Normalizers of Primitive Permutation Groups

Let $G$ be a transitive normal subgroup of a permutation group $A$ of finite degree $n$. The factor group $A/G$ can be considered as a certain Galois group and one would like to bound its size. One of the results of the paper is that $|A/G| < n$ if $G$ is primitive unless $n = 3^{4}$, $5^4$, $3^8$, $5^8$, or $3^{16}$. This bound is sharp when $n$ is prime. In fact, when $G$ is primitive, $|\mathrm{Out}(G)| < n$ unless $G$ is a member of a given infinite sequence of primitive groups and $n$ is different from the previously listed integers. Many other results of this flavor are established not only for permutation groups but also for linear groups and Galois groups.Comment: 44 pages, grant numbers updated, referee's comments include

Congruence modularity implies cyclic terms for finite algebras

An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar

inTrack: High Precision Tracking of Mobile Sensor Nodes

Radio-interferometric ranging is a novel technique that allows for fine-grained node localization in networks of inexpensive COTS nodes. In this paper, we show that the approach can also be applied to precision tracking of mobile sensor nodes. We introduce inTrack, a cooperative tracking system based on radio-interferometry that features high accuracy, long range and low-power operation. The system utilizes a set of nodes placed at known locations to track a mobile sensor. We analyze how target speed and measurement errors affect the accuracy of the computed locations. To demonstrate the feasibility of our approach, we describe our prototype implementation using Berkeley motes. We evaluate the system using data from both simulations and field tests

A note on the probability of generating alternating or symmetric groups

We improve on recent estimates for the probability of generating the alternating and symmetric groups $\mathrm{Alt}(n)$ and $\mathrm{Sym}(n)$. In particular we find the sharp lower bound, if the probability is given by a quadratic in $n^{-1}$. This leads to improved bounds on the largest number $h(\mathrm{Alt}(n))$ such that a direct product of $h(\mathrm{Alt}(n))$ copies of $\mathrm{Alt}(n)$ can be generated by two elements

Modeling and Simulating a Novel Biohydrogen Production Technology as an Integrated Part of a Municipal Wastewater Treatment Plant

A series of mathematical models and simulations was developed and performed using BioWin software suit in order to determine the suitability of implementing a biohydrogen production technology in an existing wastewater treatment plant. The evaluation of the performance of these approach was based on biohydrogen yield and effluent quality. The simulations show high biohydrogen production rates, with picks during the summer months, while most of the effluent environmental parameters remain at the same or even lower levels compared with the currently used technology