• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.13-29
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• 2021

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.

• KSTLE International Journal
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• v.8 no.1
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• pp.1-6
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• 2007

Chromatic device was developed using light emitting diodes, optic fibers and photodiodes. Chromatic ratio and total contamination parameters based on transmitted light intensity in Red, Green, and Blue wavelengths were used for oil chemical and particulate contamination assessment. Chromatic ratio criterion was found independent of the particulate contamination of oil; but depended on chemical degradation, being more sensitive for synthetic than mineral hydraulic oil. Total contamination index of the sensor depended on both the chemical degradation and particulate contamination of the oil; being most sensitive in blue wavelength, and least in the red. Test results for synthetic hydraulic oils monitored corroborated with results of other tests such as viscosity, total acid number, elemental optical emission spectroscopy, particulate counts and UV-VIS photospectrometry. Chromatic ratio showed a clearer indication of oil degradation, compared to key monitoring parameters such as total acid number, viscosity and particle counts. The results showed that these parameters are effective criteria for the condition monitoring of synthetic hydraulic oils.

• Journal of the Korean Society of Tobacco Science
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• v.23 no.2
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• pp.149-155
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• 2001

This study was carried out to evaluate the correlations among degree of carbonization, chemical components and chromatic characteristics, and to establish the criterion of carbonizaion in leaf tobacco during aging storage. The flue-cured (B2O) and burley (B2T) leaf tobaccos were redried with conventional practices for each other type, and moisture contents of leaf tobaccos were adjusted to 13, 15, 17 and 19% after redrying. The leaf tobaccos were packed in carton box and stored for 8 months in the controlled-environment rooms($35^{\circ}C$, 65% R.H. and $40^{\circ}C$, 80% R.H.). Degree of carbonization, chemical components, and chromatic characteristics(L ; black-white, a ; red to green, b ; yellow to blue) were invetigated every month. Carbonization Index (C.I.) was established as (equation omitted) in accordance with degree of carbonization in two types. The C.I. value of flue-cured leaf(56.5) for slight carbonization was higher than that of burley leaf(48.0). C.I. and rate of usable leaf, L and b were positively correlated in two types. C.I. was significantly shown positive correlation with pH in two types. The correlations between the predicted and the observed values of slight carbonizating times(month after storage) using C.I. and pH were positive significant in two types. The results suggest that cabonization index may be useful to forecast and prevent the carbonization, and pH may be useful to estimate cabonization indirectly for flue-cured and burley leaves during aging storage.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.127-133
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• 2005

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.

• Current Optics and Photonics
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• v.3 no.1
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• pp.78-85
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• 2019

The remote phosphor structure has been proven to bear greater luminous efficiency than both the conformal phosphor and in-cup phosphor structures; however, controlling its color quality is much more challenging. To solve this dilemma, various researchers have proposed dual-layer phosphor and triple-layer phosphor configuration as techniques to enhance the display brightness of white LEDs (WLEDs). Likewise, this study picked one of these configurations to utilize in multichip WLEDs with five distinct color temperatures in the range from 5600 to 8500 K, for the purpose of improving the optical properties of WLEDs, such as color rendering index (CRI), color quality scale (CQS), luminous efficacy (LE), and chromatic homogeneity. According to the results of this research, the triple-layer phosphor configuration has superior performance compared to other configurations in terms of CRI, CQS, and LE, and yields higher chromatic stability for WLEDs.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.357-366
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• 2007

