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Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
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Volume 9 Issue 1 January - June 2020

Research Paper

An In-Depth Model for Determining Teaching Efficacy through the use of Qualitative Single Subject Design, Student Learning Outcomes, Associative Statistics, and Mixed Methods Post Hoc Data Analysis Methodology

James Edward Osler II* , Mahmud Mansaray**

*-** North Carolina Central University, Durham, North Carolina, United States.

Osler, J. E., II. and Mansaray, M. (2020). An In-Depth Model for Determining Teaching Efficacy through the use of Qualitative Single Subject Design, Student Learning Outcomes, Associative Statistics, and Mixed Methods Post Hoc Data Analysis Methodology. i-manager's Journal on Mathematics, 9(1), 1-17. https://doi.org/10.26634/jmat.9.1.17400

Abstract

Many universities and colleges in the United States and elsewhere are increasingly concerned about enhancing the comprehension and knowledge of their students, particularly in the classroom. One method of enhancing student success is teaching effectiveness. The overarching objective of this research paper is to propose a novel research model that examines the relationship between teaching effectiveness and student learning outcomes qualitatively and then analyzes the outcomes of the researcher further using a mixed method data analysis methodology. This new model will first use a unique and in–depth qualitative case study methodology especially designed for the instructional setting. The anticipated qualitative initial data collecting techniques will include but not be limited to the following: observations, personal interviews, qualitative survey questionnaires, research field notes, document review, etc. The secondary data analysis model will use the mixed methods (Qualitative and Quantitative) Triostatistics Tri–Squared Test to further validate the research investigation outcomes. The initial data gathering qualitative model uses assumed data and applied statistical Cross–Tabulation and Chi–Square Tests, including a theoretical analysis of the open–ended responses and field notes recorded from participants (a sample of 32 students presently enrolled in a Semester–long English ENG 1200–01 course at a public university in North Carolina). The associative statistical findings found a positive relationship between teaching effectiveness and student learning. The outcomes of this study will increase the current lack of information on the use of qualitative and mixed methods research designs in determining teaching efficacy and its effects on student achievement in the social and behavioral sciences. This new model expands on existing measures by providing new measures to more carefully examine teaching effectiveness and its effect on student learning.

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Research Paper

On I2-Cauchy Double Sequences in Fuzzy N-Normed Spaces

Muhammed Recai Turkmen *

Department of Mathematics, Faculty of Education, Afyon Kocatepe University, Afyonkarahisar, Turkey.

Turkmen, M. R. (2020). On I2-Cauchy Double Sequences in Fuzzy N-Normed Spaces. i-manager's Journal on Mathematics, 9(1), 18-27. https://doi.org/10.26634/jmat.9.1.17735

Abstract

In this paper, the concepts of I₂ -Cauchy, I₂* -Cauchy double sequences in fuzzy n-normed spaces were introduced and some properties and relations of them were studied. We show that if a double sequence (x_mr) in X is an I₂* -double Cauchy sequence, then it is I₂ -double Cauchy sequence, where I₂ denotes the ideal of subsets of N×N.

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Research Paper

Bernstein Tau Method for Bessel and Diffusion Equations

V. Appala Naidu* , G. V. S. R. Deekshitulu **

* Department of Mathematics, Government College for Men, Kadapa, Andhra Pradesh, India.

** Department of Mathematics, University College of Engineering Kakinada, Kakinada, Andhra Pradesh, India.

Naidu, V. A., and Deekshitulu, G. V. S. R. (2020). Bernstein Tau Method for Bessel and Diffusion Equations. i-manager's Journal on Mathematics, 9(1), 28-37. https://doi.org/10.26634/jmat.9.1.17604

Abstract

Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. The aim of the present paper is to solve the higher-order linear differential and partial differential equations using Bernstein operational matrix of differentiation and Tau method. The nature of simplicity and efficiency of numerical technique has been demonstrated by considering Bessel equation of order zero and diffusion equation. The novelty of the work in this paper is to obtain an approximate solution to second order parabolic differential equation using an algorithm involving Bernstein basis polynomials and Tau method. The approximate solutions obtained by the present method are compared with the exact solutions, and the numerical results of other methods.

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[22]. Tohidi, E., Erfani, K., Gachpazan, M., & Shateyi, S. (2013). A new Tau method for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation. Journal of Applied Mathematics, 2013, 9. https://doi.org/10. 1155/2013/850170

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Research Paper

Common Fixed Point Results in Fuzzy Metric Spaces with Applications in Dynamic Programming

Dr Pranjali* , Shailesh Dhar Diwan**

* Department of Mathematics, Shri Shankaracharya Institute Of Professional Management And Technology, Raipur, Chhattisgarh, India.

** Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

Sharma, P., and Diwan, S. D. (2020). Common Fixed Point Results in Fuzzy Metric Spaces with Applications in Dynamic Programming. i-manager's Journal on Mathematics, 9(1), 38-48. https://doi.org/10.26634/jmat.9.1.17585

Abstract

In this paper we propose several common fixed point theorems for self mappings satisfying CLR_g or CLR_ST properties and weak compatibility in FMS (fuzzy metric spaces). Next, we provide some examples to support our results. Furthermore, as an application of our results we present some system of functional equations that arises in dynamic programming and prove the existence of solutions of such equations and uniqueness of the solutions of such functional equations.

References

[1]. Aamri, M., & El Moutawakil, D. (2002). Some new common fixed point theorems under strict contractive conditions. Journal of Mathematical Analysis and Applications, 270(1), 181-188.

[2]. Ali, J., Imdad, M., & Bahuguna, D. (2010). Common fixed point theorems in Menger spaces with common property (EA). Computers & Mathematics with Applications, 60(12), 3152-3159. https://doi.org/10.1016/j.camwa.2010.10.020

[3]. Baskaran, R., & Subrahmanyam, P. (1986). A note on the solution of a class of functional equations. Applicable Analysis, 22(3-4), 235-241.

