• 자원환경지질
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• 제5권3호
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• pp.133-144
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• 1972

The mine of our present concern is situated at Shim-ri, Gusan-myon, Changwon-gun, Kyongsang-namdo, with lattitude $128^{\circ}35^{\prime}{\sim}36^{\prime}N$ and longitude $35^{\circ}03^{\prime}{\sim}04^{\prime}E$. This mine has not been noticed until the intermittent geological survey for the ore deposits were initiated from September, 1967 till 1970. The main mineralized zones, No.1 and No.2 zones, were studied by the diamond drilling of 9 holes down to the total depth of 1,140m, and found to have ore reserves of Cu 1.99% ore, estimated to reach around $358,000{\frac{M}{T}}$ (proved $117,000{\frac{M}{T}}$, indicated $241,000{\frac{M}{T}}$), which triggered the new exploitation of this mine. Geological composition of the district near the mine is mainly from the andesite belonging to the Silla Series of Kyongsang System and the distribution is broadly spread. Ore deposits are the hydrothermal one, filling the shear zone formed alongside the andesite main joint. There are two stripes of copper bearing mineralized zone which are about 40~70 meters apart and parallel to each other, in addition to which two others are expected. The strike of the main mineralized zone lies at $N15^{\circ}{\sim}20^{\circ}W$, the dip at $60^{\circ}{\sim}70^{\circ}NE$. The principal components of the ore mineral are chalcopyrite, bornite and as secondary, cuprite, tenorite, azurite and malachite. Pyrite, magnetite, specular hematite, very little of galena, sphalerite, quartz, epidote, zoisite, chlorite and calcite are found as gangue mineral. Confirmed by the drilling, the main mineralized zone, No.1 zone, has the length of 320m, average width of 1.62m, Ag 26g/t, Cu 1.84% and the average width of the ore zone except the narrow barren andesite horse interposed in the mineralized zone is 1.32m with Ag 32g/t and Cu 2.26%. The mineralized zone No.2 is 340m long, 1.00m wide with Ag 30g/t and Cu 2.15%. Neglecting the barren andesite horse the width is 0.73m with Ag 42g/t and Cu 2.94%.

• 대한수학회논문집
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• 제33권4호
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• The Journal of Advanced Prosthodontics
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• 제11권4호
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• pp.193-201
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• 2019

PURPOSE. The aim of the present study was to evaluate the color changes of an autopolymerizing PMMA resin used for interim fixed restorations, reinforced with $SiO_2$ nanoparticles. MATERIALS AND METHODS. Silica nanoparticles were blended with the PMMA resin powder through high-energy ball milling. Four shades of PMMA resin were used (A3, B3, C3, D3) and total color differences were calculated through the equations ${\Delta}E_{ab}=[({\Delta}L*)^2+({\Delta}a*)^2+({\Delta}b*)^2]^{1/2}$ and ${\Delta}E_{00}=[(\frac{{\Delta}L^{\prime}}{K_LS_L})^2+(\frac{{\Delta}C^{\prime}}{K_CS_C})^2+(\frac{{\Delta}H^{\prime}}{K_HS_H})^2+R_T(\frac{{\Delta}C^{\prime}}{K_CS_C})(\frac{{\Delta}H^{\prime}}{K_HS_H})]^{1/2}$. Statistically significant differences between ${\Delta}E_{ab}$ and the clinically acceptable values of 3.3 and 2.7 and those between ${\Delta}E_{00}$ and the clinically acceptable value of 1.8 were evaluated with one sample t-test (P<.05). Differences among the different shades were assessed through One-Way ANOVA and Bonferroni multiple comparison tests. RESULTS. Significantly lower values were detected for all groups concerning ${\Delta}E_{ab}$ compared to the intraorally clinical acceptable values of 3.3 and 2.7. Significantly lower mean values were detected for groups B3, C3, and D3, concerning ${\Delta}E_{00}$ compared to the intraorally clinical acceptant value of 1.8. Color pigments in red-brown (A3) and red-grey (D3) shades affect the total color change to a greater extent after the reinforcement with $SiO_2$ nanoparticles compared to the red-yellow (B3) shade. CONCLUSION. Within the limitations of this in vitro study, it can be suggested that reinforcing PMMA with $SiO_2$ nanoparticles at 0.25 wt% slightly affects the optical properties of the PMMA resin without being clinically perceivable.

