• East Asian mathematical journal
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• v.25 no.2
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.373-386
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• 2014

Let (R,m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth($M/I^nM$) = d for $n{\gg}0$. Also we show that, if dim(R) = d and $I_1{\subset}\;{\cdots}\;{\subset}I_n$ is a chain of ideals of R such that $R/I_k$ is maximal Cohen-Macaulay for all k, then $n{\leq}{\ell}_R(R/(a_1,{\ldots},a_d)R)$ for every system of parameters $a1,{\ldots},a_d$ of R. Also, in the case where dim(R) = 2, we prove that the ideal transform $D_m(R/p)$ is minimax balanced big Cohen-Macaulay, for every $p{\in}Assh_R$(R), and we give some equivalent conditions for this ideal transform being maximal Cohen-Macaulay.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.149-156
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• 1999

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0. In this note a weak law of large number of the form $({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$ is established, where $\{{\nu}_n,\;n{\geq}1\}$ is a suitable sequence.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.117-126
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• 2003

Let {$X_{nk}$\mid$1\;{\leq}\;k\;{\leq}\;n,\;n\;{\geq}\;1$} be an array of row negatively associated (NA) random variables which satisfy $P($\mid$X_{nk}$\mid$\;>\;x)\;{\leq}\;P($\mid$X$\mid$\;>\;x)$. For weighed sums ${{\Sigma}_{k=1}}^{Tn}\;a_kX_{nk}$ indexed by random variables {$T_n$\mid$n\;{\geq}$1$}, we establish a general weak law of large numbers (WLLN) of the form $({{\Sigma}_{k=1}}^{Tn}\;a_kX_{nk}\;-\;v_{[nk]})\;/b_{[an]}$ under some suitable conditions, where $\{a_n$\mid$n\;\geq\;1\},\; \{b_n$\mid$n\;\geq\;1\}$ are sequences of constants with $a_n\;>\;0,\;0\;<\;b_n\;\rightarrow \;\infty,\;n\;{\geq}\;1$, and {$v_{an}$\mid$n\;{\geq}\;1$} is an array of random variables, and the symbol [x] denotes the greatest integer in x.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1383-1392
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• 2020

Let H_n be the n-th harmonic number and let ν_n be its denominator. Shiu proved that there are infinitely many positive integers n with ν_n = ν_n+1. Recently, Wu and Chen proved that the set of positive integers n with ν_n = ν_n+1 has density one. They also proved that the same result is true for the denominators of alternating harmonic numbers. In this paper, we prove that the result is true for the denominators of 𝜀-harmonic numbers, where 𝜀 = {𝜀_i}^∞_i=1 is a pure recurring sequence with 𝜀_i ∈ {-1, 1}.

• Journal of Sericultural and Entomological Science
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• v.40 no.1
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• pp.52-59
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• 1998

For the construction of plasmid and bmNPV sarrying the FRT recognition site for the FLP recombinases, we synthesized the wild type FRT dligonucleotides. The target FRT sequences consist of three 13bp repeated DNA sequences; two repeats in a direct orientation and one inverted relative to the other two. In addition, there is an 8bp spacer region between the repeats which determune the orientation of the FRT recombination site. In order to place the FRT site both in target BmNPV genome and the transfer vector, we constructed a plasmid, FRT site both in the target BmNPv genome and the transfer vector, we constructed a plasmid, pFRT$\beta$-gal, carrying the FRT sites within the cloning sites of pSV vector and a recombinant BmNPV, vFRTPH, carrying the FRT sites at a downstream of polyhedrin promotor, respectively. In order to test the functionality of the FLP/FRT site-specific recombination system, vFRTPH, pFRT$\beta$-gal and pHsFLP DNA were co-transfected into BmN-4 cells. The resulting recombinant virus was designated a vFRT$\beta$2-gal. From construction analysis of the vFRT$\beta$2-gal with PCR technique it was concluded that the entire pFRT$\beta$-gal plasmid with $\beta$-galactosidase gene and origines of replication flanked by two functional hybrid FRT sequences. The efficiency of recombination was 8.7%, which was higher than that(2.2%) of recombination between a conventional transfer vector and the wild type BmNPV.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• The KIPS Transactions:PartB
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• v.10B no.5
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• pp.485-490
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• 2003

In this paper, we propose the possibility of introducing chaotic sequences into digital watermarking systems as potential substitutes to commonly used pseudo noise sequences. Chaotic sequences have several good properties including the availability of a great number of them, the ease of their generation, as well as their sensitive dependence on their initial conditions. And the quantization does not destroy the good property. So this paper proposes a method that transforms Hangul text to chaotic sequence. And we presents how the Hangul text is expressed by an implied data and the implied data is regenerated into the original text. In this paper, we use this implied Hangul text for watermarking.

• Mycobiology
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• v.40 no.2
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• pp.107-110
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• 2012

Genes encoding the cellobiohydrolase enzyme (CBHI), designated as cbhI, were isolated from the basidiomycetes Auricularia fuscosuccinea, Pleurotus giganteus, P. eryngii, P. ostreatus, and P. sajor-caju. Initially, the fungal genomic DNA was extracted using a modified cetyltrimethyl ammonium bromide (CTAB) protocol and used as a DNA template. The cbhI genes were then amplified and cloned using the pGEM-T Easy Vector Systems. The sizes of these PCR amplicons were between 700~800 bp. The DNA sequences obtained were similar showing high identity to the cbhI gene family. These cbhI genes were partial consisting of three coding regions and two introns. The deduced amino acid sequences exhibited significant similarity to those of fungal CBHI enzymes belonging to glycosyl hydrolase family 7.

• BMB Reports
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• v.28 no.1
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• pp.6-11
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• 1995

A new lectin, named TRA, was purified from Trichosanthes kirilowii root by acid-treated Sepharose 6B, Mono-Q, and TSK-gel 3000SW column sequential chromatography. The lectin appeared homogeneous by native gel electrophoresis at pH 4.3 and gave two protein bands of Mr=31 and 28 kDa by SDS-PAGE. The N-terminal amino acid sequences of the polypeptides of TRA have not been reported in amino acid sequences of the lectins. TRA lectin formed a precipitate with asialofetuin, neuraminidase-treated fetuin. A sugar inhibition assay indicated that N-acetyl-D-galactosamine, among the monosaccharides tested, was the most potent inhibitor of TRA-induced hemagglutination. Asialofetuin showed a 260-times stronger inhibitory activity than N-acetyl-D-galactosamine. TRA lectin also showed agglutination with normal leukocytes and lymphoma cells, but not with premature hemopoietic cells. These results suggest that TRA is a novel plant lectin.