• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.661-690
• /
• 2019

The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-$Lindel{\ddot{o}}fness$, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi-$Lindel{\ddot{o}}fness$. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-$Lindel{\ddot{o}}f$ spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.

• Journal of Korea Water Resources Association
• /
• v.34 no.2
• /
• pp.155-167
• /
• 2001

The effects of bank crest width, slope steepness, soil properties, and soil compactness on the characteristics of levee breach due to overlfow were investigated through a series of experiments. Generally, the major factors influencing the breach phenomenon are compactness, soil properties. crest width, and slope steepness, in that order. Using proper soil, and ensuring enough compactness in bank construction are very essential for extending breach duration and reducing peak overflow ranges for the values of breach duration, breach width, width-to-depth ratio, and side slope of the breach section, proposed by Singh, MacDonald and Fread based on the field data for earth dam breaks were reasonable. We found that those criteria could also be applied to the phenomenon of levee breaching.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2011.10a
• /
• pp.915-917
• /
• 2011

In this paper, a comparison of superpixel characteristics for each color feature space. The superpixel is consist of several pixels with same features such as luminance, color, textures etc. The superpixel can be used on image processing and analysis with large image size to speed up the process. We compare the superpixel characteristics by means of compactness using Berkeley image database(BSD-300).

• Communications of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.357-368
• /
• 2012

We introduce the concepts of fuzzy ${\delta}$-interior and show that the set of all fuzzy ${\delta}$-open sets is also a fuzzy topology, which is called the fuzzy ${\delta}$-topology. We obtain equivalent forms of fuzzy ${\delta}$-continuity. More-over, the notions of fuzzy ${\delta}$-compactness and fuzzy locally ${\delta}$-compactness are defined and their basic properties under fuzzy ${\delta}$-continuous mappings are investigated.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.495-517
• /
• 2022

Let M_α be a bilinear fractional maximal operator and BM_α be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators M^j_α,β and BM^j_α,β (j = 1, 2), the fractional maximal iterated commutator ${\mathcal{M}}_{{\alpha},{\vec{b}}}$, and $BM_{{\alpha},{\vec{b}}}$, where b ∈ BMO(ℝ^d) and ${\vec{b}}\;=\;(b_1,b_2)\;{\in}\;BMO({\mathbb{R}}^d)\;{\times}\;BMO({\mathbb{R}}^d)$. In particular, we improve the well-known results to a larger scale for 1/2 < q < ∞ and give positive answers to the questions in [2].

• Honam Mathematical Journal
• /
• v.23 no.1
• /
• pp.29-39
• /
• 2001

Let $\mathcal{B}$ be a Banach space of analytic functions defined on the open unit disk. Assume S is a bounded operator defined on $\mathcal{B}$ such that S is in the commutant of $M_zn$ or $SM_zn=-M_znS$ for some positive integer n. We give necessary and sufficient condition between compactness of $SM_z+cM_zS$ where c = 1, -1, i, -i, and the structure of S. Also we characterize the commutant of $M_zn$ for some positive integer n.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.433-450
• /
• 2009

We introduce a new concept of intuitionistic fuzzy topological subspace, which coincides with the usual concept of intuitionistic fuzzy topological subspace due to Samanta and Mondal [18] in the case that $\mu=X_A$ for A $\subseteq$ X. Also, we introduce and study some concepts such as continuity, separation axioms, compactness and connectedness in this sense.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.287-304
• /
• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• Journal of Ocean Engineering and Technology
• /
• v.17 no.5 s.54
• /
• pp.19-24
• /
• 2003

The question of wave source identification in a wave maker problem is the primary objective of the this paper. With the observed wave elevation, the existence of the wave maker velocity is discussed with the help of the mathematical theory of inverse problems. Utilizing the property of the Strum-Liouville system and compactness, the uniqueness and the ill-posedness(in the sense of stability) for the identification are proved.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.527-540
• /
• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.