Barbilian spaces: The history of a geometric idea

Barbilian spaces are metric spaces with a metric induced by a special procedure of metrization that is inspired by the study of the models of non-Euclidean geometry. In this note we discuss the history of Barbilian spaces and the evolution of the theory. We point out that some of the current references to work done in Barbilian spaces refer to Barbilian's contribution from 1934, while his construction has been greatly extended in four works published in Romanian in 1959–1962.     

Investigation of the stability of a natural circulation two-pass boiler

In this paper, the results of a theoretical analysis of the static flow instability, namely the reverse flow, for a two-pass steam generator (see Fig. 1) will be presented. The aim of the work was the development of design criteria to avoid the reversal of flow. To determine the critical heat absorption ratio between the two riser systems of a two-pass boiler several dynamic simulations of a warm start-up of the two-pass boiler with different heat absorption ratios, different heat profiles along the lower heated riser system 1 and modified geometry of the boiler (influence of the flow resistance) are done. On the basis of the results of this investigations it can be shown that for every natural circulation system with unequally heated risers and a common downcomer a special critical heat absorption ratio exists. The investigations clearly indicate that such types of steam generators should be designed only in that way that the operation below the critical heat absorption ratio is possible. The modification of the flow resistance in the riser systems can help to extend the range of stable operation.     

Efficient white light emission by upconversion in Yb(3+)-, Er(3+)- and Tm(3+)-doped Y2BaZnO5

We report efficient white upconversion luminescence in Yb(3+)-, Er(3+)- and Tm(3+)-doped monophasic and biphasic Y(2)BaZnO(5) phosphors under 977 nm near-infrared excitation and at low excitation power densities (down to ～25 mW mm(-2)).     

Nonlinear interferometric vibrational imaging for fast label-free visualization of molecular domains in skin

The most prevalent molecular constituents of skin are spatially mapped by the use of nonlinear interferometric vibrational imaging, a coherent anti-Stokes Raman scattering (CARS)-based technique. Raman-like profiles over the range from 2,800 to 3,000 cm⁻¹ are acquired by means of completely suppressing the non-resonant background, allowing the generation of images based on the molecule-specific spectral profiles over the probed region with high spatial resolution. A simple algorithm that maps spectral content to color allows the visualization of histology in a manner analogous to that obtained with more conventional staining procedures (e.g., hematoxylin-eosin), but faster and with the benefit of having access to localized spectra, which could further enhance the potential for diagnosis of diseases, especially during the early stages of development.     

Revisiting the foundations of Barbilian?s metrization procedure

In the present work we prove that one of Barbilian?s theorems from 1960 regarding the metrization procedure in the plane admits a natural extension depending on a bilinear form and the relative position of two Apollonian hyperspheres. This result allows us to pursue two fundamental ideas. First, that all the distances with constant curvature can be described by Barbilian?s metrization principle. Secondly, that all the Riemannian metric corresponding to these distances can be obtained with the same unique procedure derived from the main theorem in the text (Theorem 2.5). We show how the hyperbolic metric of the disk, the hyperbolic metric on the exterior of the disk and the hyperbolic metric on the half-plane can be obtained in the same way using Theorem 2.5, which appears here for the first time and is an extension of a Barbilian classical result (Barbilian, 1960 [7]). Furthermore, we obtain metrics corresponding to quadratic forms with signature that includes minus. By considering the norms provided by either Lorentz or Minkowski (pseudo-)inner product as influence functions, two oscillant distances can be generated in some subsets of Lorentz or Minkowski plane. The extension of 1960 Barbilian?s theorem mentioned above allow us to obtain the metrics attached to these two Barbilian distances on corresponding subsets of Lorentz and Minkowski 2-dimensional spaces. The geometric study concludes that these metrics are generalized Lagrange metrics. A result concerning the distance induced by a Riemannian metric as a local Barbilian distance is also proved.     

Maternal obesity does not influence human milk protein 15N natural isotope abundance

ABSTRACT

Obesity increases protein metabolism with a potential effect on nitrogen isotope fractionation. The aim of this study was to test the influence of obesity on human milk extracted protein ¹⁵N natural isotope abundance (NIA) at one month post-partum and to compare human milk extracted protein ¹⁵N NIA and bulk infant hair ¹⁵N NIA. This cross-sectional observational study involved 16 obese mothers (body mass index (BMI)?≥?30?kg?m^?2 before pregnancy) matched with 16 normal-weight mothers (18.5?kg?m^?2?≤?BMI?<?25?kg?m^?2) for age and pregnancy characteristics. Human milk extracted protein and bulk infant hair ¹⁵N NIA were determined by isotope ratio monitoring by mass spectrometry interfaced to an elemental analyser (IRM-EA/MS). No significant difference was found in human milk protein ¹⁵N NIA values between obese and normal-weight mothers (8.93?±?0.48?‰ vs. 8.95?±?0.27?‰). However, human milk protein ¹⁵N NIA was significantly lower than bulk infant hair ¹⁵N NIA: 8.94?±?0.38?‰ vs. 9.66?±?0.69?‰, respectively. On the basis of these results, it is concluded that human milk protein ¹⁵N NIA measured at one month post-partum is not influenced by maternal obesity. These findings suggest that ¹⁵N NIA may be exploited to study metabolism without considering maternal obesity as a confounder.     

Abstracts

Abstract

Isothermal annealing of amorphous Si and Ge has been performed by picosecond pulsed laser irradiation of free-standing films. It is found that the laser induced nucleation rate is about 10²¹-5.10²² cm^?3 s^?1 (Si) and 10²³-10²⁵ cm^?3 s^?1 (Ge) near the melting point. Arrhenius plots of the nucleation rate show that nucleation is thermally activated with an activation energy of about ΔE = 1.8 ± 0.1 eV (Ge) and ΔE = 2.47 ± 0.15 eV (Si).     

Origin of the variability of the mechanical properties of silk fibers: 4. Order/crystallinity along silkworm and spider fibers

The poor crystallinity of proteic fibers has fuelled an ongoing debate over their exact organization. We present a full‐range Raman comparison of Nephila madagascariensis spider and Bombyx mori silkworm silks that sheds some new light on that matter. On the one hand, a large variability is observed along the fibers in the −200 to 200 cm⁻¹ spectral window, which is sensitive to the long‐range order signature of polyamide chains. This questions the validity of previous literature data considering silk fiber as a homogeneous material. On the other hand, the ‘amide I’ band is almost independent of the targeted point, which sets a limit to this widely used structure probe. In‐line mapping of the fibers showed that the extension of the ordered zones ranges between 1 and 3 µm. The correlation between the macromechanical behavior (the stress–strain curves) and the nanomechanics (Raman low wavenumber signatures) under controlled tensile strain demonstrates a Prevorsek's type microstructure: the macromolecular chains belong to both ordered and amorphous ‘regions’. Copyright © 2014 John Wiley & Sons, Ltd.