iosr-Jm   Volume-17 ~ Issue-4 ~ Jul. – Aug. 2021

Abstract: In this paper we analyze the agricultural data by CCR Model through Data Envelopment Analysis (DEA) for the Telangana state. To know the agriculture Technical Efficiency (T.E) of the farmers district wise in Telangana state. The Performance of the districts is presented along with the Peer, Reference Set, Potential Improvements (PI) and Technical efficiency Performance of the state by CCR Model through DEA approach.

Key words: CCR Model, Constant returns to Scale , Data Envelopment Analysis, Peers, Performance, Potential Improvement, Reference set, Technical Efficiency.

[1]. Rutter , M. & Maughan B., '' School effectiveness findings 1970-2002 '', Journal of School Psychology ,vol.40, No.6, pp.451-475,2002.
[2]. Kwimbere, F.J. , '' Measuring efficiency in not-for-profit organizations: an attempt to evaluate efficiency in selected UK university departments''. M.Sc. thesis, School of Management, University of Bath,1987.
[3]. Johnes, J, ''Performance assessment in higher Education in Britain'', European Journal of Operational Research, vol. 2, pp. 18–33,1996.
[4]. M. Goverdhan, Raju Nellutla, V. V Haragopal, ''A Critical Data Envelopment Analysis of Hospital efficiency in India '' , International Journal of Scientific Research, Vol-5,issue2,pp.471-475, 2016.
[5]. Raju Nellutla, V. V Haragopal , '' Technical efficiency Management wise Schools in Secondary School Examinations of Andhra Pradesh State by CCR Model'' , IOSR Journal of Mathematics, Vol-13,issue1,pp.1-8,2017..

Abstract:The modification of surface wave elevation and fluctuating wave pressure of waves in front of a vertical wall are examined. Consequently the Fourier and Stokes series are infused, Stokes coefficients playing a major role. Thus, the expansion is a stochastic family with the coefficients randomly distributed within specified limits. From the expansion, the wave crest elevation height and fluctuating wave pressure are calculated in front of a vertical wall and the data are in agreement with observations. Further, from the random nonlinearity parameters derived from the stochastic family, exceedence probability sketch is constructed are in agreement with observed wave heights.

Key words: Wave elevation, Fluctuating wave pressure, Probability of the execeedances

[1]. Longuet-Higgins M.S. (1963) The effect of nonlinearities on statistical distribution in the theory of sea waves. J. Fluid Mech. Vol.
17 pp 459-480.
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[3]. Tayfun M.A., (1986). On Narrow-band nonlinear Representation of Ocean waves. J. Geophy Res, Vol.91, No. 06. pp 7743-7752
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[5]. Ejinkonye I.O.,(2009) On the statistical properties of non-linear waves. J. of NAMP Vol. 14, pp 67-72.

Abstract: Differential geometry of curves studies the properties of curves and higher-dimensional curved spaces using tools from calculus and linear algebra. This study has two aspects: the classical differential
geometry which started with the beginnings of calculus and the global differential geometry which is the study of the influence of the local properties on the behavior of the entire curve. The local properties involves the properties which depend only on the behavior of the curve in the neighborhood of a point. The methods which have shown themselves to be adequate in the study of such properties are the methods of differential calculus. Due to this, the curves considered in differential geometry will be defined by functions which can be differentiated a certain number of times. The other aspect is the so-called global differential geometry which study the influence of the local properties on the behavior of the entire curve or surface. This paper aims to give an advanced introduction to the theory of curves, and those that are curved in general.

Key words: Arc-length, Curvature, Curves, Differential Geometry, Parametrized, Planes, Torsion

[1]. Banchoff, T.F. and S.T. Lovett, Differential geometry of curves and surfaces. 2016: Chapman and Hall/CRC.
[2]. Kinyua, K.D. and K.J. Gikonyo, Differential Geometry: An Introduction to the Theory of Curves. International Journal of
Theoretical and Applied Mathematics, 2017. 3(6): p. 225.
[3]. Abbena, E., S. Salamon, and A. Gray, Modern differential geometry of curves and surfaces with Mathematica. 2017: Chapman and
Hall/CRC.
[4]. Do Carmo, M.P., Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition. 2016: Courier Dover
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Abstract: In this paper, we investigated the dynamics of a reaction diffusion epidemic model with specific nonlinear incidence rate. This specific nonlinear incidence rate includes the traditional bilinear incidence rate, the bedding ton-De Angelis functional response, and Crowley Martin functional response. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. Eventually, we come to the conclusion that medical solutions had obtained and evaluated the relevant mathematical findings. Ultimately, we conclude that the application part coincides with a mathematical model and the result is linked to the medical report. In the future, this paper will be beneficial in the medical field.

Key words: Cortisol, Epidemic model, Partial differential equation, HPA axis, Depression

[1]. Ahmed A.H, Calvird M, Gordon R.D, Taylor P.J, Ward .G, Pimenta .E, Young .R, Stowasser .M (2011) Effects of two selective serotonim reuptake inhibitor antidepressants, sertraline and escitalopram, on aldosterone/renin ratio in normotensive depressed make patients. J Clin Enddocrinol Metab 96:1039-1045. https://doi.org/10.1210/jc.2010-2603
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[3]. Deuschle M, Hamann B, Meichel C, Krumm B,Lederbogen F, Kniest A, Colla M, Heuser I (2003) Antideprressive treatment with amitriptyline and paroxetine: effects on saliva cortisol concentrations. J Clin Psychopharmacol 23:201-205.
[4]. Dziurkowska E, Wesolowski M, Dzirukowski M (2013). Salivary cortisol in women with major depressive disorder under selective serotonin reuptake inhibitors therapy. Auch Women Ment Health 16:139-147. https://doi.org/10.1007/s00737-013-0329-z
[5]. Hernandez ME, Mendieta D, Perez-Tapia M, Bojalil R, Estrada-Garcia I, Estrada-Parra S, Pavon L (2013) Effects of selective serotonin reuptake inhibitors and immunomodulator on cytokines levels: an altetnative therapy for patients with major depressive disorder. Clin Dev Immunol 2013:267871. https://doi.org/10.1155/2013/167871.

