• Korean Journal of Mathematics
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• 제32권1호
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• pp.83-95
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• 2024

The Quaternionic Dirac operator proves instrumental in tackling various challenges within spectral geometry processing and shape analysis. This work involves the introduction of the quaternionic Dirac operator on a symplectic submanifold of an exact symplectic product manifold. The self adjointness of the symplectic quaternionic Dirac operator is observed. This operator is verified for spin ${\frac{1}{2}}$ particles. It factorizes the Hodge Laplace operator on the symplectic submanifold of an exact symplectic product manifold. For achieving this a new complex structure and an almost quaternionic structure are formulated on this exact symplectic product manifold.

• Fibers and Polymers
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• 제2권2호
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• pp.64-70
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• 2001

A three-dimensional, porous collagen/chitosan complex sponge was prepared to closely simulate basic extracellular matrix (ECM) constitutes, collagen and glycosaminoglycan. The complex sponge was prepared by a lyophilization method and had the regular network with highly porous structure, suitable for cell adhesion and growth. The pores were well interconnected, and their distribution was fairly homogeneous. The complex sponge was crosslinked using 1-ethyl-3-(3-dimethyl aminopropyl) carbodiimide (EDC) and N-hydroxysuccinimide (NHS) to increase its boilogical stability and enhance its mechanical properties. The crosslinking medium has a great effect on the inner structure of the sponge. The homogeneous, porous structure of the sponge was remarkably collapsed in an aqueous crosslinking medium. However, the morphology of the sponge remained almost intact in a water/ethanol mixture crosslinking milieu. Mechanical properties of the collagen/chitosan sponge were significantly enhanced by EDC-mediated crosslinking. The potential of the sponge as a scaffold for tissue engineering was investigated using a Chinese hamster ovary cell (CHO-K1) line.

• East Asian mathematical journal
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• 제40권1호
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• pp.1-23
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• 2024

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c). We denote by A, K and L the second fundamental forms with respect to the unit normal vector C, D and E respectively, where C is the distinguished normal vector, and by R_𝜉 = R(𝜉, ·)𝜉 the structure Jacobi operator. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(≠ 2c) and any vector fields X and Y , and at the same time R_𝜉K = KR_𝜉 and ∇_{𝜙∇𝜉𝜉}R_𝜉 = 0. In this paper, we prove that if it satisfies ∇_𝜉R_𝜉 = 0 on M, then M is a real hypersurface of type (A) in M_n(c) provided that the scalar curvature $\bar{r}$ of M holds $\bar{r}-2(n-1)c{\leq}0$.

• 대한수학회논문집
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• 제26권4호
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• pp.635-647
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• 2011

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$. We provide several new results on such a real half lightlike submanifold M by using the F-structure of M induced by the almost complex structure J of $\bar{M}$.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 하계종합학술대회 논문집(4)
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• pp.385-388
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• 2002

This paper proposes a new GSC (Generalized Sidelobe Canceller) structure, called HLMS-GSC. Compared to Griffiths and Jim's GSC structure, the number of complex multiplication required is reduced to one half. The simulation results show that the minimum mean square errors and performance of nulling jammers by using HLMS-GSC are almost the same compared to Griffiths and Jim's GSC, although the complexity is reduced significantly. As a result, the proposed adaptive beamformer is good for real time implementation, since it has low complexity compared to previous GSC structures.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 하계종합학술대회 논문집(4)
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• pp.389-392
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• 2002

This paper propose a new GSC (Generalized Sidelobe Canceller) structure, called HFLMS-GSC. The number of complex multiplication required is reduced to one half compared to FLMS-GSC. The simulation results show that mean square error converging and jamming signal removing characteristics are almost the same compared to FLMS-GSC, although the complexity is reduced significantly. As a result, the proposed structure is good for real time implementation, since it has low complexity compared to previous GSC structures.

