• 대한수학회지
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• 제43권1호
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• pp.65-76
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• 2006

Let $\tau$ be a hereditary torsion theory and let p be a prime ideal of a commutative ring R. We study the existence of (minimal) $\tau-injective$ submodules of the injective hull of R/p.

• East Asian mathematical journal
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• 제23권2호
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• pp.197-206
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• 2007

The purpose of this paper is to show some results of M. Bresar and J. Vukman concerning orthogonal derivations of semiprime rings in [3] for (${\sigma},\;{\tau}$)-derivations and generalized (${\sigma},\;{\tau}$)-derivations in $\Gamma$-rings.

• 한국재료학회지
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• 제5권1호
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• pp.22-35
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• 1995

본 연구는 Mn-Al 합금계에서 $\tau$상의 분율이 가장 높은 기준 조성을 결정하고 이 기준 조성중 Mn 원자의 일부를 Cu와 Fe 원자로 치환하였을 때 $\tau$상의 안정성과 자기적 성질의 변화를 조사하엿다. Mn-Al 합금계에서 $\tau$상의 분률과 자기적 특성이 가장 높은 조성은 $Mn_{0.56}Al_{0.44}$이었다. $Mn_{0.56-X}M_{X}Al_{0.44}$ 합금계의 결정구조는 M=Cu의 경우, 노냉시편과 소둔시편은 x $\leq$ 0.08 범위에서 $\tau$상과 $\beta$-Mn상이 나타났고, 0.10 $\leq x \leq$ 0.12 범위에서는 $\tau$상과 $\kappa$상이 나타났으며, 0.15 $\leq$ 0.20 범위에서는 $\kappa$상만이 존재하였다. 급속응고시편은 x=0.04에서 $\varepsilon$상과 $\tau$상이 공존하였고, x=0.06 및 x=0.08에서는 $\kappa$상과 $\tau$상이 공존하였으며 x=0.12와 x=0.20에서는 $\kappa$ 상만이 존재하였다. M=Fe의 경우, 노냉시편은 x < 0.08 범위에서 $\tau$상, $\beta$-Mn상 및 $\gamma_{2}$상이 나타났고, x > 0.10 범위에서는 $\kappa$상과 $\beta$-Mn$상이 나타났다. 급속응고시편은 x $\leq$ 범위에서는 $\varepsilon$상과 $\gamma_{2}$상이 나타났지만, 미량의 $\tau$상과 $\kappa$상도 존재함을 알 수 있었다. X=0.12와 x=0.20에서는 $\kappa$상만이 존재하엿다. $Mn_{0.56}Al_{0.44}$ 합금에서 노냉시편과 소둔시편의 포화자화값은 40-45(emu/g)이었으며 curie 온도는 약 650K였다. 급속응고 시편의 포화자화값은 약 50-52(emu/g), Curie 온도는 약 644K엿다. 소둔시편 및 급냉리본 모두 큰 잔류자화/포화자화 비(~0.7)를 나타냈으며, 특히 급냉리본의 경우 77K에서 큰 잔류자화값(~48emu/g)을 보여주었다. $Mn_{0.56-X}M_{X}Al_{0.44}$ 합금계의 자기장에 따른 자화값의 변화는 강자성이 형태를 보여주었고 자화값은 강자성과 $\tau$상과 $\kappa$상의 분율에 따라 결정되며 M=Cu일때, 최대자발자화값은 x=0.15에서 약 64.5(emu/g)이었다. M=Fe일 때 자화값은 x=0.15에서 최대자발자화값($\sigma_{0.0}$=66.4emu/g)이 나타났으며 $\tau$상 영역에서의 값보다 높았다. Curie 온도는 M=Cu, Fe에 관계없이 x가 증가함에 따라 감소하였다.

• 대한수학회지
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• 제47권3호
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• pp.523-535
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• 2010

In this paper, we show that Jordan $\tau$-centralizers and local $\tau$-centralizers are $\tau$-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if $\cal{L}$ is a CDCSL and $\cal{M}$ is a dual normal unital Banach $alg\cal{L}$-bimodule, then every local generalized derivation of above type from $alg\cal{L}$ into $\cal{M}$ is a generalized derivation.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.599-604
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• 2015

Kendall's tau statistic has been applied to test an association of bivariate random variables. However, incomplete bivariate data with a truncation and a censoring results in incomparable or unorderable pairs. With such a partial information, Tsai (1990) suggested a conditional tau statistic and a test procedure for a quasi independence that was extended to more diverse cases such as double truncation and a semi-competing risk data. In this paper, we also employed a conditional tau statistic to estimate an association of bivariate interval censored data. The suggested method shows a better result in simulation studies than Betensky and Finkelstein's multiple imputation method except a case in cases with strong associations. The association of incubation time and infection time from an AIDS cohort study is estimated as a real data example.

• 대한수학회보
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• 제49권4호
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• pp.693-704
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• 2012

We consider Weierstrass functions and divisor functions arising from $q$-series. Using these we can obtain new identities for divisor functions. Farkas [3] provided a relation between the sums of divisors satisfying congruence conditions and the sums of numbers of divisors satisfying congruence conditions. In the proof he took logarithmic derivative to theta functions and used the heat equation. In this note, however, we obtain a similar result by differentiating further. For any $n{\geq}1$, we have $$k{\cdot}{\tau}_{2;k,l}(n)=2n{\cdot}E_{\frac{k-l}{2}}(n;k)+l{\cdot}{\tau}_{1;k,l}(n)+2k{\cdot}{\sum_{j=1}^{n-1}}E_{\frac{k-1}{2}(j;k){\tau}_{1;k,l}(n-j)$$. Finally, we shall give a table for $E_1(N;3)$, ${\sigma}(N)$, ${\tau}_{1;3,1}(N)$ and ${\tau}_{2;3,1}(N)$ ($1{\leq}N{\leq}50$) and state simulation results for them.

• 대한수학회지
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• 제40권6호
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• pp.977-998
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• 2003

Let k be an imaginary quadratic field, η the complex upper half plane, and let $\tau$ $\in$ η $textsc{k}$, p = $e^{{\pi}i{\tau}}$. In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever $\tau$ are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j($\tau$). And we construct an elliptic curve E : $y^2$ = $x^3$ ＋ 3 $x^2$ ＋ {3-(j/256)}x ＋ 1 with j = j($\tau$) $\neq$ 0 and P = (equation omitted) $\in$ E.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.173-188
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• 2014

In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.13-30
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• 2007

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

• 대한수학회지
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• 제54권6호
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• pp.1853-1878
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• 2017

Let $\{U(t,s)\}_{t{\geq}s}$ be a periodic evolutionary process with period ${\tau}$ > 0 on a Banach space X. Also, let L be the generator of the evolution semigroup associated with $\{U(t,s)\}_{t{\geq}s}$ on the phase space $P_{\tau}(X)$ of all ${\tau}$-periodic continuous X-valued functions. Some kind of variation-of-constants formula for the solution u of the equation $({\alpha}I-L)^nu=f$ will be given together with the conditions on $f{\in}P_{\tau}(X)$ for the existence of coefficients in the formula involving the monodromy operator $U(0,-{\tau})$. Also, examples of ODEs and PDEs are presented as its application.