Symmetric Presentations of Coxeter Groups

We apply the techniques of symmetric generation to establish the standard presentations of the finite simply laced irreducible finite Coxeter groups, that is the Coxeter groups of types An, Dn and En, and show that these are naturally arrived at purely through consideration of certain natural actions of symmetric groups. We go on to use these techniques to provide explicit representations of these groups.Comment: This is the predecessor of arXiv:0901.2660v1. To appear in the Proceedings of the Edinburgh Mathematical Societ

Are Income Tax Breaks for Seniors Good for State Economic Growth?

In this brief, authors Ben Brewer, Karen Conway, and Jon Rork discuss the findings of their recently published study that investigates, directly, the impact on state economic growth of expanding income tax breaks for seniors. All state income tax systems contain provisions that reduce the state income tax burden for elderly households, and most modest-income elderly households owe little in state income taxes. Each year state legislatures consider expansions to these tax provisions, which tend to benefit primarily upper-income elderly households, with advocates suggesting such changes will be “good” for the state, in part by retaining and attracting elderly residents. Reducing the tax burden for higher-income groups—including the elderly—spurs state economic growth much less than reducing the tax burden for lower-income households. To provide economic relief to low-income elderly households, states would need to enact income-based refundable tax credits similar to the Earned Income Tax Credit available to low-income working households. The authors’ study suggests that expanding such tax credits would likely be more beneficial for economic growth

Weak Disorder in Fibonacci Sequences

We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1-epsilon, but follow a different recursion rule with a small probability epsilon. We focus on the weak disorder limit and obtain the Lyapunov exponent, that characterizes the typical growth of the sequence elements, using perturbation theory. The limiting distribution for the ratio of consecutive sequence elements is obtained as well. A number of variations to the basic Fibonacci recursion including shift, doubling, and copying are considered.Comment: 4 pages, 2 figure

Random Geometric Series

Integer sequences where each element is determined by a previous randomly chosen element are investigated analytically. In particular, the random geometric series x_n=2x_p with 0<=p<=n-1 is studied. At large n, the moments grow algebraically, n^beta(s) with beta(s)=2^s-1, while the typical behavior is x_n n^ln 2. The probability distribution is obtained explicitly in terms of the Stirling numbers of the first kind and it approaches a log-normal distribution asymptotically.Comment: 6 pages, 2 figure

Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR

Potassium-mediated zincation of ferrocene and ruthenocene : potassium, the architect behind supramolecular structural variations

Direct zincation of ferrocene and ruthenocene by the synergic base [PMDETA.K(μ-TMP)(μ-Me)Zn(Me)] produces the monozincated complexes [{PMDETA.K(μ-Me)2Zn(Fc)}∞] and [{PMDETA.K(μ-Me)2Zn(Rc)}2] respectively, having similar monomeric (dinuclear) units but aggregating supramolecularly in very different polymeric and dimeric forms

LCOGT Network Observatory Operations

We describe the operational capabilities of the Las Cumbres Observatory Global Telescope Network. We summarize our hardware and software for maintaining and monitoring network health. We focus on methodologies to utilize the automated system to monitor availability of sites, instruments and telescopes, to monitor performance, permit automatic recovery, and provide automatic error reporting. The same jTCS control system is used on telescopes of apertures 0.4m, 0.8m, 1m and 2m, and for multiple instruments on each. We describe our network operational model, including workloads, and illustrate our current tools, and operational performance indicators, including telemetry and metrics reporting from on-site reductions. The system was conceived and designed to establish effective, reliable autonomous operations, with automatic monitoring and recovery - minimizing human intervention while maintaining quality. We illustrate how far we have been able to achieve that.Comment: 13 pages, 9 figure

Growth and Structure of Stochastic Sequences

We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences leads to a wide variety of behaviors ranging from stretched exponential to log-normal to algebraic growth. Interestingly, the set of all possible sequence values has an intricate structure.Comment: 4 pages, 4 figure