• Korean Journal of Mathematics
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• v.28 no.4
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• pp.819-845
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• 2020

In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.161-167
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• 2005

In this note we consider the projective property $\sigma(Re(T))\;=\;Re\;(\sigma$(T))$ of p-hyponormal operators and log-hyponormal operators.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.24 no.11
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• pp.777-783
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• 2012

The hardness and strength test was performed to make the manufacturing process of SA213 P92 boiler pipe steel. And the microstructure change was studied to find out the cause of room temperature property of P92 steel, ie, low hardness and strength property. The room temperature property of P92 steel depends on the improper normalizing and cooling rate. Especially, Ferrite was formed and the steel had low hardness when the temperature was decreased slowly under the cooling rate $1^{\circ}C$/min after normalizing at the temperature around $A_{c1}$ to $A_{c3}$. The critical heat treatment temperature and cooling rate was over $900^{\circ}C$ and over $10^{\circ}C$/min to satisfy the minimum yield and tensile stress which was laid down by ASME Code.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1981-1988
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• 2013

We say a positive integer n satisfies the Lehmer property if ${\phi}(n)$ divides n - 1, where ${\phi}(n)$ is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form $D_{p,n}=np^n+1$, for a prime p and a positive integer n, or of the form ${\alpha}2^{\beta}+1$ for ${\alpha}{\leq}{\beta}$ does not satisfy the Lehmer property.

• Journal of Environmental Science International
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• v.11 no.12
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• pp.1315-1320
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• 2002

Since the enzymatic degradation of microbial poly[(R)-3-hydroxybutyrate-co-3-hydroxyvalerate] (P(3HB-co-3HV)) initially occurs by a surface erosion process, a degradation behavior could be controlled by the change of surface property. In order to control the rate of enzymatic degradation, plasma gas discharge and blending techniques were used to modify the surface of microbial P(3HB-co-3HV). The surface hydrophobic property of P(3HB-co-3HV) film was introduced by CF$_3$H plasma exposure. Also, the addition of small amount of polystyrene as a non-degradable polymer with lower surface energy to P(3HB-co-3HV) has been studied. The enzymatic degradation was carried out at 37 $^{\circ}C$ in 0.1 M potassium phosphate buffer (pH 7.4) in the presence of an extracellular PHB depolymerase purified from Alcaligenes facalis T1. Both results showed the significant retardation of enzymatic erosion due to the hydrophobicity and the enzyme inactivity of the fluorinated- and PS-enriched surface layers.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.227-232
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• 1992

In this paper we prove that if (.ohm., .SIGMA., .mu.) is a non-purely atomic measure space and X is strictly convex, then X has the asymptotic-norming property II if and only if $L_{p}$ (X, .mu.), 1 < p < .inf., has the asymptotic-norming property II. And we prove that if $X^{*}$ is an Asplund space and strictly convex, then for any p, 1 < p < .inf., $X^{*}$ has the .omega.$^{*}$-ANP-II if and only if $L_{p}$ ( $X^{*}$, .mu.) has the .omega.$^{*}$-ANP-II.*/-ANP-II.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.11a
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• pp.252-255
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• 1997

In this paper, we will propose the methodology of data analysis using the fuzzy property set model. In real world, the data can be represented with the object. $\theta$. and the property, $\pi$, and its has-property relation, P. Then, the conceptual space can be defined with the chosen properties. Each object has a unique location in the conceptual space. In Fuzzy mode, the fuzzy property, and fuzzy conceptual space can be redefined. To analyze data using the fuzzy property set model, the rough set need to be defined in the fuzzy conceptual space.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.63-72
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• 2004

It is known that each natural number can be written uniquely as a sum of Fibonacci numbers with suitably increasing indices. In 1960, Daykin showed that the sequence of Fibonacci numbers is the only sequence with this property. Consider here the problem of representing each natural number uniquely as a sum of positive integers taken from certain sequence allowing a fixed number, $\cal{l}\geq2$, of repetitions. It is shown that the $(\cal{l}+1)$-adic expansion is the only such representation possible.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.65-70
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• 2016

J. G. Stampfli proved that if a bounded linear operator T on a Hilbert space ${\mathfrak{H}}$ satisfies ($G_1$) property, then the Riesz projection $P_{\lambda}$ associated with ${\lambda}{\in}iso{\sigma}$(T) is self-adjoint and $P_{\lambda}{\mathfrak{H}}=(T-{\lambda})^{-1}(0)=(T^*-{\bar{\lambda}})^{-1}(0)$. In this note we show that Stampfli''s result is generalized to an nilpotent extension of an operator having ($G_1$) property.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.145-152
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• 2009

In this paper, we introduce a new property of a topological space which is weaker than sequential compactness and give some necessary and sufficient conditions for a $Fr{\acute{e}}chet$-Urysohn space with the property to be sequentially compact.