International Journal of Mathematics And its Applications

Number 1, 2019

1-8
Weighted Composition of m-Quasi k-Paranormal Operators

Authors: D. Senthilkumar and P. Tamil Selvi

Abstract

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Number of views: 243

In this paper we discuss the conditions for a composition operator and a weighted composition operator to be m-quasi k-paranormal operator and also the characterization of m-quasi k-paranormal operator on weighted Hardy space.

9-14
Some New Modifications of Adomian Technique for Nonlinear Volterra Integral Equations

Authors: Khawlah Hashim Hussain

Abstract

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Number of views: 183

In this paper, the nonlinear Volterra integral equations are solved by using new modifications of the Adomian decomposition technique. The approximate solution of this equation is calculated in the form of a series with easily computable components. The accuracy of the proposed techniques are examined by comparison with exact results. The test problems are presented to illustrate the reliability and performance of the techniques.

15-22
Fractional Differential Operator of Generalized Mittag-Leffler Function Using Jacobi Polynomial

Authors: Aakansha Vyas and P. K. Mishra

Abstract

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Number of views: 195

The paper is devoted to the study of generalized fractional calculus of the generalized Mittag-Leffler function $E^{\delta } _{\upsilon ,\rho } \left(z\right)$ which is an entire function of the form \[E^{\delta } _{\upsilon ,\rho } \left(z\right)=\sum\limits_{s=0}^{\infty } \frac{\left(\delta \right)_{s} z^{s} }{{\rm \Gamma }\left(\upsilon s+\rho \right)\; s!} \] Where $\upsilon >0$ and $\rho >0$. For $\delta =1$, it is reduces to Mittag-Leffler function $E_{\upsilon ,\rho } \left(z\right)$. We have shown that the generalized fractional calculus operators transform such function with power multipliers in to generalized Wright function. Some elegant results obtained by Kilbas and Saigo [11], Saxena and Saigo [24] are the special cases of the result derived in this paper.

23-30
On $\mathbb{R}$-Complex Finsler Space with Matsumoto Metric

Authors: S. M. Vanithalakshmi, S. K. Narasimhamurthy and M. K. Roopa

Abstract

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Number of views: 164

In this paper, we determined the fundemental tensor fields $( \tilde g_{ij}, \tilde g_{i\bar j})$ and inverse of these tensor fields, their determinant. Further, we studied some properties of non-Hermitian $\mathbb{R}$-complex Finsler space with Matsumoto metric.

31-39
Chirps Construct on Sobolev Spaces and the Behavior of their ${\left\|\hspace{.5cm}\right\|}_{L^2[-\varepsilon,\varepsilon]}$ and ${\left\|\hspace{.5cm}\right\|}_{H^s[-\varepsilon ,\varepsilon ]}$ Norm

Authors: T. Elbouayachi

Abstract

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Number of views: 165

The main idea of this work is to characterize chirps construct on Sobolev spaces by studying the behavior of ${\left\|f\right\|}_{L^2[-\varepsilon ,\varepsilon ]}$ or ${\left\|f\right\|}_{H^s[-\varepsilon ,\varepsilon ]}$. We expect that the behavior is in order of ${\varepsilon }^{\alpha +\left(\beta +1\right)(\left|s\right|+\frac{1}{2})}$ when $s$ tend to $-\infty $, and we believe that we have equivalence between this and the definition of chirps construct on Sobolev spaces. The formula of a chirp is given in the form ${f\left(x\right)=\left|x\right|}^{\alpha }g({\left|x\right|}^{-\beta })$, where $\beta >0$ and $g$ is an indefinitely oscillating function on $L^2$ or $H^s$. Which means that $g$ has for all $m$ integer one primitive of the order $m$ in the same space.

41-52
Lebegue-Bochner Spaces and Evolution Triples

Authors: Jula Kabeto Bunkure

Abstract

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Number of views: 192

The functional-analytic approach to the solution of partial differential equations requires knowledge of the properties of spaces of functions of one or several real variables. A large class of infinite dimensional dynamical systems (evolution systems) can be modeled as an abstract differential equation defined on a suitable Banach space or on a suitable manifold therein. The advantage of such an abstract formulation lies not only on its generality but also in the insight that can be gained about the many common unifying properties that tie together apparently diverse problems. It is clear that such a study relies on the knowledge of various spaces of vector valued functions (i.e., of Banach space valued functions). For this reason some facts about vector valued functions is introduced. We introduce the various notions of measurability for such functions and then based on them we define the different integrals corresponding to them. A function $f:\Omega \to X$ is strongly measurable if and only if it is the uniform limit almost everywhere of a sequence of countable-valued, $\Sigma$-measurable functions. If X is separable and $f: \Omega\to X$, be a function then the following three properties are equivalent: (a) f is strongly measurable; (b) f is weakly measurable; (c) f is Borel measurable. A strongly measurable function $f: \Omega\to X$, is Bochner integrable if and only if the function $\omega\to \left\|f\left(\omega \right)\right\|_X$ is Lebesgue integrable (i.e., $\left\|f\left(.\right)\right\|_X\in L^{1}(\Omega)$). The emphasis of the project is on the so-called Bochner integral, which generalizes in a very natural way the classical Lebesgue integral to vector valued functions. We continue with vector valued functions and introduce the so-called Lebesgue-Bochner spaces, which extend to vector valued functions of the well known Lebesgue $L^{p}$-spaces. We also consider evolution triples and the function spaces associated with them. Evolution triples provide a suitable analytical framework for the study of a large class of linear and nonlinear evolution equations.

