• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.29-39
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• 2001

For a Poisson Hopf algebra A, we find a natural Hopf structure in the Poisson enveloping algebra U(A) of A. As an application, we show that the Poisson enveloping algebra U(S(L)), where S(L) is the symmetric algebra of a Lie algebra L, has a Hopf structure such that a sub-Hopf algebra of U(S(L)) is Hopf-isomorphic to the universal enveloping algebra of L.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.527-541
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• 2001

We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).

• 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 $M_n(c)$.

• 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 Q^m = SO_m+2/SO_mSO₂. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric Q^m = SO_m+2/SO_mSO₂ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric Q^m with either symmetric (parallel), or recurrent structure Jacobi operator.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.55-60
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• 2021

Let M be a real hypersurface in a complex space form Mn(c), c ≠ 0. In this paper we prove that if the structure tensor field is Codazzi type, then M is a Hopf hypersurface. We characterize such Hopf hypersurfaces of Mn(c).

• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.247-252
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• 2021

Let M be a real hypersurface in a complex space form M_n(c), c ≠ 0. In this paper, we prove that if (∇_Xϕ)Y + (∇_Yϕ)X = 0 holds on M, then M is a Hopf hypersurface, where ϕ is the tangential projection of the complex structure of M_n(c). We characterize such Hopf hypersurfaces of M_n(c).

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.157-172
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• 2007

In this paper, we prove that if the structure Jacobi operator $R_{\xi}-parallel\;and\;R_{\xi}$ commutes with the Ricci tensor S, then a real hypersurface with non-negative scalar curvature of a nonflat complex space form $M_{n}(C)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_{n}(C)$.

• Journal of information and communication convergence engineering
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• v.9 no.5
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• pp.500-504
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• 2011

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. The new algorithm was applied into the identification of an unknown system for evaluating the performance of the proposed method. We compared the Wiener-Hopf solution with the equivalent Wiener-Hopf solution. The simulation results were similar to those obtained in the theoretical analysis. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.1-15
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• 2010

Let M be a real hypersurface with almost contact metric structure $(\phi,g,\xi,\eta)$ in a complex space form $M_n(c)$, $c\neq0$. In this paper we prove that if $R_{\xi}L_{\xi}g=0$ holds on M, then M is a Hopf hypersurface in $M_n(c)$, where $R_{\xi}$ and $L_{\xi}$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $\xi$ respectively. We characterize such Hopf hypersurfaces of $M_n(c)$.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.747-761
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• 2010

It is known that there are no real hypersurfaces with parallel structure Jacobi operator $R_{\xi}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $R_{\xi}$ which are weaker than ${\nabla}R_{\xi}$ = 0. Under further condition $S\phi={\phi}S$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.