• 대한수학회보
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• 제56권1호
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• pp.169-178
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• 2019

Let $M^{2n+1}$, $n{\geq}1$, be a smooth manifold with a pseudoconvex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $M={\mathcal{S}}_0{\supset}{\mathcal{S}}_1{\supset}{\cdots}{\supset}{\mathcal{S}}_n$, where $S_q$ is the set of points where the Levi-form has nullity ${\geq}q$. We prove that ${\mathcal{S}}{_q}^{\prime}s$ are locally given as common zero sets of the coefficients $A_j$, $j=0,1,{\ldots},q-1$, of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.353-366
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• 2024

A total coloring of a graph G is an assignment of colors to both the vertices and edges of G, such that no two adjacent or incident vertices and edges of G are assigned the same colors. In this paper, we have discussed the total coloring of M(T_n), M(D_n), M(DT_n), M(AT_n), M(DA(T_n)), M(Q_n), M(AQ_n) and also obtained the total chromatic number of M(T_n), M(D_n), M(DT_n), M(AT_n), M(DA(T_n)), M(Q_n), M(AQ_n).

• 대한수학회논문집
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• 제33권4호
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.505-514
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• 2019

In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.

• 대한수학회보
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• 제61권4호
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• pp.959-968
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• 2024

Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = sup_z∈ⅅ(1 - |z|²)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where f_r(z) = f(rz) and ||·||ʙ_q is the Besov seminorm given by ║f║ʙ_q = (∫_𝔻 |f'(z)|^q(1-|z|²)^q-2dA(z)). These results improve previous results of Clunie and MacGregor.

• 한국수자원학회논문집
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• 제49권12호
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• pp.1015-1025
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• 2016

일반적으로 도심지 배수시설로 설치되는 맨홀은 중간맨홀, $90^{\circ}$ 접합맨홀, 3방향 합류맨홀 및 4방향 합류맨홀 등 다양한 접합 형태를 가지고 있다. 특히 도시유역의 중․하류부에 주로 설치되는 4방향 합류맨홀에서의 과부하흐름은 에너지 손실을 발생시켜 도심지의 침수피해를 가중시키는 주요 원인이다. 그러므로 과부하 4방향 합류맨홀에서의 흐름특성 분석 및 손실계수의 산정이 필요하다. 본 연구에서는 현황조사 결과를 고려하여 수리실험 장치를 제작하였으며, 맨홀 및 관경은 하수도 시설기준을 준용하여 1/5로 축소 제작하였다. 선정된 실험조건인 맨홀 형상 조건(사각형, 원형), 유출유량($Q_{out}$)에 대한 측면유입유량($Q_{lat}$)의 비($Q_{lat}/Q_{out}$) 및 실험 유량(2.0, 3.0, 4.0, $4.8{\ell}/sec$)을 변화시키면서 실험을 실시하였다. 실험결과 측면유량비가 증가할수록 손실계수는 증가하였으며, 사각형 맨홀보다 원형 맨홀에서의 손실계수가 다소 낮게 산정되었다. 그러나 유출유량 변화에 따른 손실계수의 변화는 미미하였다. 측면유량비에 따른 과부하 4방향 합류맨홀의 손실계수는 0.4~0.8로 산정되었다. 또한, 측면유량비 변화를 고려한 4방향 합류맨홀에서의 손실계수 산정식을 제시하였다.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.583-590
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• 2008

In this article, we focuss on. sequences of polynomials with {$\pm1$} coefficients constructed by recursive argument that is known as Rudin-Shapiro polynomials. The asymptotic behavior of these polynomials defines as the ratio of their 2q-norm with 2-norm to be dominated by some number depending on q or "the best" by an absolute constant. In this work we first show the conjecture holds for some finite numbers of m and then introduce a technique that give the result for any positive odd integer m whenever it holds for all pervious even numbers.

• 대한수학회보
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• 제35권4호
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• pp.683-687
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• 1998

Suppose X is a subspace of $(\sum_{n=1} ^{\infty} X_n)_{c_0}$, dim $X_n<{\infty}$, which has the metric compact approximation property. It is proved that if Y is a Banach space of cotype q for some $2{\leq}1<{\infty}$ then K(X,Y) is an M-ideal in L(X,Y).

• 대한수학회논문집
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• 제21권1호
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• pp.37-43
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• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

• 한국미생물·생명공학회지
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• 제19권1호
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• pp.76-81
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• 1991

2l 발효조에서 pH6.9, 온도 $32^{\circ}C$일 때 당밀배지를 이용하여 Corynebacterium glutamicum의 영양요구성 유사체 내성변이주에 의한 라이신 발효시 산화환원 전위 (ORP)가 라이신 발효속도의 특성에 미치는 영향을 조사하였다. 희석률이 0.1$h ^1$일때 탄소원이 제한되건 로이신이 제한되건 산소가 제한되지 않는 한 최대의 대당수율 24를 보였으며, 이 때의 산화환원 전윈 값은 -60mV와 -100mV 범위에 해당하였다. 산화화원 전위 값이 -130mV의 매우 낮은 용존산소 조건하에서는 대당수율 밀 $q_s, q_p$ 등의 발효 반응속도 상수값들이 크게 감소하였으며 glvcine, alanine, valine을 포함하는 발효 부산물의 축적량이 매우 높아졌다.