• 대한수학회논문집
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• 제11권4호
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• pp.1067-1075
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• 1996

We show that every ultrapure space is weakly star reducible, and that every countably compact weakly star reducible space is compact. We also pose open problems.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.665-671
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• 2000

A matrix whose entries consist of the symbols +.- and 0 is called a sign pattern matrix . In 1994 , Eschenbach gave a graph theoretic characterization of irreducible sign idempotent pattern matrices. In this paper, we give a characterization of reducible sign idempotent matrices. We show that reducible sign idempotent matrices, whose digraph is contained in an irreducible sign idempotent matrix, has all nonnegative entries up to equivalences. this extend the previous result.

• 호남수학학술지
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• 제33권3호
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• pp.355-366
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• 2011

In this paper we investigate criteria that for an irreducible monic quadratic polynomial f(x) ${\in}$ $\mathbb{Q}$[x], $f{\circ}g$ is reducible over $\mathbb{Q}$ for an irreducible polynomial g(x) ${\in}$ $\mathbb{Q}$[x]. Odoni intrigued the discussion about an explicit form of irreducible polynomials f(x) such that $f{\cric}f$ is reducible. We construct a system of infitely many such polynomials.

• 대한수학회지
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• 제57권5호
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• pp.1187-1237
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• 2020

Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2003년도 추계학술발표회
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• pp.56-63
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• 2003

Fractional composition and mobility of sediments some heavy metals in Okdong stream are investigated. The fractional scheme for sediment heavy metal was made for five chemically defined heavy metal forms as adsorbed fraction, carbonate fraction, reducible fraction, organic fraction, and residual fraction (Tessier et at., 1979). The most abundant fraction of the sediment heavy metal is reducible and secondly abundant organic fraction. Adsorbed fraction is minor part of the total heavy metals. Mobilization of sediment heavy metals in stream Okdong is occur 19.8∼56.7% of total cadmium concentrate. The most abundant fraction of the sediment metal is organic fraction in Cu, Pb metals investigated. Labile fraction of sediment metals are 0.5%∼48.5% of total Zn, 2.6%∼48.1% of total Pb, 0.2∼36.9% of total Cu respectively, Most of labile fraction consists of reducible fraction for Cd, Zn, adsorbed fraction for Pb, reducible fraction for Cu, adsorbed fraction for Ni. The Mobilization of Zn and Cu is most likely to occur when oxygen depletes and that of Pb and Ni occurs when physical impact, oxygen depletion and pH reduction.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2016년도 제50회 동계 정기학술대회 초록집
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• pp.430.1-430.1
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• 2016

We present the concept of reducible fugitive material that conformally surrounds core Cu nanowire (NW) to fabricate transparent conducting electrode (TCE). Reducing atmosphere can corrodes/erodes the underlying/surrounding layers and might cause undesirable reactions such impurity doing and contamination, so that hydrogen-/forming gas based annealing is impractical to make device. In this regards, we introduce novel reducible shell conformally surrounding indivial CuNW to provide a protection against the oxidation when exposed to both air and solvent. Uniform copper lactate shell formation is readily achievable by injecting lactic acid to the CuNW dispersion as the acid reacts with the surface oxide/hydroxide or pure copper. Cu lactate shell prevents the core CuNW from the oxidation during the storage and/or film formation, so that the core-shell CuNW maintains without signficant oxidation for long time. Upon simple thermal annealing under vacuum or in nitrogen atmosphere, the Cu lactate shell is easily decomposed to pure Cu, providing an effective way to produce pure CuNW network TCE with typically sheet resistance of $19.8{\Omega}/sq$ and optical transmittance of 85.5% at 550 nm. Our reducible copper lactate core-shell Cu nanowires have the great advantage in fabrication of device such as composite transparent electrodes or solar cells.

• 한국지하수토양환경학회지:지하수토양환경
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• 제10권2호
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• pp.44-51
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• 2005

옥동천 퇴적물을 대상으로 중금속의 존재형태 및 이동성에 관하여 조사하였다. 퇴적물내의 중금속의 존재형태는 adsorbed fraction, carbonate fraction, reducible fraction, organic fraction, and residual fraction 다섯 가지 형태로 분류하였으며, 존재형태 중 제일 많은 부분을 차지하는 부분은 reducible fraction이며 다음으로 organic fraction라 residual fraction으로 나타났다. Adsorbed fraction은 중금속의 존재형태 미미한 부분으로 나타났다. 옥동천 퇴적물내 의 총 카드뮴 중 수체로 이동 가능한 부분은 $19.8{\sim}56.7%$이며, 구리, 납의 경우 대부분이 organic fraction으로 나타났다. 구리와 납의 경우 이동 가능한 형태는 납의 경우 총 납의 농도 중 $2.6{\sim}48.1%$, 구리는 $0.2{\sim}36.9%$로 나타났으며, 아연은 $0.5{\sim}48.5%$로 나타났다. 카드뮴, 아연, 구리의 경우 이동 가능한 부분 중 대부분이 reducible fraction이며, 납과 니켈의 경우 adsorbed fraction으로 나타났다. 구리와 아연의 이동이 기능한 경우는 수중의 산소의 유무에 의해 결정되며, 납이나 니켈의 경우 수중에서의 물리적 영향, 수소이온의 농도가 증가, 산소의 고갈 등에 의해 수층으로 이동할 가능성이 높다.

• 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.

• 대한수학회지
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• 제54권4호
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• pp.1231-1242
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• 2017

In this paper, we show that, under some conditions, self-maps of product spaces can be represented by the composition of two specific self-maps if their induced homomorphism on the i-th homotopy group is an automorphism for all i in some section of positive integers. As an application, we obtain closeness numbers of several product spaces.

• 충청수학회지
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• 제27권1호
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• pp.39-46
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• 2014

We completely classify the dimension of secant varieties $Sec_1(\mathbb{X}_{{\lambda},2})$ to the variety of reducible forms in $\mathbf{k}[x_0,x_1,x_2]$ when ${\lambda}=(1,{\cdots},1,3,{\cdots},3$), and also show that they are all non-defective.