• Korean Journal of Mathematics
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• 제12권1호
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• pp.41-47
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• 2004

We introduce the $K_0$-proximity space as a generalization of the Efremovi$\check{c}$-proximity space. We try to show every ultrafilter in $K_0$-proximity space generates a cluster and every Cauchy cluster is a point cluster.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권4호
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• pp.1351-1372
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• 2022

A self-organizing multiple unmanned aerial vehicles (multi-UAVs) deployment based on virtual forces has a difficulty in ensuring the quality-of-experience (QoE) of users because of the difference between the assumed center for users in a hotspot and an actual center for users in the hotspot. This discrepancy is aggravated in a non-uniform and mobile user distribution. To address this problem, we propose a new density based virtual force (D-VF) multi-UAVs deployment algorithm which employs a mean opinion score (MOS) as a metric of QoE. Because MOS is based on signal-to-noise ratio (SNR), a sum of users' MOS is a good metric not only to secure a wide service area but to enhance the link quality between multi-UAVs and users. The proposed algorithm improves users' QoE by combining virtual forces with a random search force for the exploration of finding multi-UAVs' positions which maximize the sum of users' MOS. In simulation results, the proposed deployment algorithm shows the convergence of the multi-UAVs into the position of maximizing MOS. Therefore, the proposed algorithm outperforms the conventional virtual force-based deployment scheme in terms of QoE for non-uniform user distribution scenarios.

• 대한수학회지
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• 제41권1호
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• pp.1-20
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• 2004

Let A be a uniform algebra, and let $\phi$ be a self-map of the spectrum $M_A$ of A that induces a composition operator $C_{\phi}$, on A. It is shown that the image of $M_A$ under some iterate ${\phi}^n$ of \phi is hyperbolically bounded if and only if \phi has a finite number of attracting cycles to which the iterates of $\phi$ converge. On the other hand, the image of the spectrum of A under $\phi$ is not hyperbolically bounded if and only if there is a subspace of $A^{**}$ "almost" isometric to ${\ell}_{\infty}$ on which ${C_{\phi}}^{**}$ "almost" an isometry. A corollary of these characterizations is that if $C_{\phi}$ is weakly compact, and if the spectrum of A is connected, then $\phi$ has a unique fixed point, to which the iterates of $\phi$ converge. The corresponding theorem for compact composition operators was proved in 1980 by H. Kamowitz [17].

• 충청수학회지
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• 제29권3호
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• pp.417-428
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• 2016

We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying ${\varphi}$-contractive conditions or ${\psi}$-${\phi}$-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.

• 대한수학회지
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• 제32권3호
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• pp.427-446
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• 1995

Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.

• 한국정밀공학회지
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• 제14권3호
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• pp.130-136
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• 1997

The velocity distrubution at the exit of extrusion die depends on the width of bearing land very much. When uniform bearing land without flow guide is used, the material which is extended through the same die does not, deflect to the constant direction, but when the flow guide is equipped and then the volume compensation is done accurately, the material deflects to one constant direction. Therfore, the part of problem can be known exactly, and extrusion products of straight shape can be produced by the corrected bearing land width.

• 한국환경과학회지
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• 제16권5호
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• pp.549-559
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• 2007

Vegetation surveys were performed at 45 plots along 10 highways cut slopes in South Korea. Total floral inventory, species richness and exotic plant percentage were obtained within each plot. Life history and life form of each species appeared were analyzed. Community types were classified using hierarchical cluster analysis and detrended correspondence analysis and non-metric multidimensional scaling were conducted from vegetation matrix. 292 species of vascular plants were discovered and the number of natives and exotics were 226 and 66, respectively. There were no significant differences of species richness and exotic plant percentage between cut slopes and rest areas. Hierarchical cluster analysis indicated five clear vegetation associations in cut slopes and rest areas. Detrended correspondence analysis indicated that species composition of total and native plants were similar along the highway cut slopes whereas exotic plants were distributed differentially along the highway cut slopes. in non-metric multidimensional scaling, the studied sites were more separated from each other on the basis of their species composition than the results of detrended correspondence analysis with respect to total, native and exotic plants. The both ordination represented that exotic plants have not been made uniform yet on cut slopes and rest areas by highway corridor in spite of diverse chronosequences after highway construction termination (1 to 22 years). This study showed that the distribution of species composition in exotic plants was different and localized on cut slopes and rest areas of highway in this representative peninsula area of North East Asia and the invasion of exotic plants can retard the process of plant species homogenization.

• 대한수학회보
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• 제30권2호
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• pp.179-185
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• 1993

In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

• 대한수학회보
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• 제52권5호
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• pp.1737-1751
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• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• 대한수학회논문집
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• 제11권3호
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• pp.725-742
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• 1996

In this paper we give some sharp expressions of the weakly convergent sequence coefficient WCS(X) of a Banach space X. They are used to prove fixed point theorems for involution mappings T from a weakly compact convex subset C of a Banach space X with WCS(X) > 1 into itself which $T^2$ are both of asymptotically nonexpansive type and weakly asymptotically regular on C. We also show that if X satisfies the semi-Opial property, then every nonexpansive mapping $T : C \to C$ has a fixed point. Further, some questions for asymtotically nonexpansive mappings are raised.