• The Journal of the Korea Contents Association
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• v.6 no.4
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• pp.63-68
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• 2006

For the almost co티am convergent series $S_n$ of independent random variables, by investigating the limiting behavior of the tail series, $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$, the rate of convergence of the series $S_n$ to a random variable S is studied in this paper. More specifically, the equivalence between the tail series weak law of large numbers and a limit law is established for a quasi-monotone decreasing sequence, thereby extending a result of Previous work to the wider class of the norming constants.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.91-109
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• 1995

The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.293-308
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• 2004

Let K be a nonempty convex subset of an arbitrary Banach space X and $T\;:\;K\;{\rightarrow}\;K$ be a uniformly continuous strictly hemi-contractive operator with bounded range. We prove that certain Ishikawa iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. We also establish similar convergence and almost stability results for strictly hemi-contractive operator $T\;:\;K\;{\rightarrow}\;K$, where K is a nonempty convex subset of arbitrary uniformly smooth Banach space X. The convergence results presented in this paper extend, improve and unify the corresponding results in Chang [1], Chang, Cho, Lee & Kang [2], Chidume [3, 4, 5, 6, 7, 8], Chidume & Osilike [9, 10, 11, 12], Liu [19], Schu [25], Tan & Xu [26], Xu [28], Zhou [29], Zhou & Jia [30] and others.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.185-190
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• 2005

For the almost certainly convergent series $S_n$ of independent random variables the limiting behavior of tail series ${T_n}{\equiv}S-S_{n-1}$ is reviewed. More specifically, tail series strong laws of large number and tail series weak laws of large numbers will be introduced, and their relationship will be investigated. Then, the relationship will also be extended to the case of Banach space valued random elements, by investigating the duality between the limiting behavior of the tail series of random variables and that of random elements.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.455-469
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• 2002

The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.2_2
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• pp.233-238
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• 2022

This study evaluated the fatigue limit depending on microcracks using 0.57 wt.% carbon steel with different Vickers hardness. The fatigue limit was almost constant up to a certain limit regardless of the carbon content. However, the fatigue limit decreased rapidly as the size of the crack increased. As the crack aspect ratio was smaller, the fatigue limit of the depth (point A) a lot decreased. The fatigue limit ratio of the depth decreased significantly because the crack propagation in the depth direction was fast as the crack aspect ratio became smaller. On the other hand, the fatigue limit ratio of surface cracks increased as the crack aspect ratio decreased.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.771-778
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• 2006

Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung ([12]).

• Honam Mathematical Journal
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• v.31 no.4
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• pp.505-513
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• 2009

Let {$X_k;k{\in}N^d$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $p{\alpha}$ > 1 and ${\alpha}$ > ${\frac{1}{2}}$ $E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})$ < ${\infty}$ if and only if ${\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P$($max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}$ > ${\epsilon}{\mid}n{\mid}$) < ${\infty}$ for all ${\epsilon}$ > 0, where log$^+$x = max{1,log x}.

• The Korean Journal of Food & Health Convergence
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• v.5 no.6
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• pp.5-9
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• 2019

Desalination requires large energy. This experiment deals to desalinate brackish water through solar panels. The discharge from desalination plants is almost entirely water, and .01 percent is salt. Desalination is a process that extracts minerals from saline water. Solar-powered desalination technologies can be used to treat non-traditional water sources to increase water supplies in rural, arid areas. Water scarceness is a rising dilemma for large regions of the world. Access to safe, fresh and pure clean drinking water is one of the most important and prime troubles in different parts of the world. Among many of water cleansing technologies solar desalination/distillation/purification is one of the most sustainable and striking method engaged to congregate the supply of clean and pure drinkable water in remote areas at a very sound cost. Six types of dripper having discharge 3 - 8 lh-1 were installed one by one and measured discharge and volume of clean water indicated that at 6 lh-1 untreated water discharge have maximum evaporation and volume of clean water was 19.2 lh-1 at same temperature and radiations. Now strategy was developed that when increased the temperature the intake discharge of untreated water must be increased and salt drained water two times more than treated water.

• Applied Science and Convergence Technology
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• v.25 no.6
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• pp.162-165
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• 2016

APhotocatalysis process uses ambient oxygen from air and irradiation, fundamentally UV light, to generate oxidation and reduction which can degrade almost all harmful organic and inorganic compounds to nontoxic substances. This study was focused on enhancement of photocatalytic activity which improves the photocatlytic efficiency with $TiO_2$ particle by mixing of certain amounts of Zn particles. We analyzed degradation of organic pollutant materials such as toluene and phenol with the mixed photocatalysis by using UV-visible spectrophotometer and obtained a result that photocatalytic activity is increased with increasing amount of Zn particle. Especially, in the case of $TiO_2$ (1 mmol) and Zn (0.1 mmol) mixture photocatalyst, we obtained at least 2 times higher photocatalytic activity compared with the commercially available $TiO_2$ photocatalyst (Degussa P-25), indicating that our mixed photocatalyts (Zn-doped $TiO_2$) is very effective of removing both organic dye and pollutants and the conversion rate of toluene is much faster than that of phenol.