• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.187-199
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• 2024

In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the C^v-reducible and generalized C^v-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is C^v-reducible if and only if it is C-reducible and satisfies the 𝕋-condition. We study the generalized C^v-reducible Finsler manifold with a scalar π-form 𝔸. We show that a Finsler manifold (M, L) is generalized C^v-reducible with 𝔸 if and only if it is C-reducible and 𝕋 = 𝔸. Moreover, we prove that a Landsberg generalized C^v-reducible Finsler manifold with a scalar π-form 𝔸 is Berwaldian. Finally, we consider a special C^v-reducible Finsler manifold and conclude that a Finsler manifold is a special C^v-reducible if and only if it is special semi-C-reducible with vanishing 𝕋-tensor.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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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 Internet Computing and Services
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• v.6 no.6
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• pp.117-125
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• 2005

The dominator tree presents the dominance frontier from directed graph to the tree. we present the effective algorithm for constructing the dominator tree from arbitrary directed graph. The reducible flow graph was reduced to dominator tree after dominator calculation. And the irreducible flow graph was constructed to dominator-join graph using join-edge information of information table. For reducing the dominator tree from dominator-join graph, we implement the effective sequency reducible algorithm and delay reducible algorithm. As a result of implementation, we can see that the delay reducible algorithm takes less execution time than the sequency reducible algorithm. Therefore, we can reduce the flow graph to dominator tree effectively.

• Journal of applied mathematics & informatics
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• v.7 no.2
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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.

• Honam Mathematical Journal
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• v.33 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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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.

• Journal of Soil and Groundwater Environment
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• v.10 no.2
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• pp.44-51
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• 2005

Fractional composition and mobility of some heavy metals in sediments from Okdong stream are investigated. The fractional scheme for heavy metals in the sediment was established for five chemically defined heavy metal forms as adsorbed fraction, carbonate fraction, reducible fraction, organic fraction, and residual fraction. The most abundant fraction heavy metals in the sediments is reducible and secondly abundant is organic fraction. Adsorbed fraction is minor part of the total heavy metals. Mobilization of heavy metals in the sediments from Okdong stream occur $19.8{\sim}56.7%$ 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 $0.5{\sim}48.5%$ of total Zn, $2.6{\sim}48.1%$ of total Pb, and $0.2{\sim}36.9%$ 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.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.09a
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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.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.457-464
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• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.