• Honam Mathematical Journal
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• v.32 no.1
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• pp.113-129
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• 2010

Inclusion and exclusion is used in many papers to count certain objects exactly or asymptotically. Also it is used to derive the Bonferroni inequalities in probabilistic area [6]. Inclusion and exclusion on finitely many types of properties is first used in R. Meyer [7] in probability form and first used in the paper of McKay, Palmer, Read and Robinson [8] as a form of counting version of inclusion and exclusion on two types of properties. In this paper, we provide a proof for inclusion and exclusion on finitely many types of properties in counting version. As an example, the asymptotic number of general cubic graphs via inclusion and exclusion formula is given for this generalization.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.801-809
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• 2013

In this paper, we construct nilpotent semigroups S such that $S^n=\{0\}$, $S^{n-1}{\neq}\{0\}$ and ${\Gamma}(S)$ is a refinement of the star graph $K_{1,n-3}$ with center $c$ together with finitely many or infinitely many end vertices adjacent to $c$, for each finite positive integer $n{\geq}5$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $n=5$, 6 and in finite cases.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.101-109
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• 2012

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of one-dimensional family of genus 3 nonhyperelliptic curves over finite fields. We also provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian of $C:y^3=x^4+{\alpha}$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ (mod 3) and $p{\neq}1$ (mod 4). Moreover, we give some implementation results using Gaudry-Schost method. A 162-bit order is computed in 97 s on a Pentium IV 2.13 GHz computer using our algorithm.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.803-810
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• 2000

Let N($d_1,...,{\;}d_n;c_1,...,{\;}c_n$) be the number of solutions $(x_1,...,{\;}x_n){\in}F^{n}_p$ of the diagonal equation $c_lx_1^{d_1}+c_2x_2^{d_2}+{\cdots}+c_nx_n^{d_n}{\;}={\;}0{\;}n{\geq},{\;}c_j{\;}{\in}{\;}F^{*}_q,{\;}j=1,2,...,{\;}n$ where $d_j{\;}>{\;}1{\;}and{\;}d_j{\;}$\mid${\;}q{\;}-{\;}1$ for all j = 1,2,..., n. In this paper, we find all n-tuples ($d_1,...,{\;}d_n$) such that the reduced form of ($d_1,...,{\;}d_n$) and N($d_1,...,{\;}d_n;c_1,...,{\;}c_n$) are the same as in the theorem obtained by Sun Qi [3]. Improving this, we also get an explicit formula for the number of solutions of the diagonal equation, unver a certain natural restriction on the exponents.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.611-626
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• 2013

In the paper we study the finite-time ruin probability in a general risk model with constant interest force, in which the claim sizes are pairwise quasi-asymptotically independent and arrive according to an arbitrary counting process, and the premium process is a general stochastic process. For the case that the claim-size distribution belongs to the consistent variation class, we obtain an asymptotic formula for the finite-time ruin probability, which holds uniformly for all time horizons varying in a relevant infinite interval. The obtained result also includes an asymptotic formula for the infinite-time ruin probability.

• The KSFM Journal of Fluid Machinery
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• v.16 no.4
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• pp.15-21
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• 2013

This study aims to estimate the fatigue resistance of small wind composite blade using the fatigue life estimation formula in the GL guideline. For this, firstly, we estimated a turbine blade's bending moment spectrum by using wind profile wind profile and BEMT. And fatigue tests were performed to obtain the S-N curve of composite materials used in blade. In addition, a finite element analysis was used to identify fatigue critical locations and fatigue stress spectrum. And the fatigue resistance of composite blade were evaluated using the rainflow cycle counting, and Goodman diagram and the fatigue life estimation formula in the GL guideline.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Journal of Physiology & Pathology in Korean Medicine
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• v.27 no.5
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• pp.617-624
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• 2013

The purpose of this study is to investigate the protective effects of 25 herbal formulas on acetaminophen (APAP) or D-galactosamine (D-GalN)-induced hepatotoxicity in primary rat hepatocytes. Cell viability was measured using by Cell Counting Kit-8. 15 kinds of herbal formulas significantly reversed the cell viabilities of D-GalN-treated rat hepatocytes compared with D-GalN alone (p<0.05). In particular, 9 herbal formulas (Bangpungtongseong-san, Bojungikgi-tang, Galgeun-tang, Gumiganghwal-tang, Guibi-tang, Sagunja-tang, Samsoeum, Pyeongwi-san and Yijin-tang) showed the potent protective effects. However, 8 herbal formula exerted weak protective effects and 2 herbal formula did not exert effects on hepatotoxicity by D-GalN. On APAP-induced hepatotoxicity, 7 kinds of herbal formulas increased the viabilities of hepatocytes compare with APAP alone (p<0.05). These results could be provide a valuable information for the future in vivo or clinical studies to predict the hepatoprotective effects of herbal formulas.

• KIPS Transactions on Software and Data Engineering
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• v.9 no.1
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• pp.33-38
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• 2020

This paper proposes a technique for counting construction materials by analyzing an image acquired by a Drone. The proposed technique use drone log which includes drone and camera information, RCNN for predicting construction material type, dummy area and Photogrammetry for counting the number of construction material. The existing research has large error ranges for predicting construction material detection and material dummy area, because of a lack of training data. To reduce the error ranges and improve prediction stability, this paper increases the training data with a method of data augmentation, but only uses rotated training data for data augmentation to prevent overfitting of the training model. For the quantity calculation, we use a drone log containing drones and camera information such as Yaw and FOV, RCNN model to find the pile of building materials in the image and to predict the type. And we synthesize all the information and apply it to the formula suggested in the paper to calculate the actual quantity of material pile. The superiority of the proposed method is demonstrated through experiments.