• Journal of applied mathematics & informatics
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• v.8 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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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 $\Gamma_g$.

• Honam Mathematical Journal
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• v.40 no.3
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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.

• Honam Mathematical Journal
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• v.40 no.3
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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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• v.59 no.2
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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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• v.40 no.3_4
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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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• v.15 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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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.

• Journal of KIISE:Databases
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• v.33 no.2
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• pp.175-187
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• 2006

The data cube is an aggregation operator that computes group-bys for all possible combination of dimension attributes. %on the number of the dimension attributes is n, a data cube computes $2^n$ group-bys. Each group-by in a data cube is called a cuboid. Data cubes are often precomputed and stored as materialized views in data warehouses. These data cubes need to be updated when source relation change. The incremental maintenance of a data cube is to compute and propagate only its changes. To compute the change of a data cube of $2^n$ cuboids, previous works compute a delta cube that has the same number of cuboids as the original data cube. Thus, as the number of dimension attributes increases, the cost of computing a delta cube increases significantly. Each cuboid in a delta cube is called a delta cuboid. In this paper. we propose an incremental cube maintenance method that can maintain a data cube by using only $_nC_{{\lceil}n/2{\rceil}}$ delta cuboids. As a result, the cost of computing a delta cube is substantially reduced. Through various experiments, we show the performance advantages of our method over previous methods.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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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 $N{\geq}3$.