• 대한수학회보
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• 제56권5호
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• pp.1143-1157
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• 2019

Let $T_aD_b(n)$ and $T_aD^{\prime}_b(n)$ denote respectively the number of representations of a positive integer n by $a(x^2-x)/2+b(4y^2-3y)$ and $a(x^2-x)/2+b(4y^2-y)$. Similarly, let $S_aD_b(n)$ and $S_aD^{\prime}_b(n)$ denote respectively the number of representations of n by $ax^2+b(4y^2-3y)$ and $ax^2+b(4y^2-y)$. In this paper, we prove 162 formulas for these functions.

• 한국세라믹학회지
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• 제40권5호
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• pp.455-459
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• 2003

LPE(Liquid Phase Epitaxial)법을 이용하여 성장시킨 B $i_2$S $r_2$Ca(C $u_{1-x}$ N $i_{x}$ )$_2$ $O_{8+}$$\delta$/ 막(film)을 break junction 법을 이용하여 터널링 분광을 측정하였다. Ni 조성비 $\chi$$_{L}$의 증가에 따라 에너지 간격 2$\Delta$의 크기는 증가하였다. 에너지 간격 2$\Delta$(4.2 K)는 54.4~64 meV, 2$\Delta$/ $k_{B}$ $T_{c}$ $^{zero}$는 7.36~10.14로 BCS 이론에 의한 값 보다 큰 결과를 얻었다. 융액(melting solution) 속의 Ni 조성비 $\chi$$_{L}$의 증가에 따라, 임계온도 $T_{c}$ $^{zero}$와 격자상수 c-축의 길이는 감소하는 경향을 보였다.을 보였다.$^{zero}$와 격자상수 c-축의 길이는 감소하는 경향을 보였다.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.631-644
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• 2021

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds $$\frac{{\partial}u}{{\partial}t}={\Delta}u+a(x,t)u^p+b(x,t)u^q$$ where, 0 < p, q < 1 are real constants and a(x, t) and b(x, t) are functions which are C² in the x-variable and C¹ in the t-variable. We shall get an interesting Harnack inequality as an application.

• 대한수학회지
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• 제47권3호
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• pp.455-466
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• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.

• 한국전자파학회논문지
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• 제20권10호
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• pp.1042-1049
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• 2009

본 논문에서는 광대 역 X-Band 추적 레이더의 모노펄스 비교기(comparator)에 적용 가능한 도파관 magic-T 설계 및 최적화 문제에 대해서 고찰하였다. 다층으로 구성된 도체 실린더(cylinder)를 이용하여 기존의 X-Band magic-T에 비해 광대역의 임피던스 정합을 구현하였다. 최적화된 파라미터 도출을 위해 유전 알고리즘과 particle swarm optimization을 결합한 하이브리드 최적화 알고리즘을 설계에 적용하였으며, 최적 설계된 도파관 magic-T는 모든 도파관 포트에 대해, 최소 12% 이상의 대역폭에서 -20 dB 이하의 반사 특성을 나타내었다. 전력 분배 손실은 0.2 dB 이하이며 전력 분배 편차 또한 0.1 dB 이하로 우수한 특성을 보여주었다. 또한 측정된 결과는 시뮬레이션 결과와 잘 일치하는 것을 확인하였다. 마지막으로, 적층 실린더의 차수를 증가시켜 5단 및 7단 적층 된 구조에 대한 대역폭 성능도 분석하였다.

• 대한수학회보
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• 제20권2호
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• pp.87-93
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• 1983

Let X and Y be normed linear spaces. An operator T defined on X with the range in Y is continuous in the sense that if a sequence {x$_{n}$} in X converges to x for the weak topology .sigma.(X.X') then {Tx$_{n}$} converges to Tx for the norm topology in Y. We shall denote the class of such operators by WC(X, Y). For example, if T is a compact operator then T.mem.WC(X, Y). In this note we discuss relationships between WC(X, Y) and the class of weakly of bounded linear operators B(X, Y). In the last section, we will consider some characters for an operator in WC(X, Y).).

• 대한수학회보
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• 제36권2호
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• pp.225-231
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• 1999

Let Mf(x) be the Hardy-Littlewood maximal function on $\mathbb{R}^n$. Let $\Phi$ and $\Psi$ be functions satisfying $\Phi$(t) = ${\int^t}_0$a(s)ds and $\Psi(t)$ = ${\int^t}_0$b(s)ds, where a(s) and b(s) are positive continuous such that ${\int^\infty}_0\frac{a(s)}{s}ds$ = $\infty$ and b(s) is quasi-increasing. We show that if there exists a constant $c_1$ so that ${\int^s}_0\frac{a(t)}{t}dt\;c_1b(c_1s)$ for all $s\geq0$, then there exists a constant $c_1$ such that(0.1) $\int_{\mathbb{R^{n}}$ $\Phi(Mf(x))dx\;\leq\;c_2$ $\int_\mathbb{R^{n}}$$\Psi(c_2\midf(x)\mid)dx$ for all $f\epsilonL^1(R^n_$. Conversely, if there exists a constant $c_2$ satisfying the condition (0.1), then there exists a constant $c_1$ so that ${\int^s}_\delta\frac{a(t)}{t}dt=;\leq\;c_1b(c_1s$ for all $\delta$ > 0 and $s\geq\delta$.

• Progress in Superconductivity
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• 제3권2호
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• pp.213-217
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• 2002

We have fabricated successfully single-filament composite $MgB_2$/SUS tapes, as an ultrarobust conductor type. The fabrication of the $MgB_2$/SUS tapes was performed by power-in-tube (PIT) process such as swaging and cold rolling. The critical transition temperatures $T_{c}$~38.5 K and ~36 K were observed for the sintered and the nonsintered $MgB_2$/SUS tapes, respectively In addition, the isothermal magnetization M(H) of the sintered $MgB_2$/SUS tapes was measured at temperatures T (between 5 and 50 K) in fields up to 6 T, employing a PPMS-9 (Quantum Design). The persistent current density (J$T_{P}$) values were obtained from the M(H) data, using Bean model, fur the sintered $MgB_2$/SUS tapes. The estimated values were higher than ~ 6$\times$ $10^{5}$ $A/\textrm{cm}^2$ at T = 5 K, with H : 0 G. We also investigated the cross section of the sintered tapes, by using SEM and EDX. An evidence of weak reaction on boundary between $MgB_2$ and SUS tube is found in the SEM and EDX.X.X.X.

• 대한수학회논문집
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• 제11권2호
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• pp.377-383
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• 1996

For a given separable space X which contains no copy of $C_0$ and a weakly compact T, we show that a Dunford integrable function $f : [a,b] \to X$ is intrinsically-separable valued if and only if f is McShane integrable. Also, for a given separable space X which contains no copy of $C_0$, a weakly compact T and a Dunford integrable function f we show that if there exists a sequence $(f_n)$ of McShane integrable functions from [a,b] to X such that for each $x^* \in X^*, x^*f_n \to x^*f$ a.e., then f is McShane integrable. Finally, let X contain no copy of $C_0$. If $f : [a,b] \to X$ is McShane integrable, then F is a countably additive on $\sum$.