• Journal of applied mathematics & informatics
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• v.33 no.5_6
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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.

• Korean Journal of Computational Design and Engineering
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• v.8 no.2
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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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• v.28 no.3_4
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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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• v.30 no.1_2
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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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• v.27 no.5_6
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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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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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.

• Journal of the Korean Institute of Gas
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• v.2 no.2
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• pp.55-60
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• 1998

In this study, we investigated the dust explosion characteristics by determining minimum ignition energy and explosion limit for this experiment, we used pine-tree dust which was used widely for the filler of thermosetting resin. The experiment was accomplished according to the variation of discharge gap, dust concentration, particle size and humidity. The result of this experiment are as follows; (1) The relation between the discharge gap and ignition energy was that ignition energy decreased according as the discharge gap became small, but increased when the discharge gap was below 4mm and suddenly became infinite when the discharge gap was below. So, we knew that this infinite value was limit discharge gap. (2) When the dust concentration increase and the particle size became microscopic it was easy to explore and in the same particle size, if the humidity increase the minimum ingnition energy decreased.

• East Asian mathematical journal
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• v.31 no.5
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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).

• Journal of the Korean Society of Environmental Restoration Technology
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• v.14 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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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 $b^{(r+1)}_n$.