• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• 한국CDE학회논문집
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• 제8권2호
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• pp.75-83
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• 2003

In this paper, OSP(Octal Space Partitioning) tree is proposed for the real time culling of infinite sets of geometries in interactive Virtual Environment applications. And MSVBSP(Modified Shadow Volume BSP) tree is suggested for the occlusion culling. Experimental results show that the OSP and MSVBSP tree are efficiently implemented in real time rendering of interactive geometries.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.893-908
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• 2010

In this paper we prove the existence of spanning 3-trees in a 3-connected infinite locally finite VAP-free plane graph. Together with the results of Barnette and the author, this yields that every finite or infinite 3-connected locally finite VAP-free plane graph contains a spanning 3-tree.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.83-92
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• 2012

In this paper, a generalized Shannon-McMillan theorem for the nonhomogeneous Markov chains indexed by an infinite tree which has a uniformly bounded degree is discussed by constructing a nonnegative martingale and analytical methods. As corollaries, some Shannon-Mcmillan theorems for the nonhomogeneous Markov chains indexed by a homogeneous tree and the nonhomogeneous Markov chain are obtained. Some results which have been obtained are extended.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1307-1318
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• 2009

An infinite locally finite plane graph is an LV-graph if it is 3-connected and VAP-free. In this paper, as a preparatory work for solving the problem concerning the existence of a spanning 3-tree in an LV-graph, we investigate the existence of a spanning 3-forest in a bridge of type 0,1 or 2 of a tight semi ring in an LV-graph satisfying certain conditions.

• 대한수학회보
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• 제54권3호
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• pp.747-761
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• 2017

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.

• 한국가스학회지
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• 제2권2호
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• pp.55-60
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• 1998

열경화성 수지의 충전제로 많이 사용되고 있는 소나무 분진을 시료로 분진폭발의 최소착화에너지와 폭발한계를 측정하여 분진폭발 특성을 고찰하였다. 실험은 전극간 거리, 분진운 농도, 분진입도 및 수분 등에 대한 실험을 행하였다. 그 결과 전극간 거리가 4mm 이하로 되면 증가하는 경향을 나타내었으며, 2mm 이하에서는 착화에너지가 갑자기 무한대로 되어 이 값이 한계전극 거리임을 알았다. 또한 분진운 농도가 증가하고 분진 입도가 미세할수록 폭발성이 용이하였으며, 동일한 입도의 분진에서 수분 함유량이 증가할수록 최소착화에너지가 증가하였다.

• East Asian mathematical journal
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• 제31권5호
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• pp.695-706
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• 2015

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

• 한국환경복원기술학회지
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• 제14권4호
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• pp.41-54
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• 2011

Tree roots can enhance soil shear strength and slope stability. However, there has been a limited study about root reinforcement of major tree species in Korea because of some experimental difficulties. Thus, this study was conducted to analyze the performance of Japanese larch (Larix kaempferi) and Korean pine (Pinus koraiensis) which are two common plantation species in Korea. Profile wall method was used to measure the spatial distribution of root system and its diameter within 15 soil walls of Japanese larch stand and 13 soil walls of Korean pine stand in Taehwa University Forest, Seoul National University, Korea. Root tensile properties of each species were assessed in the laboratory, and root reinforcements were estimated by Wu model. The study observed that the number and cross-sectional area (CSA) of root in both species could tend to decrease with soil depth. Especially, CSA were well-fitted to exponential functions of soil depth. Mean root area ratios (RAR) were 0.03% and 0.10% for Japanese larch and Korean pine, respectively. Estimated root reinforcement from Wu model were, on the average, 4.04 kPa for Japanese larch and 12.26 kPa for Korean pine. Overall, it was concluded that root reinforcement increased the factor of safety (Fs) of slope for small-scale landslide as the result of two-dimensional (2-D) infinite slope stability analysis considering vegetation effects.

• 대한수학회지
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• 제53권1호
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• pp.187-199
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• 2016

The r-ary number sequences given by $$(b^{(r)}_n)_{n{\geq}0}=\Large{\frac{1}{(r-1)n+1}}(^{rn}_n)$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}(^{2n}_n)$. Their history goes back at least to Lambert [8] in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various r first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give r-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between $b^{(r)}_n$ and $b^{(r+1)}_n$.