• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.455-470
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• 2005

This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.477-484
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• 2010

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1) and (2), then compactness, countable compactness and sequential compactness are equivalent in X; (1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.29-40
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• 2001

In this note, we get the conditions such that strong continuity ${\Rightarrow}$ weak continuity plus interiority condition( wc+ic), and continuity ${\Rightarrow}$ wc+ic are true. And we investigate some equivalent conditions with weak continuity, some properties of weak continuity. And we show that almost compactness is preserved by weakly continuous function, and we improve some known results with respect to strong continuity.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.661-690
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• 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 the Korean Mathematical Society
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• v.56 no.5
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• pp.1419-1439
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• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.28 no.8
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• pp.316-324
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• 2016

This study investigated a compact regenerative evaporative cooler (REC). To achieve practical applications of an REC, it is very important to consider the compactness as well as the cooling performance. Therefore, a prototype of the REC was designed and fabricated to improve the compactness by reducing the length through the insertion of fins in both the dry and wet channels. The REC prototype was tested in terms of performance evaluation under various operating conditions. An analytical model was also developed to analyze the effects of the axial conduction through the solid body of the REC, the wetness of the surface in the wet channel, and the thermal capacity of the evaporation water flow. The model was validated by comparing the results of a simulation with experimental data. The numerical simulation was based on the model to analyze the performance of the REC and to suggest methods to improve the cooling performance of the REC. Finally, the performance of the present REC was compared to that obtained in previous experimental studies. The results showed that the REC prototype in the present study is the most compact and achieves the highest cooling performance.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.315-330
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• 2007

In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.649-657
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• 2023

In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].