iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: Let 𝑅 be a prime ring,𝐼 be a non-zero ideal and 𝛼 any mapping on𝑅, and 𝜎,𝜏 be a automorphisms of 𝑅. Suppose that 𝐺 and 𝐹 are two generalized (𝜎,𝜏)-derivation on 𝑅 associated with (𝜎,𝜏)-derivation𝑔and𝑑on𝑅 respectively and 𝜏(𝐼)≠0. In this paper, we studied the following identities in prime rings:

Keywords: Prime ring, Derivation, Generalized derivation, (𝜎,𝜏)-derivation, Generalized (𝜎,𝜏)-d erivation

[1]. Ashraf,M., Rehman, N.: "On commutativity of rings with derivations", Results Math. 42(2002), 3-8.
[2]. Bresar,M.: "On the distance of the composition of two derivations to the generalized derivations", Glasgow Math. J. 33(1991), 89-93.
[3]. Charg,G., Sharma, R. K.: "On generalized (𝛼,𝛽)- derivations in prime rings", Rend. Circ. Mat. Palermo, doi: 10.1007/s12215-015-0227-5(2015), 1-10.
[4]. Daif,M.N., Bell, H.E.: "Remarks on derivations on semiprime rings", Internat J. Math. Math. Sci. 15(1992), 205-206.
[5]. Golbasi,O., Koc, E.: "Generalized derivations of Lie ideals in prime rings", Turk. J. Math. 35(2011), 23-28.

Abstract: Recently in [6], the authors have introduced the notion of semiring valued graphs, which is a generalization of both the crisp graph and fuzzy graph. In [3] the authors have studied the regularity conditions on S - valued graphs. In [7] the authors have studied the notion of vertex degree regularity on S - valued graphs. In this paper, we study the edge degree regularity of S - valued graphs.

Keywords: Semirings, Graphs, S-valued graphs, dS - edge regular graph.

[1]. Bondy J A and Murty U S R Graph Theory with Applications, North Holland, New York (1982 ).
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Mathematics.ISSN 0973-1768 Volume 11, Number 5 (2015),pp. 2971-2978.
[4]. Jonathan Golan Semirings and Their Applications, Kluwer Academic Publishers, London.
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Abstract: Interval estimation and hypothesis testing for the difference between two quantiles are investigated, using simulation, in this article. The underlying distributions that will be considered are the Weibull and Burr- Type-X. The estimation procedures will be based on the generalized confidence interval procedure, while the hypothesis testing will be based on the generalized p-values procedure. Simulation will be carried to check on the accuracy of both procedures.

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[3]. Guo, H. and Krishnamoorthy, K. (2005) Comparison between two quantiles: The Normal and Exponential cases, Communications in Statistics-Simulation and Computation, 34, 2, 243 – 252.
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Abstract: Oscillation criteria for certain fourth order quasilinear difference equations are obtained. Examples are provided to illustrate the results. AMS Subject classification: 39A10

Keywords: Oscillation theorems, Fourth order difference equation, Nonoscillation

[1] R.P.Agarwal, M.Bohner, S.R.Grace and D.O.Regan,Discrete Oscillation Theory,Hindawi Publ.NewYork,2005.
[2] E.Thandapani,S.Pandian and R.Dhanasekaran and J.R Graef,Asymptotic results for a class of fourth order quasilinear difference equations ,J.Diff. Eqn. Appl.,13 (2007), 1085-1103.
[3] R.P.Agarwal and J.V. Manojlovic,Asymptotic behavior of positive solutions of fourth order nonlinear difference equations,Ukrainian Math.J.60(2008),6-28.
[4] B.Smith and W.E.Taylor Jr.,Oscillatory and asymptotic behavior of fourth order difference equations, Rocky Mountain J.Math. 16(1986),401406.
[5] E.Thandapani and M.Vijaya Oscillatory and asymptotic behavior of fourth order quasilinear difference equations , Electronic journal od qualitative Theory of Differential Equations , 64 (2009), 1-15

Abstract: The population growth of Assam is very high which is even higher than the country's average growth. It is observed that there is an inter district disparities in the growth of population in Assam. Five districts of lower Assam, i.e. Dhuburi, Goalpara, Darrang,Barpeta, Bongaigaon two districts of Barak valley i.e. Karimganj, Hailakandi and two district of Middle Assam i.e. Nagaon and Marigaon, are showing very significant growth of population. Muslims dominated the above nine districts recording growth rate ranging from 20 per cent to 24 percent during the last decade against national average of 18 percent.

