Semigroup properties of factors in the polar decomposition or the operator De-Moivre formula

We give necessary and sufficient conditions under which the factors in the polar decomposition of a semigroup homomorphism are themselves semigroup homomorphisms.

     

Concentration of hydroxyl groups in dental apatites: a solid-state 1H MAS NMR study using inverse 31P -->1H cross-polarization

The concentration of structural hydroxyl groups in the apatite mineral of enamel, dentin and cementum of healthy human teeth was estimated by reference to stoichiometric hydroxyapatite to be 73 +/- 3, 18 +/- 2 and 18 +/- 1%, respectively.     

Periodic segment implies infinitely many periodic solutions

In this note we show that the existence of a periodic segment for a non-autonomous ODE with periodic coefficients implies the existence of infinitely many periodic solutions inside this segment provided that a sequence of Lefschetz numbers of iterations of an associated map is not constant. In the case when this sequence is bounded we have to impose a geometric condition on the segment to get solutions by use of symbolic dynamics.

     

11th Conference on Solid and Liquid Crystals—Material Science and Applications

Abstract

The eleventh conference in a series of biennial meetings was organized by Professor Jozef Zmija group from the Institute of Technical Physics WAT, Warsaw, Poland. It was supported by the State Committee of Scientific Research (KBN), the Polish chapter of the International Society for Optical Engineering (SPIE) and the Committee of Crystallography, Polish Academy of Sciences. These conferences have become more international, and this meeting, organized just outside Zakopana, in the Tatra mountains attracted more than 210 scientists, 51 from abroad.     

Dynamical phase transition in a model for evolution with migration

We study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way migration. Our key finding is a dynamical phase transition at a critical value of the migration rate, at which the time to reach the steady state diverges. The genetic composition of the population is qualitatively different above and below the transition. Using results from localization theory, we show that the critical migration rate may be very small-demonstrating that evolutionary outcomes can be very sensitive to even a small amount of migration.     

Efficiency of 1H --> 31P NMR cross-polarization in bone apatite and its mineral standards

Human bone mineral was studied using solid-state ³¹P NMR with cross-polarization (CP) from protons. The CP efficiency was determined for trabecular and cortical bone tissue from human adults and compared with synthetic mineral standards. The study shows the similarity between carbonatoapatite of type B and bone mineral as shown by their CP behaviour. The method can be used for the characterization of synthetic apatite-based implant materials.     

Stimulated Brillouin scattering in highly birefringent microstructure fiber: experimental analysis

We report on an experimental analysis of stimulated Brillouin scattering (SBS) in a 20-m-long highly birefringent microstructure fiber for sensing applications. In particular, an experimental setup based on Brillouin optical frequency-domain analysis, operating at a wavelength of 1550 nm, has been employed in order to analyze the distribution of Brillouin frequency shift along the fiber, as well as to study the dependence of Brillouin frequency shift on optical polarization, temperature, and strain. Our results indicate that, for any fixed polarization, the fiber has a dual-peaked Brillouin spectrum. A study about the origin of these two peaks is presented.     

Sur la congruence des ensembles de points et ses généralisations

Sans résumé Conférence tenue à l'Université de Zurich le 22 Mai 1946.