• Journal of the Korean Data and Information Science Society
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• 제7권2호
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• pp.273-281
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• 1996

It is derived that conditions of counting process ($\{N(t){\mid}t\;{\geq}\;0\}$) in which the number of events in time interval [0, t] has a (n, n+1)-generalized Poisson distribution with parameters (${\theta}t,\;{\lambda}$) and a generalized inflated Poisson distribution with parameters (${\{\lambda}t,\;{\omega}\}$.

• 대한수학회지
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• 제59권1호
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• pp.129-150
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• 2022

Let L = -∆ + V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator P^L_t,σ, 0 < σ < 1, associated with L. We estimate the gradient and the time-fractional derivatives of the kernel of P^L_t,σ, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space 𝒞^𝛄_L (ℝⁿ) via P^L_t,σ.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.91-121
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• 2014

Let X and Y be vector spaces. It is shown that a mapping $f:X{\rightarrow}Y$ satisfies the functional equation ${\ddag}$ $$2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^jx_j}{2d})-2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^{j+1}x_j}{2d})=2\sum_{j=2}^{2d}(-1)^jf(x_j)$$ if and only if the mapping $f:X{\rightarrow}Y$ is additive, and prove the Cauchy-Rassias stability of the functional equation (${\ddag}$) in Banach modules over a unital $C^*$-algebra, and in Poisson Banach modules over a unital Poisson $C^*$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras. As an application, we show that every almost homomorphism $h:\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h(d^nuy)=h(d^nu)h(y)$ or $h(d^nu{\circ}y)=h(d^nu){\circ}h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and n = 0, 1, 2, ${\cdots}$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras, and of Lie $JC^*$-algebra derivations in Lie $JC^*$-algebras.

• Journal of Preventive Medicine and Public Health
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• 제57권2호
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• pp.108-119
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• 2024

Objectives: Abrupt changes in air pollution levels associated with the coronavirus disease 2019 (COVID-19) outbreak present a unique opportunity to evaluate the effects of air pollution on influenza risk, at a time when emission sources were less active and personal hygiene practices were more rigorous. Methods: This time-series study examined the relationship between influenza cases (n=22 874) and air pollutant concentrations from 2018 to 2021, comparing the timeframes before and during the COVID-19 pandemic in and around Thailand's Khon Kaen province. Poisson generalized additive modeling was employed to estimate the relative risk of hospitalization for influenza associated with air pollutant levels. Results: Before the COVID-19 outbreak, both the average daily number of influenza hospitalizations and particulate matter with an aerodynamic diameter of 2.5 ㎛ or less (PM_2.5) concentration exceeded those later observed during the pandemic (p<0.001). In single-pollutant models, a 10 ㎍/m³ increase in PM_2.5 before COVID-19 was significantly associated with increased influenza risk upon exposure to cumulative-day lags, specifically lags 0-5 and 0-6 (p<0.01). After adjustment for co-pollutants, PM_2.5 demonstrated the strongest effects at lags 0 and 4, with elevated risk found across all cumulative-day lags (0-1, 0-2, 0-3, 0-4, 0-5, and 0-6) and significantly greater risk in the winter and summer at lag 0-5 (p<0.01). However, the PM_2.5 level was not significantly associated with influenza risk during the COVID-19 outbreak. Conclusions: Lockdown measures implemented during the COVID-19 pandemic could mitigate the risk of PM_2.5-induced influenza. Effective regulatory actions in the context of COVID-19 may decrease PM_2.5 emissions and improve hygiene practices, thereby reducing influenza hospitalizations.