• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.187-192
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• 2009

In this paper, we introduce the notions of $s{\gamma}$-generalized closed sets and $s{\gamma}$-generalized sets, and investigate some properties for such notions.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.25-28
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• 2002

We introduce the notion of $s{\gamma}$-sets, and we investigate some properties of $s{\gamma}$-sets. In particular, we characterize the $s{\gamma}$-closure by terms of supra-convergence of filters.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.81-98
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• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.5
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• pp.118-124
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• 2007

The efficiency of the hybrid systems which are composed of compound planetary gear sets depend on the amount of the recirculating energy among the motors and battery. This paper studies the analysis of the system efficiency with the parameters, ${\alpha},\;{\beta},\;{\gamma_a},\;{\gamma_b}$ and $\gamma_s$. The efficiency of the systems and the relative torque, speed and power of the power resources are represented by these parameters. The recuperating parameter $\kappa$ which makes the systems generalized is introduced, so the efficiencies of the modes such as the hybrid mode, the engine mode, the motoring mode and the recuperating mode are analyzed with simple equations. The tendency of the system efficiency according to the variations of the $\gamma_s$ and $\kappa$ are studied, by which it can be possible to reduce the loss of the power because the strategies for avoiding the singular speed ratio $\gamma_s$ are helpful for the system efficiency and specific value of $\kappa$ can increase the efficiency of the systems.

• International Journal of Computer Science & Network Security
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• v.24 no.1
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.