• 대한수학회보
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• 제37권1호
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• pp.181-189
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• 2000

Let (X, J) be a closed, connected almost complex four-manifold. Let $X_1$ be the complement of an open disc in X and let ${\varepsilon}_1$be the contact structure on the boundary ${\varepsilon}X_1$ which is compatible with a symplectic structure on $X_1$, Then we show that (X, J) is symplectic if and only if the contact structure ${\varepsilon}_1$ on ${\varepsilon}X_1$ is isomorphic to the standard contact structure on the 3-sphere $S^3$ and ${\varepsilon}X_1$is J-concave. Also we show that there is a contact structure ${\varepsilon}_0\ on\ S^2\times\ S^1$which is not strongly symplectically fillable but symplectically fillable, and that $(S^2{\times}S^1,\;{\varepsilon})$ has infinitely many non-diffeomorphic minimal fillings whose restrictions on$\S^2\times\ S^1$are ${\sigma}$ where ${\sigma}$ is the restriction of the standard symplectic structure on $S^2{\times}D^2$.

• 호남수학학술지
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• 제5권1호
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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).

• 한국어류학회지
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• 제22권1호
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• pp.56-60
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• 2010

기름종개와 왕종개로부터 기원한 단성생식집단인 Cobitis hankugensis-Iksookimia longicorpa complex는 대부분 암컷으로만 구성되어 있으며 최근에 1종류의 2배체와 2종류의 3배체집단이 확인되었다. 이들의 난막구조를 조사한 결과 3가지 종류로 구분될 수 있었다. 융모형은 이들의 부모종인 왕종개에서 확인되었으며, 과립형은 기름종개와 3배체집단, 그리고 과립을 가진 융모형은 2배체집단에서 나타났다. 특히 과립형을 가지는 3집단에서는 그들의 길이와 밀도에서 서로 차이를 보였다. 이러한 구조들은 cobitid complex에서 처음 보고될 뿐 아니라 2배체, 3배체 complex집단을 분류하는 데 이용될 수 있다.

• Bulletin of the Korean Chemical Society
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• 제13권4호
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• pp.363-367
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• 1992

The crystal structure of (1,3,6,9,11,14-hexaazatricycol[12.2.1.$1^{6,9}$]octadecane)copper(Ⅱ) perchlorate, Cu($C_{12}H_{26}N_6$)$(ClO_4)_2$, has been determined by the X-ray diffraction methods. The crystal data are as follows: Mr=516.9, triclinic, ${\alpha}=8.572\;(2)$, b=8.499 (3), c=15.204 (3) ${\AA}$, ${\alpha}=80.42\;(5),\;{\beta}=73.57\;(3),\;{\gamma}=69.82\;(4)^{\circ},\;V=994.2\;{\AA}^3,\;D_C=1.726\;gcm^{-3}$, space group $P{\tilde{1}},\;Z=2,\;{\mu}=21.27\;cm^{-1}&, F(000)=534 and T=297 K. The structure was solved by direct methods and refined by full-matrix least-squares methods to and R value of 0.081 for 1608 observed reflections measured with graphite-mono-chromated Mo Ka radiation on a diffractometer. There are two independent complexes in the unit cell. The two copper ions lie at the special positions (1/2, 0, 0) and (0, 1/2, 1/2)and each complex possesses crystallographic center of symmetry. Each Cu ion is coordinated to four nitrogen donors if the hexaazamacrotricyclic ligand and weakly interacts with two oxygen atoms of the perchlorate ions to form a tetragonally distorted octahedral coordination geometry. The Cu_N (sec), Cu_N(tert) and Cu_O coordination distances are 1.985 (14), 2.055 (14) and 2.757 (13) ${\AA}$ for the complex A and 1.996 (10), 2.040 (11) and 2.660 (13) ${\AA}$ for the complex B, respectively. The macrocycles in the two independent cations assume a similar conformation with the average r.m.s. deviation of 0.073 ${\AA}$. Two 1,3-diazacyclopentane ring moieties of the hexaazamacrotricyclic ligand are placed oppositely and almost perpendicularly to the square coordination plane of the ruffled 14-membered macrocycle. The secondary N atoms are hydrogen-bonded to the perchlorate O atoms with distances of 3.017 (23) and 3.025 (19) ${\AA}$ for the complexes A and B, respectively.