• 한국컴퓨터산업학회논문지
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• 제2권10호
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• pp.1301-1308
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• 2001

이 논문에서는 기존의 number-theoretic 순환함수와 연계된 word-theoretic 순환함수 및 술어(predicates)들의 Grzegorzyk 클래스를 논한다. 특히 small 클래스 $\xi\sum{n}$($n\leq2$)에서의 특성은 그에 대응하는 number-theoretic small 클래스 $\xi\sum{n}$과는 매우 틀린 특성을 보인다 [2]. 흥미 있는 문제 중의 하나인 $\xi\sum{0}$ 등급에서의 동치문제는 undecidable 임을 증명한다.

• 호남수학학술지
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• 제31권2호
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• pp.185-201
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• 2009

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In this paper, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant.

• 호남수학학술지
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• 제30권3호
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• pp.535-550
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• 2008

Let M be a real hypersurface of a complex space form with almost contact metric structure $({\phi},{\xi},{\eta},g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.173-181
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• 1995

Our objective is to investigate approximate controllability of a class of partial integrodifferential systems. This work continuous the investigations of [8]. As a model for this class one may take the equation $\frac{\partialy(t,\;\xi)}{\partialt}\;=\;\frac{\partial}{\partial\xi}(a(t,\;\xi\frac{\partialy(t,\;\xi)}{\partial\xi})\;+\;F(t,\;y(t\;-\;r,\;\xi),\;{{\int_0}^t}\;k(t,\;s,\;y(s\;-\;r,\;\xi))ds)\;+\;b(\xi)u(t),\;0\;\leq\;\xi\;\leq\;1,\;\leq\;t\;\leq\;T$ with initial-boundary conditions y(t,\;0)\;=\;y(t,\;1)\;=\;0,\;0\;\leq\;t\;\leq\;T,\;y(t,\;\xi)\;=\;\phi(t,\;\xi),\;0\;\leq\;1,\;-r\;\leq\;t\;\leq\;0$.(omitted)

• 대한수학회보
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• 제48권6호
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• pp.1315-1327
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• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.475-484
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• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

• 대한수학회지
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• 제59권2호
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• pp.353-365
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• 2022

Let 𝓐 be the collection of analytic functions f defined in 𝔻 := {ξ ∈ ℂ : |ξ| < 1} such that f(0) = f'(0) - 1 = 0. Using the concept of subordination (≺), we define $$S^*_{\ell}\;:=\;\{f{\in}A:\;\frac{{\xi}f^{\prime}({\xi})}{f({\xi})}{\prec}{\Phi}_{\ell}(\xi)=1+{\sqrt{2}{\xi}}+{\frac{{\xi}^2}{2}},\;{\xi}{\in}{\mathbb{D}}\}$$, where the function 𝚽_ℓ(ξ) maps 𝔻 univalently onto the region Ω_ℓ bounded by the limacon curve (9u² + 9v² - 18u + 5)² - 16(9u² + 9v² - 6u + 1) = 0. For 0 < r < 1, let 𝔻_r := {ξ ∈ ℂ : |ξ| < r} and 𝒢 be some geometrically defined subfamily of 𝓐. In this paper, we find the largest number 𝜌 ∈ (0, 1) and some function f₀ ∈ 𝒢 such that for each f ∈ 𝒢 𝓛_f (𝔻_r) ⊂ Ω_ℓ for every 0 < r ≤ 𝜌, and $${\mathcal{L} _{f_0}}({\partial}{\mathbb{D}_{\rho})\;{\cap}\;{\partial}{\Omega}_{\ell}\;{\not=}\;{\emptyset}$$, where the function 𝓛_f : 𝔻 → ℂ is given by $${\mathcal{L}}_f({\xi})\;:=\;{\frac{{\xi}f^{\prime}(\xi)}{f(\xi)}},\;f{\in}{\mathcal{A}}$$. Moreover, certain graphical illustrations are provided in support of the results discussed in this paper.

• Journal of Microbiology and Biotechnology
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• 제29권2호
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• pp.244-255
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• 2019

Xylose isomerase (XI; E.C. 5.3.1.5) catalyzes the isomerization of xylose to xylulose, which can be used to produce bioethanol through fermentation. Therefore, XI has recently gained attention as a key catalyst in the bioenergy industry. Here, we identified, purified, and characterized a XI (PbXI) from the psychrophilic soil microorganism, Paenibacillus sp. R4. Surprisingly, activity assay results showed that PbXI is not a cold-active enzyme, but displays optimal activity at $60^{\circ}C$. We solved the crystal structure of PbXI at $1.94-{\AA}$ resolution to investigate the origin of its thermostability. The PbXI structure shows a $({\beta}/{\alpha})_8$-barrel fold with tight tetrameric interactions and it has three divalent metal ions (CaI, CaII, and CaIII). Two metal ions (CaI and CaII) located in the active site are known to be involved in the enzymatic reaction. The third metal ion (CaIII), located near the ${\beta}4-{\alpha}6$ loop region, was newly identified and is thought to be important for the stability of PbXI. Compared with previously determined thermostable and mesophilic XI structures, the ${\beta}1-{\alpha}2$ loop structures near the substrate binding pocket of PbXI were remarkably different. Site-directed mutagenesis studies suggested that the flexible ${\beta}1-{\alpha}2$ loop region is essential for PbXI activity. Our findings provide valuable insights that can be applied in protein engineering to generate low-temperature purpose-specific XI enzymes.

• International Journal of Fluid Machinery and Systems
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• 제8권3호
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• pp.220-220
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• 2015

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.541-575
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• 2016

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we prove that if the structure Jacobi operator $R_{\xi}= R({\cdot},{\xi}){\xi}$ is ${\phi}{\nabla}_{\xi}{\xi}$-parallel and $R_{\xi}$ commute with the structure tensor ${\phi}$, then M is a homogeneous real hypersurface of Type A provided that $TrR_{\xi}$ is constant.