• 대한수학회보
• /
• 제31권2호
• /
• pp.193-200
• /
• 1994

Let x : $M^{n}$ .rarw. $E^{m}$ be an isometric immersion of a manifold $M^{n}$ into the Euclidean space $E^{m}$ and .DELTA. the Laplacian of $M^{n}$ defined by -div.omicron.grad. The family of such immersions satisfying the condition .DELTA.x = .lambda.x, .lambda..mem.R, is characterized by a well known result ot Takahashi (8]): they are either minimal in $E^{m}$ or minimal in some Euclidean hypersphere. As a generalization of Takahashi's result, many authors ([3,6,7]) studied the hypersurfaces $M^{n}$ in $E^{n+1}$ satisfying .DELTA.x = Ax + b, where A is a square matrix and b is a vector in $E^{n+1}$, and they proved independently that such hypersurfaces are either minimal in $E^{n+1}$ or hyperspheres or spherical cylinders. Since .DELTA.x = -nH, the submanifolds mentioned above satisfy .DELTA.H = .lambda.H or .DELTA.H = AH, where H is the mean curvature vector field of M. And the family of hypersurfaces satisfying .DELTA.H = .lambda.H was explored for some cases in [4]. In this paper, we classify space curves x : R .rarw. $E^{3}$ satisfying .DELTA.x = Ax + b or .DELTA.H = AH, and find conditions for such curves to be equivalent.alent.alent.

• 대한기계학회논문집
• /
• 제13권5호
• /
• pp.1012-1022
• /
• 1989

본 연구에서는 열원인 내관의 온도가 불균일한 경사진 동심환상공간에서의 열전달 특성을 $R_{a}$ =3*$10^{4T,P}$1r=7.0, 내외관의 반경비 0.6일 때 경사각도 0。,30。그리고 60。에 대하여 3차원 수치해석으로 연구하였으며 균일온도분포인 경우 와 비교 고찰하였다.

• 대한치과기공학회지
• /
• 제23권1호
• /
• pp.85-93
• /
• 2001

The purpose of this study was to evaluate the effects of commercial home-tooth bleaching agents on the color of tooth. Twenty five sound extracted teeth were randomly divided into five groups. The color differences between before and after treatment with five types of tooth bleaching agents (7.5% hydrogen peroxide Nite White $Excel^{(R)}$, 10% carbamide peroxide Nite White $Excel^{(R)}$, 16% carbamide peroxide Nite White $Excel^{(R)}$, 10% carbamide peroxide Insta-BriteTM, 20% carbamide peroxide Insta-$Brite^{TM}$) were evaluated. The results were as follows: 1. By 2 week home tooth bleaching agent applications, the values ($L^*$) of bovine teeth increased as high as 4.38 $\sim$ 8.80 when comparing to those of the samples before treatment, and the color difference (${\Delta}E^*$) showed as high as 10.16 $\sim$ 15.04. 2. 16% carbamide peroxide Nite White Excel induced significantly greater ${\Delta}L^*$ than other test edgroups except for 7.5% hydrogen peroxide Day White Excel, and significantly greater ${\Delta}E^*$ than other tested groups by 2 week bleaching agent treatments (p<0.01). 3. 16% carbamide peroxide Nite White Excel(${\Delta}L^*$=8.80, ${\Delta}E^*$=15.04) induced significantly greater ${\Delta}L^*$ and ${\Delta}E^*$ than 10% carbamide peroxide Nite White Excel(${\Delta}L^*$=5.01, ${\Delta}E^*$=10.16)(p<0.01), but significant difference between 10% carbamide peroxide Insta-Brite(${\Delta}L^*$=4.38, ${\Delta}E^*$=10.51) and 20% carbamide peroxide Insta-Brite(${\Delta}L^*$=5.63, ${\Delta}E^*$=11.23) was not shown in ${\Delta}L^*$ and ${\Delta}E^*$(p>0.01). 4. 16% carbamide peroxide Nite White Excel(${\Delta}L^*$=8.80, ${\Delta}E^*$=15.04) which were applied in night time induced significantly greater ${\Delta}L^*$ and ${\Delta}E^*$ than 7.5% hydrogen peroxide Day White Excel(${\Delta}L^*$=8.47, ${\Delta}E^*$=12.75) which were applied in day time. Conclusions: These results demonstrate that all the commercial home-tooth bleaching agents have appreciable bleaching effect on teeth, and the effects of home-tooth bleaching agents which are used during night time are affected by content of carbamide peroxide. Especially the whitening effect of home tooth bleaching agents that are used through night time is greater than that of short time-applying tooth bleaching agent.

• 한국정보디스플레이학회:학술대회논문집
• /
• 한국정보디스플레이학회 2003년도 International Meeting on Information Display
• /
• pp.347-350
• /
• 2003

Optimization of the luminance, luminous efficiency, and address voltage margin characteristics has been made on the delta color array PDP with various hexagonal shape subpixels. The optimal subpixel and electrode designs are obtained for the 42-inch high-definition PDP ($1,366{\times}768$) with the fine pixel pitch less than 0.7 mm. The hexagonal delta array structure shows more improved characteristics than that of the normal delta array structure with rectangular shape subpixels.

