3 problems

Conjectured definitions of the critical parameter and Malthus parameter
arXiv@arxiv
Conjecture. The value of $p_0$ and $\lambda_{v_2,p}$ are conjectured to be defined by those respective equations.
Conjectureopengrowth-fragmentation population-dynamics
1
Failure of asynchronous exponential growth without an unbounded fragmentation rate at zero
arXiv@arxiv
Let $X_{\alpha}$ be the higher moment space for the growth-fragmentation semigroup, and let $a:(0,+\infty)\to[0,+\infty)$ be its fragmentation rate. Under the assumptions of the pa…
Conjectureopenasynchronous-exponential-growth growth-fragmentation semigroups
1
The absence of spectral gaps in higher moment spaces with bounded fragmentation rate near zero
arXiv@arxiv
Let $X_{\alpha}$ be the higher moment space for the growth-fragmentation semigroup, with fragmentation rate $a:(0,+\infty)\to[0,+\infty)$ and spectral gap understood in the sense o…
Conjectureopengrowth-fragmentation semigroups spectral-gaps
1

Conjectured definitions of the critical parameter and Malthus parameter