Search results
Results from the WOW.Com Content Network
for some , < we say that G has a polynomial growth rate. The infimum k 0 {\displaystyle k_{0}} of such k' s is called the order of polynomial growth . According to Gromov's theorem , a group of polynomial growth is a virtually nilpotent group , i.e. it has a nilpotent subgroup of finite index .
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. [1] More precisely, the reciprocal function 1 / x {\displaystyle 1/x} has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x → 0 {\displaystyle x\to 0} is infinite: any ...
The growth rate of a group is a well-defined notion from asymptotic analysis. To say that a finitely generated group has polynomial growth means the number of elements of length at most n (relative to a symmetric generating set) is bounded above by a polynomial function p(n). The order of growth is then the least degree of any such polynomial ...
Figure 1: A bi-phasic bacterial growth curve.. A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size or biomass (in population ecology and demography, for population growth analysis), individual body height or biomass (in physiology, for growth analysis of individuals).
Moreover, the function makes use of initial growth rate, which is commonly seen in populations of bacterial and cancer cells, which undergo the log phase and grow rapidly in numbers. Despite its popularity, the function initial rate of tumor growth is difficult to predetermine given the varying microcosms present with a patient, or varying ...
Many pairs (b, τ) of a dimensionless non-negative number b and an amount of time τ (a physical quantity which can be expressed as the product of a number of units and a unit of time) represent the same growth rate, with τ proportional to log b. For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ.
Economic growth, the increase in value of the goods and services produced by an economy; Compound annual growth rate or CAGR, a measure of financial growth; Population growth rate, change in population over time; Growth rate (group theory), a property of a group in group theory
As resources become more limited, the growth rate tapers off, and eventually, once growth rates are at the carrying capacity of the environment, the population size will taper off. [6] This S-shaped curve observed in logistic growth is a more accurate model than exponential growth for observing real-life population growth of organisms. [8]