We prove that any finitely generated solvable group of zero entropy contains a nilpotent subgroup of finite index. In particular, any finitely generated solvable group of exponential growth is of uniformly exponential growth.

The quantitative characterization of bacterial growth has attracted substantial research attention since Monod’s pioneering study. Theoretical and experimental work have uncovered several laws for describing the exponential growth phase, in which the number of cells grows exponentially. However, microorganism growth also exhibits lag, stationary, and death phases under starvation conditions, in...

We assessed parameters of advanced diffusion weighted imaging (DWI) models for the prediction of the tumor growth rate in 55 head and neck squamous cell carcinoma (HNSCC) patients. The DWI acquisition used single-shot spin-echo echo-planar imaging with 12 b-values (0-2000). We calculated 14 DWI parameters using mono-exponential, bi-exponential, tri-exponential, stretched exponential and diffusi...

Maximizing cell growth rate and cell yield are among the most important features of a successful mammalian cell culture production process. To minimize time and resources needed to scale up cell mass it is important to maintain the cultures in exponential growth at every scale. Here we report results comparing viable cell counts, packed cell volume, intracellular nucleotide ratios, cell cycle a...

Stable ductile crack growth in 3 mm thick AISI 304 stainless steel specimens has been investigated experimentally and numerically. Multi-linear Isotropic Hardening method coupled with the Von-Mises yield criterion was adopted for modeling elasto-plastic behavior of the material. Mode-I CT fracture specimens have been tested to generate experimental load-displacement-crack growth data during sta...

Earth's capacity to support people is determined both by natural constraints and by human choices concerning economics, environment, culture (including values and politics), and demography. Human carrying capacity is therefore dynamic and uncertain. Human choice is not captured by ecological notions of carrying capacity that are appropriate for nonhuman populations. Simple mathematical models o...