• Honam Mathematical Journal
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• v.33 no.2
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• pp.279-300
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• 2011

For a subset system M on any poset, M-Scott notions, such as M-way below relation,M-continuity,M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset is M-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satisfies the property of interpolation then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.54-58
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• 2010

We introduce the concepts of interval-valued fuzzy $m{\alpha}$-open sets and interval-valued fuzzy $m{\alpha}$-continuous mappings. And we study some characterizations and properties of such concepts.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.603-611
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\alpha}$-open set on a fuzzy minimal space and some basic properties. We also introduce the concepts of fuzzy $r$-M ${\alpha}$-continuous and fuzzy $r$-M($M^*$) ${\alpha}$-open mappings, and investigate characterization for such mappings.

• Kyungpook Mathematical Journal
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• v.31 no.2
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• pp.275-287
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• 1991

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.787-805
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• 2023

Let (Ω, µ) be a measure space and {τ_α}_α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space 𝓗 of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that $$\sup\limits_{{\alpha},{\beta}{\in}{\Omega},{\alpha}{\neq}{\beta}}\,{\mid}{\langle}{\tau}_{\alpha},\,{\tau}_{\beta}{\rangle}{\mid}^{2m}\,{\geq}\,{\frac{1}{({\mu}{\times}{\mu})(({\Omega}{\times}{\Omega}{\backslash}{\Delta})}\;\[\frac{{\mu}({\Omega})^2}{\({d+m-1 \atop m}\)}-({\mu}{\times}{\mu})({\Delta})\],\;{\forall}m{\in}{\mathbb{N}}.$$ This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

• Microbiology and Biotechnology Letters
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• v.27 no.1
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• pp.46-53
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• 1999

The purpose of this study was to optimize the conditions of continuous mixed culture of C.butyricum and R. spaeroides K-7, which were able to produce hydrogen using biomass-dreived substrate. To investigate the possibility of continuous culture, semi-continuous culture was carried out for 20 days. In semi-continuous culture using the reactor system, the replacement rate of fresh medium was 30% of total medium volume for the highest hydrogen evolution. In continuous culture, the optimum dilution rate was determined to be 0.05$h^{-1}$. The continuous culture produced 3.1 times as compared with the hydrogen on batch culture. On the other hand, the continuous mixed culture produced 1.3~2.1 times as much as hydrogen of the continuous monoculture of C. butyricum. When 10g of glucose in the media (1l) was supplied as a carbon source on continuous culture, mixed culture of C. butyricum and R. sphaeroides K-7 increased hydrogen evolution rate. Because considerable amount of glutamate was contained in waste water of glutamate fermentation, utilization of glutamate was examined in mixed culture. As a result of examination, production of hydorgen was slightly inhibited by high concentration of glutamate, more than 20mM, on continuous monoculture of R. sphaeroides K-7. On the other hand, both on continuous monoculture of C. butyricum and on mixed culture of C. butyricum and R. sphaeroides K-7, production of hydrogen was not inhibited by high concentration of glutamate such as 100mM. Hence this suggests that high concentration of waste water can be used as good substrate for hydrogen production on monoculture of C. butyricum and mixed culture of C. butyricum and R. sphaeroides K-7.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.33-37
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• 2011

We introduce the concepts of interval-valued fuzzy m${\beta}$-open sets and interval-valued fuzzy m${\beta}$-continuous mappings. And we study some characterizations and properties of such concepts.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.263-271
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\beta}$-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy $r-M$ ${\beta}$-continuous mapping which is a generalization of fuzzy $r-M$ continuous mapping and fuzzy $r-M$ semicontinuous mapping, and investigate characterization for the continuity.

• Journal of Korean Society of Steel Construction
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• v.17 no.2 s.75
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• pp.195-206
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• 2005

Experimental research was performed on the 6m-6m two-span, continuous composite beams. Background research for the crack width control of continuous composite bridges in the Eurocode-4 is reviewed and equationsfor the calculation of crack width considering tension stiffening are presented. The behavior of the continuous composite beams was investigated using the initial and stabilized cracking process of the concrete slab in tension. Test results showed that the current requirement of minimum reinforcement for ductility in Korea Highway Bridge Design Codes could be reduced. The flexural stiffness of cracked continuous composite beams can be evaluated by the uncracked section analysis until the stabilized cracking stage. An empirical equation for the relationship between the stress of tensile reinforcements and crack width was obtained from the test results.