iosr-Jm   Volume-15 ~ Issue-2 ~ March-April 2019

Abstract: In this paper, we analyze the existing rules for constructing derivatives of the scalar and tensor functions of the tensor argument with respect to the tensor argument and the theoretical positions underlying the construction of these rules. We perform a comparative analysis of these rules and the results obtained in the framework of these rules. Considering the existing approaches, we pay due attention to the earliest of them which for some reason is not reflected in later publications on the issue under consideration, and we give to this approach the further development. The rules for constructing the derivatives..........

Key Word: Differentiation with respect to a tensor, Rules for differentiation and forms of derivatives, Scalar and tensor functions of tensor argument

[1]. A.A. Rogovoy, Formalized approach to construction of the state equations for complex media under finite deformations, Continuum
Mechanics and Thermodynamics, 24, 2012, 81-114. http://dx.doi.org/10.1007/s00161-011-0220-y.
[2]. A. Rogovoy and O. Stolbova, Modeling the magnetic field control of phase transition in ferromagnetic shape memory alloys,
International Journal of Plasticity, 85, 2016, 130-155. http://dx.doi.org/ 10.1016/j.ijplas.2016.07.006.
[3]. B.E. Pobedrya, Lectures on Tensor Analysis (Moscow: Moscow State University, 1974, in Russian).
[4]. P.K. Rashevsky, Riemannian Geometry and Tensor Analysis (Moscow: Nauka, 1967, in Russian).
[5]. I.S. Sokolnikov, Tensor Analysis (Moscow: Nauka, 1971, in Russian).

Abstract: By having used of differential subordination, it has been investigated in the present paper, subordination relations, inclusion relations, distortion theorem and inequality properties are discussed of the class𝕄𝔹(𝜶,𝝀,𝓵,𝝁,𝜜,𝜝). In this paper it has been introduced some new classes 𝕄𝔹(𝜶,𝝀,𝓵,𝝁,𝜜,𝜝) of meromorphic functions which are defined by means a meromorphic function using a new operator.

[1]. Aouf, M. K. and Mostafa, A. O. (2008) Certain subclass of p-valent meromorphic functions involving certain operator, J. Inequal. Pure and Appl. Math.,, (9), Article 45, 8pp.
[2]. Aqlan, E., Jahangiri, J. M. and Kulkarni, S. R. (2003) Certain integral operator applied to meromorphic p-valent functions, J. of Nat. Geom., 24, 111-120.
[3]. Dziok, J. and Srivastava, H. M. (1993) Classes of analytic functions associated with the generalized hypergeometric functions, Appl. Math. Comput., 103, 1-13.
[4]. Dziok, J. and Srivastava, H. M. (2002) Some subclasses of analytic functions with fixed arguments of coefficients associated with generalized hypergeometric function. Adv. Stud, Contemp. Math., 5, 115-125.
[5]. Dziok, J. and Srivastava, H. M. (2003) Certain subclasses of analytic functions associated with the generalized hypergeometric functions. IntegralTrans. Spec. Funct., 14, 7-18.

Abstract: The aim of this article was to compare Pearson's Chi-square to Uniform (U), Column (C), Row (R), and R+C ordinal contingency tables models. Data on gender, university attended for B.Sc., B.Sc. and M.Sc. grades of 116 M.Sc. graduates were collected from Department of Statistics, University of Ilorin, Nigeria. Model estimation was carried out by maximum likelihood method and goodness of fit was assessed by likelihood ratio statistic. Pearson's chi-square rejected the null hypothesis of independence in all cases; the U model rejected in 2 of 6 cases while R rejected in 4 cases. The C model rejected in 3 cases while R+C rejected in 5 out of 6 cases. Pearson's chi-square reached same..........

Keywords: Contingency table, Chi-square, Row model, Colum model, Likelihood ratio

[1]. Agresti, A. (2007). An Introduction to Categorical Data Analysis (2nd ed.). New Jersey: John Wiley.
[2]. Aktas, S. & Saracbasi, T. (2003). Analysis of triangular contingency tables. Hacettepe J. of Math. & Stat., 32, 43-51.
[3]. Altunay, S.A. & Saracbasi, T. (2009). Estimation of symmetric disagreement using a uniform association model for ordinal
agreement data. ASTA Advances in Sta. Anal., 93(3), 335-343.
[4]. Camminatiello, I., D'Ambra, A. & Sannacchiaro, A. (2014). The association in a two-way contingency table through log
odds ratio analysis: the case of Sarno river pollution. Springer Plus, 3. DOI 10.1186/2193-1801-3-384.
[5]. Eshima, N., Tubata, M. & Tsujitani,, M. (2001). Property of the RC(M) association model and a summary measure of
association in the contingency table. J. Japan Stat. Soc., 31(1), 15-26..

Abstract: In this paper, the controllability of a class of nonlinear integro-differential equation with implicit derivatives is investigated. We employ the Darbo fixed point theorem to investigate our result. Also , we give example to illustrate to obtained result.

Keyword: Nonlinear integrodifferential equation, Darbo fixed point theorem, controllability

[1]. Aghajani, A., Banas, J., andSabzali, N. (2013). Some generalizations of Darbo fixed point theorem and applications. Bulletin of the
Belgian Mathematical Society-Simon Stevin, 20(2); 345-358.
[2]. Balachandran, K., and Dauer, J. P. (2002). Controllability of nonlinear systems in Banach spaces: a survey. Journal of Optimization
Theory and Applications, 115(1): 7-28.
[3]. Balachandran, K., andSomasundaram, D. (1983). Controllability of a class of nonlinear systems with distributed delays in
control. Kybernetika, 19(6): 475-482.
[4]. Balachandran, K., and Somasundaram, D. (1985). Relative controllability of nonlinear systems with time varying delays in
control. Kybernetika, 21(1): 65-72.
[5]. Balachandran, K., andSomasundaram, D. (1986). Controllability of nonlinear delay systems with delay depending on state
variable. Kybernetika, 22(5): 439-444..