• East Asian mathematical journal
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• 제40권1호
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• pp.1-23
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• 2024

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c). We denote by A, K and L the second fundamental forms with respect to the unit normal vector C, D and E respectively, where C is the distinguished normal vector, and by R_𝜉 = R(𝜉, ·)𝜉 the structure Jacobi operator. 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 , and at the same time R_𝜉K = KR_𝜉 and ∇_{𝜙∇𝜉𝜉}R_𝜉 = 0. In this paper, we prove that if it satisfies ∇_𝜉R_𝜉 = 0 on M, then M is a real hypersurface of type (A) in M_n(c) provided that the scalar curvature $\bar{r}$ of M holds $\bar{r}-2(n-1)c{\leq}0$.

• 대한수학회보
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• 제53권6호
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• pp.1715-1723
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• 2016

We study the characteristic Jacobi operator ${\ell}={\bar{R}({\cdot},{\xi}){\xi}$ (along the Reeb flow ${\xi}$) on the unit tangent sphere bundle $T_1M$ over a Riemannian manifold ($M^n$, g). We prove that if ${\ell}$ is pseudo-parallel, i.e., ${\bar{R}{\cdot}{\ell}=L{\mathcal{Q}}({\bar{g}},{\ell})$, by a non-positive function L, then M is locally flat. Moreover, when L is a constant and $n{\neq}16$, M is of constant curvature 0 or 1.

• Journal of Preventive Medicine and Public Health
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• 제53권6호
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• pp.405-408
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• 2020

In epidemiology, the basic reproduction number (R₀) is a term that describes the expected number of infections generated by 1 case in a susceptible population. At the beginning of the coronavirus disease 2019 (COVID-19) pandemic, R₀ was frequently referenced by the public health community and the wider public. However, this metric is often misused or misinterpreted. Moreover, the complexity of the process of estimating R₀ has caused difficulties for a substantial number of researchers. In this article, in order to increase the accessibility of this concept, we address several misconceptions related to the threshold characteristics of R₀ and the effective reproduction number (R_t). Moreover, the appropriate interpretation of the metrics is discussed. R₀ should be considered as a population-averaged value that pools the contact structure according to a stochastic transmission process. Furthermore, it is necessary to understand the unavoidable time lag for R_t due to the incubation period of the disease.