• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.141-146
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• 1997

In this paper we prove that the corona theorem for the algebra $H^{\infty}(D){\cap}D(D)$. That is, we prove that $\mathcal{M}{\setminus}{\overline{D}}$ is an empty set where $\mathcal{M}$ is the maximal ideal space of the given algebra.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.325-334
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• 2006

For $f{\in}L^2(B,d{\nu})$, ${\parallel}f{\parallel}_{BMO}=\widetilde{{\mid}f{\mid}^2}(z)-{\mid}{\tilde{f}}(z){\mid}^2$. For f continuous on B, ${\parallel}f{\parallel}_{BO}=sup\{w(f)(z):z{\in}B\}$ where $w(f)(z)=sup\{{\mid}f(z)-f(w){\mid}:{\beta}(z,w){\leq}1\}$. In this paper, we will show that if $f{\in}BMO$, then ${\parallel}f{\parallel}_{BO}{\leq}M{\parallel}f{\parallel}_{BMO}$. We will also show that if $f{\in}BO$, then ${\parallel}f{\parallel}_{BMO}{\leq}M{\parallel}f{\parallel}_{BO}^2$. A homomorphic function $f:B{\rightarrow}{\mathbb{C}}$ is called a Bloch function ($f{\in}{\mathcal{B}}$) if ${\parallel}f{\parallel}_{\mathcal{B}}=sup_{z{\in}B}\;Qf(z)$<${\infty}$. In this paper, we will show that if $f{\in}{\mathcal{B}}$, then ${\parallel}f{\parallel}_{BO}{\leq}{\parallel}f{\parallel}_{\mathcal{B}}$. We will also show that if $f{\in}BMO$ and f is holomorphic, then ${\parallel}f{\parallel}_{\mathcal{B}}^2{\leq}M{\parallel}f{\parallel}_{BMO}$.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.635-641
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• 2014

The existence and the regularity of the particle trajectory flow X(x, t) along a velocity field u on $\mathbb{R}^n$ are discussed under the BMO-blow-up condition: $${\int}_{0}^{T}{\parallel}{\omega}({\tau}){\parallel}_{BMO}d{\tau}&lt;{\infty}$$ of the vorticity ${\omega}{\equiv}{\nabla}{\times}u$. A comment on our result related with the mystery of turbulence is presented.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.495-517
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• 2022

Let M_α be a bilinear fractional maximal operator and BM_α be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators M^j_α,β and BM^j_α,β (j = 1, 2), the fractional maximal iterated commutator ${\mathcal{M}}_{{\alpha},{\vec{b}}}$, and $BM_{{\alpha},{\vec{b}}}$, where b ∈ BMO(ℝ^d) and ${\vec{b}}\;=\;(b_1,b_2)\;{\in}\;BMO({\mathbb{R}}^d)\;{\times}\;BMO({\mathbb{R}}^d)$. In particular, we improve the well-known results to a larger scale for 1/2 < q < ∞ and give positive answers to the questions in [2].

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1357-1377
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• 2017

In this article, we first give the $L^p$ boundedness of the operator $D^2L^{-1}$ with BMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator L with VMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition.

• Journal of Life Science
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• v.8 no.3
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• pp.285-293
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• 1998

We have cloned an internal fragment of the putative transoisase gene of MLE in the silkworm, Bombyx mori, using PCR method with degenerative oligonucleotide primers designed to represent regions of amino acids encoding transposase. The resulting PCR clone, designed as BmoMAR, cords a partial ORF(152 a.a.) of MLE in which interrupted by five stop codons, and the sequence of its deduced amino acids showed 37% homology with Mos1, an active mariner, from Drosophila mauritiana. Furthermore, the BmoMAR exhibits nucleotide and amino acid homology with 59% and 37% from Apis mellifera and D. mauritiana 7.9 clone, respectively. This result strongly that a MLE is present in the genome of B. mori.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.2 no.2
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• pp.49-68
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• 2007

This paper develop self pre-checkup lists for the validity of business model as web business starters can utilize to open business. In particular, self pre-checkup lists invented by Dr. Bruce Merrifield, is reapplied and modified in appropriate to internet shopping mall business. This paper complete many literature reviews to identify appropriate factors of evaluation such as about the characters of internet business, business validity testing theory for internet business model, pros and cons of e-business and startup ventures, factor analysis of technology valuation, and pros and cons for internet shopping mall. This paper define six different factors; scale of sales, the growth rate of market, competitiveness, risk portfolio, industry upside down, and social conditions, as the factors of evaluating the business attractiveness. Meanwhile, it define characters of CEO, content's power, mutual inclusion, commerce, fulfillment, marketing power as the factors of business appropriateness. This paper also conducts several case studies; company I, D, G of applying the former model. This paper sort out internet business model in imaginations by utilizing self pre-checkup lists of business evaluation. Also, the outcomes of evaluation is expected to provide meaningful future business implications.

• East Asian mathematical journal
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• v.33 no.1
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• pp.103-113
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• 2017

We provide quantitative two weight estimates for the commutator of the Hilbert transform under certain conditions on a pair of weights (u, v) and b in $Carl_{u,v}$. In [10] and [11], Bloom's inequality is shown in a modern setting, and the boundedness of the commutators is provided by assuming both weights u, v are $A_2$ and $b{\in}BMO_{\rho}$. In the present paper we show that the condition on b can be replaced by $Carl_{u,v}$ by using the joint $A^d_2$ condition.