• Journal of the Korean Society of Safety
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• v.12 no.4
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• pp.180-190
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• 1997

A new method in the fault tree analysis (FTA) for the reliability calculation is suggested. Two steps are necessary in traditional method in evaluation of the occurrence probability of top event in fault tree (FT). The first step is to find the minimal outsets, and the second one is to substitute the result into the poincare equation. In order to reduce the enormous computing time of this method, lots of rapid algorithms have been developed. Almost of all achievements were, however, based on the partial structural properties of FT. In this paper, the FT is transformed to a non-linear graph G which has the same minimal outsets of original n, and then the reliability is calculated using the domination theory. In this new method, the required number of equation terms are at most $2^n$ (n is node number of graph G), while $2^m$-1 (m is the number of minimal cutsets) calculation terms are required in the poincare equation in traditional method. Since m>>n in general. our new method reduces the calculation time significantly.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1465-1472
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• 2009

In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

• Journal of Mechanical Science and Technology
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• v.18 no.5
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• pp.857-864
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• 2004

The change in the NO emission indices (EINO) in a two-dimensional plane has been investigated, which is due to the interaction between a vortex and methane-air flames established at different equivalence ratios, by solving the field equation. After solving the field equation, the spatial distribution of G-values is obtained. The NO emission index is calculated after applying the appropriate relation between the G-values and the NO production rate or the mass fraction of methane obtained from the library of freely propagating flames created from detailed simulations. When a vortex exists in a reacting flow field, in general EINO slightly increases, whereas ElNO is lowered in the vicinity of the vortex regardless of flow direction. A change in vortex size has negligible impact on EINO$\_$T/ but increasing the vortex strength slightly increases EINO$\_$T/ in the domain of this study.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.91-100
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• 2013

This paper is a direct continuation of [1] and [2]. In this paper we investigate some properties of ES-curvature tensor and contracted ES-curvature tensor of g - $ESX_n$. Also, we study the field equations in the n-dimensional ES manifold g - $ESX_n$.

• Imaging Science in Dentistry
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• v.46 no.1
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• pp.1-7
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• 2016

Purpose: This study assessed the accuracy of age estimates produced by a regression equation derived from lower third molar development in a Thai population. Materials and Methods: The first part of this study relied on measurements taken from panoramic radiographs of 614 Thai patients aged from 9 to 20. The stage of lower left and right third molar development was observed in each radiograph and a modified Gat score was assigned. Linear regression on this data produced the following equation: Y=9.309+1.673 mG+0.303S (Y=age; mG=modified Gat score; S=sex). In the second part of this study, the predictive accuracy of this equation was evaluated using data from a second set of panoramic radiographs (539 Thai subjects, 9 to 24 years old). Each subject's age was estimated using the above equation and compared against age calculated from a provided date of birth. Estimated and known age data were analyzed using the Pearson correlation coefficient and descriptive statistics. Results: Ages estimated from lower left and lower right third molar development stage were significantly correlated with the known ages (r=0.818, 0.808, respectively, $P{\leq}0.01$). 50% of age estimates in the second part of the study fell within a range of error of ${\pm}1year$, while 75% fell within a range of error of ${\pm}2years$. The study found that the equation tends to estimate age accurately when individuals are 9 to 20 years of age. Conclusion: The equation can be used for age estimation for Thai populations when the individuals are 9 to 20 years of age.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.195-204
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• 2014

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.111-124
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• 2000

In this paper we obtain the Hyers-Ulam-Rassias stability of the Pexider equation f(x+y) =g(x)+h(y) in the spirit of Hyers, Ulam, Rassias and Gavruta.

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.199-203
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• 2016

An enzyme-free optical method is proposed for estimating high concentrations of glucose in a glucose-lactose mixture, based on a predictive equation that takes advantage of the reflective optical power observed at two discrete wavelengths. Compared to the conventional absorption spectroscopy method based on Beer's Law, which is mainly valid for concentrations below hundreds of mg/dL, the proposed scheme, which relies on reflection signals, can be applied to measure higher glucose concentrations, of even several g/dL in a glucose-lactose mixture. Two probe wavelengths of 1160 and 1300 nm were selected to provide a linear relationship between the reflective power and pure glucose/lactose concentration, where the relevant linear coefficients were derived to complete the predictive equation. Glucose concentrations from 2 to 7 g/dL in a glucose-lactose mixture were efficiently estimated, using the established predictive equation based on monitored reflective powers. The standard error of prediction was 1.17 g/dL.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.749-759
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• 2024

In this manuscript, we formulate the notion of Ω(H, θ)-contraction on a self mapping f : W → W, this contraction based on the concept of Ω-distance mappings equipped on G-metric spaces together with the concept of H-simulation functions and the class of Θ-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.