28 research outputs found
๋ณต์ ๊ทธ๋ผ์ค๋ง ๋ค์์ฒด ์ฌ์ด์ ๋งค์ฅ
ํ์๋
ผ๋ฌธ (๋ฐ์ฌ)-- ์์ธ๋ํ๊ต ๋ํ์ : ์๋ฆฌ๊ณผํ๋ถ, 2017. 2. ๊นํ์ข
.์ด ๋
ผ๋ฌธ์์๋ ๋ณต์ ๊ทธ๋ผ์ค๋ง ๋ค์์ฒด Gr(2,m) ์์ ๋ณต์ ๊ทธ๋ผ์ค๋ง ๋ค์์ฒด Gr(2,n) ์ผ๋ก ๊ฐ๋ ๋ณต์ํด์์ ๋งค์ฅ์ ์ ํ์ฑ์ ๋ํด ๊ท๋ช
ํ๊ณ ์ ํ๋ค.
๋ณต์ ๊ทธ๋ผ์ค๋ง ๋ค์์ฒด Gr(2,n) ์์ ๋ณดํธ๋ฒกํฐ๋ค๋ฐ์ ์๋๋ฒกํฐ๋ค๋ฐ์, ์ฃผ์ด์ง ๋งค์ฅ์ผ๋ก ๋์ด๋น๊ธด ๋ฒกํฐ๋ค๋ฐ์ E ๋ผ๊ณ ํ๋ฉด, ๊ฐ๋ฅํ ๋ชจ๋ E ์ ์ ์ฒ ํน์ฑ๋ฅ๋ค์ ์กฐ์ฌํจ์ผ๋ก์จ ์ด๋ฌํ ๋งค์ฅ๋ค์ ๋ํ ์ฑ์ง์ ํ์
ํ ์ ์๋ค.
๋จผ์ , ์์ผ๋ก์ ๋
ผ๋ฆฌ๋ฅผ ์ ๊ฐํ๋๋ฐ ์ ์ฉํ๊ฒ ์ฌ์ฉ๋ Gr(2,m) ์ ์ฝํธ๋ชฐ๋ก์งํ์ Z-๊ฐ๊ตฐ ๊ธฐ์ ๋ฅผ ํ๋ ์ก๊ณ , ๋ชจ๋ ์ฝํธ๋ชฐ๋ก์ง๋ฅ๋ค์ ์ด ๊ธฐ์ ์ ๋ํ ์ ํ๊ฒฐํฉ์ผ๋ก ํํํ๋ค.
๋ณต์ ๊ทธ๋ผ์ค๋ง ๋ค์์ฒด Gr(2,m) ์์ Gr(2,n) ์ผ๋ก ๊ฐ๋ ๊ฐ๊ฐ์ ๋ณต์ํด์์ ๋งค์ฅ์ ๋ํด, ๋ฒกํฐ๋ค๋ฐ E ์ ์ ์ฒ ํน์ฑ๋ฅ๋ฅผ ์ด ๊ธฐ์ ๋ก ํํํ๋ฉด, ์ธ ๊ฐ์ ์ ์๊ณ์๋ฅผ ๊ฐ์ง๋ ์ ํ๊ฒฐํฉ์ผ๋ก ์ ์ผํ๊ฒ ์ธ ์ ์๋๋ฐ, ๋งค์ฅ์ ์ ํ์ฑ์ ์ด๋ฌํ ์ ์๋ค์ ์ํด ์์ ํ ๊ฒฐ์ ๋๋ค.
์ฃผ์ด์ง ๋งค์ฅ์ผ๋ก๋ถํฐ ์ ๋๋ ๋ฒ๋ฒกํฐ๋ค๋ฐ์ ์ฒ ํน์ฑ๋ฅ์ ์ค์ผ๋ฌ ํน์ฑ๋ฅ๋ก๋ถํฐ, 3-๋ณ์ ๋์คํํ ์ค ๋ฐฉ์ ์๋ค์ ์ป์ ์ ์๊ณ , ํด์์ ๋ฒกํฐ๋ค๋ฐ์ ์ฒ ํน์ฑ๋ฅ๊ฐ ์์ด ์๋ ํ์ ๊ธฐ์ค๊ณผ ํจ๊ป ์ด ๋ฐฉ์ ์๋ค์ ํ๋ฉด, ํน์ ์ ์์ ์๊ณ๋ฅผ ๋น๋กฏํ, ์ธ ๊ฐ์ ์ ์๋ค์ด ๋ง์กฑํด์ผ ํ๋ ๋ช ๊ฐ์ง ์กฐ๊ฑด๋ค์ ์ป์ ์ ์๋ค.
์ด ์ ์ ์๊ณ๋ก๋ถํฐ W. Barth ์ A. Van de Ven ์ด ์ฆ๋ช
ํ ๊ฒฐ๊ณผ๋ค์ ๋ฒกํฐ๋ค๋ฐ E ์ ์ ์ฉํ ์ ์๊ณ , ๋ณต์ ๊ทธ๋ผ์ค๋ง ๋ค์์ฒด Gr(2,m)์์ Gr(2,n) ์ผ๋ก ๊ฐ๋ ๋ณต์ํด์์ ๋งค์ฅ์ด ํญ์ ์ ํ์ด ๋๊ธฐ ์ํ m ๊ณผ n ์ ์กฐ๊ฑด๋ค์ ๊ตฌํ ์ ์๋ค.In this thesis, we characterize the linearity of holomorphic embeddings of the complex Grassmannian Gr(2,m) into the complex Grassmannian Gr(2,n).
