• Journal of the Korean Society for Heat Treatment
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• v.21 no.1
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• pp.20-25
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• 2008

Structural studies have been performed on precipitation hardening and microstructural variations found in Ti-Al-Cr ternary $L1_0$- and $L1_2$-phase alloys using transmission electron microscopy. Both the $L1_0$ and $L1_2$ phase alloys harden by aging at 973 K after solution annealing at higher temperatures. The amount of age hardening of the $L1_2$ phase alloy is larger than that of the $L1_0$ phase alloy. The phase separation between $L1_0$ and $L1_2$ phase have not been observed by aging at 973 K. But $Al_2Ti$ was formed in each matrix alloy during aging. The crystal structure of the $Al_2Ti$ phase is a $Ga_2Zr$ type in the $L1_0$ and a $Ga_2Hf$ type in the $L1_2$ phase, respectively. At the beginning of aging the fine coherent cuboidal $Al_2Ti$-phase are formed in the $L1_0$ phase. By further aging, two variants of $Al_2Ti$ precipitates grow along the two {110} habit planes. On the other hand, in the $L1_2$ phase, the $Al_2Ti$ phase forms on the {100} planes of the $L1_2$ matrix lattice. After prolonged aging the precipitates are rearranged along a preferential direction of the matrix lattice and form a domain consisting of only one variant. It is suggested that the precipitation of $Al_2Ti$ in each matrix alloy occurs to form a morphology which efficiently relaxes the elastic strain between precipitate and matrix lattices.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.55-68
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• 2008

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form $P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m$, where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ complex matrices. Newton's method was introduced a useful tool for solving the equation P(X)=0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.255-258
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• 2009

It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

• Journal of Periodontal and Implant Science
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• v.27 no.4
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• pp.767-783
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• 1997

Guided tissue regeneration, bone graft procedures, and application of growth factors have been used to regenerate lost periodontal tissues. Recently, enamel matrix derivative has been introduced into periodontal regeneration procedures in expectation of promoting new bone and cementum formation. The purpose' of this study was to evaluate the effect of enamel matrix derivative in 1-wall intrabony defects in beagle dogs. For this purpose, each dog was anesthesized using intravenous anesthesia and mandibular 1st, 3rd premolars were extracted. 2 months later, the 1-wall intrabony defects(mesio-distal width: 4mm, depth: 4mm) were created on the distal side of 2nd premolars and mesial side of 4th premolars. The control group was treated with debridement alone, and experimental group was treated with debridement and enamel matrix derivative application. The healing processes were histologically and histometrically observed after 8 weeks and the results were as follows : 1. The length of junctional epithelium was $0.94{\pm}0.80mm$ in the control group, $0.57{\pm}0.42mm$ in the experimental group, with no statistically significant difference between groups. 2. The connective tissue attachment was $1.36{\pm}0.98mm$ in the control group. $0.38{\pm}0.43mm$ in the experimental group, with statistically significant difference between groups(P<0.05). 3. The new cementum formation was $2.49{\pm}1.06mm$ in the control group, $3.59{\pm}0.74mm$ in the experimental group. with statistically significant difference between groups(P<0.05). 4. The new bone formation was $1.92{\pm}0.97mm$ in the control group, $2.32{\pm}0.59mm$ in the experimental group. with no statistically significant difference between groups. Within the limitation to this study protocol, enamel matrix derivative application in 1-wall intrabony defect enhanced new cementum formation. Although there was no statistically significant difference, enamel matrix derivative also seems to be effective in inhibition of apical migration of junctional epithelium and new bone formation.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.25-40
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• 2021

In this article we introduce tribonacci sequence spaces c0(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine ��-, ��- and ��- duals of the spaces c0(T) and c(T). We characterize certain matrix classes (c0(T), Y) and (c(T), Y), where Y is any of the spaces c0, c or ℓ∞. Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c0(T).

