• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.115-119
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• 1997

We show that if $f_{i}$:$X_{i}$ longrightarrow Y is strongly continuous(resp. weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map), then F : $X_1 \bigoplus X_2$longrightarrow Y is strongly continuous(resp.weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map).

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.224-230
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• 2013

In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy ${\theta}$-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy ${\theta}$-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy ${\theta}$-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy ${\theta}$-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.335-346
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• 2000

This paper discusses the relation of fuzzy sets satisfying some types of fuzzy covering properties. We give some characterizations of such fuzzy sets and investigate a few properties.

• East Asian mathematical journal
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• v.24 no.4
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• pp.329-338
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• 2008

The aim of this paper is to introduce a new generalization of fuzzy faintly continuous functions called fuzzy faintly pre-continuous functions and also we have introduced and studied weakly fuzzy pre-continuous functions. Several characterizations of fuzzy faintly pre-continuous functions are given and some interesting properties of the above functions are discussed.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.33-45
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• 1999

In this paper, we are interested in studying weak covering properties in the presence of a countable compact condition. The purpose of this paper is to characterize an ideal weakly $\delta$$\theta$-refinable space and to show that every ideal weakly $\delta$$\theta$-refinable space is isocompact. Also, we consider the behavior under mappings of ideal weakly $\delta$$\theta$-refinable properties and productivity of ideal weakly $\delta$$\theta$-refinable properties.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.155-164
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• 2007

It is the objective of this paper to study further the notion of ${\Lambda}_s$-semi-${\theta}$-closed sets which is defined as the intersection of a ${\theta}$-${\Lambda}_s$-set and a semi-${\theta}$-closed set. Moreover, introduce some low separation axioms using the above notions. Also we present and study the notions of ${\Lambda}_s$-continuous functions, ${\Lambda}_s$-compact spaces and ${\Lambda}_s$-connected spaces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.244-247
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• 2002

The performance of the precision micro-positioning 4-dof stage is presented. The compact design utilizes the monolithic mechanism to achieve the translation in the Z axis and rotation in the $\theta$ z, $\theta$ x and $\theta$ y axes with high stiffness and high damping. Hysteresis, nonlinearity, and drift of the piezoelectric effects are improved by incorporating the sensors in a feedback control. Experiments demonstrate that the micro-positioning stage is capable of 2nm resolution over the travel range of 25$\mu\textrm$ m in the Z axis, 0.0l7 $\mu\textrm$ rad resolution over the 170$\mu\textrm$ rad in the $\theta$ z and 0.011 $\mu\textrm$ rad resolution over the $\mu\textrm$ rad in the $\theta$ x and $\theta$ y axes. The cross-axis interferences among the axes are at a noise range. This stage is available for positioning error compensation of the XY stage with large stroke.

• Bulletin of the Korean Chemical Society
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• v.22 no.2
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• pp.213-218
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• 2001

Presented are the STM images of self-assembled monolayer of 2-mercaptoethanol on Au(111). Striped structures of ($6{\times}3_{\frac{1}{2}}$), ($5{\times}3_{\frac{1}{2}}$), ($4{\times}3_{\frac{1}{2}}$) and compact-($5{\times}3_{\frac{1}{2}}$) were observed after annealing at $80^{\circ}C.$ Analysis of the ordered structures revealed that the basic fundamental units of the ordered structures were three crystallographically non-equivalent ($3_{\frac{1}{2}}{\times}3_{\frac{1}{2}}$) $R30^{\circ}$ assemblies, and that the way of combination of the assemblies produced the four different structures. The($6{\times}3_{\frac{1}{2}}$) structure ( $\theta$ = 0.33) was composed of one ($3_{\frac{1}{2}}{\times}3_{\frac{1}{2}}$)$R30^{\circ}$ assembly, while the ($5{\times}3_{\frac{1}{2}}$) ( $\theta$ = 0.30) and ($4{\times}3_{\frac{1}{2}}$) ( $\theta$ = 0.38) structures were consisted of two ($3_{\frac{1}{2}}{\times}3_{\frac{1}{2}}$) $R30^{\circ}$ assemblies, separated by 5a and 4a, respectively. Furthermore, the compact-(5X 3½) structure ( $\theta$ = 0.50) was obtained by overlapping three ($3_{\frac{1}{2}}{\times}3_{\frac{1}{2}}$) $R30^{\circ}$ assemblies. In spite of the diversity in the adsorption structures, all the adsorption sites of 2-mercaptoethanol were fundamentally identical. On the other hand, the unannealed primitive SAM of 2-mercaptoethanol was characterized by two observations: a short-range order keeping the adsorbed molecules at approximately $3_{\frac{1}{2}}$ a and the small domains of the striped structures supporting that the observed surface structures on the annealed surface were the extension of the primitive layer of 2-mercaptoethanol. Comparing these observations with the already published structures of ethanthiol, it was concluded that the interaction between the hydroxyl groups of 2-mercaptoethanol might play a significant role in the adsorption step of 2-mercaptoethanol on Au(111) to organize the adsorption structures different from those of ethanthiol.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.593-604
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• 2018

Recently, a new version of expansiveness which is closely attached to some certain weak version of hyperbolicity was given for $C^1$ vector fields as following: a $C^1$ vector field X will be called rescaling expansive on a compact invariant set ${\Lambda}$ of X if for any ${\epsilon}$ > 0 there is ${\delta}$ > 0 such that, for any $x,\;y{\in}{\Lambda}$ and any time reparametrization ${\theta}:{\mathbb{R}}{\rightarrow}{\mathbb{R}}$, if $d({\varphi}_t(x),\,{\varphi}_{{\theta}(t)}(y)){\leq}{\delta}{\parallel}X({\varphi}_t(x)){\parallel}$ for all $t{\in}{\mathbb{R}}$, then ${\varphi}_{{\theta}(t)}(y){\in}{\varphi}_{(-{\epsilon},{\epsilon})}({\varphi}_t(x))$ for all $t{\in}{\mathbb{R}}$. In this paper, some equivalent definitions for rescaled expansiveness are given.