• Honam Mathematical Journal
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• v.35 no.3
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• pp.541-550
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• 2013

In this paper, we strengthen the properties of approximation by points (AP) and weak approximation by points (WAP) considered by A. Pultr and A. Tozzi in 1993 to define ${\kappa}$-AP and ${\kappa}$-WAP for an infinite cardinal ${\kappa}$. We also strengthen the properties of radial and pseudoradial to define ${\kappa}$-radial and ${\kappa}$-pseudoradial for an infinite cardinal ${\kappa}$. These allow us to consider new cardinal functions related to almost closed sets; AP-number, WAP-number, radial number, and pseudoradial number. We study their properties and show the relationships between them. We also provide some examples around ${\kappa}$-AP and ${\kappa}$-WAP which are closely connected with ${\kappa}$-radial and ${\kappa}$-pseudoradial.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.37 no.5 s.113
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• pp.50-55
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• 2005

In previous report, we investigated the impact of hexeneuronic acid and some residual extractiveson lignin determination. These non-lignin components severely interfered lignin content determination which also affect on the oxygen delignification comparison between aspen and pine unbleached kraft pulps. Very different pattern was observed whether based on uncorrected conventional kappa number or based on corrected kappa number in oxygen delignification comparison. Lower kappa number aspen pulps showed poor response to oxygen delignification when kappa number was used as lignin determination method but better response with using the acid lignin method. Phenolic hydroxyl group in kraft pulps were also compared based on uncorrected or corrected kappa numberfor lignin content. Based on uncorrected kappa number, lower kappa number oxygen-delignified pulps had lower phenolic hydroxyl group. However, lower kappa number oxygen-delignified pulps showed much higher phenolic hydroxyl group based on the corrected lignin content. For accurate comparison for residual lignin properties from different pulps, lignin determination should be corrected from non-lignin components contribution to lignin.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.42 no.2
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• pp.35-40
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• 2010

Variations in hexeneuronic acid content in hardwood alkaline pulps were investigated to evaluate their contribution to kappa number. Out of diverse chemical pulps the highest hexeneuronic acid content were measured in yellow poplar kraft pulping, which was assumed to enhance ca. 7.0 of kappa number determined by acid permanganate consumption. In yellow poplar soda-anthraquinone pulping, hexeneuornic acid was contributed to increment of 5.0-6.0 kappa number. In eucalyptus alkaline pulping, hexeneuronic acid content was not significantly different from soda-anthraquinone pulping. Increment of Kappa number by hexeneuronic acid was 4.5-5.6 depending on pulping method and pulping time at target temperature.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.551-563
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• 2011

Let ${\kappa}$ be a positive integer and let G be a simple graph with vertex set V(G). A function f : V (G) ${\rightarrow}$ {-1, 1} is called a signed total ${\kappa}$-dominating function if ${\sum}_{u{\in}N({\upsilon})}f(u){\geq}{\kappa}$ for each vertex ${\upsilon}{\in}V(G)$. A set ${f_1,f_2,{\ldots},f_d}$ of signed total ${\kappa}$-dominating functions of G with the property that ${\sum}^d_{i=1}f_i({\upsilon}){\leq}1$ for each ${\upsilon}{\in}V(G)$, is called a signed total ${\kappa}$-dominating family (of functions) of G. The maximum number of functions in a signed total ${\kappa}$-dominating family of G is the signed total k-domatic number of G, denoted by $d^t_{kS}$(G). In this note we initiate the study of the signed total k-domatic numbers of graphs and present some sharp upper bounds for this parameter. We also determine the signed total signed total ${\kappa}$-domatic numbers of complete graphs and complete bipartite graphs.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.158-163
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• 2003