• Journal of Periodontal and Implant Science
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• v.49 no.4
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• pp.215-227
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• 2019

Purpose: To histologically characterize periodontal healing at 8 weeks in surgically created dehiscence defects in beagle dogs that received a collagen matrix with periodontal ligament (PDL) progenitor cells. Methods: The bilateral maxillary premolars and first molars in 6 animals were used. Standardized experimental dehiscence defects were made on the buccal side of 3 premolars, and primary culturing of PDL progenitor cells was performed on the molars. Collagen matrix was used as a scaffold and a delivery system for PDL progenitor cells. The experimental sites were grafted with collagen matrix (COL), PDL progenitor cells with collagen matrix (COL/CELL), or left without any material (CTL). Histologic and histomorphometric analyses were performed after 8 weeks. Results: The defect height from the cementoenamel junction to the most apical point of cementum removal did not significantly differ across the CTL, COL, and COL/CELL groups, at $4.57{\pm}0.28$, $4.56{\pm}0.41$, and $4.64{\pm}0.27mm$ (mean ${\pm}$ standard deviation), respectively; the corresponding values for epithelial adhesion were $1.41{\pm}0.51$, $0.85{\pm}0.29$, and $0.30{\pm}0.41mm$ (P<0.05), the heights of new bone regeneration were $1.32{\pm}0.44$, $1.65{\pm}0.52$, and $1.93{\pm}0.61mm$ (P<0.05), and the cementum regeneration values were $1.15{\pm}0.42$, $1.81{\pm}0.46$, and $2.57{\pm}0.56mm$ (P<0.05). There was significantly more new bone formation in the COL/CELL group than in the CTL group, and new cementum length was also significantly higher in the COL/CELL group. However, there were no significant differences in the width of new cementum among the groups. Conclusions: PDL progenitor cells carried by a synthetic collagen matrix may enhance periodontal regeneration, including cementum and new bone formation.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.598-609
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• 2023

The purpose of this article is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the double band matrix U (a₀, a₁, a₂; b₀, b₁, b₂), b₀, b₁, b₂≠0 on the sequence space ℓ_p (1 < p < ∞).

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.51-67
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• 2004

A matrix pair $(X_0,\;Y_0)$ is called a Hermitian nonnegative-definite(respectively, positive-definite) solution to the matrix equation $GXG^*\;+\;HYH^*\;=\;C$ with unknown X and Y if $X_{0}$ and $Y_{0}$ are Hermitian nonnegative-definite (respectively, positive-definite) and satisfy $GX_0G^*\;+\;HY_0H^*\;=\;C$. Necessary and sufficient conditions for the existence of at least a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation are investigated. A representation of the general Hermitian nonnegative-definite (respectively positive-definite) solution to the equation is also obtained when it has such solutions. Two presented examples show these advantages of the proposed approach.

• Journal of the Korean Ceramic Society
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• v.31 no.4
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• pp.375-380
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• 1994

Matrices retaining electrolyte in phosphoric acid fuel cell were prepared with SiC to SiC whisker mixing ratios of 1:0.5, 1:1, 1:1.5, 1:2, 1:3 by tape casting method. When viscosity of the slurry was 5.9 poise and the SiC to SiC whisker mixing ratios were 1:1, 1:1.5, 1:2, the ranges of porosity, acid absorbency and bubble pressure were 80~90%, 2.5~6 and 700~2200 mmH2O, respectively. Those ranges are acceptable for a practical electrolyte-retaining matrix. With increasing the mixing ratio of SiC whisker to SiC, the porosity and the vol.% of large pores in the main pore size distribution which is between 1 and 10 ${\mu}{\textrm}{m}$, increased rapidly. Impedance spectroscopy was measured to know characteristics of matrix inside and contact region of matrix to catalyst layer. When the SiC to SiC whisker mixing ratio was 1:2, hydrogen ions were transported in the matrix most effectively because of high ionic conductivity and low activation energy due to high acid absorbency in spite of high interfacial resistance. The cell current density of the cell made using the matrix was 220 mA/$\textrm{cm}^2$ at 0.7 V.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.34 no.5
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• pp.423-429
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• 2001

Prediction of the variation in annual biomass was conducted for the white croaker. Argyrosomus argentatus in Korean waters using leslie Matrix, based upon fishery data for the past 21 years and biological data, We used density-independent and density-dependent Leslie Matrix models. Similar parameters were estimated from two models except that the density-dependent model was influenced by the density effect variable, q(i,t), The eigenvalue of the white croaker population for the $1984\~1995$ period was estimated to be 0.8, indicating a declining pattern of the population. The survival rate of 0-th year class was calculated to be 0.00005. Based on the schedule of the age-specific survival rate and fecundity, the future biomass and catch was predicted for various levels of fishing mortalities (F), If F was set at 0.252/yr ($F_{35x}$) or 0.368/yr ($F_{0.1}$), the biomass and catch increased, and if F was set at 0.922 ($F_{current}$), the biomass and catch decreased, The fishing mortality at equilibrium was estimated to be 0.7/yr. Finally, the management strategy of the white croaker was discussed.