Sharpness of the Korányi approach region

We prove a Littlewood-type theorem which shows the sharpness of the Korányi approach region for the boundary behavior of Poisson-Szegö integrals on the unit ball of . Our result is stronger than Hakim and Sibony (1983).

     

Fibred spaces and non-linear connections

Summary We give the fibre structure to the two complementary distributions, one being holomonic and the other being in general non-holomonic, by assigning the structure preserving transformations of the coordinates and of the frames. By the conversion from such fibred spaces we derive the spaces of non-linear connections as their image, in which we point out that the usual conditions imposed on C_kji and the covariant differentiation of g_ji in the metric spaces of non-linear connections can be interpreted respectively as the parallel and isometric conditions imposed on the fibre of the corresponding fibred Riemannian spaces. To Enrico Bompiani on his scientific Jubilee.     

Differential geometry on almost tangent manifolds

Summary We start from a tensor field Q of type (1, 1) defined in a2n-dimensional manifold M which satisfies Q ²⁼⁰ and has rank n. The tensor field Q defines an almost tangent structure in M. We then introduce another tensor field P of the same type and having properties similar to those of Q. We then define and study the tensors H=PQ, V=QP, J=P−Q, K=P+Q, L=PQ−QP, (J, K, L) defining an almost quaternion structure of the second kind on M. We study the differential geometry on almost tangent manifolds in terms of these tensors. To ProfessorBeniamino Segre on his seventieth birthday Entrata in Redazione il 7 giugno 1973.     

Fractal dimensions for diffusion-limited aggregation

A mean-field theory is proposed for fractal dimensions of diffusion-limited aggregates grown on a substrate surface of arbitrary dimensionality. The results are in good agreement with those of the computer simulations for all dimensionalities.     

Thermodynamic mixing properties of liquids in the system Na2O-SiO2

Enthalpies of fusion have been measured by differential scanning calorimetry for a Na₂O-SiO₂ system at 50, 66.6, and 74.4 mol% SiO₂. Enthalpies of mixing of liquids obtained from different calorimetry techniques are critically evaluated. The data on calorimetric enthalpy, activity of Na₂O, cristobalite liquidus, and immiscibility gap are used to determine the enthalpy and entropy of mixing of sodium-silicate liquids are determined as a function of composition by the least squares method. The derived mixing properties are based only on the experimental data and are independent of any assumption about the structure and chemical species in liquids. The enthalpy of mixing has a minimum value of −120 kJ/mol at 35-40 mol% SiO₂ and is convex upward around 80-90 mol% SiO₂. The entropy of mixing have a maximum value of + 6 J/K-mol at 75 mol% SiO₂, and it decreases with the SiO₂ content to −5 J/K-mol at 40 mol% SiO₂. This decrease in entropy can be accounted for by ideal mixing of Q⁴, Q³, and Q^{0 + 1 + 2} (= Q⁰ + Q¹ + Q²) species in the liquids and is responsible for the negative temperature dependence of the partial molar Gibbs energy of mixing of Na₂O, observed in activity measurements. Comparison of the present results with previous values suggests that a quasi-chemical model and the Adam-Gibbs model overestimate the configurational entropy of mixing of liquids.     

Complexability of o-bisguanidinobenzenes with arsenic and phosphoric acids in solution and solid states, and the potential use of their immobilized derivatives as solid base ligands for metal salts and arsenic acid

The role of o-bisguanidinobenzenes (BGBs) as new Brønsted base ligands for arsenic and phosphoric acids was examined. In solution state, complexation was evaluated by Job’s plot in ¹H NMR experiment, indicating a 1:1 complex formation, whereas in solid state crystalline structures of complexes obtained were addressed by X-ray crystallographic analysis and/or solid state ¹³C NMR experiment, in which 1:2 complexes between the BGB and the acid components were normally formed. Based on these results, Merrifield and Hypogel^® resin-anchored BGBs were designed and prepared as the corresponding polymer-supported host ligands. Evaluation of their coordination ability with metal salts (ZnCl₂ and CoCl₂) and arsenic acid in aqueous media by ICP-MS showed that the latter Hypogel^® resin-anchored BGBs acted as effective immobilized base ligands.     

Interferometers for displacement-noise-free gravitational-wave detection

We propose a class of displacement- and laser-noise-free gravitational-wave-interferometer configurations, which does not sense nongeodesic mirror motion and laser noise, but provides a nonvanishing gravitational-wave signal. Our interferometers consist of four mirrors and two beam splitters, which form four Mach-Zehnder interferometers. By contrast to previous works, no composite mirrors with multiple reflective surfaces are required. Each mirror in our configuration is sensed redundantly, by at least two pairs of incident and reflected beams. Displacement- and laser-noise-free detection is achieved when output signals from these four interferometers are combined appropriately. Our 3-dimensional interferometer configuration has a low-frequency response proportional to f2, which is better than the f3 achievable by previous 2-dimensional configurations.     

Tripodal oxazoline-based homochiral coordination cages with internal binding sites

Homochiral coordination cages, which have two well-defined internal binding sites for ammonium and organoammonium ions, have been constructed by Pd(II)-mediated self-assembly of preorganized tripodal oxazolines containing pyridine pendant groups.     

A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea

During respiration, particles suspended in the air are inhaled and unless cleared by airway defences they can remain and affect lung health. Their size precludes the use of standard imaging modalities so we have developed synchrotron phase-contrast X-ray imaging (PCXI) methods to non-invasively monitor the behaviour of individual particles in live mouse airways. In this study we used these techniques to examine post-deposition particle behaviour in the trachea. PCXI was used to monitor the deposition and subsequent behaviour of particles of quarry dust and lead ore; fibres of asbestos and fibreglass; and hollow glass micro-spheres. Visibility was examined in vitro and ex vivo to avoid the complicating effects of surrounding tissue and respiratory or cardiac motion. Particle behaviour was then examined after deposition onto the tracheal airway surfaces of live mice. Each particle and fibre looked and behaved differently on the airway surface. Particles lodged on the airway shortly after deposition, and the rate at which this occurred was dependent on the particle type and size. After the live-imaging experiments, excised airway samples were examined using light and electron microscopy. Evidence of particle capture into the airway surface fluids and the epithelial cell layer was found. PCXI is a valuable tool for examining post-deposition particulate behaviour in the tracheal airway. These first indications that the interaction between airways and individual particles may depend on the particle type and size should provide a novel approach to studying the early effects of respired particles on airway health.     

Maximization of the total population in a reaction–diffusion model with logistic growth

This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the effect of spatial heterogeneity on the total population of a biological species at a steady state, using a reaction–diffusion logistic model. Our objective is to maximize the total population when resources are distributed in the habitat to control the intrinsic growth rate, but the total amount of resources is limited. It is shown that under some conditions, any local maximizer must be of “bang–bang” type, which gives a partial answer to the conjecture addressed by Ding et al. (Nonlinear Anal Real World Appl 11(2):688–704, 2010). To this purpose, we compute the first and second variations of the total population. When the growth rate is not of bang–bang type, it is shown in some cases that the first variation becomes nonzero and hence the resource distribution is not a local maximizer. When the first variation becomes zero, we prove that the second variation is positive. These results implies that the bang–bang property is essential for the maximization of total population.