## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
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JMD

In this note, we consider the orbits $\{pu(n^{1+\gamma})|n\in\mathbb N\}$ in $\Gamma\backslash\text{PSL}(2,\mathbb R)$, where $\Gamma$ is a non-uniform lattice in $\text{PSL}(2,\mathbb R)$ and $\{u(t)\}$ is the standard unipotent one-parameter subgroup in $\text{PSL}(2,\mathbb R)$. Under a Diophantine condition on~the initial point $p$, we can prove that the trajectory $\{pu(n^{1+\gamma})|n\in\mathbb N\}$ is equidistributed in $\Gamma\backslash\text{PSL}(2,\mathbb R)$ for small $\gamma>0$, which generalizes a result of Venkatesh [22].

DCDS-B

To mimic the striking capability of microbial culture for growth
adaptation after the onset of the novel environmental conditions, a
modified heterogeneous microbial population model in the chemostat
with essential resources is proposed which considers adaptation by
spontaneously phenotype-switching between normally growing cells and
persister cells having reduced growth rate. A basic reproductive
number $R_0$ is introduced so that the population dies out when
$R_0<1$, and when $R_0>1$ the population will be asymptotic to a
steady state of persister cells, or a steady state of only normal
cells, or a steady state corresponding to a heterogeneous population
of both normal and persister cells. Our analysis confirms that
inherent heterogeneity of bacterial populations is important in
adaption to fluctuating environments and in the persistence of
bacterial infections.

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