Uniform growth rate

In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of the original object. We apply this principle to find a uniform upper bound for the growth rate of certain groups including the mapping class group. We also find a uniform upper bound for the growth rate of the number of homotopy classes of triangulations of an oriented surface that can be obtained from a given triangulation using $m$ diagonal flips.Comment: 13 pages, 5 figures, minor revisions, final version appears in Proc. Amer. Math. So

Growth And Survival Rate Of Western White Prawns (Litopaneaus Vannamei) On Different Salinity

The research was conducted for 30 days from 23 March to 22 April 2015 which was held at the Great Hall Brackishwater Aquaculture Development Jepara, Central Java Province. The aim of this research to determine the different salinity for growth and survival rate of Western white prawns (Litopenaeus vannamei). The method used is the experimental method with completely randomized design (CRD) of the factor with 3 levels a treatment. The treatment was applied, namely P1 of salinity 15 ppt, P2 of salinity 20 ppt, P3 of salinity 25 pptThe best result showed that salinity 15 ppt. Total absolute body weight, absolute body length, daily growth rate and survival rate was 2.09 grams, 6.60 cm, 0.07 grams/day and 94.7 % respectively. Water quality parameters were recorded namely a temperature is 29.1-31.6 oC, pH 7.9-8.1 and dissolved oxygen 3.84- 4.97 ppm

On growth rate and contact homology

It is a conjecture of Colin and Honda that the number of Reeb periodic orbits of universally tight contact structures on hyperbolic manifolds grows exponentially with the period, and they speculate further that the growth rate of contact homology is polynomial on non-hyperbolic geometries. Along the line of the conjecture, for manifolds with a hyperbolic component that fibers on the circle, we prove that there are infinitely many non-isomorphic contact structures for which the number of Reeb periodic orbits of any non-degenerate Reeb vector field grows exponentially. Our result hinges on the exponential growth of contact homology which we derive as well. We also compute contact homology in some non-hyperbolic cases that exhibit polynomial growth, namely those of universally tight contact structures non-transverse to the fibers on a circle bundle

Growth rate for beta-expansions

Let $\beta>1$ and let m>\be be an integer. Each x\in I_\be:=[0,\frac{m-1}{\beta-1}] can be represented in the form $$x=\sum_{k=1}^\infty \epsilon_k\beta^{-k},$$ where $\epsilon_k\in\{0,1,...,m-1\}$ for all $k$ (a $\beta$-expansion of $x$). It is known that a.e. $x\in I_\beta$ has a continuum of distinct $\beta$-expansions. In this paper we prove that if $\beta$ is a Pisot number, then for a.e. $x$ this continuum has one and the same growth rate. We also link this rate to the Lebesgue-generic local dimension for the Bernoulli convolution parametrized by $\beta$. When $\beta<\frac{1+\sqrt5}2$, we show that the set of $\beta$-expansions grows exponentially for every internal $x$.Comment: 21 pages, 2 figure

Mach Stem Height and Growth Rate Predictions

A new, more accurate prediction of Mach stem height in steady flow is presented. In addition, starting with a regular reflection in the dual-solution domain, the growth rate of the Mach stem from the time it is first formed till it reaches its steady-state height is presented. Comparisons between theory, experiments, and computations are presented for the Mach stem height. The theory for the Mach stem growth rate in both two and three dimensions is compared to computational results. The Mach stem growth theory provides an explanation for why, once formed, a Mach stem is relatively persistent