iosr-Jm   Volume-15 ~ Issue-5 ~ Sep-Oct 2019

Abstract: Background: Diphtheria is still fatal disease even in the era of universal immunization., Heart complication (HC) ones of the serious complications, have historically had a large impact on morbidity and mortality, which probably led predictions about the evolution of epidemics have been made for centuries. Many factors may affect severity of HC and needed mentoring by clinician The objective is to identify the most-frequently used mathematical models and the diseases to which they are applied. Objective: To identify the most-frequently used mathematical models and the diseases to which they are applied. Methods: A cross-sectional study was conducted from January to December 2017 at Zainoel Abidin Hospital Banda Aceh, Indonesia. The type of HC, the mathematical...........

Key Word: diphtheria, predict of heart complication, mathematical models

[1]. Centres for Disease Control and Prevention. Diphtheria.: Available from: 2016; 2016 (Accessed: 27 December 2017) https://www.cdc.gov/diphtheria/index.html.
[2]. Ministry of Health of the Republic Indonesia (MoHRI). Menkes: Difteri menular, berbahaya dan mematikan, namun bisa dicegah dengan imunisasi: Available from: 2017; 2017 (Accessed: 27 December 2017) http://www.depkes.go.id/article/view/17121200002/menkes-difteri-menular-berbahaya-dan-mematikan-namun-bisa-dicegah-dengan-imunisasi.html.
[3]. WHO. Diphtheria reported cases Last update: 06-Sep-2017 http://apps.who.int/immunization_monitoring/globalsummary/timeseries/tsincidencediphtheria.html.
[4]. Havaldar PV, Sankpal MN, Doddannavar RP: Diphtheritic myocarditis: clinical and laboratory parameters of prognosis and fatal outcome. Ann Trop Paediatr. 2000, 20 (3): 209-215.
[5]. Mithun J. Verghese, Siva Subramanian Ramakrishnan, Anitha Saxsena Complete heart block due to diphtheritic myocarditis in the present era, Ann Pediatr Cardiol, 6 (2013), pp. 34-38.

Abstract: Migration (human) is the movement of people from one place in the world to another for the purpose of taking up permanent or semi permanent residence, usually across a political boundary in search of better living and livelihood opportunities. Migration is one of the important components of population change along with mortality and fertility. The creation of the separate state of Uttarakhand has caused a large part of the population of the rural Kumaun Region to migrate to different urban parts of the state and in the present scenario out migration is one of the major problems which the state faces. This paper is an attempt to analyse the out-migration with reference to various demographic indicators like family size, family nature, region, religion, category, facilities in the rural areas of Nainital district. The data is collected through a survey with the help of questionnaire. The multiple regression model........

Key Word: Multiple regression, demographic indicators, push & pull factors, out-migration.

[1]. Government of India: Census of India, Uttarakhand Provisional Population Figure, Uttarakhand, 2011.
[2]. Belwal, O.K., Bhatt N. & Panwar Pushpa, "Role of Socio-Economic Factors which affect the Out-migration in Rural Areas of Uttarakhand: A case study", Arya Bhatta Journal of Mathematics & Informatics, vol. 3, No.1, 2011.
[3]. Belwal, O.K., Bhatt N. & Todaria, N. P.,"Pattern of Agriculture Land Holdings and consequences of migration on Culture & Economy in Garhwal Himalaya,MUHA-2005, vol.5, 2005.
[4]. Belwal, O.K. & Bhatt N., "Effect of Socio- Economic characteristics on out-migration; A case study of Garhwal Himalayan Villages, Bio-Science Research Bulletin, 2004.
[5]. Srivastava, S.C., "Studies in Demography", Anmol Publications Pvt. Ltd., 2004..

Abstract: In this present paper based on the concept and properties of c∗-algebras valued metric spaces and gives some fixed point theorems for self-maps with contractive conditions on such spaces. as applications, existence and uniqueness results for a type of integral equation and operator equation are given. MSC: 47H10; 46L07.