We study such embeddings by finding all possible total Chern classes of the pullback bundles E of the dual bundles of the universal bundles on Gr(2,n) under these embeddings.
We first take a Z-module basis of the cohomology ring of Gr(2,m) which is useful for further works, and express every cohomology classes as a linear combination with respect to this basis.
For each holomorphic embedding of Gr(2,m) into Gr(2,n), the total Chern class of E is written uniquely as a linear combination of basis elements with three integral coefficients, the linearity of the embedding is determined completely by these integers.
We obtain several conditions on the three integers, including a upper bound of the specific integer by solving 3-variate Diophantine equations which are constructed from the Chern classes and the Euler class of the normal bundle induced by the embedding, together with a criterion of the numerical non-negativity of Chern classes of holomorphic vector bundles.
This upper bound enables us to apply W. Barth and A. Van de Ven's results to E, and we find conditions on m and n for which any holomorphic embedding of Gr(2,m) into Gr(2,n) is linear.1. Introduction 1
2. Preliminaries 12
2.1 Schubert cycles on Grassmannians 12
2.2 Vector bundles on Grassmannians 19
3. Embeddings of Gr(2,m) into Gr(2,n) 22
3.1 Linear embeddings 23
3.2 Equivalent conditions for the linearity 26
3.3 Equations in a, b and c 30
3.3.1 Euler class of N_{\mathbb{R}} 30
3.3.2 Total Chern class of N 32
3.3.3 Refined equations in \omega_{1,0} and \omega_{1,1} 36
3.4 Inequalities in a, b and c 38
3.4.1 Numerical non-negativity of Chern classes 38
3.4.2 Refined equation in \omega_{1,1} 40
3.4.3 Refined equation in \omega_{1,0} 44
4. Characterization of linear embeddings 48
4.1 General case 49
4.2 Special case 58
Bibliography 64
Abstract (in Korean) 66Docto
(The)Power relation among peers in the physical activity games
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ผ๋ฌธ(๋ฐ์ฌ)--์์ธ๋ํ๊ต ๋ํ์ :์ฒด์ก๊ต์ก๊ณผ,2003.Docto
Visual search strategies in Rugby tackle task
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ผ๋ฌธ(์์ฌ)--์์ธ๋ํ๊ต ๋ํ์ :์ฒด์ก๊ต์ก๊ณผ,2005.Maste
Deformation behavior of ฮต martensite in high Mn steels at low strain
MasterHigh Mn steels have been assessed in exceptional ability of high tensile stress with good ductility for automotive and high energy absorption industry. Their properties were attributed to deformation mechanisms called twinning induced plasticity (TWIP), formation of deformation twinning during plastic deformation, and transformation induced plasticity (TRIP), phase transformation during plastic deformation. In TRIP steels, martensitic transformation and reverse transformation were well known behavior.
Although models for TRIP phenomena was proposed at 1950s, the real time observation was limited in heating test and only a little research have been conducted with mechanical test. Relatively formation of deformation twinning and martensitic transformation were observed in detail, but reverse transformation was secondary induced plasticity at high strain. In this thesis, we observed the deformation mechanisms in ฮต phase at low strain with in-situ transmission electron microscopy (TEM) straining test. Before state the in-situ TEM result, sample designs and analysis of microstructure are explained, discussion about reverse transformation will be followed
Influence of Mn, Si and Al on the selective oxidation behavior of low carbon steel
DoctorThe selective oxidation phenomenon is inevitable during the continuous annealing of advanced high strength steel (AHSS) under the low oxygen partial pressure (POxy) atmosphere. The external and internal oxides can deteriorate the wettability and result in forming defects on the strip surface after hot dip galvanizing (HDG) process.
The oxidation behavior was investigated by many researchers in teams of the morphology of surface oxides and annealing conditions for transition between external and internal oxidation. In addition the numerical modes for internal oxidation behavior were proposed by many authors. However, the models are not yet applied in the field due to lack of the reliability.
The present study focuses on selective oxidation behavior in the steels containing single oxidant, double oxidants and triple oxidants to analyze fundamental effects of alloying elements. With cross sectional STEM observation, the morphology and oxidation behavior are investigated and comparison calculation depth to measured depth is carried out. The proper criteria for internal oxidation depth is proposed in the research, and new prediction model is suggested describing intra-oxidation depths and grain boundary oxidation depths in similar with measured values
Direct observation of transition from compact glide to cube glide during thermal straining of Al thin film on polyimide at elevated
A fast and scalable qubit-mapping method for noisy intermediate-scale quantum computers
This paper presents an efficient qubit-mapping method that redesigns a quantum circuit to overcome the limitations of qubit connectivity. We propose a recursive graph-isomorphism search to generate the scalable initial mapping. In the main mapping, we use an adaptive look-ahead window search to resolve the connectivity constraint within a short runtime. Compared with the state-of-the-art method [15], our proposed method reduced the number of additional gates by 23% on average and the runtime by 68% for the three largest benchmark circuits. Furthermore, our method improved circuit stability by reducing the circuit depth and thus can be a step forward towards fault tolerance.1