• 제목/요약/키워드: M-S2X

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PROPERTIES OF INDUCED INVERSE POLYNOMIAL MODULES OVER A SUBMONOID

  • Cho, Eunha;Jeong, Jinsun
    • Korean Journal of Mathematics
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    • 제20권3호
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    • pp.307-314
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    • 2012
  • Let M be a left R-module and R be a ring with unity, and $S=\{0,2,3,4,{\ldots}\}$ be a submonoid. Then $M[x^{-s}]=\{a_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ is an $R[x^s]$-module. In this paper we show some properties of $M[x^{-s}]$ as an $R[x^s]$-module. Let $f:M{\rightarrow}N$ be an R-linear map and $\overline{M}[x^{-s}]=\{a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ and define $N+\overline{M}[x^{-s}]=\{b_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}b_0{\in}N,\;a_i{\in}M}$. Then $N+\overline{M}[x^{-s}]$ is an $R[x^s]$-module. We show that given a short exact sequence $0{\rightarrow}L{\rightarrow}M{\rightarrow}N{\rightarrow}0$ of R-modules, $0{\rightarrow}L{\rightarrow}M[x^{-s}]{\rightarrow}N+\overline{M}[x^{-s}]{\rightarrow}0$ is a short exact sequence of $R[x^s]$-module. Then we show $E_1+\overline{E_0}[x^{-s}]$ is not an injective left $R[x^s]$-module, in general.

A SYMBOLIC POWER OF THE IDEAL OF A STANDARD 𝕜-CONFIGURATION IN 𝕡2

  • Shin, Yong-Su
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제25권1호
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    • pp.31-38
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    • 2018
  • In [4], the authors show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type ($d_1$, ${\ldots}$, $d_s$) with $d_s$ > $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(md_s-1)$ is the number of lines containing exactly $d_s-points$ of ${\mathbb{X}}$ for $m{\geq}2$. They also show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)$ is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}s+1$. In this paper, we explore a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ and find that if ${\mathbb{X}}$ is a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)=3$, which is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}2$ instead of $m{\geq}s+1$.

RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF THE EXPONENTIAL DISTRIBUTION BY RECORD VALUES

  • LEE, MIN-YOUNG;CHANG, SE-KYUNG
    • 호남수학학술지
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    • 제26권4호
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    • pp.463-469
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    • 2004
  • In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function(pdf) f(x). Let $Y_n=max\{X_1,\;X_2,\;{\cdots},\;X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of $\{X_n,\;n{\geq}1\}$, if $Y_j>Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, $n{\geq}1$, where u(n)=min\{j{\mid}j>u(n-1),\;X_j>X_{u(n-1)},\;n{\geq}2\} and u(1) = 1. Suppose $X{\in}Exp(1)$. Then $\Large{E\;\left.{\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}}\right)=\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n)}}}\right)}$ and $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$.

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MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE

  • Li, Songxiao;Lou, Zengjian;Shen, Conghui
    • 대한수학회보
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    • 제57권2호
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    • pp.429-441
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    • 2020
  • Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓αp, M(𝓓p-1p, 𝓓q-1q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓p-2+sp, 𝓓q-2+sq) = {0}. However, X ∩ 𝓓p-1p ⊆ X ∩ 𝓓q-1q and X ∩ 𝓓p-2+sp ⊆ X ∩ 𝓓q-2+sp whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 p-2+sp, X∩𝓓q-2+sq) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓p-2+sp, X ∩ 𝓓q-2+sq) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗.

EXISTENCE OF SOLUTIONS FOR FRACTIONAL p&q-KIRCHHOFF SYSTEM IN UNBOUNDED DOMAIN

  • Bao, Jinfeng;Chen, Caisheng
    • 대한수학회보
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    • 제55권5호
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    • pp.1441-1462
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    • 2018
  • In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

Ethyl Methanesulfonate처리에 의한 수도 돌연변이에 관한 연구 (Studies on the Selection of Mutation in Rice Treated with Ethyl Methanesulfonate)

