• 충청수학회지
• /
• 제21권1호
• /
• pp.139-146
• /
• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.

• Korean Journal of Mathematics
• /
• 제16권4호
• /
• pp.545-551
• /
• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

• KSBB Journal
• /
• 제26권4호
• /
• pp.305-310
• /
• 2011

This study was carried out to establish the optimum condition of cell disruption with a sonicator for the detection of the spore, Bacillus anthracis ${\Delta}$-sterne for the purpose of developing automatic fluorometer. The efficiency of sonication on the ${\Delta}$-sterne spore disruption was very weak. The ${\Delta}$-sterne spore with zirconia bead showed greater disruption than the ${\Delta}$-sterne spore alone when sonificated. The volumn of the zirconia bead added in the spore solution has little effect on the disruption efficiency. The detection limit of the ${\Delta}$-sterne spore with zirconia bead and the ${\Delta}$-sterne spore alone was $10^6$ CFU/mL and $5{\times}10^7$ CFU/mL respectively, when sample was sonicated for 20 seconds with a sonicator probe of 13 mm diameter.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.421-426
• /
• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• 대한수학회논문집
• /
• 제10권4호
• /
• pp.881-887
• /
• 1995

Let f be a measurable function on the unit ball B in $C^n$, then we define a maximal function $M_p(f), 1 \leq p < \infty$, by $$ M_p(f)(\zeta ) = \sup_{\delta > 0}(\frac{1}{\sigma(\beta(\zeta, \delta))} \int_{T(\beta(\zeta, \delta))} $\mid$f(z)$\mid$^p \frac{d\nu(z)}{(1-$\mid$z$\mid$^n})^{1/p} $$ where $\sigma$ denotes the surface area measure on S, the boundary of B, and $T(\beta(\zeta, \delta))$ denotes the tent over the ball $\beta(\zeta, \delta)$. We prove that the maximal operator $M_p$ belongs to the Muckenhoupt class $A_1$.

• 대한수학회보
• /
• 제50권4호
• /
• pp.1061-1067
• /
• 2013

In this paper, we study surfaces of revolution without parabolic points in 3-Euclidean space $\mathbb{R}^3$, satisfying the condition ${\Delta}^{II}G=f(G+C)$, where ${\Delta}^{II}$ is the Laplace operator with respect to the second fundamental form, $f$ is a smooth function on the surface and C is a constant vector. Our main results state that surfaces of revolution without parabolic points in $\mathbb{R}^3$ which satisfy the condition ${\Delta}^{II}G=fG$, coincide with surfaces of revolution with non-zero constant Gaussian curvature.

• 구강회복응용과학지
• /
• 제26권3호
• /
• pp.265-271
• /
• 2010

심미적 보철물을 제작하는 데 있어 색조의 선택은 중요한 단계이다. 이러한 색조선택과정은 광원, 표면, 관찰자 의 능력, 주변 배경색상, 관찰각도, 명암적응력 등과 같은 다양한 원인에 의해 좌우된다. 색조를 선택하는 시점에 따라 치아의 건조정도는 달라지게 되므로 본 실험에서는 치아 건조정도가 자연치아의 색조에 미치는 영향에 대해 살펴보고자 하였다. 구강내 색조측정기를 이용하여 구강가글 즉시 측정한 군을 실험군으로 구강가글 10초 후, 1분 후, 5분 후, 30초간 건조 후 색조를 측정하여 ${\Delta}E$값을 비교하였다. 각 실험군사이 ${\Delta}E$값은 유의할 만한 차이를 보였으나 대부분의 경우 구강내에서 시각적으로 구별할 수 없는 정도의 근접치를 보였다. 실험결과 시각적인 방법으로 색조 견본을 이용하는 방법은 건조정도에 따른 색조 차이가 없는 것으로 사료되고 기계를 이용하는 경우 건조정도가 색조 선택에 유의할 만한 영향을 줄 것이라고 사료된다.

• 한국세라믹학회:학술대회논문집
• /
• 한국세라믹학회 2000년도 추계총회,초청강연,특별강연,연구발표회
• /
• pp.129.2-129
• /
• 2000

• 방사성폐기물학회지
• /
• 제6권4호
• /
• pp.297-306
• /
• 2008

본 연구는 방사성 폐기물 처분장의 지하수 화학 조건을 조절하는 수리지구화학 특성을 규명할 목적으로 수행되었다. 이를 위해 처분장 주변의 관측공 중 12개의 관측공이 선정되었으며, 이들 시료를 심도별로 총 46 지점에서 채취하였다. 또한 지표수 3점과 해수 1점의 시료도 채취하였다. 채취된 시료는 양/음이온 분석이 수행되었으며, 물과 용질의 기원을 규명할 추적자로서 산소-수소, 삼중수소, 탄소, 황 동위원소도 분석되었다. 산소-수소 동위원소 분석 결과 지표수와 지하수는 모두 강우 기원임을 보여주었으며, 삼중수소 농도는 깊이가 깊어짐에 따라 감소하고는 있으나 높은 삼중수소 농도는 최근에 충진된 물임을 나타내고 있었다. 양/음이온 분석 결과를 통한 수질 유형 분석에서는 연구 지역 지하수는 Ca-Na-$HCO_3$ 유형과 Na-Cl-$SO_4$ 유형이 대표적이었으며, 상관 분석 결과 이들 이온은 해염, 물-암석 반응의 영향을 받은 것으로 판단된다. 특히 연구 지역에서 Na 비율이 높은 이유는 양이온 교환 반응에 의해 이루어지고 있음을 보여 주었다. 연구 지역의 산화-환원 조건의 경우에는 심도가 깊어짐에 따라 낮은 DO와 Eh 값을 나타내어 환원 환경이 형성되었음을 나타내며, 높은 Fe와 Mn의 농도는 Fe와 Mn 산화물의 환원 반응이 산화-환원 조건을 조절하고 있음을 보여주었다.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2003년도 추계학술대회
• /
• pp.1115-1120
• /
• 2003

The recent tendency in the automobile industries is toward light weighting vehicle body to improve the problems by environmental pollution as well as improving fuel cost. The effective way to reduce the weight of vehicle body seems to be application of new materials for body structure and such trend is remarkable. Among the various materials for vehicle body, stainless steel sheet (for example, 301L and 304L), TRIP steel and cold rolled steel sheets are under the interests. However, in order to guarantee reliability of new material and to establish the long life design criteria of body structure, it is important and require condition to assess spot weldability of them and fatigue strength of spot welded lap joints which were fabricated under optimized spot welding condition. And, recently, a new issue in the design of the spot welded structure is to predict economically fatigue design criterion without additional fatigue tests. In general, for fatigue design of the spot-welded thin sheet structure, additional fatigue tests according to the welding condition, material, joint type, and fatigue loading condition are generally required. This indicates that much cost and time for it should be consumed. Therefore, in this paper, the maximum stresses at nugget edge of spot weld were calculated through nonlinear finite element analysis first. And next, obtained the ${\Delta}P-N_{f}$ relation through the actual fatigue tests on spot welded lap joints of similar and dissimilar high strength steel sheets. And then, the ${\Delta}P-N_{f}$ relation was rearranged in the ${\Delta}{\sigma}-N_{f}$ relation. From this ${\Delta}{\sigma}-N_{f}$ relation, developed the fatigue design technology for spot welded lap joints of them welded using the optimized welding conditions.