• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• 대한수학회지
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• 제34권1호
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• pp.87-118
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• 1997

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

• 호남수학학술지
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• 제40권3호
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• pp.391-400
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• 2018

The object of this paper to construct a new class $$A^m_{{\mu},{\lambda},{\delta}}({\alpha},{\beta},{\gamma},t,{\Psi})$$ of bi-univalent functions of complex order defined in the open unit disc. The second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass are determined. Several special consequences of the results are also indicated.

• 호남수학학술지
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• 제40권3호
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• pp.433-446
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• 2018

In this present investigation, we introduce a new class of harmonic univalent functions of the form $f=h+{\bar{g}}$ in the open unit disk ${\Delta}$. We get basic properties, like, necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for these classes of functions.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.341-352
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• 2019

Let M be an n-dimensional closed Riemannian manifold with metric g, $d{\mu}=e^{-{\phi}(x)}d{\nu}$ be the weighted measure and ${\Delta}_{p,{\phi}}$ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.785-794
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• 2022

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.

• Journal of Gastric Cancer
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• 제15권2호
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• pp.105-112
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• 2015

Purpose: Intracorporeal anastomosis is the most difficult procedure during pure single-incision distal gastrectomy (SIDG) that affects its generalization. We introduced unaided delta-shaped anastomosis (uDelta), a novel anastomosis technique, for gastroduodenostomy after pure SIDG, and compared the results with those of previously reported Roux-en-Y anastomosis (RY). Materials and Methods: Between March 2014 and March 2015, SIDG with D1+ lymph node dissection was performed for early gastric cancer through a 2.5-cm transumbilical incision without any additional port. uDelta was performed by the operator alone, without any intracorporeal assistance. Results: uDelta was performed on 11 patents, and uncut RY was performed on 5-patients without open or multiport conversion. R0 resection was performed in all cases. No significant differences were observed in mean age and body mass index between patients who underwent uDelta or RY. Mean operation times were $214.5{\pm}36.2$ minutes for uDelta and $240.8{\pm}65.9$ minutes for RY, which was not significantly different. Reconstruction time for uDelta was shorter than that for RY, with marginal statistical significance ($26.1{\pm}8.3$ minutes vs. $38.0{\pm}9.1$ minutes, P=0.05). There were no intraoperative transfusions, 30-day mortality, or anastomosis-related complications in either group. Average length of hospital stay was $8.2{\pm}1.9$ days in the uDelta group and $7.2{\pm}0.8$ days in the RY group (P=0.320). Conclusions: After carefully considering indications, uDelta can be a feasible and can be a reproducible reconstruction method after SIDG in early gastric cancer.

• 대한수학회보
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• 제24권1호
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• pp.23-26
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• 1987

The aim of this note is to study some properties of Schrodinger operators, the magnetic case, $H_{0}$ (a)=1/2(-i.del.-a)$^{2}$; H(a)= $H_{0}$ (a)+V, where a=( $a_{1}$,.., $a_{n}$ ).mem. $L^{2}$$_{loc}$ and V is a potential energy. Also, we are interested in solutions, .psi., of H(a).psi.=E.psi. in the sense that (.psi., $e^{-tH}$(a).PSI.)= $e^{-tE}$(.psi.,.PSI.) for all .PSI..mem. $C_{0}$ $^{\infty}$( $R^{n}$ ) (see B. Simon [1]). In section 2, under some conditions, we find that a semibounded quadratic form of H9a) exists and that the Schrodinger operator H(a) with Re V.geq.0 is accretive on a form domain Q( $H_{0}$ (a)). But, it is well-known that the Schrodinger operator H=1/2.DELTA.+V with Re V.geq.0 is accretive on $C_{0}$ $^{\infty}$( $R^{n}$ ) in N Okazawa [4]. In section 3, we want to discuss $L^{p}$ estimates of Schrodinger semigroups.ups.

• 한국정보과학회논문지:데이타베이스
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• 제33권2호
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• pp.175-187
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• 2006

데이타 큐브는 차원 애트리뷰트의 모든 가능한 조합에 대해 데이타를 집단화하는 연산자이다. 차원 애트리뷰트의 수가 n일 때, 데이타 큐브는 $2^n$개의 group-by를 계산한다. 데이타 큐브에 포함된 각각의 group-by를 큐보이드(cuboid)라 부른다. 데이타 큐브는 흔히 미리 계산되어 형태 뷰(materialized view)의 형태로 데이타 웨어하우스에 저장된다. 이러한 데이타 큐브는 소스 릴레이션이 변경되면 이를 반영하기 위해 갱신되어야 한다. 데이타 큐브의 점진적 관리는 데이타 큐브의 변경될 내용만을 계산하여 이를 데이타 큐브에 반영하는 방법을 의미한다. $2^n$개의 큐보이드로 이루어진 큐브의 변경될 내용을 계산하기 위하여, 기존의 방법들은 데이타 큐브와 동일한 개수의 큐보이드를 가지는 변경 큐브를 계산한다. 따라서, 차원 애트리뷰트의 수가 증가할수록 변경 큐브를 계산하는 비용이 매우 커지게 된다. 변경 큐브에 포함된 각 큐보이드들을 변경 큐보이드(delta cuboid)라 부른다. 본 논문에서는 $2^n$개의 변경 큐보이드 대신 $_nC_{{\lceil}n/2{\rceil}}$개의 변경 큐보이드만을 사용하여 데이타 큐브를 갱신하는 방법을 제안한다. 이에 따라 제안하는 방법은 변경 큐브를 계산하는 비용을 크게 줄일 수 있다. 성능 평가 결과는 제안하는 방법이 기존의 방법에 비해 더 좋은 성능을 가지고 있음을 보여준다.

• 대한수학회보
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• 제50권3호
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.