• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.817-824
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• 2017

In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.

• Journal of the military operations research society of Korea
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• v.24 no.1
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Microbiology and Biotechnology Letters
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• v.33 no.3
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• pp.226-230
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• 2005

The microbial community during composting of gargage was analyzed using 16S rDNA PCR - DGCE (denaturing gradient gel electrophoresis). Pseudomonas spp. was found throughout the process, and thermophilic Bacillus spp. was dominated at the thermophilic stage. Six thermophilic bacteria were isolated and identified as B. caldoxylolyticus, B. thermoalkalophilus, and B. thermodenitrificans.

• Multiscale and Multiphysics Mechanics
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• v.1 no.2
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• pp.171-188
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• 2016

Gradient enhanced theories of crystal plasticity enjoy great research interest. The focus of this work is on thermodynamically consistent modeling of grain size dependent hardening effects. In this contribution, we develop a model framework for damage coupled to gradient enhanced crystal thermoplasticity. The damage initiation is directly linked to the accumulated plastic slip. The theoretical setting is that of finite strains. Numerical results on single-crystalline metal showing the development of damage conclude the paper.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1411-1429
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• 2016

We consider the nite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R({\nabla}u_h)$ possesses the superconvergence: ${\parallel}{\nabla}u-R({\nabla}u_h){\parallel}=O(h^2){\parallel}u{\parallel}_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.853-865
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• 2019

In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $${\Delta}_Vu+cu^{\alpha}=0$$, where c, ${\alpha}$ are two real constants and $c{\neq}0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.635-682
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• 2023

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise Hölder continuous but locally Hölder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient Hölder continuity which was obtained by the previous results.

• Asia Marketing Journal
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• v.16 no.1
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• pp.1-12
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• 2014

The goal-gradient hypothesis states that the tendency to approach a goal increases with the increasing proximity of the goal (Hull 1932). It was initially supported with an evidence of animal experiments and since then, several papers have investigated the goal-gradient hypothesis in humans. Although there are some evidences related to the goal-gradient hypothesis in human behaviors, none of previous studies can properly explain its underlying mechanism, and what's more, they were not able to suggest useful managerial applications in human behaviors. From these perspectives, this work points out that there are some theoretical weaknesses to apply the goal-gradient hypothesis into the complicated human decision-making behaviors and proposes an alternative theoretical mechanismthat underlies the goal-gradient hypothesis in human. Finally, it offers insights into managerial implications of the goal-gradient hypothesis in the marketing field. This study focuses on the changes in motivations for achieving goals, in terms of how approaches to goals vary according to temporal distance from those goals. Specifically, the temporal construal theory (Liberman and Trope 1998) is considered as the underlying mechanism of the goal-gradient in that the temporal construal theory argues how the temporal distance from a goal makes people change their associated values regarding to that goal. According to the temporal construal theory, the value of distant future outcomes (near future outcomes) is construed on the basis of abstract and central features (concrete and peripheral features), and it argues that distant future situations are construed on a higher level than near future situations. This means that the value associated with the high-level construal is enhanced over delay, whereas the value associated with the low-level construal is discounted over delay. Our propositions suggest that the goal-gradient behavior in human can be motivated by the different aspects or characteristics of the goal as time changes based on the temporal construal theory. Thus, the following propositions are proposed. P 1-1: If the goal is far away, consumers put more value on the central features that are more associated with the desirability of the goal. P 1-2: If the goal is far away, consumers put more effort into accomplishing the goal that has more central features, regardless of its peripheral features. P 2-1: If a goal is near, consumers put more value on the peripheral features that are more associated with the feasibility of the goal. P 2-2: If a goal is near, consumers put more effort into accomplishing the goal that has more peripheral features, regardless of its central features. We hope to provide sufficient managerial implications for the companies as our research aims to show how consumers react differently as they progress toward the goal. Proposed propositions may provide guidance for companies developing a loyalty program, enabling them to understand what kinds of benefits or services they should provide or emphasize to consumers in loyalty programs on the basis of the time-dependent changes in outcome values (such as gifts, reward coupons). The effects of temporal distance from a goal should inform companies' marketing activities and help themto determine where emphasis should be placed in designing the benefits of their loyalty program.