Key Word: C∗-algebra; C∗-algebra-valued metric; contractive mapping; fixed point theorem

[1]. Murphy, GJ: C∗-Algebras and Operator Theory. Academic Press, London (1990)
[2]. Xu, QH, Bieke, TED, Chen, ZQ: Introduction to Operator Algebras and Noncommutative Lp Spaces. Science Press, Beijing (2010) (in Chinese)
[3]. O'Regan, D, Petrusel, A: Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl. 341(2), 1241-1252 (2008)
[4]. Caballero, J, Harjani, J, Sadarangani, K: Contractive-like mapping principles in ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory Appl. 2010, Article ID 916064 (2010)
[5]. Huang, LG, Zhang, X: Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332(2), 1468-1476 (2007)..

Abstract: The present study investigates the use of conjunction in the mathematics books. Authors developeda database of conjunction to study the uses and effects of conjunctionin Mathematicians writing. 'A Course of Pure Mathematics', a work bygreat English Mathematician G. H. Hardy is compared with a book 'Topics in Algebra' by another famous mathematician I. N. Herstein in the perspective of used conjunctions. Frequencies of various categories of conjunctions are counted and each category is given with a weight and highest weight category is identified. A visual representation of analysis through graphs is given.

[1]. Abu Ayyash, E. (2013). The role of cohesive devices and the interplay of theme and rheme in consolidating the argument. Arab World English Journal , 235-251.
[2]. Ali, M. (2016). Using cohesive devices during the course of lectures "the lectures‟ role". International Research Journal of Social Sciences , 33-36.
[3]. Baker, M. (1992). In other words: A coursebook on translation. London: Routledge.
[4]. Bamberg, B. (1984). Assessing Coherence: A Reanalysis of Essays Written for the National Assessment of Educational Progress, 1969-1979. Research in the Teaching of English , 305-319.
[5]. Bolton, K. N. (2003). A corpus-based study of connectors in student writing. International Journal of Corpus Linguistic , 165-182.
[6]. Brown, G. &. (1983). Discourse Analysis. Cambridge: Cambridge University Press..

Abstract: The object of the present paper is to characterize 3-dimensional generalized (  k , μ )–contact metric manifolds satisfying certain curvature conditions on T-curvature tensor. 2000 Mathematics Subject Classification: 53C15, 53C25......

Key Word: T-curvature tensor, (  k , μ)–contact metric manifold, 3-dimensional generalized (  k , μ )–contact metric manifolds, N(k)-contact metric manifolds, manifolds.

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Abstract: Violence against women is one of the most problematic issues that hinder the development and growth of societies. This researcher paper aims to deciding the most important reasons that lead to violence against women in the context of Saudi Arabia. This objective is achieved by using exploratory factor analysis which is used to explain the relationship among the variables and to decrease the number of variables. This factor analysis is applied on a sample that includes 800 women from different regions of Saudi Arabia. The study consists of 18 variables. Correlation.....

Key Word: Domestic violence, Factor Analysis, Scree Test, Extraction, Eigenvalues

[1]. Russo, N. F., &Pirlott, A. (2006). Gender‐Based Violence: Concepts, Methods, and Findings. Annals of the new york academy of sciences, 1087(1), 178-205.
[2]. Van der Straten, A., King, R., Grinstead, O., Vittinghoff, E., Serufilira, A., & Allen, S. (1998). Sexual coercion, physical violence, and HIV infection among women in steady relationships in Kigali, Rwanda. AIDS and Behavior, 2(1), 61-73.
[3]. Williams, B., Onsman, A., & Brown, T. (2010). Exploratory factor analysis: A five-step guide for novices. Australasian Journal of Paramedicine, 8(3).
[4]. Henson, R. K., & Roberts, J. K. (2006). Use of exploratory factor analysis in published research: Common errors and some comment on improved practice. Educational and Psychological measurement, 66(3), 393-416.
[5]. Watkins, M. W. (2018). Exploratory factor analysis: A guide to best practice. Journal of Black Psychology, 44(3), 219-246

Abstract: This paper deals with the study of constructing sequences of diophantine triples (a,b,c) based on two given pronic numbers such that the product of any two elements of the set added by a polynomial with integer coefficient is a perfect square.

