• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1269-1283
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• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.141-153
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• 2014

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.567-577
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• 2014

In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form $\mathbb{M}^{n+1}(c)$ (c = 1, 0,-1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in $\mathbb{S}^{n+1}(1)$ with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.87-93
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• 1983

Let X and Y be normed linear spaces. An operator T defined on X with the range in Y is continuous in the sense that if a sequence {x$_{n}$} in X converges to x for the weak topology .sigma.(X.X') then {Tx$_{n}$} converges to Tx for the norm topology in Y. We shall denote the class of such operators by WC(X, Y). For example, if T is a compact operator then T.mem.WC(X, Y). In this note we discuss relationships between WC(X, Y) and the class of weakly of bounded linear operators B(X, Y). In the last section, we will consider some characters for an operator in WC(X, Y).).

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.319-329
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• 2012

For a norm 1 function ${\sigma}$ in the Fourier-Stieltjes algebra of a locally compact group we define the space of ${\sigma}$-harmonic operators in the non-commutative $L^p$-space associated to the group von Neumann algebra of G. We will investigate some properties of the space and will obtain a precise description of it.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.269-286
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• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• Korean Journal of Culture and Social Issue
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• v.27 no.3
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• pp.217-236
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• 2021

The present study examined the mediating role of the subjective norm about social distancing in the relationship between individuals' collectivistic orientation and their social distancing behavior during the early COVID-19 crisis in Korea. A total of 445 South Korean adults residing in Korea participated in a survey during which level 2 to 2.5 prevention policies were being enforced. Results indicated, as expected, that collectivism positively predicted the perceptions of subjective norm that supports social distancing, which in turn predicted positively individuals' participation in social distancing as prescribed by the central government. This result emerged regardless of the individuals' perception of personal vulnerability to COVID-19. We discuss implications of these findings and directions for future research regarding the link between individualism-collectivism and the behavioral immune system, along with the role of social distancing in effectively curbing the spread of corona virus during the pandemic.

• Journal of Korean Biological Nursing Science
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• v.13 no.2
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• pp.102-108
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• 2011

Purpose: The purpose of this study was to examine the effects of first clinical training on stress, anxiety and changes in autonomic nervous system in nursing students. Methods: Seventy-four nursing students were assigned to the experimental group (n=36) that had two weeks of clinical training, and the control group (n=38) that had only two weeks of regular classes. Perceived stress, state anxiety and heart rate variability (HRV) were measured at the beginning and end of the experiment. Results: Perceived stress in the experimental group was significantly higher than in the control group. However, State anxiety was not significantly different between the two groups. All indices of HRV except LF/HF ratio were significantly different between the two groups. LF norm in the experimental group was significantly higher than in the control group, and HF norm in the experimental group was significantly lower than in the control group. Conclusion: Based on these results, it can be suggested that clinical training increases the perceived stress and affects the changes in autonomic nervous system in nursing students.