• Title/Summary/Keyword: m-structure

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PHY Frame Structure Design for M2M Direct Communications (M2M 단말간 직접통신을 위한 PHY 프레임구조 설계)

  • Oh, Changyoon
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.2
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    • pp.20-26
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    • 2013
  • We propose PHY Frame Structure for M2M direct communications in licensed frequency band. Especially, the proposed PHY Frame Structure coexists in the same licensed frequency band as currently operating cellular systems. Recently, Machine to Machine (M2M) service markets, including SmartGrid, Mobile Health, and Smart Car, are being rapidly expanded. Supporting M2M services in a specific case can waste Radio Resource in cellular systems. For example, when two M2M terminals communicating to each other are closely located, direct communication is radio resource efficient. In this paper, we set the requirement of maintaining the existing PHY frame structure in cellular systems to meet the backward compatibility. Based on this backward compatibility requirement, PHY frame structure for M2M direct communications is developed while satisfying coexistence with current operating cellular system. The proposed PHY frame structure meets backward compatibility. Accordingly, it is expected that the proposed M2M frame structure is useful for its frequency resource efficiency.

A NEW CLASSIFICATION OF REAL HYPERSURFACES WITH REEB PARALLEL STRUCTURE JACOBI OPERATOR IN THE COMPLEX QUADRIC

  • Lee, Hyunjin;Suh, Young Jin
    • 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 Qm from the equation of Gauss and some important formulas for the structure Jacobi operator Rξ and its derivatives ∇Rξ under the Levi-Civita connection ∇ of M. Next we give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, ∇ξRξ = 0, in the complex quadric Qm 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 Qm, for m ≥ 3.

DEFORMATION SPACES OF CONVEX REAL-PROJECTIVE STRUCTURES AND HYPERBOLIC AFFINE STRUCTURES

  • Darvishzadeh, Mehdi-Reza;William M.Goldman
    • Journal of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.625-639
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    • 1996
  • A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

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ξ-PARALLEL STRUCTURE JACOBI OPERATORS OF REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM

  • KIM, NAM-GIL;KI, U-HANG
    • Honam Mathematical Journal
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    • v.28 no.4
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    • pp.573-589
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    • 2006
  • Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ in a non flat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is ${\xi}$-parallel and the Ricci tensor S commutes with the structure operator $\phi$, then a real hypersurface in $M_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_n(c)$.

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Effect of Valence Electron Concentration on Elastic Properties of 4d Transition Metal Carbides MC (M = Y, Zr, Nb, and Rh)

  • Kang, Dae-Bok
    • Bulletin of the Korean Chemical Society
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    • v.34 no.7
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    • pp.2171-2175
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    • 2013
  • The electronic structure and elastic properties of the 4d transition metal carbides MC (M = Y, Zr, Nb, Rh) were studied by means of extended H$\ddot{u}$ckel tight-binding band electronic structure calculations. As the valence electron population of M increases, the bulk modulus of the MC compounds in the rocksalt structure does not increase monotonically. The dominant covalent bonding in these compounds is found to be M-C bonding, which mainly arises from the interaction between M 4d and C 2p orbitals. The bonding characteristics between M and C atoms affecting the variation of the bulk modulus can be understood on the basis of their electronic structure. The increasing bulk modulus from YC to NbC is associated with stronger interactions between M 4d and C 2p orbitals and the successive filling of M 4d-C 2p bonding states. The decreased bulk modulus for RhC is related to the partial occupation of Rh-C antibonding states.

Submanifolds of Codimension 3 in a Complex Space Form with Commuting Structure Jacobi Operator

  • Ki, U-Hang;Song, Hyunjung
    • Kyungpook Mathematical Journal
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    • v.62 no.1
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    • pp.133-166
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    • 2022
  • Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form Mn+1(c) for c ≠ 0. We denote by S and R𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R𝜉𝜙 = 𝜙R𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in Mn(c) (⊂ Mn+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 IN A COMPLEX SPACE FORM IN TERMS OF THE STRUCTURE JACOBI OPERATOR

  • Ki, U-Hang;Kurihara, Hiroyuki
    • Communications of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.229-257
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    • 2022
  • Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form Mn+1(c), c ≠ 0. We denote by A and R𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R𝜉A = AR𝜉 and at the same time ∇𝜉R𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

STRUCTURE JACOBI OPERATORS OF SEMI-INVARINAT SUBMANIFOLDS IN A COMPLEX SPACE FORM II

  • Ki, U-Hang;Kim, Soo Jin
    • East Asian mathematical journal
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    • v.38 no.1
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    • pp.43-63
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    • 2022
  • Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (φ, ξ, η, g) in a complex space form Mn+1(c). We denote by Rξ the structure Jacobi operator with respect to the structure vector field ξ and by ${\bar{r}}$ the scalar curvature of M. Suppose that Rξ is φ∇ξξ-parallel and at the same time the third fundamental form t satisfies dt(X, Y) = 2θg(φX, Y) for a scalar θ(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies Rξφ = φRξ, then M is a Hopf hypersurface of type (A) in Mn+1(c) provided that ${\bar{r}-2(n-1)c}$ ≤ 0.

COMMUTING STRUCTURE JACOBI OPERATOR FOR SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 IN COMPLEX SPACE FORMS

  • KI, U-Hang;SONG, Hyunjung
    • East Asian mathematical journal
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    • v.38 no.5
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    • pp.549-581
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    • 2022
  • Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form Mn+1(c), c≠ 0. We denote by S and R𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that M satisfies R𝜉S = SR𝜉 and at the same time R𝜉𝜙 = 𝜙R𝜉, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

SEMI-SYMMETRIC STRUCTURE JACOBI OPERATOR FOR REAL HYPERSURFACES IN THE COMPLEX QUADRIC

  • Imsoon Jeong;Gyu Jong Kim;Changhwa Woo
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.4
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    • pp.849-861
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    • 2023
  • In this paper, we introduce the notion of semi-symmetric structure Jacobi operator for Hopf real hypersufaces in the complex quadric Qm = SOm+2/SOmSO2. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric Qm = SOm+2/SOmSO2 with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric Qm with either symmetric (parallel), or recurrent structure Jacobi operator.