• Honam Mathematical Journal
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• v.41 no.4
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• pp.745-756
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• 2019

In this paper, we establish the log convexity and Turán type inequalities of extended (p, q)-beta functions. Likewise, we present the log-convexity, the monotonicity and Turán type inequalities for extended (p, q)-confluent hypergeometric function by utilizing the inequalities of extended (p, q)-beta functions.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.719-731
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• 2020

In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.573-583
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• 2019

This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Some properties for the ratio of the modified Lommel functions with the Lommel function, sinh and cosh are also discussed. As a consequence, $Tur{\acute{a}}n$ type and reverse $Tur{\acute{a}}n$ type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1845-1856
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• 2016

In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some $Tur{\acute{a}}n$ type inequalities are deduced.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.575-598
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• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• Nuclear Engineering and Technology
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• v.49 no.3
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• pp.484-494
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• 2017

In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.