• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.341-354
• /
• 2023

In this article, an alternating Fibonacci sequence is defined from a second-order linear homogeneous recurrence relation with constant coefficients. Then, the determinant, inverse, and eigenvalues of the circulant matrices with entries in the first row having the formation of the sequence are formulated explicitly in a simple way. In this study, the method for deriving the formulation of the determinant and inverse is simply using traditional elementary row or column operations. For the eigenvalues, the known formulation from the case of general circulant matrices is simplified by considering the specialty of the sequence and using cyclic group properties. We also propose algorithms for the formulation to show how efficient the computations are.

• Journal of the Korean Society of Safety
• /
• v.35 no.4
• /
• pp.64-73
• /
• 2020

As Korean government and safety-related organizations make continuous efforts to reduce the number of industrial accidents, accident rate has steadily declined since 2010, thereby recording 0.48% in 2017. However, the number of fatalities due to industrial accidents was 1,987 in 2017, which means that more efforts should be made to reduce the number of industrial accidents. As an essential activity for enhancing the system safety, accident analysis can be effectively used for reducing the number of industrial accidents. Accident analysis aims to understand the process of an accident scenario and to identify the plausible causes of the accident. Accident analysis offers useful information for developing measures for preventing the recurrence of an accident or its similar accidents. However, it seems that the current practice of accident analysis in Korean manufacturing companies takes a simplistic accident model, which is based on a linear and deterministic cause-effect relation. Considering the actual complexities underlying accidents, this would be problematic; it could be more significant in the case of human error-related accidents. Accordingly, it is necessary to use a more elaborated accident model for addressing the complexity and nature of human-error related accidents more systematically. Regarding this, HFACS(Human Factors Analysis and Classification System) can be a viable accident analysis method. It is based on the Swiss cheese model and offers a range of causal factors of a human error-related accident, some of which can be judged as the plausible causes of an accident. HFACS has been widely used in several work domains(e.g. aviation and rail industry) and can be effectively used in Korean industries. However, as HFACS was originally developed in aviation industry, the taxonomy of causal factors may not be easily applied to accidents in Korean industries, particularly manufacturing companies. In addition, the typical characteristics of Korean industries need to be reflected as well. With this issue in mind, we developed HFACS-K as a method for analyzing accidents happening in Korean industries. This paper reports the process of developing HFACS-K, the structure and contents of HFACS-K, and a case study for demonstrating its usefulness.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.50 no.10
• /
• pp.188-198
• /
• 2013

Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.