• Korean Journal of Mathematics
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• 제4권1호
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• pp.45-49
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• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• 대한수학회보
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• 제58권4호
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• pp.983-1002
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• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• 대한수학회지
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• 제33권4호
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.127-132
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• 1995

[1] Show that ∫$\_$0/$\^$1/ [∫$\_$0/$\^$1/ f($\chi$,y)dy] d$\chi$ = ∫$\_$0/$\^$1/[∫$\_$0/$\^$1/ f($\chi$,y)d$\chi$] Counterexample: If pk denotes the k-th prime number, let S(pk) = (equation omitted), let S = ∪$\_$k=1/$\^$$\infty$/ S(pk), and let Q = [0, 1]${\times}$[0, 1]. Define f on Q as follows; f($\chi$, y) = 0 ($\chi$, y)$\in$S, f($\chi$, y) = 1 ($\chi$, y)$\in$Q - S.(omitted)

• 호남수학학술지
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• 제16권1호
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2003년도 춘계학술대회 논문집 센서 박막재료 반도체 세라믹
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• pp.277-281
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• 2003

Effects of $CaF_2$ addition as a filler on the high frequency dielectric properties and sintering of CaO-$Al_2O_3-SiO_2-B_2O_3$(CASB) and ZnO-MgO-$B_2O_3-SiO_2$(ZMBS) glass composites were investigated. The optimal glass composition in the CASB system was 33.0CaO-$17.0Al_2O_3-35.0SiO_2-15.0B_O_3$(in wt%). The corresponding dielectric properties were k=8.1 and $Q{\times}fo$=1,200GHz. The sintering temperature was $800{\mu}m$. In case of 2MBS system, 25.0ZnO-25.0MgO-20.0$B_2O_3-30.0SiO_2$(in wt%) glass showed k=6.8 and $Q{\times}fo$=5,200GHz when it was sintered at $750^{\circ}C$. The maximum amount of $CaF_2$ in the CASB and 2MBS glass system without any detrimental effect on the sintering was 25.0 v/o and 15.0 v/o, respectively. The addition of $CaF_2$ in the glass systems improved the high frequency dielectric properties. In case of CASB+$CaF_2$ composite, k was 7.1 and $Q{\times}fo$ was 2,300GHz. And in case of 2MBS+$CaF_2$ composite, k was 5.9 and $Q{\times}fo$ was 8,100GHz. $CaF_2$ addition also reduced sintering temperature. Effects of $CaF_2$ on the dielectric and sintering properties was analyzed in terms of viscosity and crystallization behavior changes due to the interaction between $CaF_2$ and the glass systems.

• 지구물리
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• 제3권3호
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• pp.193-200
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• 2000

지진파가 전달되면 진폭이 감쇠되는 정도를 나타내는 감쇠상수 $Q^{-1}$는 지구내부 물질의 물리적 성질을 나타내는 중요한 척도이며, 구조물의 내진설계에 있어서 지반의 강진동을 정량적으로 예측하기 위해 필수적이다. 경상북도 덕정리에 위치한 지진관측기기에 기록된 80지진과 76단일 관측망 기록자료를 바탕으로 한국남동부의 P, S 실체파 감쇠상수를 Coda확장규격화법에 의해 구하였다. 구하여진 $Q_P^{-1}$및 $Q_S^{-1}$는 각각 1.5Hz에서 $1{\times}10^{-2}$ 와 $9{\times}10^{-3}$, 24 Hz에서 $6{\times}10^{-4}$ 와 $5{\times}10^{-4}$로 줄어들고, $Q_P^{-1}=0.01\;f^{-1.07}$ 및 $Q_S^{-1}=0.01\;f^{-1.03}$의 강한 주파수 의존성을 보였다.

• 대한수학회논문집
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• 제24권3호
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• 호남수학학술지
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• 제17권1호
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)