On critical cardinalities related to QQ-sets

In this note we collect some known information and prove new results about the small uncountable cardinal $\mathfrak q_0$. The cardinal $\mathfrak q_0$ is defined as the smallest cardinality $|A|$ of a subset $A\subset \mathbb R$ which is not a $Q$-set (a subspace $A\subset\mathbb R$ is called a $Q$-set if each subset $B\subset A$ is of type $F_\sigma$ in $A$). We present a simple proof of a folklore fact that $\mathfrak p\le\mathfrak q_0\le\min\{\mathfrak b,\mathrm{non}(\mathcal N),\log(\mathfrak c^+)\}$, and also establish the consistency of a number of strict inequalities between the cardinal $\mathfrak q_0$ and other standard small uncountable cardinals. This is done by combining some known forcing results. A new result of the paper is the consistency of $\mathfrak{p} < \mathfrak{lr} < \mathfrak{q}_0$, where $\mathfrak{lr}$ denotes the linear refinement number. Another new result is the upper bound $\mathfrak q_0\le\mathrm{non}(\mathcal I)$ holding for any $\mathfrak q_0$-flexible cccc $\sigma$-ideal $\mathcal I$ on $\mathbb R$.Comment: 8 page

Species traits and the form of individual species–energy relationships

Environmental energy availability explains much of the spatial variation in species richness at regional scales. While numerous mechanisms that may drive such total species–energy relationships have been identified, knowledge of their relative contributions is scant. Here, we adopt a novel approach to identify these drivers that exploits the composite nature of species richness, i.e. its summation from individual species distributions. We construct individual species–energy relationships (ISERs) for each species in the British breeding avifauna using both solar (temperature) and productive energy metrics (normalized difference vegetation index) as measures of environmental energy availability. We use the slopes of these relationships and the resultant change in deviance, relative to a null model, as measures of their strength and use them as response variables in multiple regressions that use ecological traits as predictors. The commonest species exhibit the strongest ISERs, which is counter to the prediction derived from the more individuals hypothesis. There is no evidence that predatory species have stronger ISERs, which is incompatible with the suggestion that high levels of energy availability increase the length of the food chain allowing larger numbers of predators to exist. We find some evidence that species with narrow niche breadths have stronger ISERs, thus providing one of the few pieces of supportive evidence that high-energy availability promotes species richness by increasing the occurrence of specialist species that use a narrow range of resources

Effects of Changes in Surface Water Regime and/or Land Use on the Vertical Distribution of Water Available for Wetland Vegetation: Dynamic Model of the Zone of Aeration (Appendix to Part 1 of Completion Report for Project A-023-ARK)

Appendix to Part 1 of Completion Report for Project A-023-AR

Quantum chaos in nanoelectromechanical systems

We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems (NEMS) and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate's surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian Orthogonal Ensemble (GOE) or the Gaussian Unitary Ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.Comment: 14 pages, two column

Computer Aided Aroma Design. II. Quantitative structure-odour relationship

Computer Aided Aroma Design (CAAD) is likely to become a hot issue as the REACH EC document targets many aroma compounds to require substitution. The two crucial steps in CAMD are the generation of candidate molecules and the estimation of properties, which can be difficult when complex molecular structures like odours are sought and their odour quality are definitely subjective or their odour intensity are partly subjective as stated in Rossitier’s review (1996). The CAAD methodology and a novel molecular framework were presented in part I. Part II focuses on a classification methodology to characterize the odour quality of molecules based on Structure – Odour Relation (SOR). Using 2D and 3D molecular descriptors, Linear Discriminant Analysis (LDA) and Artificial Neural Network are compared in favour of LDA. The classification into balsamic / non balsamic quality was satisfactorily solved. The classification among five sub notes of the balsamic quality was less successful, partly due to the selection of the Aldrich’s Catalog as the reference classification. For the second case, it is shown that the sweet sub note considered in Aldrich’s Catalog is not a relevant sub note, confirming the alternative and popular classification of Jaubert et al., (1995), the field of odours

Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory

The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green's functions involving the temporal component of the gauge field without approximation, given appropriate input.Comment: 20 pages, no figure