• 호남수학학술지
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• 제32권1호
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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.

• 대한수학회보
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• 제50권3호
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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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• 제30권1_2호
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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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• 제29권4호
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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.

• 대한수학회보
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• 제37권4호
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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.

• 대한수학회보
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• 제50권2호
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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.

• 한국유체기계학회 논문집
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• 제16권4호
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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.

• 대한수학회지
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• 제56권6호
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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.

• 동의생리병리학회지
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• 제27권5호
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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.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제9권1호
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• pp.33-38
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• 2020

본 논문에서는 드론에 의하여 획득된 영상을 분석하여 건축자재의 수량을 측정하는 기술을 제안한다. 제안하는 기술은 드론 및 카메라 정보가 담겨있는 드론 로그와 영상 내 건축자재더미 종류와 영역을 예측하는 RCNN, 실제적인 수량 계산을 위한 사진측량법을 사용한다. 기존 연구에선 학습 데이터의 부족으로, 자재 종류 및 건축자재더미 영역 예측 정확도의 오류 범위가 컸다. 논문에서는 이러한 오류 범위를 줄이고 예측 안정성을 높이기 위해 자료 증가 방법으로 학습 데이터를 증가시킨다. 자료 증가는 학습 모델의 과적합을 막기 위해 회전에 의한 증가 방법만 사용한다. 수량 계산 방법으로는 Yaw, FOV 등의 드론 및 카메라 정보가 담겨있는 드론 로그와 영상 내 건축자재더미 영역을 찾고, 종류를 예측해 줄 RCNN 모델을 사용하고, 이 모든 정보를 종합해 논문에서 제안하는 수식에 적용하여 자재더미의 실제적인 수량을 계산한다. 제안하는 방법의 우수성은 실험을 통하여 확인한다.