• 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.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.23-30
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• 2014

For two positive integers r and s, $\mathcal{G}$(n; r; ${\theta}_s$) denotes to the class of graphs on n vertices containing no r of edge disjoint ${\theta}_s$-graphs and f(n; r; ${\theta}_s$) = max{${\varepsilon}(G)$ : G ${\in}$ $\mathcal{G}$(n; r; ${\theta}_s$)}. In this paper, for integers r, $k{\geq}2$, we determine f(n; r; ${\theta}_{2k+1}$) and characterize the edge maximal members in G(n; r; ${\theta}_{2k+1}$).

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1371-1376
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• 1990

The paper presents a method of constructing simple fuzzy control rules for the determination of stabilizing signals of automatic voltage regulator and governor, which are controllers of electric power systems. Fuzzy control rules are simplified by considering a coordinate transformation with the rotation angle .theta. on the phase plane, and by expanding the range of membership functions. Also, two rotation angles .theta. $_{1}$ and .theta. $_{2}$ are selected for the linearizable region and the nonlinear one of the system, respectively. Here, .theta. $_{1}$ is chosen by the pole assignment method, and .theta. $_{2}$ by a performance index. Fuzzy inference is applied to the connection of two rotation angles .theta. $_{1}$ and .theta. $_{1}$ by regarding the distance from the desired equilibrium point as a variable of condition parts. The control effect is demonstrated by an application of the proposed method to one-machine infinite-bus power system.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1025-1036
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• 2010

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1043-1059
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• 2019

In this paper, we use some theta function identities involving two parameters h_n,k and h'_n,k for the theta function φ to establish new evaluations of Ramanujan's cubic continued fraction.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• 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 Chungcheong Mathematical Society
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• v.20 no.2
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• pp.97-107
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• 2007

Ramanujan gave six identities involving ${\theta}$-function expansion. We extended these identities by introducing a free parameter. We also give the interpretation of one of the identities using theory of partitions.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.27-36
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• 2006

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. We introduce the concept of linear ${\theta}$-derivations on $JB^*$-triples, and prove the Cauchy-Rassias stability of linear ${\theta}$-derivations on $JB^*$-triples.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.435-437
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• 2009

In this paper we prove that every Jordan $\theta$-derivation on a Lie triple system is a $\theta$-derivation. Specially, we conclude that every Jordan derivation on a Lie triple system is a derivation.