• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.481-494
• /
• 1996

We introduced the generalized Sobolev space $H_\omega^s$ in [4]. In this paper, we introduce the space $H_\omega^s(\Omega)$ of the generalized distributions in $H_\omega^s$ with compact supports in $\Omega$ and the local generalized Sobolev spaces $H_{\omega loc}^s(\Omega)$ of the generalized distributions on $\Omega$ which are locally in $H_\omega^s$ and study their properties.

• Journal of applied mathematics & informatics
• /
• v.6 no.2
• /
• pp.467-486
• /
• 1999

We introduce the concepts of a generalized state machine and a generalized transformation semigroup and discuss their algebraic properties.

• Korean Journal of Mathematics
• /
• v.16 no.3
• /
• pp.291-300
• /
• 2008

In this paper, we introduce several types of r-semi-generalized fuzzy compactness and fuzzy r-compactness in fuzzy topological spaces and investigate the relations between these compactness.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1996.10a
• /
• pp.66-70
• /
• 1996

We investigate some of algebraic properties of T-generalized state machines, T-generalized transformation semigroups, coverings of T-generalized state machines and T-generalized transformation semigroups.

• The Pure and Applied Mathematics
• /
• v.16 no.2
• /
• pp.187-192
• /
• 2009

In this paper, we introduce the notions of $s{\gamma}$-generalized closed sets and $s{\gamma}$-generalized sets, and investigate some properties for such notions.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.409-415
• /
• 2011

We introduce the notion of weakly quasi generalized continuous functions, and investigate properties for the continuity.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.2
• /
• pp.125-136
• /
• 2022

The goal of this paper is to introduce the notion of generalized symmetric bi-f-derivations in lattices and to study some properties of generalized symmetric f-derivations of lattice. Moreover, we consider generalized isotone symmetric bi-f-derivations and fixed sets related to generalized symmetric bi-f-derivations.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.1
• /
• pp.79-99
• /
• 2006

In this paper, we define a class of functional defined on a very general function space $C_{a,b}[0,T]$ like a Fresnel class of an abstract Wiener space. We then define the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product of functionals on function space $C_{a,b}[0,T]$. Finally, we establish some relationships between the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $\mathcal{F}(C_{a,b}[0,T])$.

• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.117-127
• /
• 2013

As a generalization of fuzzy subsemigroups, the notion of ${\varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${\varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${\varepsilon}$-generalized fuzzy subsemigroups is also an ${\varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be ${\varepsilon}$-fuzzy idempotent is discussed. Using a given ${\varepsilon}$-generalized fuzzy subsemigroup, a new ${\varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${\varepsilon}$-generalized fuzzy subsemigroup is considered.

• Korean Journal of Mathematics
• /
• v.32 no.1
• /
• pp.27-42
• /
• 2024

In this paper we define generalized double group-groupoids and crossed modules over generalized group-groupoids. Also we prove that these algebraic structures are categorically equivalent.