• 천문학회지
• /
• 제15권2호
• /
• pp.49-58
• /
• 1982

The UBVRIHKL magnitudes on Johnson system and space motions of M dwarf stars have been collected. This sample of M stars have been distinguished on a purely kinematical basis; the one with e<0.15, young disk population, with 0.150.3 halo population. On the color-color diagrams and the color excess-orbital eccentricity diagrams, there is no distinction between the old disk stars and the young disk stars. However (I-H) color could be used to distinguish halo stars from young and old disk stars and the color excesses, ${\Delta}(U-B),\;{\Delta}(B-V),\;{\Delta}(V-R),\;{\Delta}(H-K),\;{\Delta}(K-L),\;and\;{\Delta}(B-R)$ can be used as abundance indicators only for the halo stars. But these color excesses which are measures of blue excesses, are positive for the halo stars with smaller eccentricities and become negative for those with larger eccentricities.

• Korean Journal of Mathematics
• /
• 제15권1호
• /
• pp.51-57
• /
• 2007

We prove the existence of a positive solution for the system of the following nonlinear biharmonic equations with Dirichlet boundary condition $$\{{\Delta}^2u+c{\Delta}u+av^+=s_1{\phi}_1+{\epsilon}_1h_1(x)\;in\;{\Omega},\\{\Delta}^2v+c{\Delta}v+bu^+=s_2{\phi}_1+{\epsilon}_2h_2(x)\;in\;{\Omega},$$ where $u^+= max\{u,0\}$, $c{\in}R$, $s{\in}R$, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition. Here ${\epsilon}_1$, ${\epsilon}_2$ are small numbers and $h_1(x)$, $h_2(x)$ are bounded.

• 전자공학회논문지A
• /
• 제31A권6호
• /
• pp.143-148
• /
• 1994

In order to study the effect of D.C resistivity of sample on electromagnetic loss of ferrite at microwave frequency, samples were prepared for having differences in resistivity of an order of two. Microwave permeability($\mu$), permitivity($\varepsilon$) and effective linewidth(${\Delta}H_{eff}$), and ferromagnetic resonance linewidth(${\Delta}$H) were characterized. Tan${\delta}{\mu}$, tan${\delta}{\varepsilon}$ and ${\Delta}H_{eff}$ were decreased with increasing the resistivity and (${\Delta}$H) was increased with increasing Fe concentration, which was due to an increase of anisotropy magnetic field (=Ha).

• 대한화학회지
• /
• 제17권1호
• /
• pp.1-9
• /
• 1973

區區한 Diels-Alder 反應의 구조를 규명하기 위하여 Diels-Alder 反應 基 自體의 本質에 가장 가깝다고 생각한 새로운 擬似分子化合物이라는 遷移狀態의 模型을 假定하여 Mulliken의 分子化合物의 量子力學을 適用하였다. 이 擬似分子化合物은 이온성과 Radical성을 지닌 混成體이다. 이 混成體의 波動函數는 다음 식으로 표현된다. ${\psi}_{complex} = {\psi}(R,S) + {\rho}{\psi}(R^+,S^-)$ 여기 ${\rho}$는 擬似分子化合物의 極性程度를 나타내는 것이고 이 ${\rho}$가 Diene과 Dienpohile의 反應中心原子들의 自由原子價의 차 $({\Delta}F)$에 關係함을 밝혔다. 아울러 이 ${\Delta}F$量이 Brown氏의 Lp量 및 Dewar氏의 ${\Delta}E_{deloc}$量과 直線성이 있음을 알았다. Diels-Alder反應의 可能性與否를 24組의 反應組에 對하여 豫言하였다. 따라서 우리가 假定한 遷移狀態의 模型이 眞實에 가깝다고 볼 수 있으며 결국 Diels-Alder 反應은 同時附加로 융합된 ionic-Radical mechanism으로 反應이 進行한다고 볼 수 있다.

• Kyungpook Mathematical Journal
• /
• 제56권3호
• /
• pp.777-789
• /
• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.

• Journal of applied mathematics & informatics
• /
• 제36권3_4호
• /
• pp.213-229
• /
• 2018

In this work, we establish oscillation of the second order sublinear neutral delay dynamic equations of the form:$$(r(t)((x(t)+p(t)x({\tau}(t)))^{\Delta})^{\gamma})^{\Delta}+q(t)x^{\gamma}({\alpha}(t))+v(t)x^{\gamma}({\eta}(t))=0$$ on a time scale T by means of Riccati transformation technique, under the assumptions $${\displaystyle\smashmargin{2}{\int\nolimits^{\infty}}_{t_0}}\({\frac{1}{r(t)}}\)^{\frac{1}{\gamma}}{\Delta}t={\infty}$$, and ${\displaystyle\smashmargin{2}{\int\nolimits^{\infty}}_{t_0}}\({\frac{1}{r(t)}}\)^{\frac{1}{\gamma}}{\Delta}t$ < ${\infty}$, for various ranges of p(t), where 0 < ${\gamma}{\leq}1$ is a quotient of odd positive integers.