53-58
Status of Employment in Ethiopia: Bahir Dar University Graduates Tracer Study

Authors: H. M. Fenta, P. Kibebew, S. T. Nigatu, Z. Siraye and A. Mulu

Abstract

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Number of views: 503

Background: Both graduates and Higher Education Institutions are increasingly concerned with ensuring that their academic investment results in future employability. The FDRE Ministry of Education has targeted to reach $>$ 80\% of graduates with the first degree of the regular program employed with degree-relevant employment within 1 year after their graduation. Therefore, this GTS was carried out to explore the employability rate, the average time it takes a graduate to find employment measured in months and assess if the employed graduates were employed in their field of study of 2015 and 2016 Bahir Dar University graduates with a first degree, in general. Method: The study was conducted in Bahir Dar University in 2015 and 2016 regular, first-degree graduates and stratified multistage random sampling was used to select respondents. Out of 4208 graduates, 867 graduates with a response rate of 82.5\% were selected to participate in the study. To determine the prevalence, the duration and the potential factors of employability graduates' in the labor market, both descriptive and inferential statistics were applied. Result: Seventy-nine percent of surveyed graduates were gainfully employed, of which majority (93\%) was landing with degree-relevant jobs. Most of the employment rate was taking place during 1 to 6 months in duration and the overall average duration of unemployment was 5.08 months. Moreover, the graduates from the Institute of textile and fashion technology and College of Business and Economics have a shorter spell of unemployment (3.62 and 4.41 months) respectively.

59-68
A New Generalization of Power Lomax Distribution

Authors: Sanaa Al-Marzouki

Abstract

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Number of views: 196

A new generalization of the power Lomax (PL) distribution, called exponentiated power Lomax (EPL), is introduced for modeling lifetime data. Some statistical properties of the EPL distribution are provided. Explicit expressions for the quntile, moments, moment generating function, probability weighted moments and order statistics are studied. Maximum likelihood estimation technique is employed to estimate the model parameters are presented. In addition, the superiority of the EPL distribution is illustrated with applications to two real data sets.

69-83
Assessing the Impact of Implementation of Higher Diploma Program in Ethiopian Institute of Textile and Fashion Technology(EiTEX)

Authors: Jula Kabeto Bunkure and Shimelis Adugna Tesema

Abstract

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Number of views: 219

This article determine the Higher Diploma program trained and no-trained teachers' skills in classroom instruction as well as pinning to the possible bottlenecks that hamper the successful application of the training skills. On this research a descriptive survey research design and explanatory research method where both qualitative and quantitative data gathering methods and analysis were used. The participants of the study were 20 HDP trained and 20 non-HDP trained teachers and 12 teachers on focused group discussion. The tools for collecting data or gathering data were: Questionnaire, classroom observation and Focused Group Discussion(FGD). In analyzing the quantitative data, statistical techniques of percentage, frequency count, mean and standard deviation were employed. The results indicate that HDP trained teachers were found to be better at reflective practice, implementing variety of active learning methods and assessment techniques than that of non HDP trained ones. However, both HDP trained and non HDP trained teachers have similar attitude towards the use of active learning methods and assessment techniques in their classrooms and it was found to be positive, since HDP trained teachers were found to be better at reflective practice, implementing variety of active learning methods and assessment techniques than that of non HDP trained ones. Besides, independent sample t-test and chi-square were used. The data gathered through qualitative methods was categorized and analyzed on thematic basis as raised in the objectives and the research questions. Large class size, classroom arrangement, lack of resources, and students' passive involvement were mentioned as major challenges to the implementation of a range of active learning methods and assessment techniques. Thus, the university should strengthen the HDP training to promote reflective practice, implementation of active learning methods and use of assessment techniques.

85-92
Truncated Weibull Lomax Distribution and its Statistical Inference

Authors: Sanaa Al-Marzouki and Taghreed Al-Said

Abstract

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Number of views: 149

A new three-parameter lifetime model, called the Truncated Weibull Lomax (TWL) distribution, is introduced. We investigate the density (pdf), distribution function (cdf), survival function (sf), hazard function (hrf), quantile function, r\textsuperscript{th} moment, incomplete moments and order statistics. Maximum Likelihood methods to estimate the TWL distribution parameters are studied. One real data set is applied to illustrate the flexibility of the TWL model compared with some Known models.