  • 권신한;이영일
    • 한국작물학회지
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    • 제24권2호
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    • pp.27-34
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    • 1979
  • 수도의 돌연변이를 보다 효율적으로 선발키 위한 수단을 모색코저 진흥의 성숙종자에 ethyl methanesulfonate(EMS)를 처이하여 $_{x}\textrm{M}_1식물체에 미치는 영향과 $_{x}\textrm{M}_2의 돌연변이율 등을 분얼별로 조사하고 이들 상호간의 관계를 검토해 보았다. EMS를 처리하면 $_{x}\textrm{M}_1식물체의 간장은 길어지는 반면, 분얼은 전반적으로 억제되었는데 주간과 상위 제 7, 8절의 1차분얼만은 오히려 출현율이 증가하는 치향이 있었다. 주간이 $_{x}\textrm{M}_1주내에서 최장간이 되는 율은 EMS의 농도가 높을수록 현저히 증가하였다. 분얼군별 돌연변이율은 1차분얼의 것이 가장 높아 이삭당으로 4.7%이었고, 2차분얼이 3.9%, 주간의 것이 2.5%로 가장 낮다. 또 변이율은 $_{x}\textrm{M}_1이삭의 불염율과도 관계가 있어 불염이 41~60%의 범위일 때 8.2%의 돌연변이율을 나타내어 가장 높고 이보다 높거나 낮은 군에서는 변이율이 낮았다. EMS를 돌연변이유기원으로 사용할 경우 $_{x}\textrm{M}_2 돌연변이율을 높이기 위해서는 주내에서 간장이 제일 큰 주간을 제외하고 나머지 1차 혹은 2차분얼의 이삭을 선발하되 $_{x}\textrm{M}_1이삭의 불염이 40~60%정도의 것을 취하여 다음 $_{x}\textrm{M}_2 세대를 양성하는 것이 $_{x}\textrm{M}_2의 돌연변이를 효율적으로 선발할 수 있는 수단이 될 것 같다.

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HOMOTOPY PROPERTIES OF map(ΣnℂP2, Sm)

  • Lee, Jin-ho
    • 대한수학회지
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    • 제58권3호
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    • pp.761-790
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    • 2021
  • For given spaces X and Y, let map(X, Y) and map*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map*(X, Y ; g) be the path component of map(X, Y) containing f and map*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane πn+mnℂP2) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣnℂP2, Sm) up to homotopy equivalence. We also determine the generalized Gottlieb groups Gn(ℂP2, Sm). Finally, we compute homotopy groups of mapping spaces map(ΣnℂP2, Sm; f) for all generators [f] of [ΣnℂP2, Sm], and Gottlieb groups of mapping components containing constant map map(ΣnℂP2, Sm; *).

ON THE CHARACTERISTIC S-AUTOMATA

  • PARK CHIN HONG
    • Journal of applied mathematics & informatics
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    • 제17권1_2_3호
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    • pp.779-786
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    • 2005
  • In this paper we shall discuss some properties derived from the characteristic S-automaton $_x(S)_M$, using the fact that ${\mu}_S$ is an equivalence relation on M. When $L_{m}:S{\rightarrow}M$ is a left translation and $L_{M}$ is a collection of $L_{m}'s$, we shall show $_x(S)_{M}{\cong}L_{M}$. If S is commutative, we have $_x(S)_{M{\times}N{\cong}L_{M{\times}N}$. Moreover when M and N are perfect, we have $L_{M{\times}N}{\cong}L_{M}{\times}L_{N}$ and $_x(S)_{M{\times}N}{\cong}_x(S)_{M}{\times}_x(S)_N$.

RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF THE WEIBULL DISTRIBUTION BY RECORD VALUES

  • Chang, Se-Kyung
    • Journal of applied mathematics & informatics
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    • 제23권1_2호
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    • pp.471-477
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    • 2007
  • In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

Cathodoluminescence and Longevity Properties of Potential Sr1-xMxGa2S4:Eu (M = Ba or Ca) Green Phosphors for Field Emission Displays

  • Ko, Ki-Young;Huh, Young-Duk;Do, Young-Rag
    • Bulletin of the Korean Chemical Society
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    • 제29권4호
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    • pp.822-826
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    • 2008
  • We report the cathodoluminescence and aging properties of a series of green phosphors of formula $Sr_{1-x}M_xGa_2S_4$:Eu (x = 0.0-1.0, M = Ba or Ca) that have potential applications in field emission displays (FEDs). The series of phosphors was synthesized via NaBr-aided solid-state reactions in a flowing $H_2S$ stream. A low level ($\sim$20%) of Ba or Ca substitution for Sr in $SrGa_2S_4$:Eu maintains the orthorhombic phase of pure $SrGa_2S_4$:Eu phosphors. Further, a low level ($\sim$20%) of Ba or Ca substitution for Sr in $SrGa_2S_4$:Eu provides various green colors and sufficient brightness for FED applications. Substitution of Ba or Ca for Sr in $SrGa_2S_4$:Eu also improved the stability of the phosphor when it was operated under electron-beam irradiation of 5 kV.