This paper assesses the two-equation turbulence models available in a commercial code, FLUENT, for heat transfer in a turbulent heated pipe flow. In case of flow under $Re_D=10,000$, Standard $\kappa-\epsilon$ and Realizable $\kappa-\epsilon$ models overpredict the Nusselt number about $20\%$ compared with the experimental correlation, and RNG $\kappa-\epsilon$ model overpredicts about $30\%$ when the two-layer zonal method is employed. When wall function method is adopted, all $\kappa-\epsilon$ models show better predictions. Standard $\kappa-\omega$ and SST $\kappa-\omega$ models have the dependency on the first grid point ($0.3). As Reynolds number becomes high, the predictions of all $\kappa-\epsilon$ and $\kappa-\omega$ models are in a good agreement with the experimental correlation.

• Journal of the Korean Graphic Arts Communication Society
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• v.26 no.1
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• pp.65-72
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• 2008

Kappa number and brightness were more increased with treatment of endo-xylanase than hydrogen-peroxide. In pulp bleaching process, endo-xylanse was most effective in the other enzyme treatment. Exo-xylanase was effective more than 4 unit treatment. Kappa number was tiny increased with enzyme ratio, but less than 4 unit treatment, increased with hydrogen peroxide treatment ratio. In more than 4 unit acetyl-estease treatment, Kappa number and brightness were not influenced with enzyme treatment ratio, but concentration of hydrogen-peroxide.

• Proceedings of the Korea Technical Association of the Pulp and Paper Industry Conference
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• 2006.06a
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• pp.167-172
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• 2006

High-yield Pinus radiate kraft pulps with various Kappa number were produced from flow-through laboratory pulping. The samples were prepared and scanned using a rapid scan photoacoustic Fourier transform infrared (PAS-FTIR) spectrometer. A partial-least-squares (PLS) model was established based on the spectral data collected at different mirror velocities. The model was used to predict the Kappa number of the pulps and its robustness was statistically evaluated. The outcomes indicate that the PLS model can be used to predict the Kappa number of Pinus radiata kraft pulps with a high degree of accuracy provided that the moving mirror velocity is ${\leq}\;0.5cm/s$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.821-827
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• 2003

Fully developed turbulent flow in a square duct is numerically predicted with two nonlinear low-Reynolds-number ${\kappa}-{\varepsilon}$ models. Typical predicted quantities such as axial and secondary velocities, turbulent kinetic energy and Reynolds stresses are compared in detail with each other. It is found that the nonlinear low-Reynolds-number ${\kappa}-{\varepsilon}$ model adopted in a commercial code is unable to predict accurately duct flows involving turbulence-driven secondary motion with the prediction level of secondary flows one order less than that of the experiment.

• Journal of computational fluids engineering
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• v.18 no.2
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• pp.35-40
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• 2013

Natural convection of air with Pr=0.7 between two horizontal plates with small magnitude non-uniform temperature distribution[${\in}{\Delta}Tsin({\kappa}X/H)$, H : gap width, X : horizontal coordinate] in the lower plate is numerically(${\in}=0.01$) investigated. In the conduction-dominated regime with $Ra{\leq}1700$, two upright cells are formed over one wave length($2{\pi}/{\kappa}$). For small wave number, the flow becomes unstable with increase of Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The flow patterns are classified by the number of eddies over one wave length. When ${\kappa}=1$, a transition of $2{\rightarrow}4{\rightarrow}6$ eddy flow occurs with increase of Rayleigh number, and no hysteresis phenomenon is observed. Dual and triple solutions are found for ${\kappa}=1$, and transitions of $10{\rightarrow}8$, $8{\rightarrow}6$, $6{\rightarrow}4{\rightarrow}2$ eddy flow occur with decrease of Rayleigh number.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.313-323
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• 2007

The equitable total chromatic number ${\chi}_{et}(G)$ of a graph G is the smallest integer ${\kappa}$ for which G has a total ${\kappa}$-coloring such that the number of vertices and edges in any two color classes differ by at most one. In this paper, we determine the equitable total chromatic number of one class of the graphs.