• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.43-55
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• 1997

Suppose that D is a domain in the extended complex plane $\overline{C} = C \cup {\infty}$. For each $z_0 \in C$ and $C < r < \infty$, we let $B(z_0, r) = {z \in C : $\mid$z - z_0$\mid$ < r}$ and $S(z_0, r) = \partial B(z_0, r)$. For non-empty sets A, $B \subset \overling{C}$, diam (A) is the diameter of A and d(A, B) is the distance of A and B.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.531-540
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• 2015

If T is an unbounded hyponormal operator on an infinite dimensional complex Hilbert space H with ${\rho}(T){\neq}{\phi}$, then it is shown that T satisfies Weyl's theorem, generalized Weyl's theorem, Browder's theorem and generalized Browder's theorem. The equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w) with property (b) have also been established. It is also shown that a-Browder's theorem holds for T as well as its adjoint $T^*$.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.1-17
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• 2014

Instructions for the commutative property of multiplication at elementary schools tend to be based on checking the equality between the quantities of 'a times b 'and b' times a, ' for example, $3{\times}4=12$ and $4{\times}3=12$. This article critically examined the approaches to teach the commutative property of multiplication from Kant's perspective of mathematical knowledge. According to Kant, mathematical knowledge is a priori. Yet, the numeric exploration by checking the equality between the amounts of 'a groups of b' and 'b groups of a' does not reflect the nature of apriority of mathematical knowledge. I suggest we teach the commutative property of multiplication in a way that it helps reveal the operational schema that is necessarily and generally involved in the transformation from the structure of 'a times b' to the structure of 'b times a.' Distributive reasoning is the mental operation that enables children to perform the structural transformation for the commutative property of multiplication by distributing a unit of one quantity across the other quantity. For example, 3 times 4 is transformed into 4 times 3 by distributing each unit of the quantity 3, which results in $3{\times}4=(1+1+1){\times}4=(1{\times}4)+(1{\times}4)+(1{\times}4)+(1{\times}4)=4+4+4=4{\times}3$. It is argued that the distributive reasoning is also critical in learning the subsequent mathematics concepts, such as (a whole number)${\times}10$ or 100 and fraction concept and fraction multiplication.

• Proceedings of the Korean Society of Crop Science Conference
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• 2022.10a
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• pp.184-184
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• 2022

This study was aimed to evaluate the antioxidant activity and bioactive property of extracts from a purple-colored wheat variety 'Arriheuk' (Triticum aestivum L.) wheatgrass, affected by light emitting diode irradiation (LED). The wheatgrass was cultivated for 10 days after sowing in a growth chamber under the following LED conditions: R1B1 (Red:Blue = 1:1), R7B3 (Red:Blue = 7:3), and R3B7 (Red:Blue = 3:7). We examined antioxidant activity of the hot water extracts of wheatgrass using DPPH and ABTS free radicals scavenging assays. At the concentration of 10,000 ㎍/ml, the extract from R1B1 showed the highest DPPH free radical scavenging activity(79.29%), but its ABTS free radical scavenging activity was the lowest(32.0%). To evaluate bioactive property of the wheatgrass, we examined the change of natural killer (NK) cell activity affected by the wheatgrass extracts in vitro. At the concentration of 500㎍/ml, NK cell activity was most highly enhanced by the extract from R1B1(181.6%), and the activity was 176.1% (R7B3) and 144.6%(R3B7), respectively. These results suggest that the functional property of 'Arriheuk' wheatgrass would be enhanced by LED irradiation condition.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1027-1040
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• 2012

The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.535-543
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• 2009

In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford's boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford's boundedness condition (B).

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• Korean Journal of Metals and Materials
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• v.48 no.8
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• pp.780-789
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• 2010

The aim of this study is to evaluate the microstructure and tensile property of in-situ (TiB+TiC) particulate reinforced titanium matrix composites (TMCs) synthesized by the investment casting process. Boron carbide ($1,500{\mu}m$ and $150{\mu}m$) was added to the titanium matrix during vacuum induction melting, which can provide the in-situ reaction of $5Ti+B_4C{\rightarrow}4TiB+TiC$. 0.94, 1.88 and 3.76 wt% of $B_4C$ were added to the melt. The phases identification of the in-situ synthesized TMCs was examined using scanning electron microscopy, an X-ray diffractometer, an electron probe micro-analyzer and transmission electron microscopy. Tensile properties of TMCs were investigated in accordance with the reinforcement size and volume fraction. The improvement of tensile property of titanium matrix composites was caused by load transfer from the titanium matrix to the reinforcement and by grain refinement of titanium matrix and reinforcements.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.255-260
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• 2011

In this paper, we define the intuitionistic fuzzy contraction, and obtain some fixed point theorem using common property(E.A.) and weakly compatibility in intuitionistic fuzzy metric space.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.65-72
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• 1998

We investigate a chain of properties of real function algebras along the analogous proofs of the complex cases such as the fact that any real function algebra which is both maximal and essential is pervasive. And some properties of real function algebras with a vertex property will be discussed.