Maximal Strings in the Crystal Graph of Spin Representations of the Symmetric and Alternating Groups

We define a block-reduced version of the crystal graph of spin representations of the symmetric and alternating groups, and separate it into layers, each obtained by translating the previous layer and, possibly, adding new defect zero blocks. We demonstrate that each layer has weight-preserving central symmetry, and study the sequence of weights occurring in the maximal strings.

The Broué conjecture, that a block with abelian defect group is derived equivalent to its Brauer correspondent, has been proven for blocks of cyclic defect group and verified for many other blocks. This article is part of a study of the spin block case.     

Optimizing data-acquisition schedules in physicochemical experiments : Part 1. Principle of the Method and Application to the Firt-Order Decay of an Absorbing Species

In designing an experiment aimed at the evaluation of one or more of the physicochemical parameters that characterize the behaviour of the system being studied, it is advantageous to choose the data-acquisition schedule that will maximize the precision of the desired result. Practical definitions of a precision index (for a single parameter) and an overall precision index (for the simultaneous estimation of two or more parameters) are offered, and a method is described for optimizing either. When the method is applied to synthetic data the represent the first-order decay of an absorbing species, it yields results considerably superior to those obtained from other data-acquisition schedules.     

The beta stochastic utility (β-SU)

In this article, a new model for decision making under uncertainty is presented. Here, we model human attitude toward risks to show that an individual estimate of the expected utility of a lottery follows a generalized Beta distribution with a random error that follows a similar distribution. An individual is said to maximize his stochastic utility when requested to present his preference between risky lotteries. Hypothetically, risky lotteries are those exhibiting wider ranges of rewards where human estimate will not be below the utility of the lowest reward nor above the highest of the lottery. The Beta distribution is bounded and complies to such intuitive preconditions with a variance depending on such bounds. The proposed model will overestimate/underestimate the expected utility of a lottery according to the lottery probability mass and individuals' risk attitudes. By such estimation, our model conforms to the fourfold choice pattern. The model also explains the violations present as inconsistencies in the expected utility theory, such as Allais paradox, common consequence effect, common ratio effect, and the violation of betweenness that can be found in the fourfold choice pattern. For the validation purposes, 13 datasets from literature were collected and tested. The β-SU model fits the data at least as good as other approaches such as the CPT/StEUT and presents higher prediction log-likelihoods and less sum of squared errors in most of the cases, a matter that supports the proposition that human estimates of the expected utility may be drawn out of a generalized Beta distribution.     

Photodegradation of Decabromo Diphenyl Ether Flame Retardant in Poly (Acrylonitrile Butadiene Styrene) (ABS)

Abstract

Decabromodiphenylether (DBDE) is a brominated flame retardant which belongs to the group of polybromodiphenylethers (PBDEs) often used as a fire resistant additive in various well known polymeric systems like polystyrene, poly(acrylonitrile-butadiene-styrene) (ABS), polypropylene, etc. This compound can be considered as a persistent organic pollutant and presents certain risks for the environment owing to the fact that it is bioaccumulable and not biodegradable. A detailed investigation, described here, was carried out on the effect of ultraviolet/visible radiation on DBDE in ABS with the aim to study the photolytic reactions of this molecule in the solid state, in order to improve the economic and ecological treatment of brominated plastic waste from waste electrical and electronic equipment (WEEE). This study presents new aspects of the photochemical degradation of DBDE/ABS systems in the solid state. The photodegradation of DBDE in ABS was followed by Fourier transform infrared spectroscopy (FTIR) as well as by thermogravimetrical analysis (TGA). Good agreement was obtained for the results of both analytical methods in terms of the overall photolysis of DBDE.     

Potential well escape in a galloping twin-well oscillator

Nonlinear Dynamics - When a bi-stable oscillator undergoes a supercritical Hopf bifurcation due to a galloping instability, intra-well limit cycle oscillations of small amplitude are born. The...     

Elemental analysis in solutions by radioisotope excited X-ray fluorescence

The problem of spectrochemical analysis of elements in solutions has been investigated for a number of elements across the periodic table using radioisotope-induced energy dispersive X-ray fluorescence method. In this study a low intensity¹⁰⁹Cd X-ray source was used for characteristic X-ray excitation. Experimental parameters such as saturation thickness and critical thickness have been studied to evaluate their role in this method. Minimum detection limits, sensitivities and the nature of concentration calibration at critical thickness have been obtained as a function of Z to find the limits of the method. Results obtained have been discussed in the light of theories and potential areas of applicability of the method have been indicated.     

Oxidation and reactivity of nitrogen- and phosphorus-doped heterofullerenes

Density functional theory (DFT) calculations suggest significantly different oxidation behaviour for phosphorus-doped heterofullerenes compared to their pure and nitrogen-doped counterparts, due to formation of a phosphene oxide. This oxide is not thermally labile, suggesting stable phosphofullerenes are likely to be C(59)POH and (C(59)PO)(2). In contrast, azafullerenes form stable epoxides when oxidised. We calculate the effect of oxidation on radical pairing and hydrogen passivation. Notably while the C(59)N radical behaves as a donor, C(59)PO will be an acceptor.