• 호남수학학술지
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• 제45권3호
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• pp.542-554
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• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• 대한수학회논문집
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• 제18권3호
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• 대한수학회보
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• 제29권2호
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• 대한수학회보
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• 제54권2호
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• pp.543-557
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• 2017

In this paper, we investigate the notion of q-pseudoconvexity to discuss and describe some geometric characterizations of q-pseudoconvex domains ${\Omega}{\subset}{\mathbb{C}}^n$. In particular, we establish that ${\Omega}$ is q-pseudoconvex, if and only if, for every boundary point, the Levi form of the boundary is semipositive on the intersection of the holomorphic tangent space to the boundary with any (n-q+1)-dimensional subspace $E{\subset}{\mathbb{C}}^n$. Furthermore, we prove that the Kiselman's minimum principal holds true for all q-pseudoconvex domains in ${\mathbb{C}}^p{\times}{\mathbb{C}}^n$ such that each slice is a convex tube in ${\mathbb{C}}^n$.

• 대한수학회논문집
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• 제27권3호
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• pp.557-564
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• 2012

This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

• Journal of Photoscience
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• 제4권3호
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• pp.97-103
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• 1997

The effect of temperature on the fluorescence quenching of 2-(4-Methoxyphenyl)-5-(1-naphthyl)-1,3,4-oxadiazole (MPNO1), 2-(4-Methoxyphenyl)-5-(2-naphthyl)-1,3,4-oxadiazote(MPNO2), by aniline, and 2-Phenylindole (2-PI) by CCk, in toluene by steady state method and in benzene by time-resolved method have been carried out in the temperature range 30 - 70$\circ$C. The Stem-Volmer (S-V) plots, I$_0$/I against quencher concentration [Q] at different temperanares show positive deviations. The fluorescence lifetimes determined at different temperatures show no systematic variations and the variations being within the experimental error, the average values of lifetimes $ $\tau$ (t) are taken for further calculations. Rate constants such as Stem-Volmer quenching constants K$_sv}$, quenching rate parameters k$_q$ and k'$_q$, static quenching constant V and kinetic distance r are determined using the modified Stem-Volmer equation and sphere of action static quenching model. In order to see whether the reactions are diffusion limited, equations k$_q$ = e$^{-Eq/RT}$ and k'$_q$ = e$^{-Eq/RT}$ are used to determine the values of E$_q$ and E'$_q$, the activation energies for collisional quenching and the values of E$_q$ are 14.53. 17.28 and 16.20 kJ mole$^{-1}$ for MPNO1, MPNO2 and 2-PI respectively and the values of E'$_q$ are 14.62 and 17.73 for MPNO1 and MPNO2 respectively. From the magnitudes of various quantities it has been concluded that the reactions are diffusion limited and the observed positive deviations in the S-V plot are due to static and dynamic quenching.

• 한국육종학회지
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• 제41권3호
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• pp.236-243
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• 2009

벼멸구 저항성 유전자의 mapping, 벼멸구 저항성 관련 QTL 분석, 주요 농업형질과 벼멸구 저항성과의 관계 분석 등에 관한 연구를 수행 하여 얻은 결과는 다음과 같다. 벼멸구 저항성을 가진 통일형 벼인 '삼강'과 자포니카형 벼인 '낙동'을 교배하여 양성된 $F_1$의 약을 배양하여 육성된 120 DH 계통을 유전자 지도 작성을 위한 mapping 재료로 이용 하였다. Maker 검정에서 양친에 다양성을 나타낸 SSR 73, STS 89개 등 총 162개의 marker를 이용하여 전체 길이가 1,884 cM이고 평균 marker간 거리가 11.6 cM인 연관지도를 작성하였다. 유전자지도 작성에 이용된 120 DH 계통에 대한 벼멸구 저항성 정도를 조사하여 저항성 관련 QTL을 분석한 바, 3번, 6번, 7번, 8번 그리고 12번 염색체에서 1개씩 총 5개의 QTL을 확인하고 이들을 qBPR3, qBPR6, qBPR7, qBPR8, qBPR12로 명명하였다. 간장, 수장, 수수 및 출수일수에 대한 QTL을 분석하여, 총8개의 QTL이 7개의 염색체에 위치하는 것으로 확인되었다. 벼멸구 저항성과 주요 농업형질관련 QTL과의 연관관계를 분석한 바, 3번 염색체 상의 벼멸구 저항성 QTL(qBPR3)이 간장 및 수수 관련 QTL(qCL3, qNP6)과 연관되어 있었으며, 7번 염색체 상의 qBPR7은 분상질립 관련 QTL qPGC7.1과 qPWBP7.2과 그리고 8번 염색체상의 벼멸구 저항성 QTL 역시 간장관련 QTL(qCL8)과 연관되어 있는 것으로 나타났다.