Keywords: Demographic structure, Fertility, Growth of population.

[1]. Dr. B.K.Nath,Dilip C.Nath, The Change of Religious and Language Composition in the State of Assam in Northeast India, A Statistical Analysis Since 1951 to 2001, International Journal of Scientific and Research Publications, 2(5),(2012),1-6.
[2]. D.N. Bezbaruah, Demographic Threats in Assam, The Sentinel, 2 January, (2005).
[3]. Census Report of India, Government of India, 2001, 2011.
[4]. Economic Survey, Assam, (2010-11), (2013-14).
[5]. Hsiu-ling Yang, Education, Married Women's Participation Rate, Fertility and Economic Growth, Journal of Economic Development, 25(2),(2000),101-118.

Abstract: Throughout the history of mathematics, the view of actual infinity and the view of potential infinity have taken turns to dominate. In fact, these two infinite views present two aspects of the "infinity". Both of them have great significance to the development of mathematics. Therefore, we should use dialectical thought on these two views and properly use them on mathematical studies.

Keywords: Actual infinity, potential infinity, dialectical thought

[1]. M.Kline. Mathematical Thought from Ancient To modern Times [M]. Shanghai: Shanghai Science and Technology Press，2002 (in
Chinese)
[2]. Zhu Wujia, etc. Research on Infinite Views (I) [J]. Journal of Nanjing University of Aeronautics and Astronautics, 2002，34（2）(in Chinese)
[3]. Li Xincan. Creators and Pioneers of Calculus [M]. Beijing: Higher Education Press, 2002(in Chinese)
[4]. Xu Lizhi. Xu Lizhi on Mathematical Methodologies [M]. Jinan: Shandong Education Press, 2001(in Chinese)
[5]. Zheng Junwen, Zhang Enhua. An Introduction to Mathematical Logic [M]. Hefei: Anhui Education Press, 1995(in Chinese)

Abstract: This study used a Quasi-experimental Design to determine the effects of modular instruction to third year BEED students of Eastern Samar State University (ESSU) who were exposed to lecture method and modular instruction in teaching word problem solving. Its purpose was to seek answers to the following questions: (1) Is there a significant difference in the pretest mean score? (2) Is there a significant difference in the posttest mean scores? (3)Is there a significant difference between the mean gainscores?Based on the pretest and posttest mean scores of both control and experimental groups, the following findings were formulated..............

Keywords: Effectiveness, modular; module; experimental; word problem solving

[1]. Abad, Ma. Leah I. (2006) "Training Needs & Performance of Engineering Math Teacher in the State Colleges of Region VIII: Inputs to a Proposed In-service Training Program," Unpublished MAIS Math Thesis, Leyte Institute of Technology, Tacloban City, Philippines.

[2]. Aggabao, Ambrose Hans. Development and Evaluation of Individualized Self-Instructional Modules on Selected Topics in Basic Mathematics. (Journal of Research, Isabela State University, Vol. XI, No. 1, January – December 2002).

[3]. Aquino-Danganan, Aussie. (2001) "Development and Validation of A Module in Developing Computational Skills in College Algebra" Unpublished Thesis, Tarlac State University.

[4]. Cappetta, Robert W., 2007, Reflective Abstraction and the Concept of Limit: A Quasi-Experimental Study to Improve Student Performance in College Calculus by Promoting Reflective Abstraction through Individual, Peer, Instructor and Curriculum Initiates, (Dissertation Abstract International Vol. 69 No. 2 August (541-A)).

[5]. Castillion-Boiser, Diosdada, (2000) Strategies for Teaching: A Modular Approach, Quezon City: Rex Bookstore Inc.