Let G(V, E) be a simple graph, and let f be an integer function on V with $1{\leq}f(v){\leq}d(v)$ to each vertex $v{\in}V$. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex $v{\in}V$ at least f(v) times. The f-edge cover chromatic index of G, denoted by ${\chi}'_{fc}(G)$, is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to ${\delta}_f\;or\;{\delta}_f-1,\;where\;{\delta}_f{=}^{min}_{v{\in}V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. Let G be a connected and not complete graph with ${\chi}'_{fc}(G)={\delta}_f-1$, if for each $u,\;v{\in}V\;and\;e=uv{\nin}E$, we have ${\chi}'_{fc}(G+e)>{\chi}'_{fc}(G)$, then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each $u,\;v{\in}V\;and\;e=uv{\nin}E$ there exists $w{\in}\{u,v\}\;with\;d(w)\leq{\delta}_f(f(w)+1)-2$ such that w is adjacent to at least $d(w)-{\delta}_f+1$ vertices which are all ${\delta}_f-vertex$ in G.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.9
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• pp.119-126
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• 2013

In this paper, we propose a chromatic aberration removal algorithm in image capture devices, which considers local properties of the image. Chromatic aberration is generated by the fact that the refractive index of the lens is different for different wavelengths, which produces color artifacts on strong edge due to misalignment of RGB channels. Under the characteristics of the artifacts, the proposed algorithm first estimates the regions with the apparent color artifacts as the neighborhoods of the strong edge. In the regions, the proposed algorithm removes the color artifacts by matching the edges of RGB channels. The widely used conventional methods based on global image warping could not remove the color artifacts of longitudinal chromatic aberration and purple fringing identified by the image sensor, whereas the matching process of the proposed method could reduce them. Experimental results show that the proposed algorithm outperforms the conventional methods on objective and subjective criteria.

• Textile Coloration and Finishing
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• v.19 no.1 s.92
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• pp.53-60
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• 2007

In order to optimize the process for development of super deep black fiber, the silica-containing polyester fabric, SN2000, was investigated in terms of mass reduction process by sodium hydroxide, selection of high color strength dyes, and resin treatment. As the results, the mass reduction condition which used 15g/L of sodium hydroxide at $120^{\circ}C$ was determined and Dianix Deep Black Plus was selected for the best deep coloration at around 5% owf. Contrary to the prevailed understanding that the additional use of chromatic dyes would enhance the deep coloration, four kinds of chromatic dyes such as yellow, red, blue, and green dyes did not make great effect on the deep coloration. To increase the effect, the commercial resin that has low refractive index was used additionally and the resin made it possible to lower the lightness of the fabrics down to 8.7 which was generally accepted for super highly deep black fabric.

• Journal of the Optical Society of Korea
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• v.14 no.4
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• pp.351-356
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• 2010

We investigated the combined effect of fiber chromatic dispersion and self-phase modulation (SPM) in multi-channel subcarrier multiplexed (SCM) optical transmission systems. We theoretically analyzed the transmission characteristics of the SCM signals with the effect of SPM and chromatic dispersion in a single-mode optical fiber by numerical simulations based on the nonlinear Schrodinger equation. The numerical simulation results revealed that the effect of fiber dispersion and SPM could occur independently between subcarrier channels in two-channel SCM systems for small optical modulation index (OMI) and large channel spacing. However, for large OMI, small channel spacing, and large fiber launching power, we found a performance degradation of the two-channel system compared to that of a single-channel system. These parameters are therefore important for the optimization of multi-channel SCM systems applicable to radio over fiber networks.

• Journal of the Optical Society of Korea
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• v.14 no.4
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• pp.424-430
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• 2010

In coherent anti-Stokes Raman scattering (CARS) microscopy reported until now, conventional microscope objectives are used, so that they are limited for introduction into a living body. Gradient-index (GRIN) rod lenses might be a solution for miniaturized microscope objectives for in-vivo CARS microscopy. However, due to the inherent large amount of chromatic aberration, GRIN rod lenses cannot be utilized for this purpose. CARS imaging catheter, composed of miniaturized microscope objective and fiber bundle, can be introduced into a living body for minimally invasive diagnosis. In order to design the catheter, we have to first investigate design requirements. And then, the optical design is processed with design strategies and intensive computing power to achieve the design requirements. We report the miniaturized objective lens system with diffraction-limited performance and completely corrected chromatic aberrations for an in-vivo CARS imaging catheter.