• 호남수학학술지
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• 제38권1호
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• pp.85-93
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• 2016

Let A be an abelian variety defined over a number field K and let L be a degree 3 non-Galois extension of K. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Assuming that III(A/L) is finite, we compute [III(A/K)][III($A_{\varphi}/K$)]/[III(A/L)], where [X] is the order of a finite abelian group X.

• 한국재료학회지
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• 제19권4호
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• pp.186-191
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• 2009

Thermoelectric power and resistivity are measured for the perovskite $LaNi_{1-x}Ti_xO_3$ ($x{\leq}0.5$) in the temperature range 77 K - 300 K. The measured thermoelectric power of $LaNi_{1-x}Ti_xO_3$ ($x{\leq}0.5$) increases linearly with temperature and is represented by A + BT. The x = 0.1 sample showed metallic behavior, the x = 0.3 showed metal and insulating transition around 150 K, and x = 0.5 showed insulating behavior the over the whole temperature range. The electrical resistivity of x = 0.1 shows linear temperature dependence over the whole temperature range and $T^2$ dependence. On the other hand, the electrical resistivity of x = 0.3 shows a linear relation between $ln{\rho}$ and $T^{-1/4}$ (variable range hopping mechanism) in the range of 77 K to 150 K. For x = 0.5, the temperature dependence of resistivity is characteristic of insulating materials; the resistivity data was fitted to an exponential law, such as ln(${\rho}/T$) and $T^{-1}$, which is usually attributed to a small polaron hopping mechanism. These experimental results are interpreted in terms of the spin polaron (x = 0.1) and variable range hopping (x = 0.3) or small polaron hopping (x = 0.5) of an almost localized $Ni^{3+}$ 3d polaron.

• 청정기술
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• 제19권1호
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• pp.13-21
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• 2013

다른 분율의 Cs이 포함된 Pt/$Cs_xH_{3-x}PW_{12}O_{40}$ 촉매를 제조하여 셀룰로우스의 폴리올로의 수소화분해반응를 수행하였다. 촉매의 비표면적과 Pt의 분산도는 Pt/$Cs_xH_{3-x}PW_{12}O_{40}$ 촉매의 Cs 함량이 증가함에 따라 증가하였다. 그러나 Pt/$Cs_xH_{3-x}PW_{12}O_{40}$ 촉매의 Cs의 함량이 변함에도 불구하고 비슷한 폴리올 수득률을 보였다. Pt/$Cs_xH_{3-x}PW_{12}O_{40}$ 촉매의 반응 활성은 Ni/W/SBA-15와 두 가지의 복합촉매(Pt/AC+$H_3PW_{12}O_{40}$과 Pt/AC+$Cs_{3.0}PW_{12}O_{40}$)와 비슷하였다. 이 반응을 진행하는 동안 Pt/$Cs_xH_{3-x}PW_{12}O_{40}$ 촉매로부터 헤테로폴리 음이온이 침출되는 것을 확인하였다.

• 대한수학회논문집
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• 제22권2호
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• pp.183-194
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• 2007

For an irreducible binomial polynomial $f(x)=x^n-b{\in}K[x]$ with a field K, we ask when does the mth iteration $f_m$ is irreducible but $m+1th\;f_{m+1}$ is reducible over K. Let S(n, m) be the set of b's such that $f_m$ is irreducible but $f_{m+1}$ is reducible over K. We investigate the set S(n, m) by taking K as the rational number field.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2012년도 춘계학술대회
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• pp.237-240
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• 2012

주기가 $N=2^n-1$인 이진수열은 공학과 과학의 많은 분야에서 폭넓게 사용된다. 코드분할 다중접속(CDMA) 통신시스템과 스트림암호시스템은 잘 알려진 응용분야이다. 본 논문에서는 유한체위에서 방정식 $(x+1)^d=x^d+1$의 특성을 분석한다. 특히 이 방정식의 $d$는 이진수열의 상호상관관계를 분석하는데 사용된다.

• 대한수학회지
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• 제53권2호
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• pp.447-459
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• 2016

Let D be an integral domain, {$X_{\alpha}$} be a nonempty set of indeterminates over D, and $D{\mathbb{[}}\{X_{\alpha}\}{\mathbb{]}_1}$ be the first type power series ring over D. We show that if D is a t-SFT $Pr{\ddot{u}}fer$ v-multiplication domain, then $D{\mathbb{[}}\{X_{\alpha}\}{\mathbb{]}}_{1_{D-\{0\}}}$ is a Krull domain, and $D{\mathbb{[}}\{X_{\alpha}\}{\mathbb{]}}_1$ is a $Pr{\ddot{u}}fer$ v-multiplication domain if and only if D is a Krull domain.

• 대한수학회지
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• 제48권5호
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• pp.1065-1081
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• 2011

For any field F, a polynomial f $\in$ F[$x_1,x_2,{\ldots},x_k$] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F. We present some results giving new integrally indecomposable classes of polygons. Consequently, we have some criteria giving many types of absolutely irreducible bivariate polynomials over arbitrary fields.

• Bulletin of the Korean Chemical Society
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• 제23권7호
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• pp.953-956
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• 2002

Excess molar volumes (Vm E ) of binary liquid mixtures: xC6H5CH3 + (1-x1)CH3CN or + (1-x1)C6H5NO2, or + (1-x1)C2H5NO2 have been determined as a function of mole fraction of C6H5CH3 (x) at a temperature of 303.15 K over a entire range of composition. The densities of the binary liquid mixtures were determined by pycnometrically. The VmE values of the mixtures have been found to be negative over the whole composition in order of C6H5CH3 + C6H5NO2, < C6H5CH3 + CH3CN, and < C6H5CH3 + C2H5NO2. The negative magnitude of VmE suggests the presence of intermolecular interaction in the three binary liquid mixtures.

• 대한수학회논문집
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• 제28권1호
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• pp.39-54
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• 2013

The purpose of this paper is to find a description of the cyclic codes of length $2^n$ over $\mathbb{Z}_4$. We show that any ideal of $\mathbb{Z}_4$[X]/($X^{2n}$ - 1) is generated by at most two polynomials of the standard forms. We also find an explicit description of their duals in terms of the generators.

• 대한수학회보
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• 제30권1호
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• pp.61-64
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• 1993

In this paper, we show that if R is a local-global domain then the Question holds. McDonald and Waterhouse in [6] and Estes and Guralnick in [5] introduced the concept of local-global rings (so called rings with many units) independently. A local-global ring is a commutative ring R with 1 satisfying; if a polynomial f in R[ $x_{1}$, .., $x_{n}$] represents a unit over $R_{P}$ for every maximal ideal P in R, then f represents a unit over R. Such rings include semilocal rings, or more generally, rings which are von Neumann regular mod their Jacobson radical, and the ring of all algebraic integers.s.s.