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[6]. Bhakta, P. C., & Mitra, S. (1984). Some existence theorems for functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications, 98(2), 348-362.

[7]. Chang, S. S., & Ma, Y. H. (1991). Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications, 160(2), 468-479.

[8]. Chen, S., Shi, P., & Lim, C. C. (2017). Curve arc length in fuzzy metric spaces. Fuzzy Sets and Systems, 313, 105-113.

[9]. García, J. G., Rodríguez-López, J., & Romaguera, S. (2018). On fuzzy uniformities induced by a fuzzy metric space. Fuzzy Sets and Systems, 330, 52-78.

[10]. George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399.

[11]. Gregori, V., & Sapena, A. (2002). On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 125(2), 245- 252.

[12]. Gregori, V., Miñana, J. J., & Miravet, D. (2020). Contractive sequences in fuzzy metric spaces. Fuzzy Sets and Systems, 379, 125-133.

[13]. Imdad, M., Pant, B., & Chauhan, S. (2012). Fixed point theorems in menger spaces using the CLRST property and applications. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 3(2), 225-237.

[14]. Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9, 771-779.

[15]. Jungck, G. (1976). Commuting mappings and fixed points. The American Mathematical Monthly, 83, 261-263.

[16]. Jungck, G., & Rhoades, B. E. (2006). Fixed point Theorems for occasionally weakly compatible mappings. Fixed Point Theory, 7, 286-296.

[17]. Kramosil, I., & Michálek, J. (1975). Fuzzy metrics and statistical metric spaces. Kybernetika, 11(5), 336-344.

[18]. Miheţ, D. (2010). Fixed point theorems in fuzzy metric spaces using property EA. Nonlinear Analysis: Theory, Methods & Applications, 73(7), 2184-2188.

[19]. Pant, R. P. (1994). Common fixed points of non-commuting mappings. Journal of Mathematical Analysis and Applications, 188, 436-440.

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[22]. Sintunavarat, W., & Kumam, P. (2011). Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces. Journal of Applied Mathematics. https://doi.org/10.1155/2011/637958

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Article

Fractals: A Never Ending Pattern

Reproduced from OYLA DIGITAL Magazine*

OYLA DIGITAL Magazine. (2020). Fractals: A Never Ending Pattern. i-manager's Journal on Mathematics, 9(1), 49-52.

Abstract

In everyday life, we rarely hear the mysterious word “fractal”, but we encounter them on a daily basis. Nature exhibits fractals in Trees, mountains, snow, plants, and even the circulatory system have fractal structures. Fractals can be applied in various areas from image compression algorithms to the study of blood vessels of living organisms. A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals.

References

[1]. Fractals. (2020). Fractal Foundation. Retrieved from www.fractalfoundation.org

[2]. Fractal. (n.d.). Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Fractal

i-manager's Journal on Mathematics (JMAT)

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Volume 9 Issue 1 January - June 2020

An In-Depth Model for Determining Teaching Efficacy through the use of Qualitative Single Subject Design, Student Learning Outcomes, Associative Statistics, and Mixed Methods Post Hoc Data Analysis Methodology

James Edward Osler II* , Mahmud Mansaray**

*-** North Carolina Central University, Durham, North Carolina, United States.

Abstract

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On I2-Cauchy Double Sequences in Fuzzy N-Normed Spaces

Muhammed Recai Turkmen *

Department of Mathematics, Faculty of Education, Afyon Kocatepe University, Afyonkarahisar, Turkey.

Turkmen, M. R. (2020). On I2-Cauchy Double Sequences in Fuzzy N-Normed Spaces. i-manager's Journal on Mathematics, 9(1), 18-27. https://doi.org/10.26634/jmat.9.1.17735

Abstract

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Bernstein Tau Method for Bessel and Diffusion Equations

V. Appala Naidu* , G. V. S. R. Deekshitulu **

* Department of Mathematics, Government College for Men, Kadapa, Andhra Pradesh, India. ** Department of Mathematics, University College of Engineering Kakinada, Kakinada, Andhra Pradesh, India.

Naidu, V. A., and Deekshitulu, G. V. S. R. (2020). Bernstein Tau Method for Bessel and Diffusion Equations. i-manager's Journal on Mathematics, 9(1), 28-37. https://doi.org/10.26634/jmat.9.1.17604

Abstract

References

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Common Fixed Point Results in Fuzzy Metric Spaces with Applications in Dynamic Programming

Dr Pranjali* , Shailesh Dhar Diwan**

* Department of Mathematics, Shri Shankaracharya Institute Of Professional Management And Technology, Raipur, Chhattisgarh, India. ** Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

Sharma, P., and Diwan, S. D. (2020). Common Fixed Point Results in Fuzzy Metric Spaces with Applications in Dynamic Programming. i-manager's Journal on Mathematics, 9(1), 38-48. https://doi.org/10.26634/jmat.9.1.17585

Abstract

References

Full Article (HTML)

Pdf

Fractals: A Never Ending Pattern

Reproduced from OYLA DIGITAL Magazine*

OYLA DIGITAL Magazine. (2020). Fractals: A Never Ending Pattern. i-manager's Journal on Mathematics, 9(1), 49-52.

Abstract

References

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Pdf

* Department of Mathematics, Government College for Men, Kadapa, Andhra Pradesh, India.

** Department of Mathematics, University College of Engineering Kakinada, Kakinada, Andhra Pradesh, India.

* Department of Mathematics, Shri Shankaracharya Institute Of Professional Management And Technology, Raipur, Chhattisgarh, India.

** Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.