• 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 the Korean Society for Heat Treatment
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• v.9 no.4
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• pp.252-260
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• 1996

A study was conducted to examine the precipitation phenomena of Al-2.1Li-2.9Cu alloy by differential scanning calorimetry and transmission electron microscopy. DSC curves were measured over the temperature range of $25{\sim}550^{\circ}C$ at a heating rate of $2{\sim}20^{\circ}C$/min.. Three heat evolution peaks and three heat absorption peaks were observed in the DSC curve for the as-quenched specimen. From DSC results and TEM analysis, it was proved that the precipitation sequence in the as-quenched specimen is supersaturated solid solution ${\rightarrow}$ GP zone ${\rightarrow}{\delta}^{\prime}{\rightarrow}T_1{\rightarrow}T_2$ and ${\theta}^{\prime}$ was detected in the peak aged specimen at $160^{\circ}C$. The major phase formed at peak hardeness in the aging at $160^{\circ}C$ was ${\delta}^{\prime}$ phase. The activation energies for the formation of ${\delta}^{\prime}$ and $T_1$ phases were 22.3kcal/mole and 24.3kcal/mole, respectively. These lower activation energies than those for diffusion of Cu and Li in Al are ascribed to the quenched-in excess vacancies.

• Journal of the Korean Society for Heat Treatment
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• v.6 no.3
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• pp.138-143
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• 1993

Effects of aging treatment on the microstructural evolution of a rapidly solidified Al-Li-Cu alloy were investigated by differential scanning calorimetry (DSC) and transmission electron microscopy(TEM). It was found that the precipitation sequence was: supersaturated solid solution ${\alpha}^{\prime}$ ${\rightarrow}$ metastable ${\delta}^{\prime}$ + stable precipitate $T_1$ ${\rightarrow}$ stable precipitates ${\delta}+T_1$. Two exothermic and two endothermic peaks are detected by DSC analysis. The two exothermic and endothermic peaks corresponded to ${\delta}^{\prime}$ and ${\delta}+T_1$ precipitation and dissolution reactions respectively. The enthalpy of ${\delta}^{\prime}$ precipitation decreased with increasing of aging temperature and time until the finishing point of precipitation. The activation energy for precipitation of ${\delta}^{\prime}$ was measured as 80KJ/mol and the energy for dissolution was 93KJ/mol. These values arc higher than those of AI-Li binary alloy. Peak hardness value (Hv 170) was obtamed at $210^{\circ}C$ for 1hr aging treatment which coincided with finishing point of ${\delta}^{\prime}$ precipitation.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.473-480
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• 2009

We prove the existence and multiplicity of nontrivial solutions for a fourth order problem ${\Delta}^2u+c{\Delta}u={\alpha}u-{\beta}(u+1)^-$ in ${\Omega}$, ${\Delta}u=0$ and $u=0$ on ${\partial}{\Omega}$, where ${\lambda}_1{\leq}c{\leq}{\lambda}_2$ (where $({\lambda}_i)_{i{\geq}1}$ is the sequence of the eigenvalues of $-{\Delta}$ in$H_0^1({\Omega})$) and ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. The results are proved by applying minimax arguments and linking theory.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2005.10a
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• pp.271-273
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• 2005

The ${\delta}^{15}N\;and\;{\delta}^{15}O$ data of nitrate indicates the sources of nitrate in oxic groundwater as a mixture of ammonia or urea-containing fertilizer and manure. The ${\delta}^{34}S_{sulfate}$ values indicate that sulfate Is mainly originated from fertilizers and soil S. In sub-oxic groundwater, the increased ${\delta}^{34}S_{sulfate}$ values evidently indicate that sulfate is gradually removed by microbial mediated sulfate reduction. However, iron reduction does not occur In this study area. Such a reversed redox sequence may occur In the presence of stable iron oxides such as hematite and goethite in alluvlal aquifer.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

• Journal of Science of Art and Design
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• v.2
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• pp.239-293
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• 2000

The paper aims to study how to describe the rigorous position on which semantic elements are laid, within the visual space. This purpose is, first of all, for the construction of visual syntactical semantics of the visual space. For this aim, the preliminary research begins with some definitions on : 1) visual space, visual design, visual syntactical semantic meaning, 2) position, sequence of position, 2-dim. sequence of position, and 3) 2-dim. numerical series of position, harmonious dynamic values. Here, The main issue is to define the position in general. To solve this problem, the researcher surveyed the positions on which the sets of pixemes are set up. The results are as follows ; 1. As far as the positions in visual space are concerned, they are the possible locations permitted in the visual patches. They are not the factual but the possible positions. 2.The position value that the sequential point has is not arithmetical but harmonious-dynamic, for it is not permitted for its own sake, but for the person, that is to say, for the viewer's visual perception. 3. The harmonious-dynamic value of positional sequence can be composed of the 2-dimensional successive numerical series which is, in turn, composed of the primordial 3 values x0, $\mu0$, y0. Here, the $\mu0$ is the harmonious mean value of x0 and y0. The x0 and y0 are, therefore, of the mutual dynamic relationship. 4. From this, the 2-dim general $\Delta-TABLE$ of the numerical series of position in visual design could be acquired through development of the primordial 3 values into the $X_i,\;Y_i$, orbit values.

• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.617-626
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• 2009

A series of recent papers reported that the inter-gene correlations in Affymetrix microarray data sets were strong and long-ranged, and the assumption of independence or weak dependence among gene expression signals which was often employed without justification was in conflict with actual data. Qui et al. (2005) indicated that applying the nonparametric empirical Bayes method in which test statistics were pooled across genes for performing the statistical inference resulted in the large variance of the number of differentially expressed genes. Qui et al. (2005) attributed this effect to strong and long-ranged inter-gene correlations. Klebanov and Yakovlev (2007) demonstrated that the inter-gene correlations provided a rich source of information rather than being a nuisance in the statistical analysis and they developed, by transforming the original gene expression sequence, a sequence of independent random variables which they referred to as a ${\delta}$-sequence. We note in this report using two cDNA microarray data sets experimented in this country that the strong and long-ranged inter-gene correlations were still valid in cDNA microarray data and also the ${\delta}$-sequence of independence could be derived from the cDNA microarray data. This note suggests that the inter-gene correlations be considered in the future analysis of the cDNA microarray data sets.

• The Transactions of the Korean Institute of Power Electronics
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• v.20 no.1
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• pp.19-30
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• 2015

A static synchronous compensator (STATCOM) applied to rapidly changing, highly unbalanced loads such as electric arc furnaces (EAFs), requires both positive-sequence and negative-sequence current control, which indicates fast response characteristics and can be controlled independently. Furthermore, a delta-connected STATCOM with cascaded H-bridge configuration accompanying multiple separate DC-sides, should have high performance zero-sequence current control to suppress a phase-to-phase imbalance in DC-side voltages when compensating for unbalanced load. In this paper, actual EAF data is analyzed to reflect on the design of current controllers and a pioneering zero-sequence current controller with a superb transient performance is devised, which generates an imaginary -axis component from the presumed response of forwarded reference. Via simulation and experiments, the performance of the positive, negative, and zero-sequence current control of a cascaded H-bridge STATCOM for EAF is verified.

• Economic and Environmental Geology
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• v.17 no.4
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• pp.289-298
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• 1984

Uraniferous black slates of the Okchon sequence occur in Koesan (northeast) through Miwon-Boun (middle) to the southwest off Taejon (southwest) within the Okchon fold belt. The Uraniferous balck slates in the southwest off Taejon are particularly well developed in Chubu (northeast) and Moksso-ri (middle) areas whereas they are less developed in Jinsan (southwest) area. The uraniferous beds range from less than a meter to 40 meters in thickness and range from less than 0.02% $U_3O_8$ (cut-off-grade) to 0.05% $U_3O_8$ in the southwestern district off Taejon. Electron microprobe analysis of uranium-minerals found in graphitic slate samples enables to estimate their major compositions semi-quantitatively so that uraninite, ferro-uranophane and chlopinite are tentatively identified. Uranium-minerals are closely associated with carbon and metal sulfides. Correlation analysis of trace element concentrations revealed that U and F.C., and U and Mo are lineary correlative respectively and their correlation coefficients are positively high whereas those of U and V, U and Mn, and U and Zr are negatively low, implying that uranium mineralization has been closely related with concentrations of carbon and molybdenum. Stable isotope analyses of pyrite sulfur range widely from +11.5% to -23.3% in ${\delta}^{34}S$ values whereas those of graphite carbon fall within a narrow range between -23.3% and -28.9% in ${\delta}^{13}C$ values. The wide range of ${\delta}^{34}S$ values suggests that the sulfur could be of meteoric origin rather than of igneous source. The narrow range of ${\delta}^{13}C$ values, which are close to those of coal, indicates that the graphite is organic carbon in origin. Therefore, it is concluded that the uranium mineralization in the Okchon sequence took place primarily in sedimentary environment rich in organic matter and sulfide ion, both of which served as the reducing agents to convert soluble uranyl complex to insoluble uranium dioxide.