[1]. I.G. Bashmakova, ed., Diophantus of Alexandria, Arithmetics and the Book of Polygonal Numbers, Nauka, Moscow, 1974.
[2]. A.F. Beardon and M.N. Deshpande, Diophantine triples, Math. Gazette 86, 2002, 258-260.
[3]. V. Pandichelvi, Construction of the Diophantine triple involving polygonal numbers, Impact J.Sci. Tech. , 2011, 5(1), 7-11.
[4]. M.A. Gopalan, G. Srividhya, Two special Diophantine Triples, Diophantus J.Math,2012, 1(1), 23-27.
[5]. M.A. Gopalan, V. Sangeetha and Manju Somanath, Construction of the Diophantine triple involving polygonal numbers, Sch. J.
Eng. Tech., 2014, 2(1), 19-22..

Abstract: In this Paper studies the existence of solution for a fractional order nonlinear quadratic differential equation with initial value condition in banach algebras. Moreover; we show that solutions of this equation are locally attractive. We make use of the standard tools of the hybrid fixed point theory for two operators to establish the main result.. The existence theorems for extremal solutions are also proved under certain monotonicity conditions. Finally, our results are illustrated by a concrete example..

Key Word: Fractional Order Quadratic Differential Equation, Fixed Point Theorem, LocallyAttractivitty and Extremal Solutions, Banach Space

[1]. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
[2]. Dhage B. C., A Nonlinear alternative in Banach algebras with applications to fractional differential equations, Nonlinear Funct. Anal. Appl.,8, 563-573,2004.
[3]. Dhage B. C., A nonlinear alternative in Banach Algebras with applications to functional differential equations, Nonlinear Funct. Anal. And Appal. 8(40), 563-575, 2004.
[4]. Granas A. R. B., Guenther and lee J. W., Some general existence principles for caratheodory theory of nonlinear differential equations, J. math. Pureset Appl. 70, 153-196, 1991.

J. Sabatier, O.P. Agrawal, J.A.T. Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007.

Abstract: The frequency of appearance of the Golden Ratio (Φ) in nature implies its importance as a cosmological constantand sign of beingfundamental characteristic of the Universe.Except than Leonardo Da Vinci's 'Monalisa' it appears on the sunflower seed head, flower petals, pinecones, pineapple, tree branches, shell, hurricane, tornado, ocean wave, and animal flight patterns. It is also very prominent on human body as it appears on human face, legs, arms, fingers, shoulder, height, eye-nose-lips, and all over DNA molecules and human brain as well. It is inevitable in ancient Egyptian pyramids and many of the proportions of the Parthenon. But very few of us are aware of the fact that it is part and parcel for constituting black hole's entropy equations,black hole's specific..........

Key Word: Golden Ratio, Devine Proportion, Cosmological Constant, Fundamental Constant of Nature

[1]. C. Rovelli and F. Vidotto, "Covariant Loop Quantum Gravity", Cambridge University Press 1 edition, 2014
[2]. Klee Irwina, Marcelo M. Amaralab, Raymond Aschheima, Fang Fanga, "Quantum Walk on a Spin Network and theGolden Ratio as the Fundamental Constantof Nature", Minkowski Institute Press, Published on 29 April 2017
[3]. Salvatore Giandinoto,"Superluminal Transportation of High Energy Particles Through Wormholes Using the Phi-Based Solution to the Schrödinger Wave Equation, the theorem of Residues and the Cauchy Integral Formula", Journal Published on 2007
[4]. Norman Cr., Marco Ol. &VillanuevaJ. R., "The Golden Ratio in Schwarzschild–Kottler Black Holes", The European Physical Journal, Received: 16 January 2017 / Accepted: 27 January 2017 / Published online: 23 February 2017
[5]. Weblink: https://en.wikipedia.org/wiki/Golden_ratio; collected on 2019.

Abstract: In order to solve the Nonlinear Mixed Integer Programming Problem, an improved Krill Herd algorithm(ANRKH) based on natural selection and random disturbance is proposed in this paper. Firstly, the induced weight and foraging weight based on the time-varying nonlinear decreasing strategy is proposed to improve the induced movement and foraging movement of krill. Secondly, random disturbance factor is added into the process of generating the new generation of krill herd population. And the evolution of the survival of the fittest in natural selection mechanism enhances the quality of the individuals in the krill herd population. Those steps can effectively balance the exploration and development ability of KH. Finally through the experiments of 16 test functions, this proposed algorithm compares with other algorithms. Experimental results demonstrate that this proposed algorithm has a significant advantage.

Key Word: nonlinear mixed integer programming, krill herd algorithm, time-varying weight, random disturbance, natural selection

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