• Korean Journal of Mathematics
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• v.32 no.1
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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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• v.2 no.2
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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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• v.40 no.1
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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 $\bar{r}-2(n-1)c{\leq}0$.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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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 $\bar{M}$.

• Proceedings of the IEEK Conference
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• 2002.06d
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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.

• Proceedings of the IEEK Conference
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• 2002.06d
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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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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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 $S^2{\times}D^2$.

• 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).

• Korean Journal of Ichthyology
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• v.22 no.1
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• pp.56-60
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• 2010

The Cobitis hankugensis-Iksookimia longicorpa complex from Korea has been presumed to be a unisexual lineage, originating from C. hankugensis and I. longicorpa and having almost all females. Recently, it was confirmed that the complex consisted of one diploid and two triploid complexes. From observation of their oocyte envelopes, three forms could be classified: a villous projection in I. longicorpa, a granular one in C. hankugensis and two triploid complexes, and a granule with villous one in the diploid complex. Even within the same granular projection, they showed specific features in length and density number from each other. These architectures are first observed in cobitid complexes and may playa role in identification of diploids and triploids.

• Bulletin of the Korean Chemical Society
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• v.13 no.4
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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.