• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.623-631
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• 2001

Let $\kappa$ be a real abelian field of conductor f and $\kappa$(sub)$\infty$ = ∪(sub)n$\geq$0$\kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$\phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$\geq$0, let G(sub)m,n be the Galois group Gal($\kappa$(sub)m/$\kappa$(sub)n) and C(sub)m be the group of circular units of $\kappa$(sub)m. Let l be the number of prime ideals of $\kappa$ above p. Then, for mm>n$\geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).

• Proceedings of the Korean Vacuum Society Conference
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• 2013.08a
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• pp.222-222
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• 2013

GaN 기반 반도체는 넓은 bandgap을 가지고 있어 가시광부터 자외선까지 다양한 광전소자에 유용하게 사용된다. 광전소자중 발광다이오드의 경우 대부분 사파이어 기판위에 성장된다. 하지만 사파이어와 GaN의 격자 불일치 및 열팽창 계수의 차이로 인해 고품질의 GaN를 성장하기가 어렵다. 특히 열팽창 계수의 차이는 GaN 성장 공정이 고온에서 이루어지기 때문에 성장후 상온으로 온도가 떨어질 때 웨이퍼의 bowing을 발생시키고 동시에 dislocation이나 crack과 같은 결함이 생성되 GaN 성장막의 품질을 떨어트린다. 웨이퍼의 크기가 커지면 커질수록 웨이퍼 bowing은 커져 이에 대한 연구는 중요하다. 본 논문에서 2인치 사파이어 기판위에 성장된 GaN의 bow특성을 알아보기 위해 먼저 simulation을 하였고 실제로 성장된 GaN 웨이퍼와 비교를 하였다. c-plane 사파이어 기판위에 성장된 c-plane GaN의 bow특성을 알아보기 위해 성장 온도 $1,100^{\circ}C$에서 GaN두께를 1 ${\mu}m$에서 10 ${\mu}m$까지 1 ${\mu}m$씩 변화시켜 가며 simulation을 하였다. GaN두께가 1 ${\mu}m$일때는 bow가 11 ${\mu}m$, 6 ${\mu}m$ 일때는 54.7 ${\mu}m$, 10 ${\mu}m$ 일때는 108 ${\mu}m$를 얻어 GaN두께가 1 ${\mu}m$씩 증가할 때 마다 bow가 약 10 ${\mu}m$씩 증가하였다. 성장온도에 대한 영향을 알아보기 위해 $700^{\circ}C$에서 $1,200^{\circ}C$까지 $100^{\circ}C$씩 증가시켜며 bow특성 simulation을 하였다. 6 ${\mu}m$성장된 GaN의 경우 성장온도가 $100^{\circ}C$ 씩 증가할 때 bow는 약 6 ${\mu}m$ 증가하였다. 실제 성장된 c-plane GaN웨이퍼와 비교하기 위해 GaN을 각각 3 ${\mu}m$와 6 ${\mu}m$를 성장시켰고 high resolution x-ray diffraction장비를 사용하여 bow를 측정한 결과 각각 28 ${\mu}m$와 61 ${\mu}m$ 였고 simulation결과는 각각 33 ${\mu}m$와 65.5 ${\mu}m$를 얻어 비슷한 결과를 보였다. c-plane 사파이어 기판위에 성장된 c-plane GaN는 방향에 무관하게 동일한 bow 특성을 가지는 반해 r-plane 사파이어 기판위에 성장된 a-plane GaN는 방향에 따라 다른 bow특성을 보인다. a-plane GaN 이방향성적인 bow 특성을 알아보기 위해 simulation을 하였다. $1,100^{\circ}C$에서 a-plane GaN을 성장할 때 두께가 1 ${\mu}m$ 증가할 때마다 bow가 c축 방향으로는 21.7 ${\mu}m$씩 증가하였고 m축 방향으로는 11.8 ${\mu}m$ 씩 증가하여 매우 큰 이방향성적인 bow 특성을 보였다. 실제 r-plane 사파이어 기판위에 성장된 a-plane GaN의 bow를 측정하였고 simulation 결과와 비교해 보았다.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.759-764
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• 1998

We define the rational lens algebra (equation omitted)(n) as the crossed product by an action of Z on C( $S^{2n＋l}$). Assume the fibres are $M_{ k}$/(C). We prove that (equation omitted)(n) $M_{p}$ (C) is not isomorphic to C(Prim((equation omitted)(n))) $M_{kp}$ /(C) if k > 1, and that (equation omitted)(n) $M_{p{\infty}}$ is isomorphic to C(Prim((equation omitted)(n))) $M_{k}$ /(C) $M_{p{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p. It is moreover shown that if k > 1 then (equation omitted)(n) is not stably isomorphic to C(Prim(equation omitted)(n))) $M_{k}$ (c).