Abstract: The effective teaching and learning of mathematics could be attributed to many factors. Among them include the teachers' content knowledge, the application of teaching strategies and the knowledge and experience that students bring into the teaching and learning environment. The term Pedagogical Content Knowledge (PCK) is defined as teachers' interpretations and transformations of subject matter knowledge in the context of facilitating student learning and understanding. This paper aims at highlighting some of the key elements of PCK that may enhance the teaching and learning of mathematics............

Keywords: Mathematics, teaching and learning, students' knowledge, content knowledge

[1]. Anthony, G. & Walshaw, M.(2009): Characteristics of effective teaching of mathematics: a view from the west. Journal of Mathematics Education, 2(2); 147-164.
[2]. Carpenter, T.P., Fennema, E., Petersen, P., & Carey, D. (1988): Teachers pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19(1), 385-401.
[3]. Cochran, K.F., DeRuiter, J.A. & King, R.A. (1993): Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44(1), 32-43.

Abstract: A proper edge colouring of a graph G with the elements of ℤk is said to be a twin edge k-colouring of G if the induced vertex colouring is a proper vertex colouring in which the colour of a vertex v in G is defined as the sum (in ℤk) of the colours of the edges incident with v. Twin chromatic index of G is the minimum k for which G has a twin edge k-colouring. Twin chromatic index of Wn is determined, where Wn is the wheel graph of order n.

Keywords: Edge colouring, vertex colouring

[1]. E.Andrews, L. Helenius, D. Johnsonston, J. VerWys and P.Zhang, On twin edge colourings of graphs, Discuss. Math. Graph Theory 34 (2014), 613-627.
[2]. L. Addario-Berry, R.E.L. Aldred, K. Dalal and B.A. Reed, vertex colouring edge partitions, J. Combin. Theory (B) 94 (2005) 237-244.
[3]. M. Anholcer, S. Cichaz and M. Milanic, Groupirregularity strength of connected graphs, J. Comb. Optim. (2015) 30: 1-17 Doi: 10.1007/s10878-013-9628-6
[4]. G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, irregular networks, Congr. Numer. 64 (1988) 187-192.
[5]. G. Chartrand, L.Lesniak and P.Zhang, Graphs and Digraphs: 5th Edition (Chapman & Hall/CRC, Boca Raton, FL, 2010).

Abstract: Let P be the partition of a graph G with chromatic number, P is puzzle on G, if there is a vertex coloring of G using 1,2,…  (G) Such that the sums of the numbers assigned to the partition pieces are all same. P is a puzzle if there is unique vertex coloring such that the sums are all different. We investigate the concept of some graphs are puzzling, a puzzling and neither.

Keywords: Vertex coloring, Puzzles, Partition, Fan graph, Wheel graph, Ladder graph

[1]. Daphne Gold, James Henle, Cherry Huang, Tia Lyve, Tara Marin, Jasmine Osorio, Maneka Puligandla, Bayla Weick, Jing Xia, He Yun, Jize Zhang, Puzzling and Apuzzling Graphs, AKCE International Journal of Graphs and Combinatorics 13(2016)1-10.
[2]. Gerard Butters, Frederick Henle, James Henle,Colleen McGaughey, Creating clueless Puzzles, math. Intelligencer 33 (2011) 102-107.
[3]. Sonia Brown, James Henle, Christine Niccoli, Bayla Weick, Blank Sodoku, MAA Focus 33 (2013) 27.
[4]. Béla Bollobás, Extremal Graph theory, in: LMS Monographs, vol. 11, Academic Press, New York, San Francisco, 1980.
[5]. A.Ko`zig.A. Rosa, Magic Valuations of finite graphs, Canad. Math.Bull. 13 (1970)451-461.

Abstract: The paper presents solution to Least squares equation as driven by Singular Value Decomposition (SVD) obtained from using Jacobi Similarity Transformation without recourse to Tikhonov regularization parameter. We use the LU decomposition and QR algorithm as bases of comparison for the obtained results. A polynomial fit of order five for the Least squares problem was adopted. Sample numerical data problem was obtained as a primary source at Trodan, Kogi State University, Anyigba showing the functional relationship between Temperature and Relative Humidity. It is suggested that the SVD is numerically backward stable as attested to by the LU decomposition method relative to similar results computed by QR and other known methods.

Keywords: Least squares equation, singular value decomposition, Jacobi similarity transformation algorithm, inverse problems

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