• Journal of the Korean Mathematical Society
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• v.7 no.1
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• pp.25-28
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• 1970

• Bulletin of the Korean Mathematical Society
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• v.17 no.2
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• pp.123-132
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• 1981

• Kyungpook Mathematical Journal
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• v.22 no.1
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• pp.61-65
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• 1982

• Kyungpook Mathematical Journal
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• v.22 no.1
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• pp.1-5
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• 1982

• Kyungpook Mathematical Journal
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• v.21 no.2
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• pp.271-274
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• 1981

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1285-1296
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• 2010

We give criterions for a submanifold to be an extrinsic sphere and to be a totally geodesic submanifold by observing some Frenet curves of order 2 on the submanifold. We also characterize constant isotropic immersions into arbitrary Riemannian manifolds in terms of Frenet curves of proper order 2 on submanifolds. As an application we obtain a characterization of Veronese embeddings of complex projective spaces into complex projective spaces.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.399-415
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• 2014

We study the Seifert surfaces of a link by relating the embeddings of graphs with induced graphs. As applications, we prove that every link L is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph $K_{2,n}$, where all voltage assignments on the edges of $K_{2,n}$ are 0. We also provide an algorithm to construct such a graph diagram of a given link and demonstrate the algorithm by dealing with the links $4^2_1$ and $5_2$.

• International Journal of Computer Science & Network Security
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• v.22 no.8
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• pp.399-403
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• 2022

Natural texts are analyzed to obtain their intended meaning to be classified depending on the problem under study. One way to represent words is by generating vectors of real values to encode the meaning; this is called word embedding. Similarities between word representations are measured to identify text class. Word embeddings can be created using word2vec technique. However, recently fastText was implemented to provide better results when it is used with classifiers. In this paper, we will study the performance of well-known classifiers when using both techniques for word embedding with Arabic dataset. We applied them to real data collected from Wikipedia, and we found that both word2vec and fastText had similar accuracy with all used classifiers.

• Journal of the Korean Mathematical Society
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• v.29 no.1
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• pp.165-174
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• 1992

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.7
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• pp.1726-1748
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• 2024

Trajectory planning is vital for autonomous systems like robotics and UAVs, as it determines optimal, safe paths considering physical limitations, environmental factors, and agent interactions. Recent advancements in trajectory planning and future location prediction stem from rapid progress in machine learning and optimization algorithms. In this paper, we proposed a novel framework for Spatial-temporal transformer-based feed-forward neural networks (STTFFNs). From the traffic flow local area point of view, skip-gram model is trained on trajectory data to generate embeddings that capture the high-level features of different trajectories. These embeddings can then be used as input to a transformer-based trajectory planning model, which can generate trajectories for new objects based on the embeddings of similar trajectories in the training data. In the next step, distant regions, we embedded feedforward network is responsible for generating the distant trajectories by taking as input a set of features that represent the object's current state and historical data. One advantage of using feedforward networks for distant trajectory planning is their ability to capture long-term dependencies in the data. In the final step of forecasting for future locations, the encoder and decoder are crucial parts of the proposed technique. Spatial destinations are encoded utilizing location-based social networks(LBSN) based on visiting semantic locations. The model has been specially trained to forecast future locations using precise longitude and latitude values. Following rigorous testing on two real-world datasets, Porto and Manhattan, it was discovered that the model outperformed a prediction accuracy of 8.7% previous state-of-the-art methods.