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.809-817
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• 1998

We investigate when the product of two smooth manifolds admits a weakly Lagrangian embedding. Prove that, if $M^m$ and $N^n$ are smooth manifolds such that M admits a weakly Lagrangian embedding into ${\mathbb}C^m$ whose normal bundle has a nowhere vanishing section and N admits a weakly Lagrangian immersion into ${\mathbb}C^n$, then $M \times N$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$. As a corollary, we obtain that $S^m {\times} S^n$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$ if n=1,3. We investigate the problem of whether $S^m{\times}S^n$ in general admits a weakly Lagrangian embedding into ${\mathbb} C^{m+n}$.

• The KIPS Transactions:PartA
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• v.15A no.2
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• pp.95-100
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• 2008

In this paper, we propose a new interconnection network topology, hierarchical folded hyper-star network HFH($C_n,\;C_n$), which is based on folded hyper-star network. Our results show that the proposed hierarchical folded hyper-star network performs very competitively in comparison to folded hyper-star network and hierarchical network HCN(m,m), HFN(m,m) have been previously proposed, when diameter ${\times}$ degree is used as a network cost measure. We also investigate various topological properties of HFH($C_n,\;C_n$) including connectivity, routing algorithm, diameter, broadcasting.

• Tribology and Lubricants
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• v.4 no.2
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• pp.36-43
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• 1988

Titanium carbide(TiC) and titanium nitride(TiN) flims were deposited on $Si_3N_4$-TiC composite cutting tools by chemical vapor deposition(CVD) using $TiCl_4-CH_4-H_2$ and $TiCl_4-H_2-N_2$ gas mixtures, respectively. The nonmetal to metal ratio of deposit increases with increasing $m_{C/Ti}$(mole ratio of CH$_4$ to TiCl$_4$ in the input) for TiC coatings and $m_{N/Ti}$(mole ratio of N$_2$ to TiCl$_4$ in the input) for TiN coatings. The nearly stoiahiometric films could be obtained under the deposition condition of $m_{C/Ti}$ between 1.15 and 1.61 for TiC, and that of $m_{N/Ti}$ between 25 and 28 for TiN. Also maximum microhardness of the coatings can be obtained in these ranges. The interfacial region of TiC coatings on $Si_3N_4$-TiC ceramics is wider than that of TiN coatings according to Auger depth profile analysis, which indicates good interfacial bonding for TiC. Experimental results show that TiC coatings have an randomly equiaxed structure and Columnar structure with(220) preferred orientation can be obtained for TiN coatings. And, multilayer coatings have a dense and equiaxed structure.

• Elastomers and Composites
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• v.40 no.3
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• pp.174-180
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• 2005

Sonochemical synthesis of fullerene oxides $[C_{70}O_n](n=1{\sim}2)$ by fullerene$[C_{70}]$ and metal hexacarbonyl complexes $M(CO)_6$(M=Cr, Mo, W) took place under air atmosphere. The reactivity of fullerene$[C_{70}]$ and several metal hexacarbonyl complexes $M(CO)_6$(M=Cr, Mo, W) under same ultrasonic condition increased in the order of $Mo(CO)_6$ > $W(CO)_6$ > $Cr(CO)_6$. The MALDI-TOF-MS, UV-visible spectra, and HPLC analysis confirmed that the products of sonochemical reaction were $[C_{70}O_n](n=1{\sim}2)$.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.471-479
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• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.19 no.3
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• pp.257-264
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• 1986

The Chromosomes of five cobitid fishes, Cobitis taenia taenia, C. taenia lutheri, C. taenia striata, C. longicorpus and C. koreensis were studied. The karyotypic studies were based on the observations from the flame-drying preparations. The results obtained such as the number of somatic chromosomes, the type of chromosomes according to the centromeric loci and the number of chromosomal arm(AN) were as follows: C. longicorpus, 2n=50, 12m-8sm-30a, AN=70; C. koreensis, 2n=50, 10m-12sm-28a, AN=72; C. taenia taenia, 2n=48, 14m-4sm-30a, AN=66: C. taenia lutheri, 2n=50, 10m-6sm-34a, AN=66; and C. taenia striata, 2n=50, 10m-6sm-34a, AN=66. Peculiarly, in the case of C. taenia lutheri the chromosome number of somatic diploid was found to be 48-51, however, the number of chromosomal arm was 66, irrespective of the difference in the numbers of each somatic genome. It was confirmed there exists the Robertsonian event, one of the chromosomal polymorphism in C.t. lutheri. It was remarked taxonomically that the karyotype of C. taenia taenia of Korea having 48 diploid chromosomes was not identical with that of Europe and Japan with 50 chromosomes. Based on the karyotype analysis the Korean cobitid fishes can be classified roughly into three species groups according to arm numbers and diploid numbers; 1) C. taenia taenia, C. taenia lutheri, C. taenia striata 2) C. koreensis, C. longicor pus, C. rotundicaudata and 3) C. granoei.