• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1529-1561
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• 2018

Let f and g be nonconstant meromorphic (entire, respectively) functions in the complex plane such that f and g are of finite order, let a and b be nonzero complex numbers and let n be a positive integer satisfying $n{\geq}21$ ($n{\geq}12$, respectively). We show that if the difference polynomials $f^n(z)+af(z+{\eta})$ and $g^n(z)+ag(z+{\eta})$ share b CM, and if f and g share 0 and ${\infty}$ CM, where ${\eta}{\neq}0$ is a complex number, then f and g are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.91-102
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• 2000

Let ${\gamma}{\equiv}{\gamma}^{(2n)}$ denote a sequence of complex numbers ${\gamma}{00},{\gamma}{01},\cdots,{\gamma}0, 2n,...,{\gamma}{2n},0\;with\; {\gamma}{00}\;>\;0,{\gamma}{ji}={{\overline}{\gamma_{ij}}}$,and let K denote a closed subset of the complex plane C. The truncated K complex moment problem entails finding a positive Borel measure $\mu$ such that ${\gamma}{ij}={\int}{{\overline}{z}}^{i}z^{j}d{\mu}\;(0{\leq}\;i+j\;{\leq}\;2n)$ and supp ${\mu}{\subseteq}\;K$. If n=2, then is called the quartic moment problem. In this paper, we give partial solutions for the singular quartic moment problem with rank M(2)=5 and ${{\overline}{Z}}Z{\in}\;<1,Z,{{\overline}{Z}},Z^{2},{{\overline}{Z}}^2>$.

• Journal of the Korean Chemical Society
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• v.35 no.4
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• pp.301-307
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• 1991

The solubilities of the n-propyl iodide in nitrobenzene and m-xylene have been measured at 8$^{\circ}$, 15$^{\circ}$ and 25$^{\circ}C$ in the presence and the absence of gallium iodide. When gallium iodide does not exist in the system, the solubility of n-propyl iodide in m-xylene is greater than in nitrobenzene, indicating a stronger interaction of n-propyl iodide with m-xylene than that with nitrobenzene. It could be thought that n-propyl iodide forms unstable complex with gallium iodide in the presence of gaillium iodide in the system. This complex has been assumed in various ways and evaluated, that instability constant (K value) is relatively certain under the assumption of 1:1 complex, n-C$_3H_7I{\cdot}GaI_3$. Therefore, the complex would form the following equilibrium in the solution: n-C$_3H_7{\cdot}GaI _3{\rightleftharpoons}n-C_3H_7I+1/2Ga_2I_6$ the instability of the complex of n-propyl iodide with gallium iodide is compared with similar complexes of gallium iodide with methyl iodide. The changes of enthalpy, free energy and entropy for the dissociation of the complex are also calculated.

• Bulletin of the Korean Chemical Society
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• v.6 no.6
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• pp.369-374
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• 1985

A new flexible quadridentate ligand, N,N'-dimethylethylenediamine-N,N'-di-${\alpha}$-propionic acid (dmedpa) has been synthesized, and diammine and ethylenediamine cobalt(III) complexes of dmedpa, $[Co(dmedpa)(NH_3)_2]^+$ and $[Co(dmedpa(en)]^+,$ have been prepared. Only s-cis isomer has been yielede. A known N,N'-dimethylethylediamine-N,N'-diacetic acid (dmedda) has also been prepared. Dichloro cobalt(III) complexes of both dmedda and dmedpa have been prepared. Only the s-cis isomer has been yielded in the $[Co(dmedda)Cl_2]^-$ complex, while only the uns-cis isomer has been obtained for the $[Co(dmedpa)Cl_2]^-$ complex.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Journal of the Korean Applied Science and Technology
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• v.17 no.1
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• pp.29-35
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• 2000