• 한국미생물학회:학술대회논문집
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• 한국미생물학회 2008년도 International Meeting of the Microbiological Society of Korea
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• pp.23-25
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• 2008

Serum complement proteins comprise an important system that is responsible for several innate and adaptive immune defence mechanisms. There were three well described pathways known to lead to the generation of a C3 convertase, which catalyses the proteolysis of complement component C3, and leads to the formation of C3 opsonins (C3b, iC3b and C3d) that fix to bacteria. A pivotal step in the complement pathway is the assembly of a C3 convertase, which digests the C3 complement component to form microbial-binding C3 fragments recognized by leukocytes. The spleen clears microorganisms from the blood. Individuals lacking this organ are more susceptible to Streptococcus pneumoniae. Innate resistance to S. pneumoniae has previously been shown to involve complement components C3 and C4, however this resistance has only a partial requirement for mediators of these three pathways, such as immunoglobulin, factor B and mannose-binding lectin. Therefore it was likely that spleen and complement system provide resistance against blood-borne S. pneumoniae infection through unknown mechanism. To better understand the mechanisms involved, we studied Specific intracellular adhesion molecule-grabbing nonintegrin (SIGN)-R1. SIGN-R1, is a C-type lectin that is expressed at high levels by spleen marginal-zone macrophages and lymph-node macrophages. SIGN-R1 has previously been shown to be the main receptor for bacterial dextrans, as well as for the capsular pneumococcal polysaccharide (CPS) of S. pneumoniae. We examined the specific role of this receptor in the activation of complement. Using a monoclonal antibody that selectively downregulates SIGN-R1 expression in vivo, we show that in response to S. pneumoniae or CPS, SIGN-R1 mediates the immediate proteolysis of C3 and fixation of C3 opsonins to S. pneumoniae or to marginal-zone macrophages that had taken up CPS. These data indicate that SIGN-R1 is largely responsible for the rapid C3 convertase formation induced by S. pneumoniae in the spleen of mice. Also, we found that SIGN-R1 directly binds C1q and that C3 fixation by SIGN-R1 requires C1q and C4 but not factor B or immunoglobulin. Traditionally C3 convertase can be formed by the classical C1q- and immunoglobulin-dependent pathway, the alternative factor-B-dependent pathway and the soluble mannose-binding lectin pathway. Furthermore Conditional SIGN-R1 knockout mice developed deficits in C3 catabolism when given S. pneumoniae or its capsular polysaccharide intravenously. There were marked reductions in proteolysis of serum C3, deposition of C3 on organisms within SIGN-$R1^+$ spleen macrophages, and formation of C3 ligands. The transmembrane lectin SIGN-R1 therefore contributes to innate resistance by an unusual C3 activation pathway. We propose that in the SIGN-R1 mediated complement activation pathway, after binding to polysaccharide, SIGN-R1 captures C1q. SIGN-R1 can then, in association with several other complement proteins including C4, lead to the formation of a C3 convertase and fixation of C3. Therefore, this new pathway for C3 fixation by SIGN-R1, which is unusual as it is a classical C1q-dependent pathway that does not require immuno globulin, contributes to innate immune resistance to certain encapsulated microorganisms.

• 전자공학회논문지D
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• 제35D권2호
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• pp.52-59
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• 1998

The ZnS:Mn thin film electroluminescent(TFEL) devices fabricated by ALE system were investigated. Yellow-orange light emission was observed when the applied voltage exceeded 134 V and luminance increased sharply as the applied voltage increased. Luminance of 568 Cd/c $m^{2}$ was obtained under 1 KHz sinusoidal voltage wave application at the peak applied voltage of 230 V. The peak wavelength of the emissionwas 577 nm. The C-V, Q-V, $Q_{t}$ - $F_{p}$ , L- $Q_{cond}$, and V- $Q_{pol}$ have been measured under theapplication of the trapezoidal wave with its pulse width varying 0 to 75 .mu.sec. The phoshor and the insulator capacitance of the TFEL device under test were 24.3 nF/c $m^{2}$ and 9 nF/c $m^{2}$, respectively. It was observed that the threshold voltage changed from 137V to 100V as the pulse width varied from 0 to 75 .mu.sec. The L- $Q_{cond}$ characteristics showed that the light emission increased in proportion to the $Q_{cond}$. The luminance increased from 386 Cd/ $m^{2}$ to 607 Cd/ $m^{2}$ when the $Q^{+}$$_{cond}$ increased from 1.3 .mu.C/c $m^{2}$ to 2.3 .mu.C/c $m^{2}$. The V- $Q_{pol}$ characteristics showed that the V was inversely proportional to $Q_{pol}$./. th/ was inversely proportional to $Q_{pol}$./. pol/./.

• 대한수학회지
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• 제56권1호
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• pp.197-224
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• 2019

Let A be a $JB^*$-triple with Banach dual space $A^*$ and bi-dual the $JBW^*$-triple $A^{**}$. Elements x of $A^*$ of norm one may be regarded as normalised 'Q-measures' defined on the complete ortho-lattice ${\tilde{\mathcal{U}}}(A^{**})$ of tripotents in $A^{**}$. A Q-measure x possesses a support e(x) in ${\tilde{\mathcal{U}}}(A^{**})$ and a compact support $e_c(x)$ in the complete atomic lattice ${\tilde{\mathcal{U}}}_c(A)$ of elements of ${\tilde{\mathcal{U}}}(A^{**})$ compact relative to A. Necessary and sufficient conditions for an element v of ${\tilde{\mathcal{U}}}_c(A)$ to be a compact support tripotent $e_c(x)$ are given, one of which is related to the Q-covering numbers of v by families of elements of ${\tilde{\mathcal{U}}}_c(A)$.