiu. Intrduction of mathematical physics equations (the second edition) [M]. Beijing: Higher
Education Press, 2003.(In Chinese)
[2]. E. DiBeneddetto, Degenerate Parabolic Equations, New York: Springer-Verlag, 1993.
[3]. ChaohaoGu,Daqian Li, ShuxingChen. Mathematics physics equation (the third edition) [M]. Beijing: Higher Education Press,
2012.(In Chinese)
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Press, 2006.(In Chinese)

Abstract:Qingdun is a kind of Poker game originated from Zhoushan city, Zhejiang province, It's a component of local distinctive culture[1].But some rules of the game is still incomplete. We see there is no references in the probability calculation about complex poker in most of literature. .In this paper, we mainly research probability of some card type......
Keywords: Qingdun , probability ,simulate , prior probability, posterior probability

[1]. Zhang Tongkuan, the Research of Zhoushan Qingdun Sports,Sports Culture Guide,2011,(5) :32-35.
[2]. Chen Wei,Division Thought Event in Probability Theory and It Application,COLLEGE MATHEMATICS, 2011, 27(2) :159-161
[3]. Mao Shisong,Cheng Yiming,Pu Xiaolong,probability theory and mathematical statistics, Second Edition. Beijing: Higher Education Press, Feb 2011 :32-39 .
[4]. Chen Si, Research on programming algorithm based on poker probability, Science&Technology Vision, 2013 (14) :38-40.
[5]. Sha Xiuyan,Xin Jie,Teaching practice and exploration in probability theory and mathematical statistics,COLLEGE MATHEMATICS, 2013, 29(4) : 9-12

Abstract: 3 + 5 + 7 + 9 + 11 + 13 is a summation series of six integers in arithmetic progression. If we put the sign of equality (=) between 9 and 11 replacing the plus sign (+) then we find: 3 + 5 + 7 + 9 = 11 + 13. The paper describes the general forms of such equalities and their amazing properties.

Keywords: integer; summation; identity; arithmetic progression.

[1]. Arithmetic and geometric progressions, http://www.mathcentre.ac.uk. [2]. Arithmetic Sequences and Series, http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm

Abstract: Bifurcation control has gained increasing attention in the last decade. This paper makes an attempt to highlight a simple and unified state-feedback methodology for developing Hopf bifurcation linear or nonlinear controls for continuous-time systems. The control task can be either shifting an existing bifurcation or creating a new one. Some numerical simulations are included to illustrate the methodology and verify the theoretical results.
Keywords: Eigenvalues, Hopf bifurcation, Control.

[1]. G. Chen , K. Yap and J. Lu, "Feedback Control of Hopf Bifurcation " IEEE Trans. on Circ. pp. 639-641,1998.
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Abstract:In 1993, Satyanarayana [8] has defined generalized hypergeometric functions through p q; ;(a ) H (x,w) n; ;(b )    by using difference operator technique. In this paper we established unification of several multilateral generating relations of certain special functions has been established through a bilateral generating relation for generalized hypergeometric functions, p q ; ;(a ) H (x,w) n; ;(b )   .

[1]. Deepa Agrawal, A Pseudo Orthogonal Modified Version of Jacobi Polynomials, Ph.D. Thesis, Banaras Hindu
[2]. University, Varanasi, 1992.
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[4]. operator, Soochow J. Math.,19(1993), 163-171.
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Abstract: This study aimed to investigate the impact of the use of Geogebra software on the academic achievement and visual thinking skills for eighth-grade students. To achieve the objectives of the study, the researcher used the quasi-experimental design, in which the study tools consisted an achievement test and a test for visual thinking skills applied to a sample of 70 eighth grade students, by which it was distributed evenly over two groups (experimental and control group).......
Keywords: Geogebra software ; Academic achievement; Visual thinking skills.

[1]. Abu Thabet, Ajtaad Abdel Razek Hamed (2013). The effectiveness of using Geogebra software and teaching aids in the immediate and delayed achievement of the basic ninth grade students in mathematics in public schools in Nablus, Master Thesis, School of Graduate Studies, An-Najah University, Palestine.
[2]. Balawi, Ayed (2012). A training program based on interactive programs in teaching and learning of mathematics, Ph.D. thesis unpublished, Umm Al Qura University, Saudi Arabia.
[3]. Al-Jasser Saleh Mekheled (2011). The impact of using software based on Geogebra software on the achievement of sixth-grade students in mathematics from elementary school in Arar, Ph.D. thesis is published, the College of Education, Umm Al Qura University, Makkah.
[4]. Hamada, Ahmed (2006). The impact of using educational computer games in teaching Geometry unit on the development of achievement and visual thinking of the fifth graders in math, unpublished Master Thesis, University of Alexandria, Egypt.

Abstract: In this paper paper we present a delay differential equation model for the dynamics between proliferating cells and quiescent cells. This model includes the positivity and boundedness of the solution. Stability has been investigated for trivial and nontrivial steady states. We analyze the sensitivity on performed parameters for the dynamical system. Using He's variational iteration method to obtain approximate solutions for the given dynamical model.

[1]. P. Krishnapriya, M. Pitchaimani, Optimal control of mixed immunotherapy and chemotherapy of tumours with discrete delay,
International Journal of Dynamics and Control, Springer-Verlag Berlin Heidelberg, DOI 10.1007/s40435-015-0221-y (2016).
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Abstract: In this article, a new method of analysis of the second order multivariable state-space and singular systems using Leapfrog method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the second order multivariable state-space and singular systems has been considered and the solutions were obtained using methods taken from the literature [8] and Leapfrog method........
Keywords:Differential equations, system of differential equations, second order multivariable state-space and singular systems, Single-term Haar wavelet series, Leapfrog Method.

[1]. C. W. Gear, ―Numerical initial value problems in ordinary differential equations‖, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1971.
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Abstract: Receiver Operating Characteristic (ROC) Curve is one of the renowned statistical techniques to assess the accuracy of a diagnostic test to discriminate between healthy and diseased subjects. In this paper, two component Normal-Mixture ROC curve is studied and its properties are discussed to know the characteristics of the ROC Curve. Area under the Curve (AUC) of Normal-Mixture ROC Curve and Confidence Interval of AUC are also derived. The proposed model is validated by using the simulation studies. Keywords: Normal-Mixture distribution, ROC Curve, AUC, Confidence Interval of Area Under the ROC Curve, MLE of AUC of ROC Curve via Expectation Maximization (EM) algorithm and Monte Carlo simulation.

[1]. Newcomb S. (1886), A generalized theory of the combination of observations so as to obtain the best result, Amer. J. Math., 8, 343-346.
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Abstract: Design thinking is a recognized method for practical, inventive resolution of problems. It gives easy and workable solutions when applied properly. One needs keen observations and a creative eye for details to apply design thinking. It creates an intent for improved future result. In this regard it is a form of solution-based, or solution-focused thinking. It is based on well-formed goals and objectives by considering both present and future conditions and parameters of the problem, alternative solutions in most cases are explored simultaneously. Progressive firms all over the world are keen to use design thinking and are making an effort to use it.
Keywords: Way of thinking, Indira Nooyi, PepsiCO, Mauro Porcini, Six Sigma, IDEO, Design-led innovation

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