Some sharp estimates for convex hypersurfaces of pinched normal curvature

For a convex domain $D$ bounded by the hypersurface $\partial D$ in a space of constant curvature we give sharp bounds on the width $R-r$ of a spherical shell with radii $R$ and $r$ that can enclose $\partial D$, provided that normal curvatures of $\partial D$ are pinched by two positive constants. Furthermore, in the Euclidean case we also present sharp estimates for the quotient $R/r$. From the obtained estimates we derive stability results for almost umbilical hypersurfaces in the constant curvature spaces.Comment: 2 figure

Atmospheric impacts on daytime urban heat island

Daytime urban heat island effects can be weak compared to night time and even reversed (as in the case of cool islands, where urban locations display lower temperatures than at a rural site), mostly due to shading effects from buildings, vegetation, and other possible obstructions. The study of the relationship between the sky-view factor, an indicator of urban geometry in terms of sky openness, and urban heat island intensity generally focus on night time periods; only a few report on the daytime effect of the SVF. Such effect will also vary according to background atmospheric conditions of the period of measurements. This article is a commentary on a recent publication by the authors on a study of diurnal intra-urban temperature differences in a location with Koeppen’s Cfb climate

Assessment of predicted versus measured thermal comfort and optimal comfort ranges in the outdoor environment in the temperate climate of Glasgow, UK

In a warming world, the risk of overheating is significant in temperate climate areas such as Glasgow, UK where adaptation to overheating is low. An easy-to-use thermal comfort evaluation is therefore a necessary first step towards developing effective coping mechanisms. In this study, we explore the effectiveness of Predicted Mean Vote, Predicted Percentage of Dissatisfied and Physiologically Equivalent Temperature, together with air temperature in mimicking actual thermal sensation votes of street users obtained in 2011 in Glasgow City Centre. The Predicted Mean Vote/Predicted Percentage of Dissatisfied indices developed for controlled indoors show a surprising similarity to actual thermal sensation votes derived from outdoor surveys, than the Physiologically Equivalent Temperature developed specifically for the outdoors. The method of calculation of mean radiant temperature is the key to improved performance of Physiologically Equivalent Temperature, with fish-eye lens photographs improving its performance. The results also show air temperature alone has nearly equal predictive power of the actual thermal sensation. A preliminary comfort range for Glasgow is also derived and its limitations are explored. Practical application: The strong relation between thermal sensation votes and air temperature (Ta) enables future thermal comfort studies to predict the thermal comfort using easy-to-access Ta only. A current thermal comfort study in Glasgow aiming at developing a link between urban morphology and Ta is already using this strong relation to predict outdoor thermal comfort in the city centre. This helps to establish a correlation between these three factors. </jats:p

Integrable and superintegrable systems with spin

A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of motion. The Pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first-order integral exists.Comment: 12 page

A sausage body is a unique solution for a reverse isoperimetric problem

We consider the class of $\lambda$-concave bodies in $\mathbb R^{n+1}$; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/\lambda$ that lies locally (around the boundary point) inside the body. In this class we solve a reverse isoperimetric problem: we show that the convex hull of two balls of radius $1/\lambda$ (a sausage body) is a unique volume minimizer among all $\lambda$-concave bodies of given surface area. This is in a surprising contrast to the standard isoperimetric problem for which, as it is well-known, the unique maximizer is a ball. We solve the reverse isoperimetric problem by proving a reverse quermassintegral inequality, the second main result of this paper.Comment: 1 figur

Elemental technetium as a cosmic-ray clock

Several radioactive isotopes have been proposed as clocks for the study of the mean cosmic ray confinement time, T sub e. Measurements of Be-10 and Al-26 give a value for T sub e of about 10 Myr when one uses a leaky box cosmic ray propagation model. It is important to obtain additional measurements of T sub e from other radioactive isotopes in order to check whether the confinement is the same throughout the periodic table. The possible use of Tc (Z = 43) as a cosmic clock is investigated. Since all isotopes of Tc are radioactive, one might be able to group these isotopes and use the elemental abundance as a whole. The results of the calculations are somewhat inconclusive for two reasons. First, the beta + decay half lives of two of the Tc isotopes relevant to our calculation are not known. Second, the dependence of the Tc abundance on the mean confinement time is rather weak when one considers the number of events expected in 4 trays of plastic track detectors. However, a future, finite measurement of the Beta + half lives and the possible use of the entire collecting area of the HNC to detect Tc nuclei could make the use of Tc as a cosmic ray clock more attractive

A Combinatorial classification of postcritically fixed Newton maps

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental ingredient is the proof that for every Newton map (postcritically finite or not) every connected component of the basin of an attracting fixed point can be connected to $\infty$ through a finite chain of such components.Comment: 37 pages, 5 figures, published in Ergodic Theory and Dynamical Systems (2018). This is the final author file before publication. Text overlap with earlier arxiv file observed by arxiv system relates to an earlier version that was erroneously uploaded separately. arXiv admin note: text overlap with arXiv:math/070117