Abstract: The paper is done to study the Spread of disease in prey-predator population. For these problem a Dynamical system of differential Equations has been proposed. The Positivity, Boundedness and existence of model solutions of the Equation has been analyzed and proved. Existence of all possible Equilibrium has been checked and computed. Stability Analysis of all Equilibrium points of the model has been done. Moreover Local and global stability of disease free and endemic equilibrium points are established with concept of Jacobian matrix and Routh Hurwitz criterion respectively. Numerical simulations are presented to clarify analytical results..

Key words: Spread of disease, predator-prey system, Local Stability, global stability , Simulation Study

[1]. Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao. Mathematical Eco-Epidemic Model on Prey-Predator System. IOSR Journal of Mathematics (IOSR-JM), 16(1), (2020): pp. 22-34.
[2]. Sachin Kumar and Harsha Kharbanda. Stability Analysis Of Prey-Predator Model With Infection, Migration and Vaccination In Prey, arXiv:1709.10319vl [math.DS], 29 Sep 2017.[3]. Paritosh Bhattacharya, Susmita Paul and K .S. Choudhury (2015). Mathematical Modeling of Ecological Networks, Structure and Interaction of Prey and Predator, Palestine Journal of Mathematics Vol. 4(2), 335–347.
[4]. C. M. Silva (2017). Existence of periodic solutions for periodic eco-epidemic models with disease in the prey, J. Math. Anal. Appl. 453(1), 383–397.
[5]. J. Chattopadhyay and O. Arino. A predator-prey model with disease in the prey, Nonlinear Analysis, 36 (1999), 747–766.

Abstract:The concept of commutativity degree for finite groups is an aspect of abstract algebra that places the subject on a numerical scale.Cody, C (2010) has determined the maximum sizeof the centre of finite groups while Anna, C (2010)obtained the equivalent in terms of commutativity degree. In this paper we obtained the commutativity degrees of finite groups of order less that one hundred where the groups have orders of the form a b G  p q , a  b using the conjugacy classes via the class equation as instruments where p is an even prime while q is an odd prime such that q  10 , 2  a  6 and 0  b  2 ..

Key words: Group; Commutativity; Centre; Conjugacy class; Prime

[1]. Anna, C. (2010). Commutativity degree of finite groups. Unprinted Thesis: Wake Forest University , Winston – Salem, North Carolina.
[2]. Cody, C. . Commutativity in non abelian groups. www.whitman.edu/mathematics/ .../2010/seniorproject.codyclifton. 2010: Retrieved on 2/9/2012. 1-18.
[3]. Herstein, I. N.. Topics in Algebra. Massachusetts USA: Blaisdell Publishing Company. 1964
[4]. Houshang, B. and Hamid, M.. A note on p-groups of order ≤p4. Proc.Indian Acad. Sci. (Math. Sci.), 2009: 119(2): 137-143.
[5]. Jelten, N.B. and Momoh, S.U.. Minimum and maximum number of irreducible representations of prime degree of non abelian group using the centre. Journal of Natural Sciences Research. 2014.4(10):63 - 59.

Abstract: We consider a stochastic evolution equation on a separable Hilbert space..........

Key words: Brownian Motion, Evolution Equation, Hilbert space, Lévy Process, Stochastic Evolution Equation.

[1]. Chojnowska- Michalik, A. and Goldys, B., Existence, uniqueness and invariant measures for stochastic semilinear equations in Hilbert spaces, Probab. Th. Rel. Fields 102 (1995), 331–356.
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[4]. Da Prato, G. and Zabczyk, J., Ergodicity for Infinite Dimensional Systems, (Cambridge University Press, Cambridge, 1996).
[5]. Es- Sarhir, A. and Farkas, B., Invariant measures and regularity properties of perturbed Ornstein-Uhlenbeck semigroups, J. Diff. Equ. 233 (2007), 87–104.

Abstract:The concept of commutativity degree for finite groups is an aspect of abstract algebra that places the subject on a numerical scale.Cody, C (2010) has determined the maximum sizeof the centre of finite groups while Anna, C (2010)obtained the equivalent in terms of commutativity degree. In this paper we obtained the commutativity........

Key words: Group; Commutativity; Centre; Conjugacy class; Prime

[1]. Anna, C. (2010). Commutativity degree of finite groups. Unprinted Thesis: Wake Forest University , Winston – Salem, North Carolina.
[2]. Cody, C. . Commutativity in non abelian groups. www.whitman.edu/mathematics/ .../2010/seniorproject.codyclifton. 2010: Retrieved on 2/9/2012. 1-18.
[3]. Herstein, I. N.. Topics in Algebra. Massachusetts USA: Blaisdell Publishing Company. 1964
[4]. Houshang, B. and Hamid, M.. A note on p-groups of order ≤p4. Proc.Indian Acad. Sci. (Math. Sci.), 2009: 119(2): 137-143.
[5]. Jelten, N.B. and Momoh, S.U.. Minimum and maximum number of irreducible representations of prime degree of non abelian group using the centre. Journal of Natural Sciences Research. 2014.4(10):63 - 59.