• 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 ${\mathbb} C^{m+n}$.

• 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.

• Annual Conference on Human and Language Technology
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• 2017.10a
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• pp.60-63
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• 2017

자연어처리에 딥 러닝을 적용하기 위해 사용되는 Word embedding은 단어를 벡터 공간상에 표현하는 것으로 차원축소 효과와 더불어 유사한 의미의 단어는 유사한 벡터 값을 갖는다는 장점이 있다. 이러한 word embedding은 대용량 코퍼스를 학습해야 좋은 성능을 얻을 수 있기 때문에 기존에 많이 사용되던 word2vec 모델은 대용량 코퍼스 학습을 위해 모델을 단순화 하여 주로 단어의 등장 비율에 중점적으로 맞추어 학습하게 되어 단어의 위치 정보를 이용하지 않는다는 단점이 있다. 본 논문에서는 기존의 word embedding 학습 모델을 단어의 위치정보를 이용하여 학습 할 수 있도록 수정하였다. 실험 결과 단어의 위치정보를 이용하여 word embedding을 학습 하였을 경우 word-analogy의 syntactic 성능이 크게 향상되며 어순이 바뀔 수 있는 한국어에서 특히 큰 효과를 보였다.

• 한국어정보학회:학술대회논문집
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• 2017.10a
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• pp.60-63
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• 2017

자연어처리에 딥 러닝을 적용하기 위해 사용되는 Word embedding은 단어를 벡터 공간상에 표현하는 것으로 차원축소 효과와 더불어 유사한 의미의 단어는 유사한 벡터 값을 갖는다는 장점이 있다. 이러한 word embedding은 대용량 코퍼스를 학습해야 좋은 성능을 얻을 수 있기 때문에 기존에 많이 사용되던 word2vec 모델은 대용량 코퍼스 학습을 위해 모델을 단순화 하여 주로 단어의 등장 비율에 중점적으로 맞추어 학습하게 되어 단어의 위치 정보를 이용하지 않는다는 단점이 있다. 본 논문에서는 기존의 word embedding 학습 모델을 단어의 위치정보를 이용하여 학습 할 수 있도록 수정하였다. 실험 결과 단어의 위치정보를 이용하여 word embedding을 학습 하였을 경우 word-analogy의 syntactic 성능이 크게 향상되며 어순이 바뀔 수 있는 한국어에서 특히 큰 효과를 보였다.

• KIPS Transactions on Computer and Communication Systems
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• v.2 no.4
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• pp.151-154
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• 2013

In this paper, we will analyze embedding between Folded Hypercube and HFH. We will show Folded Hypercube $FQ_{2n}$ can be embedded into HFH($C_n,C_n$) with dilation 4, expansion $\frac{(C_n)^2}{2^{2n}}$ and HFH($C_d,C_d$) can be embedded into $FQ_{4d-2}$ with dilation O(d).

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.435-445
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• 2003

In this paper we consider Sobolev-type embedding theorems for harmonic and holomorphic Sobolev spaces on a bounded domain with $C^2$ boundary.

• The Journal of Korean Association of Computer Education
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• v.17 no.2
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• pp.115-124
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• 2014

Hypercube and star graph are widely known as interconnection network. The embedding of an interconnection network is a mapping of a network G into other network H. The possibility of embedding interconnection network G into H with a low cost, has an advantage of efficient algorithms usage in network H, which was developed in network G. In this paper, we provide an embedding algorithm between HCN and HON. HCN(n,n) can be embedded into HON($C_{n+1},C_{n+1}$) with dilation 3 and HON($C_d,C_d$) can be embedded into HCN(2d-1,2d-1) with dilation O(d). Also, star graph can be embedded to half pancake's value of dilation 11, expansion 1, and average dilation 8. Thus, the result means that various algorithms designed for HCN and Star graph can be efficiently executed on HON and half pancake, respectively.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1027-1034
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• 2017

In this paper, we propose a new function embedding method that can measure mathematical projections of probability amplitude, probability, average expectation and matrix elements of stationary-state unit matrix at all control operation points of quantum gates. The function embedding method in this paper is to embed orthogonal normalization condition of probability amplitude for each control operating point into a binary scalar operator by using Dirac symbol and Kronecker delta symbol. Such a function embedding method is a very effective means of controlling the arithmetic power function of a unitary gate in a unitary transformation which expresses a quantum gate function as a tensor product of a single quantum. We present the results of evolutionary operation and projective measurement when we apply the proposed function embedding method to the ternary 2-qutrit cNOT gate and compare it with the existing methods.

• The KIPS Transactions:PartA
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• v.16A no.4
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• pp.299-306
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• 2009

Hierarchical Folded HyperStar Network has lower network cost than HCN(n,n) and HFN(n,n) which are hierarchical networks with the same number of nodes. In this paper, we analyze embedding between Hierarchical Folded HyperStar HFH($C_n,C_n$) and Hypercube, HCN(n,n), HFN(n,n). The results of embedding are that HCN(n,n), HFN(n,n) and Hypercube $Q_{2n}$ can be embedded into HFH($C_n,C_n$) with expansion $\frac{C^n}{2^{2n}}$ and dilation 2, 3, and 4, respectively. Also, HFH($C_n,C_n$) can be embedded into HFN(2n,2n) with dilation 1. These results mean so many developed algorithms in Hypercube, HCN(n,n), HFN(n,n) can be used efficiently in HFH($C_n,C_n$).

• The KIPS Transactions:PartC
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• v.14C no.1 s.111
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• pp.39-44
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• 2007

In this paper, we propose a reversible watermarking method to recover an original image after the watermark has been extracted. Most watermarking algorithms cause degradation of image quality in original digital content in the process of embedding watermark. In the proposed algorithm, the original image can be obtained when the degradation is removed from the watermarked image after extracting watermark information. In the proposed method, we utilize histogram shifting concept and Location Map structure. We could solve the Filp-Flop problem by using Location Map structure and enlarge the information embedding capacity by embedding recursively. Experimental results demonstrate that the embedding information as large as 120k bits can be realized while the invisibility as high as 41dB can be maintained.