• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.59-63
• /
• 2010

In this paper, we introduce the concept of weakly-ultra-${\alpha}{\psi}$-separation of two sets in a topological space using ${\alpha}{\psi}$-open sets. The ${\alpha}{\psi}$-closure and the ${\alpha}{\psi}$-kernel are defined in terms of this weakly ultra-${\alpha}{\psi}$-separation. We also investigate some of the properties of the ${\alpha}{\psi}$-kernel and the ${\alpha}{\psi}$-closure.

• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• pp.223-234
• /
• 2005

We introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of quasi-smooth ${\alpha}$- compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.101-112
• /
• 2006

In this paper, we introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of weak quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Korean Journal of Mathematics
• /
• v.14 no.2
• /
• pp.233-240
• /
• 2006

In this paper we introduce the concepts of several types of $weak^*$ quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and investigate some of their properties.

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.143-153
• /
• 2004

In [3] and [6] the concepts of smooth closure, smooth interior, smooth ${\alpha}-closure$ and smooth ${\alpha}-interior$ of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth ${\alpha}-compactness$ in terms of these concepts introduced in [3] and [61 and investigate some of their properties.

• Korean Journal of Mathematics
• /
• v.11 no.2
• /
• pp.127-136
• /
• 2003

In this paper we obtain some properties of the weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of $weak^*$ smooth compactness in smooth topological spaces and investigate some of their properties.

• KOREAN JOURNAL OF CROP SCIENCE
• /
• v.53 no.2
• /
• pp.137-143
• /
• 2008

Rapid canopy closure (RCC) is one of the physiological attributes that may enhance genetic yield potential of rice (Oryza sativa L.) in a growing season. Crop growth before canopy closure could be described by an exponential equation of $y\;=\;{\alpha}{\cdot}{\exp}({\beta}{\cdot}t)$ where $\alpha$ is the crop leaf area index (LAI) or shoot dry weight (DW), t is the thermal time, $\beta$ is the LAI or DW at the beginning of the exponential growth and is the relative growth rate of LAI ($m^2m^{-2}^{\circ}C^{-1}$) or DW($gg^{-2}^{\circ}C^{-1}$). Field experiment using 22 cultivars revealed that the exponential growth phase before canopy closure can be divided into two sections; an earlier section during which crop dry weight and LAI of varieties are highly dependent on $\alpha$ and a second section where crop dry weight and LAI are highly dependent on $\beta$. Grain weight had significantly positive correlation with $\alpha$ parameter and dry weight and LAI during early exponential phase. The parameter $\beta$ of the exponential growth curve had positive and significant correlation with the LAI and dry weight during the late exponential growth phase, grain number per unit area, and grain yield. There was genotypic difference for RCC parameters, $\alpha$ and $\beta$, indicating the possibility of genetic improvement for these traits.

• Honam Mathematical Journal
• /
• v.25 no.1
• /
• pp.131-139
• /
• 2003

The notion of intuitionistic fuzzy ${\alpha}$-continuity is introduced, and its characterization is given.

• Journal of Chest Surgery
• /
• v.34 no.6
• /
• pp.485-489
• /
• 2001

Background: The most important factor in preventing sternal complications is stable sternal approximation. We have tried to find the most effective sternal closure method by examining the incidence of sternal dehiscence with or without infection in patients with cardiac surgery through median sternotomy. Material and Method: This study was performed in 489 patients over 45 years of age with median sternotomy for open cardiac surgery. Simple closure with interrupted 6 wires was performed in 159 patients, figure-of-8 closure technique in 119, overlapping interrupted closure using 10 wires in 150, and combined closure technique of interrupted simple closure and figure-of-8 suture closure in 61. Two hundred thirty-four patients underwent valve and aortic operations and 213 patients coronary artery bypass surgery. Result: Sternal dehiscence with or without infection occurred in 12 (2.5 %) patients. The complication developed in 5 of 159 patients (3.1%) with six interrupted simple closure, in 4 of 119 patients (3.4%) with figure-of-8 closure, and in 3 of 150 patients (2.0%) with overlapping interrupted closure using 10 wires, but there was no complication in 61 patients with combined closure technique (relative risk for other closure techniques, p<0.05). There was no significant difference in the incidence of the sternal complication between valve and aortic operation group and coronary artery bypass group (3.0% vs 2.3%, not significant), but diabetes mellitus was a significant independent risk factor (odds ratio and multivariate analysis, p<0.05). Conclusion: The sternal closure technique that combines simple interrupted suture closure and figure-of-8 suture closure may be a more useful technique to enhance sternal stabilization compared to other closure techniques, such as simple interrupted closure, 8-figure closure, and overlapping interrupted closure.

• Journal of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.867-879
• /
• 2012

For ${\beta}$ > 1, let $T_{\beta}$ : [0, 1] ${\rightarrow}$ [0, 1) be the ${\beta}$-transformation. We consider an invariant $T_{\beta}$-orbit closure contained in a closed interval with diameter 1/${\beta}$, then define a function ${\Xi}({\alpha},{\beta})$ by the supremum such $T_{\beta}$-orbit with frequency ${\alpha}$ in base ${\beta}$, i.e., the maximum value in $T_{\beta}$-orbit closure. This paper effectively determines the maximal domain of ${\Xi}$, and explicitly specifies all possible minimal intervals containing $T_{\beta}$-orbits.