In this study, ultra-thin films of (N-docosyl quinolinium)-TCNQ(1:2) complex were prepared on the hydrophilic substrate by Langmuir-Blodgett(LB) technique. The characteristics of ${\pi}-A$ isotherms were studied to find optimum conditions of deposition by varying temperature of subphase, compression speed of barrier and amount of spreading solution. Using UV-vis spectra, capacitance and thickness, deposition of LB films was confirmed together with the thickness of the naturally oxidized aluminum film inside a device and dielectric constant of (N-docosyl quinolinium)-TCNQ(1:2) complex. The dielectric constant of LB film was about $4.59{\sim}5.58$. The electrical properties of (N-docosyl quinolinium)-TCNQ(1:2) complex were investigated at room temperature. The conductivity of this film measured by the direction of either vertical or horizontal axis was found to have a quite different value.

• Honam Mathematical Journal
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• v.5 no.1
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• pp.45-69
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• 1983

The hermitian structures on complex manifolds have been studied by several mathematicians ([1], [2], and [3]), and the Kähler structure on hermitian manifolds have been so much too ([6], [12], and [15]). There has been some gradual progress in studying the invariant forms on Grassmann manifolds ([17]). The purpose of this dissertation is to prove the Theorem 3.4 and the Theorem 4.7, with relation to the nature of complex Grassmann manifolds. In $\S$ 2. in order to prove the Theorem 4.7, which will be explicated further in $\S$ 4, the concepts of the hermitian structure, connection and curvature have been defined. and the characteristic nature about these were proved. (Proposition 2.3, 2.4, 2.9, 2.11, and 2.12) Two characteristics were proved in $\S$ 3. They are almost not proved before: particularly. we proved the Theorem 3.3 : $G_{k}(C^{n+k})=\frac{GL(n+k,C)}{GL(k,n,C)}=\frac{U(n+k)}{U(k){\times}U(n)}$ In $\S$ 4. we explained and proved the Theorem 4. 7 : i) Complex Grassmann manifolds are Kahlerian. ii) This Kähler form is $\pi$-fold of curvature form in hyperplane section bundle. Prior to this proof. some propositions and lemmas were proved at the same time. (Proposition 4.2, Lemma 4.3, Corollary 4.4 and Lemma 4.5).

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.535-539
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• 2007

Given operators X and Y acting on a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX=Y. In this article, we show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $X=(x_{ij})\;and\;Y=(y_{ij})$ be operators in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that AX=Y. (2) There is a bounded sequence $\{\alpha_n\}\;in\;\mathbb{C}$ such that $y_{ij}=\alpha_jx_{ij}\;for\;i,\;j\;{\in}\;\mathbb{N}$. Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax=y. We show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $x=(x_i)\;and\;y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that Ax=y. (2) There is a bounded sequence $\{\alpha_n\}$ in $\mathbb{C}$ such that $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• Journal of the Korean Chemical Society
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• v.68 no.1
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• pp.25-31
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• 2024

The p97 adenosine triphosphatase is a key player in protein homeostasis, responsible for unfolding ubiquitylated substrates. It engages with various adaptor proteins through its N-terminal domain, with the p97-p47 complex attracting particular attention for its involvement in membrane remodeling. Although the structures of p97 in complex with the Ubiquitin regulatory X (UBX) domain from various adaptors have been reported, the stoichiometry is conflicting. Here, we report the crystal structure of the p97 N-D1 hexamer in complex with the p47 UBX domain at a resolution of 2.7 Å. The structure reveals a stoichiometry of 6:6 between the p97 N-D1 and the p47 UBX domain. These findings provide valuable insights into the binding stoichiometry of p97 N-D1 and p47 UBX domain, which are crucial for understanding the role of p97 and adaptor proteins in cellular processes such as the ubiquitin-proteasome pathway, membrane fusion, and cell cycle regulation.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.137-149
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• 2020

Let γ⁽ⁿ⁾ ≡ {γ_ij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ⁽ⁿ⁾. For an odd number n, it is known that γ⁽ⁿ⁾ has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.