• East Asian mathematical journal
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• v.29 no.3
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• International Journal of Control, Automation, and Systems
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• v.4 no.4
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• pp.438-447
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• 2006

Fuzzy controller's design depends mainly on the rule base and membership functions over the controller's input and output ranges. This paper presents two different approaches to deal with these design issues. A simple and efficient approach; namely, Fuzzy Subtractive Clustering is used to identify the rule base needed to realize Fuzzy PI and PD type controllers. This technique provides a mechanism to obtain the reduced rule set covering the whole input/output space as well as membership functions for each input variable. But it is found that some membership functions projected from different clusters have high degree of similarity. The number of membership functions of each input variable is then reduced using a similarity measure. In this paper, the fuzzy subtractive clustering approach is shown to reduce 49 rules to 8 rules and number of membership functions to 4 and 6 for input variables (error and change in error) maintaining almost the same level of performance. Simulation on a wide range of linear and nonlinear processes is carried out and results are compared with fuzzy PI and PD type controllers without clustering in terms of several performance measures such as peak overshoot, settling time, rise time, integral absolute error (IAE) and integral-of-time multiplied absolute error (ITAE) and in each case the proposed schemes shows an identical performance.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.169-187
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• 2022

There have been provided a surprisingly large number of summation formulae for generalized hypergeometric functions and series incorporating a variety of elementary and special functions in their various combinations. In this paper, we aim to consider certain generalized hypergeometric function ₃F₂ with particular arguments, through which a number of summation formulas for _p+1F_p(1) are provided. We then establish a power series whose coefficients are involved in generalized hypergeometric functions with unit argument. Also, we demonstrate that the generalized hypergeometric functions with unit argument mentioned before may be expressed in terms of Bell polynomials. Further, we explore several special instances of our primary identities, among numerous others, and raise a problem that naturally emerges throughout the course of this investigation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.720-730
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• 2002

Automated design of large structures requires efficient and accurate optimization algorithms because of a large number of design variables and design constraints. The objective of this study is to examine the characteristics of the Kreisselmeier -Steinhauser envelope function and to investigate va tidily of accumulating constraint functions into a small number of constraint functions or even into a single constraint function. The commercial package DOT is adopted as a local optimizer. The optimum results using the envelope function are compared with those of the conventional method for a number of numerical examples and the differences between them are shown to be negligible.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.545-555
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• 2009

In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.69-81
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• 2016

For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set $\{1,2,{\ldots},k\}$ such that for any vertex $v{\in}V(D)$ with $f(v)={\emptyset}$ the condition ${\cup}_{u{\in}N^-(v)}$ $f(u)=\{1,2,{\ldots},k\}$ is fulfilled, where $N^-(v)$ is the set of in-neighbors of v. A set $\{f_1,f_2,{\ldots},f_d\}$ of k-rainbow dominating functions on D with the property that $\sum_{i=1}^{d}{\mid}f_i(v){\mid}{\leq}k$ for each $v{\in}V(D)$, is called a k-rainbow dominating family (of functions) on D. The maximum number of functions in a k-rainbow dominating family on D is the k-rainbow domatic number of D, denoted by $d_{rk}(D)$. In this paper we initiate the study of the k-rainbow domatic number in digraphs, and we present some bounds for $d_{rk}(D)$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.659-665
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• 2013

In this note, the $q$-extension of the twisted Lerch Euler zeta functions considered by Jang [Bull. Korean Math. Soc. 47 (2010), no. 6, 1181-1188] is further investigated, and the generalized multiplication theorem for the $q$-extension of the twisted Lerch Euler zeta functions is given. As applications, some well-known results in the references are deduced as special cases.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.675-683
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• 2000

As a by-product of [4], we give algebraic integers of certain values of quotients of Weierstrass $\delta'(\tau),\delta'(\tau)$-functions. We also show that special values of elliptic functions are transcendental numbers.

• Proceedings of the Korean System Dynamics Society
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• 2007.06a
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• pp.113-129
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• 2007

Due to criminal aspects spreading nation wide, their intelligence level increasing and becoming digitalized, the citizens' interest in and desire for crime security have increased. Until now, the preceding researches have been focused on finding the specific variables that have direct effects on the demand for police manpower through regression analysis and attempted to predict number of needs. However, there have never been any researches producing the accurate number of demands for crimes and human resources needed for each work load. Therefore, this research have analyzed each police station functions by interviewing the persons in charge and selected the main duty for each functions. From this, by using the method of system dynamics, this research was able to predict the standard number of manpower needed for each police station functions. Also, by making a model for each 235 police stations, the best efficient employment plan for police stations and district agencies have been further discussed based on the computer simulation results.

• Korean System Dynamics Review
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• v.8 no.1
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• pp.49-66
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• 2007

Due to criminal aspects spreading nation wide, their intelligence level increasing and becoming digitalized, the citizens' interest in and desire for crime security have increased. Until now, the preceding researches have been focused on finding the specific variables that have direct effects on the demand for police manpower through regression analysis and attempted to predict number of needs. However, there have never been any researches producing the accurate number of demands for crimes and human resources needed for each work load. Therefore, this research have analyzed each police station functions by interviewing the persons in charge and selected the main duty for each functions. From this, by using the method of system dynamics, this research was able to predict the standard number of manpower needed for each police station functions. Also, by making a model for each 235 police stations, the best efficient employment plan for police stations and district agencies have been further discussed based on the computer simulation results.