Growth rates of bacteria in rivers

Three different methods for determining bacterial growth rate in rivers are described. Two of the methods are for bacteria in suspension: a recirculating experimental channel method and a radioactive tracer technique using super(35)SO sub(4). The third method is for bacteria attached to surfaces and specifically considers the surface of the common duckweed Lemna minor)

Growth rates for persistently excited linear systems

We consider a family of linear control systems $\dot{x}=Ax+\alpha Bu$ where $\alpha$ belongs to a given class of persistently exciting signals. We seek maximal $\alpha$-uniform stabilisation and destabilisation by means of linear feedbacks $u=Kx$. We extend previous results obtained for bidimensional single-input linear control systems to the general case as follows: if the pair $(A,B)$ verifies a certain Lie bracket generating condition, then the maximal rate of convergence of $(A,B)$ is equal to the maximal rate of divergence of $(-A,-B)$. We also provide more precise results in the general single-input case, where the above result is obtained under the sole assumption of controllability of the pair $(A,B)$

Growth rates for subclasses of Av(321)

Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates

Knowledge Spillovers and TFP Growth Rates

In this paper I calibrate unobserved labor-generated knowledge spillovers within and between six large macroeconomic sectors covering the U.S. civilian economy from 1948 to 1991. Using quality-adjusted data I show that manufacturing and trade & transportation are the main source of knowledge flows to the overall economy for the entire period. However, the productivity slowdown of the early seventies coincides with trade & transportation taking over manufacturing as the main source and destination of post-73 knowledge flows. Furthermore, I compute the gap between the market and the optimal allocation of labor across sectors, and the wedge between market and optimal wages by sector. I find that, for the whole period, optimal employment in manufacturing and trade & transportation is, respectively, 20% and 27% above market. As a result optimal output in these sectors is 12% and 16% higher than the market’s, and optimal wages in manufacturing are 54% above market wages.Knowledge spillovers; productivity; human capital; learning; wages.

Subdegree growth rates of infinite primitive permutation groups

A transitive group $G$ of permutations of a set $\Omega$ is primitive if the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. If $\alpha \in \Omega$, then the orbits of the stabiliser $G_\alpha$ on $\Omega$ are called the $\alpha$-suborbits of $G$; when $G$ acts transitively the cardinalities of these $\alpha$-suborbits are the subdegrees of $G$. If $G$ acts primitively on an infinite set $\Omega$, and all the suborbits of $G$ are finite, Adeleke and Neumann asked if, after enumerating the subdegrees of $G$ as a non-decreasing sequence $1 = m_0 \leq m_1 \leq ...$, the subdegree growth rates of infinite primitive groups that act distance-transitively on locally finite distance-transitive graphs are extremal, and conjecture there might exist a number $c$ which perhaps depends upon $G$, perhaps only on $m$, such that $m_r \leq c(m-2)^{r-1}$. In this paper it is shown that such an enumeration is not desirable, as there exist infinite primitive permutation groups possessing no infinite subdegree, in which two distinct subdegrees are each equal to the cardinality of infinitely many suborbits. The examples used to show this provide several novel methods for constructing infinite primitive graphs. A revised enumeration method is then proposed, and it is shown that, under this, Adeleke and Neumann's question may be answered, at least for groups exhibiting suitable rates of growth.Comment: 41 page

Growth rates of permutation classes: categorization up to the uncountability threshold

In the antecedent paper to this it was established that there is an algebraic number $\xi\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $\xi$, there are only countably many less than $\xi$. Here we provide a complete characterization of the growth rates less than $\xi$. In particular, this classification establishes that $\xi$ is the least accumulation point from above of growth rates and that all growth rates less than or equal to $\xi$ are achieved by finitely based classes. A significant part of this classification is achieved via a reconstruction result for sum indecomposable permutations. We conclude by refuting a suggestion of Klazar, showing that $\xi$ is an accumulation point from above of growth rates of finitely based permutation classes.Comment: To appear in Israel J. Mat