iosr-Jm   Volume-16 ~ Issue-1 ~ Jan – Feb 2020

Abstract: In this paper, some relations of order, L-order, L*-order of composite entire and meromorphic functions with relative lower order, relative L-lower order, relative L*-lower order of a meromorphic function with respect to an entire function are established. AMS Subject Classification (2010) : 30D20,30D30,30D35..

Keywords and Phrases : Entire function, Meromorphic function, Slowly changing function, order, L-order, L*- order, relative lower order, relative L-lower order, relative L*-lower order.

[1]. L. Bernal : Crecimiento relativo de funciones enteras. Contribuci´on al estudio de lasfunciones enteras con ´ındice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
[2]. L. Bernal : Orden relative de crecimiento de funciones enteras , Collect. Math., Vol. 39 (1988), pp.209-229.
[3]. W. Bergweiler : On the Nevanlinna characteristic of a composite function, Complex Variables, Vol. 10 (1988), pp. 225-236.
[4]. W. Bergweiler : On the growth rate of composite meromorphic functions, Complex Variables, Vol. 14 (1990), pp. 187-196.
[5]. S. K. Datta and T. Biswas : On a Result of Bergweiler, International Journal of Pure and Applied Mathematics, Vol. 51 No. 1 (2009), pp. 33-37.

Abstract: In Integral transform, The Laplace transform has wide application to study of differential equation. We study some partial differential equations and analyze flow of temperature in to a rod by using Double Laplace Transform and getting a length independent temperature relation.

Kew words: Laplace Transform, Circuit, current, temperature, time, length etc.

[1]. C.Fox , Applications of Mellin's Transformation to the integral equations ,(1933)
[2]. C. Fox Application of Mellin Transformation to Integral Equation, 3rd March, 1934,pp 495-502.
[3]. Debnath, J. C., N-dimensional Laplace transforms with associated transforms and boundary value problems. Ph. D. thesis, Iowa StateUniversity, 1988.
[4]. Pipes, L. S., The summation of Fourier Series by Operational Methods, Journal of Applied Physics, Vol. 21, No. 4,1950, p. 298-301.
[5]. S. M. Khairnar, R. M. Pise, J. N. Salunke ,Bi Lateral Laplace Mellin Integral Transform and Its Applications, Imt. J. of Pure & Appl. Sci. Tech. , 1 (2), 2010, pp 114-126

Abstract: In this paper, the author finds the coefficient bounds and the Hankel determinant of Generalized distribution function involving Jackson' q-derivative operator using the subordination principle.

[1]. Al-Abadi, M. A. & Darus, M. (1933). Hankel determinant for certain class of analytic function defined by generalized derivative operator, Tankang Journal of Mathematics, 43(4), 445 – 453.
[2]. Aldweby, H. & Darus, M. (2013). A subclass of Harmonic univalent functions associated with q-analogue of Dziok-strivastara operator ISRN. Math anal. 10, 382312.
[3]. Al-Rufai, O. & Darus, M. (2009). Second Hankel Determinant for certain class of analytic function defined by a fractional operator. European Journal of Scientific Research, 28(2), 234 – 241.
[4]. Aydogan, M., Kahramaner, Y. & Polatoglu, Y. (2013). Close-to convex functions defined by fractional operator. Appl math sci, 7, 2769 – 2775.
[5]. Babalola, K. O. (2010). On third order Hankel determinant for some classes of univalent functions. Inequality Theory and Applications, 6, 1 – 7..

Abstract: In the present work we study the situation in Brazil regarding sexually transmitted diseases, indicating those groups of people for which certain diseases are more common. A system of differential equations is introduced that simulates the process of transmission of the different diseases in case homosexuals of both sexes appear; systems in a neighborhood of equilibrium positions are studied and the behavior of their trajectories is concluded; if we infer the future situation regarding the number of patients

Keywords: Sexually transmitted, model, disease, patient.

[1]. Bailey N. T. J., The Mathematical Theory of Infectious Diseases, 2nd ed., Hafner, New York,1975 (1).
[2]. Bailey N. T. J, The Mathematical Theory of Infectious Diseases, 2nd ed., Hafner, New York,1975 (2).
[3]. Becker N., Analysis of Infectious Disease Data, Chapman and Hall, New York, 1989.
[4]. Bongaarts J., A model of the spread of HIV infection and the demographic impact of AIDS,Stat. Med., 8 (1989), pp. 103–120.
[5]. Burnett M. and White D. O., Natural History of Infectious Disease, 4th ed., Cambridge University Press, Cambridge, UK, 1974.

