• 한국수학사학회지
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• 제23권3호
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• pp.121-140
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• 2010

본 논문은 속도, 온도, 농도, 밀도, 단가, 일인당 국민소득 등의 내포량의 평균을 구할 때, 내포량마다 다른 공식을 적용하여 구해야 하는 불편함을 해소하기 위하여, 지레의 원리를 이용하여 두 내포량의 평균 공식 $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$를 유도하였고, 이 공식의 관계적 이해를 돕기 위해 지레의 원리를 이용한 조작적 학습법을 제시하였다. 비의 의미의 분수는 그 수치만으로 덧셈을 할 수가 없어 비가법적이라고 한 것을 비중을 적용하여 계산할 수 있음을 보인 것이다. 또한 두 양에서뿐만 아니라 여러 양의 덧셈도 단 한번의 공식에의 적용으로 해결할 수 있도록 확장 적용시킨 $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$ (단, $f_1+f_2+{\cdots}+f_n=N$) 은 새로운 공식이 가중평균을 구하는 공식이었다는 것을 밝혔다. 또한 통계학에서 의문거리였던 하위 제표의 방향성과 다른 모습을 보이는 상위제표의 통계자료에 대한 심프슨의 파라독스의 의문점을 가중평균의 원리를 이용하여 밝혔다.

• 대한수학회논문집
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• 제37권4호
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• 충청수학회지
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• 제24권4호
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• pp.703-712
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• 2011

In this paper, we investigate the stability of a cubic functional equation $$f(x+ny)+f(x-ny)+f(nx)=n^2f(x+y)+n^2f(x-y)+(n^3-2n^2+2)f(x)$$ in p-Banach spaces and in Banach modules, where $n{\geq}2$ is an integer.

• 대한수학회지
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• 제33권3호
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• pp.601-607
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• 1996

For functions $f(z) = \sum_{n = 0}^{\infty}a_n z^n$ and $g(z) = \sum_{n = 0}^{\infty} b_n z^n$ analytic in the unit disk $\Delta = {z : $\mid$z$\mid$ < 1}$, the convolution $f * g$ is defined by $(f * g)(z) = \sum_{n = 0}^{\infty}a_n b_n z^n$. Let S denote the family of functions $f(z) = z + \cdots$ analytic and univalent in $\Delta$ and K, St, C the subfamilies that are respectively convex, starlike, and close-to-convex.

• 대한수학회지
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• 제52권4호
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• pp.685-697
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• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.435-441
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• 2016

Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.

• 대한수학회논문집
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• 제12권1호
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.

• 대한수학회지
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• 제51권1호
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• pp.55-65
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• 2014

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

• 대한기계학회논문집
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• 제7권2호
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• pp.204-211
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• 1983

To investigate the effects of oscillatory feed cutting on the chip breaking and surface roughness and circularity, A prototype unit developed for the experiment is used. The results obtained are as follows. (1) It is obtained the region of chip breaking as Ftmin $f_{+min}$0.03mm ( = 0.3f). (2) The surface roughness becomes worse with increasing the value of A/f, but the type of variation with respect to n/N differs from the case of A/f>1, f<1. (3) The circularity of workpiece is increasing from the fundamental mode of n/N=i to the maximum value of n/N=i+0.5, and becomes worse with increasing the value of A/f. (4) From the viewpoint of above details and tool mechanics, the condition of A/f=1.0 and n/N=i.+-. .delta. (0.3<.delta.<0.4) is recommended.