• Proceedings of the Optical Society of Korea Conference
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• 2008.07a
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• pp.297-298
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• 2008

• Proceedings of the Optical Society of Korea Conference
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• 2006.07a
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• pp.63-66
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• 2006

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.525-535
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• 2017

In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.339-350
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• 2005

We obtain the following two inequalities on a strongly pseudoconvex domain $\Omega\;in\;\mathbb{C}^n\;:\;for\;f\;{\in}\;O(\Omega)$ $$\int_{0}^{{\delta}0}t^{a{\mid}a{\mid}+b}M_p^a(t, D^{a}f)dt\lesssim\int_{0}^{{\delta}0}t^{b}M_p^a(t,\;f)dt\;\int_{O}^{{\delta}O}t_{b}M_p^a(t,\;f)dt\lesssim\sum_{j=0}^{m}\int_{O}^{{\delta}O}t^{am+b}M_{p}^{a}\(t,\;\aleph^{i}f\)dt$$. In [9], Shi proved these results for the unit ball in $\mathbb{C}^n$. These are generalizations of some classical results of Hardy and Littlewood.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.321-331
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• 2019

The present paper deals with a study of infinitesimal CL-transformations on Kenmotsu manifolds, whose metric is Yamabe soliton and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Among others, we find a necessary and sufficient condition of a Yamabe soliton on Kenmotsu manifold with respect to CL-connection to be Yamabe soliton on Kenmotsu manifold with respect to Levi-Civita connection. We found the necessary and sufficient condition for the Yamabe soliton structure to be invariant under Schouten-Van Kampen connection. Finally, we constructed an example of steady Yamabe soliton on 3-dimensional Kenmotsu manifolds with respect to Schouten-Van Kampen connection.

• Journal for History of Mathematics
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• v.32 no.1
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• pp.1-15
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• 2019

We divide the timeline of the history of Finsler geometry, which dates back to Riemann's inaugural lecture in 1854, into three periods (hibernation, hiatus, rebirth) and we study formation of Romanian Finsler school around Iasi, Romania during the hiatus period. We look for the history centered around Radu Miron who is a third generation geometer of Iasi University and the mathematical heritage there through five generations. We also investigate mathematical impact of T. Levi-Civita, D. Hilbert, ${\acute{E}}$ Cartan who are considered as top mathematicians at their time.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.895-920
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• 2021

In this paper, first we introduce the full expression of the Riemannian curvature tensor of a real hypersurface M in the complex quadric Q^m from the equation of Gauss and some important formulas for the structure Jacobi operator R_ξ and its derivatives ∇R_ξ under the Levi-Civita connection ∇ of M. Next we give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, ∇_ξR_ξ = 0, in the complex quadric Q^m for m ≥ 3. In addition, we also consider a new notion of 𝒞-parallel structure Jacobi operator of M and give a nonexistence theorem for Hopf real hypersurfaces with 𝒞-parallel structure Jacobi operator in Q^m, for m ≥ 3.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.149-164
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• 2021

By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds. We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections. Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection. Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection. Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.77-87
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• 2005

Smith(2001) calls for practice-based professional development for teachers of mathematics. This paper discusses laboratory class as a model for conducting professional development program for a group f elementary school mathematics teachers. The laboratory class seeks to promote teachers' generative growth (Carpenter & Levi, 1999) and all the core and structural features (Garet, Porter, Desimone, Birman & Kwang, 2001) of a professional development are also engaged in this program and the ultimate goal is for teachers to be reflective in their practices to be generative (Carpenter & Leher, 1999) in their teaching and learning. This paper also discusses the design of the laboratory class based on the principles of reflective thinking and psychological observation by Dewey to connect theory with practice.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.4
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• pp.1527-1552
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• 2018

The rapidly-evolving demand of applications using wireless sensor networks in several areas such as building and industrial automation or smart cities, among other, makes it necessary to determine and provide QoS support mechanisms which can satisfy the requirements of applications. In this paper we propose a mechanism that establishes different QoS levels, based on Publish/Subscribe model for wireless networks to meet application requirements, to provide reliable delivery of packet and timeliness. The first level delivers packets in a best effort way. The second one intends to provide reliable packet delivery with a novel approach for Retransmission Timeout (RTO) calculation, which adjusts the RTO depending on the subscriber Packet Delivery Ratio (PDR). The third one provides the same reliable packet delivery as the second one, but in addition, it provides data aggregation trying to be efficient in terms of energy consumption and the use of network bandwidth. The last one provides timeliness in the packet delivery. We evaluate each QoS Level with several performance metrics such as PDR, Message Delivery Ratio, Duplicated and Retransmitted Packet Ratio and Packet Timeliness Ratio to demonstrate that our proposal provides significant improvements based on the increase of the PDR obtained.