Abstract: Assignment problems arise in different situation in our daily life where we have to assign n objects to m-other objects in such a way that can minimize the cost or maximize the profits. The assignment problems are a well studied topic in Operation Research especially in Optimization Problems. These problems find numerous application in production planning, telecommunication, economic …etc. It is done in such a way that the cost or time or distance involved in the process is to be minimized and the profits or returns are to be maximized. From here I can define two types of the assignments problems:
1- The Balanced assignment problems in which we are to assign number of resources (suppose equals N) to the same number of activities also equals N.
2- The Unbalanced

Keywords: Assignment Problems, Balanced and Unbalanced assignment Problems, Constraints, Objective Function, Optimal Solution and Dummy Cell.

[1]. M.Missmar. A New Technique for Solving the Assignment Problems Using Vogel Method. Internation Journal of Advance Research in Science and Engineering. Vol.No..06,Issue No.08,August 2017
[2]. http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf
[3]. Revised Ones Assignment Method For Solving Assignment Problem. Journal of Statics and AppliedMathematics ISSN:0976- 8807&E-ISSN:0976-8815,volume 4,Issue1,2013, pp-147-150,
[4]. N. Sujatha1,A. V. S. N. Murthy. An Advanced Method for Finding Optimal Solutionof Assignment Problem, International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064
[5]. http://www.uobabylon.edu.iq/eprints/publication_5_26416_36.pdf.

Abstract: Functional equalities are very difficult and are frequently exploited in regional, national and international olympiads (of high-school or university level). The development used to application in several
areas - not only in mathematics but also in other disciplines. Functional equalities are applied computers, economics, polynomials, engineering, information theory, reproducing scoring system, taxation, etc. In recent
years, many author studied functional equations. In this paper, we establish some functional equalities induced bymean of arbitrary degrees tomean of arbitrary degrees and apply to solve some mathematical problems ..

Keywords: Functional, functional equalities, arithmetic mean, quadratic mean, mean of arbitrary degrees

[1]. B. J. Venkatachala. (2002). Functional equations - A problem solving aproach. PRISM.
[2]. Christopher G. Mall. (2000). Functional equations and how to solve them, Springer.
[3]. Nguyen, V.M. (1966. Lectures on functional equations and their applications, Academic Press, New York/San Francisco/London.
[4]. NicolateNeamtu. (1998). About some classical functional equations, Tr. J. of Mathematics, 22 , 119 - 126, Tubitak.
[5]. PL. Kannappan. (2000). Functional equations and Inequalities with applications.SpringerMonogaphs in Mathematics.
[6]. T. Acze'l. (1966). Lectures on functional equations and their applications, Academic Pres, New York/San Francisco/London.

Abstract: Expression and facial pattern understanding are one of the major key leading research happening theses day, from the neural net to a simple comparison of images this action can be performed in various formats depending on the need and the accuracy of the neural network possible. The neural network present also possesses, the flexibility and functionality of recognizing highly complex facial expressions. The collective database of images is used as a reference base for training and to make the entire system give highly accurate results. The trained model and the final output helps in generating output in terms of programmed results and terms of accurate data pointers. This high-performance data can be used to perform functional programming and applications like expression-based lights and appliances control.................

Keywords: Pattern Recognition, Facial expression, Trained Model.

[1]. Yongmian Zhang and Qiang Ji, "Active and dynamic information fusion for facial expression understanding from image sequences," in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 5, pp. 699-714, May 2005.
[2]. Y. Ou, T. Kuan, A. Tsai, J. Wang, and J. Chiou, "Sunnfering understanding system based on facial expression and human action," 2016 International Conference on Orange Technologies (ICOT), Melbourne, VIC, 2016, pp. 52-55.
[3]. G. H. Weber et al., "Visual Exploration of Three-Dimensional Gene Expression Using Physical Views and Linked Abstract Views," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 6, no. 2, pp. 296-309, April-June 2009.
[4]. M. Ceresa, M. Masseroli, and A. Campi, "A Web-enabled Database of Human Gene Expression Controlled Annotations for Gene List Functional Evaluation," 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Lyon, 2007, pp. 394-397.
[5]. Y. Chen, T. Shimizu, and M. Okada, "Fundamental study on a structural understanding of mathematical expressions," IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028), Tokyo, Japan, 1999, pp. 910-914 vol.2.

Abstract: The achievement of households food security status are measured following four well established components like food availability, food accessibility, food stability and food utilization for all people at all time have noticed in most of the research works. The continuous supply of the aforesaid components may not imply the attainment of food security. Even if the food security is dependent on a household access to enough food it is measured by actual dietary intake of all household members it may be estimated by examining the daily calorie intake gained from carbohydrate, protein, fat and other sources of ingredients. As such the food secured households are they who get recommended calories from their daily food intake. According to the objectives of this research we were intended to measure the food security status using the aforesaid calorie intake by developing a food security index with the help of established consumption boundary.............

