• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.733-745
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• 2007

We prove the $L^p(1 boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega{\in}L(log^+L)^{1/2}(S^{n-1})$. The result is an improvement and extension of some known results.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.283-296
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• 2001

The Heisenberg inequality associated with the uncertainty principle is extended to an infinite dimensional abstract Wiener space (H, B) with an abstract Wiener measure p$_1$. For $\phi$ $\in$ L$^2$(p$_1$) and T$\in$L(B, H), it is shown that (※Equations, See Full-text), where F(sub)$\phi$ is the Fourier-Wiener transform of $\phi$. The conditions when the equality holds also discussed.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.29-40
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• 2010

In this paper, we study a generalization of the Banach space B($l_2$) of all bounded linear operators on $l_2$. Over this space, we present some reasonable ways to define Schatten-type classes which are generalizations of the classical Schatten classes of compact operators on $l_2$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.543-552
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• 2012

In this paper, we will show that if ${\mu}$ is a Borel measure on the unit disk D such that ${\int}_{D}\frac{d{\mu}(z)}{(1-\left|z\right|^2)^{p\alpha}}$ < ${\infty}$ where 0 < ${\alpha},{\rho}$ < ${\infty}$, then a bounded sequence of functions {$f_n$} in the $\alpha$-Bloch space $\mathcal{B}{\alpha}$ has a convergent subsequence in the space $D_p({\mu})$ of analytic functions f on D satisfying $f^{\prime}\;{\in}\;L^p(D,{\mu})$. Also, we will find some conditions such that ${\int}_D\frac{d\mu(z)}{(1-\left|z\right|^2)^p$.

• Microbiology and Biotechnology Letters
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• v.25 no.3
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• pp.258-265
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• 1997

The effects of medium pH and culture temperature on the expression and secretion of inulinase and invertase were investigated with recombinant Saccharomyces cerevisiae cells. These cells were obtained by transformation of 2$\mu$-based plasmids pYI10 and pYS10 which contain Kluyveromyces marxianus inulinase gene (INU1A) and S. cerevisiae invertase gene (SUC2), respectively, in the downstream of GAL1 promoter. The expression level and localization of inulinase and invertase were not affected significantly by the initial medium pH: secretion efficiencies of inulinase and invertase into the medium were about 90% and 60%, respectively, in the pH ranges of 4.0 to 6.5. However, the expression and secretion of both enzymes were strongly dependent on the culture temperature. The highest expression (7.7 units/mL) and secretion (6.7 units/mL) of inulinase were observed at 28$\circ$C and 30$\circ$C. As a consequence of decreased localization of inulinase in the periplasmic space, the secretion efficiency increased from 68% at 20$\circ$C, to 95% at 35$\circ$C,. The total expression level and secretion efficiency of invertase increased from 19 units/mL and 55% at 20$\circ$C to 25 units/mL and 68% at 35$\circ$C, respectively. Irrespective of the culture temperature, the invertase activity in the cellular fraction (periplasmic space and cytoplasmic fractions) was kept constant at around 33-45%.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1103-1107
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• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.481-495
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• 2009

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.430-443
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• 2005

A general construction algorithm of the Grassmann space parameters in linear systems - so-called, the Plucker matrix, 'L' in m-input, p-output, n-th order static output feedback systems and the Plucker matrix, $'L^{aug}'$ in augmented (m+d)-input, (p+d)-output, (n+d)-th order static output feedback systems - is presented for numerical checking of necessary conditions of complete static and complete minimum d-th order dynamic output feedback pole-assignments, respectively, and also for discernment of deterministic computation condition of their pole-assignable real solutions. Through the construction of L, it is shown that certain generically pole-assignable strictly proper mp > n system is actually none pole-assignable over any (real and complex) output feedbacks, by intrinsic rank deficiency of some submatrix of L. And it is also concretely illustrated that this none pole-assignable mp > n system by static output feedback can be arbitrary pole-assignable system via minimum d-th order dynamic output feedback, which is constructed by deterministic computation under full­rank of some submatrix of $L^{aug}$.