• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.17-27
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• 2010

A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are balanced and all prime-valent regular Cayley maps on abelian groups are either balanced or anti-balanced. Furthermore, we prove that there is no prime-valent regular Cayley map on any dicyclic group.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.13-27
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• 2024

A regular t-balanced Cayley map on a group Γ is an embedding of a Cayley graph on Γ into a surface with certain special symmetric properties. We completely classify regular t-balanced Cayley maps for a class of split metacyclic 2-groups.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.9
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• pp.3298-3321
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• 2021

A lot of data hiding schemes have been proposed to embed secret data in the plain cover images or compressed images of various formats, including JPEG, AMBTC, VQ, etc. In this paper, we propose a production process of mosaic images based on three regular images of coffee beans. A primary image is first mimicked by the process to produce a mosaic cover image. A two-layer steganography is applied to hide secret data in the mosaic image. Based on the low visual quality of the mosaic cover image, its PSNR value can be improved about 1.5 dB after embedding 3 bpp. This is achieved by leveraging the newly proposed polarized search mask and the concepts of strong embedding and weak embedding. Applying steganography to the mosaic cover images is a completely new idea and it is promising.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.6 no.2
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• pp.257-263
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• 2002

A graph embedding problem has been studied for applications of resource allocation and mapping the underlying data structure of a parallel algorithm into the interconnection architecture of massively parallel processing systems. In this paper, we consider the embedding problem of the pyramid into the regular 2-dimensional mesh interconnection network topology. We propose a new embedding function which can embed the pyramid of height N into 2$^{N}$ x2$^{N}$ 2-dimensional mesh with dilation max{2$^{N1}$-2. [3.2$^{N4}$＋1)/2, 2$^{N3}$＋2. [3.2$^{N4}$＋1)/2]}. This means an improvement in the dilation measure from 2$^{N}$ $^1$in the previous result into about (5/8) . 2$^{N1}$ under the same condition.condition.

• Language and Information
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• v.5 no.2
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• pp.1-8
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• 2001

Natural language string sets are known to require a grammar with a generative capacity slightly beyond that of Context Free Grammars. Proofs regarding complexity of natural language have involved particular properties of languages like English, Swiss German and Bambara. While it is not very difficult to prove that Korean is more complex than the simplest of the many infinite sets, no proof has been given of this in the literature. I identify two types of center embedding in Korean and use them in proving that Korean is not a regular set, i.e. that no FSA's can recognize its string set. The regular language i salam i (i salam ul$)^j$ michi (key ha)^k$ essta is intersected with Korean, to give {i salam i (i salam ul$)^j$ michi (key ha$)^k$ essta i $$\mid$$ j, k $\geq$ 0 and j $\leq$ k}. This latter language is proved to be nonregular. As the class of regular sets is closed under intersection, Korean cannot be regular.

• The KIPS Transactions:PartA
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• v.10A no.6
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• pp.627-634
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• 2003

In this paper, we consider a graph-theoretic problem,, the so-called "graph embedding problem" that maps the vertices and edges of the given guest graph model into the corresponding vertices and paths of the host graph under the condition of maintaining better performance parameters such as dilation, congestion, and expansion. We firstly propose a new mapping function which can embed the pyramid model with height N into the 3-dimensional mesh massively parallel processor system with the height $(4^{(N+1)/3}+2)/3$ and the regular 2-dimensional mesh of one side $2^{(2N-1)/3}$, and analyze the performance of the embedding in terms of the dilation parameter that reflects the number of communication steps between two adjacent vertices under the embedding. We prove that the dilation of the embedding is $2{\cdot}4^{(N-2)/3}+4)/3$. This is superior to the previous result of $4^{N+183}+2)/3$ under the same condition.condition.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.23
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• pp.10509-10512
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• 2015

Objective: To investigate the differential features of CT images in children with neuroblastomas (N) and ganglioneuroblastomas (G). Materials and Methods: Clinical data of 12 children in group G and 15 in group N undergoing CT examination and definitely diagnosed by pathology were retrospectively analyzed. The focal conditions were observed and compared in the two groups, including location, size, boundaries, morphology, enhanced degree and mode, abdominal vascular involvement, presence or absence of spanning the midline, infiltration of peripheral organs, angiography manifestations in tumors or surroundings, presence or absence of calcification and vascular tumor emboli as well as metastases of distal organs and lymph nodes. Results: In group N, the incidence of tumors in the adrenal area was conspicuously higher than in group G (P<0.05), while that of tumors with regular morphology and clear boundaries was significantly lower than in group G (P<0.01); Angiography manifestation rate and incidences of vascular embedding, lymph node metastasis, infiltration and organic metastasis in group N were all markedly higher than in group G (P<0.05). There was no statistical significance between the two groups in terms of focal size, presence or absence of calcification and spanning the midline, and enhanced degree and mode, as well as vascular tumor emboli (P>0.05). Conclusions: Mostly located in adrenal areas and with vascular embedding as a primary manifestation, the neuroblastoma extremely readily metastases to lymph nodes and other organs as well as infiltrating local tissues, with dilation on angiography frequent in or around the tumors. With vascular displacement as a primary manifestation, ganglioneuroblastoma has a regular morphology and clear boundaries.

• Journal of Electrical Engineering and Technology
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• v.8 no.2
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• pp.271-281
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• 2013

In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincar$\acute{e}$ transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.