Keywords: Daily Calorie Intake, Food security index, KMO statistics, Bartlett's test of Sphericity and Factor analysis.

[1]. Baffes, J., and M. Gautam (2001).Assessing Sustainability of Rice Production Growth in Bangladesh. Food Policy, Vol. 26, pp. 515-542.
[2]. Begum, M. E. A., M. I. Hossain, and L. D. Haese (2013).Food Security in Bangladesh: Present Status and Trend. Progressive Agriculture, Vol. 24(1 and 2), pp. 263-271.
[3]. Chen Y. and Lu C. (2018). A Comparative Analysis on Food Security in Bangladesh, India and Myanmar. Sustainability 2018, 10, 405. pp. 2-13
[4]. Deb U.K., Hossain M. and Jones S. (2009). Rethinking Food Security Strategy:Self-sufficiency or Self-reliance.
[5]. Debebe Habtewold. 1995. Food security: A Brief Review of Concepts and Indicators. In: Multa. D., Wolday. A., Simeon. E. and Tesfaye. Z. (cds.), Food security. Nutrition and Poverty Alleviation in Ethiopia Problems and Prospects (pp. 1-18), Addis Ababa: Agricultural Economics society of Ethiopia.

Abstract: In the present paper some aspects of surface, curvature, Dupins indicatrix, Weingarten Equations are studied. The importance of this study lies in the fact that Mean and Gaussian curvature is established with the help of the coefficient of first and second fundamental form.

Keywords: Curvature, Curvature Directions and Quadratic form of curvature directions, Mean & Gaussian curvature, Dupin Indicatrix and Asymptotic Direction, Weingarten Equations

[1]. Boothby, W. An Introduction to Differentiable Manifolds and Differential Geometry, Academic Press, NewYork, 1975.
[2]. M. Deserno, Notes on Difierential Geometry with special emphasis on surfaces in R3, Los Angeles, USA, 2004.
[3]. Ahmed, K. M., Md. Showkat Ali, 2008. A study of spaces of constant curvature on Riemannian manifolds, Dhaka Uni. J. Sci. 56(1): 65-67.
[4]. M. P. do-Carmo, Differential Geometry of curves and surfaces, Prentice-Hall, Inc., Englewood Cliffs, New Zealand, USA, 1976.
[5]. M. Raussen, Elementary Differential Geometry: Curves and Surfaces, Aalborg University, Denmark, 2008.

Abstract: In this paper a mathematical model is formulated to analyze the transmission of AIDS with drug resistance. The total population under consideration is divided into seven compartments viz., Susceptable, Primary, Asymptomatic, Symptomatic, Resistant, and AIDS compartments. The well-possedness of the formulated model isproved. The local stabilities of the model are analyzed using Routh Hurwitz criterion. Next generation matrix method is used to find the basic reproduction number. The study has shwn that natural death rate is the most sensitive parameter in the model formulated.The transmission rate is one of the factors that determines the extinction or persistence of disease in the population. Finally, numerical solutions of the model equations are simulated using MATLAB.

Keywords: HIV, Basic Reproduction Number, Stability Analysis, Routh Hurwitz criterion, well-possedness

[1]. Kumama Regassa, Purnachandra Rao Koya. Modeling and Analysis of Population Dynamics of Human Cells Pertaining to HIV/AIDS withTreatment. American Journal of Applied Mathematics. Vol. 7, No. 4, 2019, pp. 127-136. doi: 10.11648/j.ajam.20190704.14
[2]. Kumama Regassa Cheneke, Geremew Kenassa Edessa, Purnachandra Rao Koya.Global Stability and Sensitivity Analysis of the Dynamics of Human Population Subjected to HIV/AIDS with Treatment. IOSR Journal of Mathematics (IOSR-JM).Volume 15, Issue 6 Ser. III (Nov – Dec 2019), PP 34-51. DOI: 10.9790/5728-1506033451.
[3]. Kumama Regassa Cheneke, Geremew Kenassa Edessa, Purnachandra Rao Koya. Impact of Treatment and Isolation on the Dynamics of HIV Transmission. IOSR Journal of Mathematics (IOSR-JM). Volume 15, Issue 6 Ser. V (Nov – Dec 2019), PP 73-72. DOI: 10.9790/5728-1506055372.
[4]. Daabo1,M.I., Makinde, O.D., Seidu, B. (2013). Modeling the combined effects of careless susceptible and infective immigrants on the transmission dynamics of HIV/AIDS epidemics. Journal of Public Health and Epidemiology. 5, 362-369.