• Korean Journal of Mathematics
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• v.14 no.2
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• pp.161-168
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• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• East Asian mathematical journal
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• v.31 no.5
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• pp.695-706
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• 2015

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.487-496
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• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.407-416
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• 2008

In this paper, we study property ($B_2$) and property ($D_2$) and their implications.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.759-764
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• 2004

Let X = {a} ${\cup}$ {$a_{i}$ ${$\mid$}$i $\in$ N} be a subspace of Euclidean space $E^2$ such that $lim_{{i}{\longrightarrow}{$\infty}}a_{i}$ = a and $a_{i}\;{\neq}\;a_{j}$ for $i{\neq}j$. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y) of all homeomorphisms on Y, where Y = {a, b} ${\cup}$ {$a_{i}{$\mid$}i{\in}Z$} is a subspace of $E^2$ such that $lim_{i}$-$\infty$ $a_{i}$ = b and $lim_{{i}{\longrightarrow}{$\infty}}a_{i}$ = a with the following properties; $a_{i}{\neq}a_{j}$ for $i{\neq}j$ and $a{\neq}b$.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.645-667
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• 2019

It has been little known when an Artinian point quotient has the strong Lefschetz property. In this paper, we find the Artinian point star configuration quotient having the strong Lefschetz property. We prove that if ${\mathbb{X}}$ is a star configuration in ${\mathbb{P}}^2$ of type s defined by forms (a-quadratic forms and (s - a)-linear forms) and ${\mathbb{Y}}$ is a star configuration in ${\mathbb{P}}^2$ of type t defined by forms (b-quadratic forms and (t - b)-linear forms) for $b=deg({\mathbb{X}})$ or $deg({\mathbb{X}})-1$, then the Artinian ring $R/(I{\mathbb_{X}}+I{\mathbb_{Y}})$ has the strong Lefschetz property. We also show that if ${\mathbb{X}}$ is a set of (n+ 1)-general points in ${\mathbb{P}}^n$, then the Artinian quotient A of a coordinate ring of ${\mathbb{X}}$ has the strong Lefschetz property.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.1-6
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• 2008

Duggal-Jeon-Kubrusly([2]) introduced Hilbert space operator T satisfying property ${\mid}T{\mid}^2{\leq}{\mid}T^2{\mid}$, where ${\mid}T{\mid}=(T^*T)^{1/2}$. In this paper we extend this property to general version, namely property B(n). In addition, we construct examples which distinguish the classes of operators with property B(n) for each $n{\in}\mathbb{N}$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2368-2373
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• 1994

The advancement of the mechanical properties of metal materials caused by a recent high technology contributes to the stability and productivity of mechanical structures. However, the advanced mechanical properties depends on the conditions of crystal boundaries and the improvement of the texture. Although the tensile strength and a hardness of a steel would be increased by the adding B, it seems to be a marked decreases of the toughness which caused in the weaken workability. This study is concerned with a characteristics of the B compound which will be mixed with $H_3BO_3$ and the metallic magnesium. What affected in the mechanical property and texture is checked by the strength and the texture test. As a result, it is shown that the improvement of the mechanical property and the texture homogeneity. In addition, it seems that a molten metal which is added by the B compound is deoxized and cleansed.

• The Journal of the Korean Society for Microbiology
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• v.20 no.1
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• pp.109-113
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• 1985

It was well known that B. pertussis cells possess protective antigen, histamine sensitizing factor, heatstable and labile toxin, hemagglutinin, agglutinogen and the others. Previous reports involving above antigenic properties of B. pertussis have been carried out for several years. However, leucocyte promoting property was not yet investigated. In this report, the results of studies on the leucocytosis, particulary the lymphocytosis, produced in mice by injecting pertussis vaccine were presented. Especially leucocyte promoting property and histamine sensitizing property of B. pertussis vaccine treated at various temperatures were compared. The relationship between the leucocyte promoting property and histamine sensitizing property was investigated. Results were as follows. 1. Although leucocytosis was significantly rised in both 0.5ml injection and 0.1ml injection of pertussis vaccine than in control, at the higher dose (0.5ml injection) an elevation in white cell count was more significant. The leucocyte responce to pertussis vaccine was greater following 0.5 ml injection than following 0.1ml injection. 2. Lymphocytosis was significantly rised in both 0.5ml injection and 0.1ml injection of pertussis vaccine than in control. At higher dose (0.5ml injection), an elevation in lymphocyte count was more significant. 3. Order of elevation in differential leucocyte counts was lymphocyte, polymorphonuclear leucocyte and monocyte. 4. The leucocyte response to pertussis vaccine was 2 fold greater following intravenous injection than following subcutaneous injection. 5. Decrease leucocyte promoting activity and histamine sensitizing activity resulted from exposure to temperature above $56^{\circ}C$. Histamine sensitizing activity of pertussis vaccine treated at various temperatures paralleled leucocyte promoting activity.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.23-32
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• 1998

In the present paper the author studies the decomposition property ($\delta$) of the bounded linear operators.