• 대한수학회보
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• 제38권2호
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• pp.223-230
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• 2001

In this parper, we considered the uniqueness of positive time-solution to equation ${\Box}_g$u(t,$\chi$) - $c_n$u(t,$\chi$) + $c_n$u(t,$\chi$)$^[\frac{n+3}{n-3}]$ = 0, where $c_n$ = $\frac{n-1}{4n}$ and ${\Box}_g$ is the d'Alembertian for a Lorentzian warped manifold M = {a,$\infty$] $\times_f$ N.

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.513-518
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• 2003

In this paper, we have proved a theorem on Hausdorff summability of Fourier series which generalizes various known results. We prove that if $${\int}_{o}^{t}\;{\mid}{\phi}(u){\mid}\;du=o(t)\;as\;t{\rightarrow}0\; and\;\lim_{n{\rightarrow}{\infty}}{\int}^{\eta}_{{\pi}/n}{\frac{{\mid}{\phi}(t)-{\phi}(t+{\pi}/n){\mid}}{t}}dt=o(n)$$ where 0 < ${\eta}$ < 1, then the Fourier series is (H, ${\mu}_n$) summable to s at t = x where the sequence ${\mu}_n$ is given by ${\mu}_n={\int}^1_0x^n{\chi}(x)\;dx\;n=0,1,2\;and\;K_n(t)=\limits\sum_{{\nu}=0}^n(\array {n\\{\nu}})({\Delta}^{{n}-{\nu}}{\mu}_{\nu}){\frac{sin{\nu}t}{t}}$.

• 호남수학학술지
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• 제16권1호
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• 멤브레인
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• 제2권1호
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• pp.59-66
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• 1992

십자류 흐름 평판형 cell에서 비대칭 cellulose acetate 막으로 PEG #6000 및 dextran 70T 용액의 한외여과를 압력차와 도입용액 농도 변화에 따라 실험하여 막투과량 및 용질 배제도를 측정하고, 막투과량에 미치는 농도분극층 저항을 고찰하였다. 이 결과 농도분극층 저항 $R_{b1}$을 농도분극층내의 고분자 용액의 평균 농도 $C_{b1}$과 상관시켜 다음의 무차원 관계식으로 나타낼 수 있었다. $\frac{R_{b1}}{{R_m}}=\alpha[\frac{\rho_{b1}}{C_{b1}}]^\beta$

• 한국식품과학회지
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• 제18권4호
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• pp.306-312
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• 1986

마이야르 반응의 색변화를 이해하고자 0.8M의 당과 0.8M의 글리신반응액을 $70-100^{\circ}C$의 범위에서 반응시킬때 색의 변화를 Hunter값인 L, a 및 b값으로 측정하였다. 측정된 Hunter값들의 전반적인 변화경향은 유사하였으나 당의 종류 및 반응온도에 의해 변화속도가 크게 영향을 받았다. 색의 변화를 3단계로 구분하면 초기에는 L값이 서서히 감소함과 동시에 a값은 감소하여 -값을 나타내었고 b값은 급격히 증가하여 최고치에 도달하였다. 중기에서는 L값과 b값은 급속히 감소하면서 a값은 급속히 증가하였으며 최종기에서는 L값과 b값의 감소속도가 완만하게 되었고 a값은 급격하게 감소하였다. 반응시간에 따른 색의 변화를 예측하고져 Hunter값은 $\frac{1}{1/\sqrt{(L_{t}-L_{\circ})^2\;+\;(a_t-a_{\circ})^2\;+\;(b_t-b_{\circ})^2}}=a(\frac{1}{t})+b$의 식, 그리고 CIE 표준색채계에서는 $\frac{1}{\sqrt{X\;+\;Y\;+\;Z}}=a(\frac{1}{t})+b$의 직선관계식으로 계산하였을때 이들은 반응시간과 변화된 색 사이에 높은 상관관계가 변화된 색 사이에 높은 상관관계가 있음이 밝혀졌다. 또한 Hunter 값들 간의 관계, 즉L과a, L과b 그리고 a와b 값들간의 관계도 그림으로서 비교하였다.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.109-116
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• 1997

In the present paper we consider an abstract partial dif-ferential equation of the form $\frac{\partial^2u}{{\partial}t^2}-\frac{\partial^2u}{{\partial}x^2}+A(x.t)u=f(x, t)$, where ${A(x, t):(x, t){\epsilon}\bar{G} }$ is a family of linear closed operators and $G=GU{\partial}G$, G is a suitable bounded region in the (x, t)-plane with bound-are ${\partial}G$. It is assumed that u is given on the boundary ${\partial}G$. The objective of this paper is to study the considered Dirichlet problem for a wide class of operators $A(x, t)$. A Dirichlet problem for non-elliptic partial differential equations of higher orders is also considerde.