Generation of strongly chaotic beats

The letter proposes a procedure for generation of strongly chaotic beats that have been hardly obtainable hitherto. The beats are generated in a nonlinear optical system governing second-harmonic generation of light. The proposition is based on the concept of an optical coupler but can be easily adopted to other nonlinear systems and Chua's circuits.Comment: 10 pages, 4 figures, accepted for publication in Int.J.Bif.Chao

Structure determination of a brownmillerite Ca2Co2O5 thin film by Precession Electron Diffraction

Calcium cobaltite thin films with a ratio Ca/Co=1 were grown on (101)-NdGaO3 substrate by the pulsed laser deposition technique. The structure of the deposited metastable phase is solved using a precession electron diffraction 3D dataset recorded from a cross-sectional sample. It is shown that an ordered oxygen-deficient Ca2Co2O5+d perovskite of the brownmillerite-type with lattice parameters a= 0.546nm, b=1.488nm and c=0.546nm (SG: Ibm2) has been stabilized using the substrate induced strain. The structure and microstructure of this metastable cobaltite is further discussed and compared to related bulk materials based on our transmission electron microscopy investigationsComment: 13 pages, 10 figures, 2 tables, accepted in Phys. Rev.

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size $3n+1$ are in a bijection with binary trees of size $n$.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Nanostructured poly(benzimidazole) membranes by N-alkylation

Modification of poly(benzimidazole) (PBI) by N-alkylation leads to polymers capable of undergoing microphase separation. Polymers with different amounts of C18 alkyl chains have been prepared. The polymers were analyzed by spectroscopy, thermal analysis, electron microscopy and X-ray scattering. The impact of the amount of alkyl chains on the observed microphase separation was analyzed. Membranes prepared from the polymers do show microphase separation, as evidenced by scattering experiments. While no clear morphology could be derived for the domains in the native state, evidence for the formation of lamellar morphologies upon doping with phosphoric acid is provided. Finally, the proton conductivity of alkyl-modified PBI is compared with that of pure PBI, showing that the introduction of alkyl side chains does not result in significant conductivity changes

On the adequacy of qualifying Roger Penrose as a complex Pythagorean

The aim of the presented article is to provide an in-depth analysis of the adequacy of designating Penrose as a complex Pythagorean in view of his much more common designation as a Platonist. Firstly, the original doctrine of the Pythagoreans will be briefly surveyed with the special emphasis on the relation between the doctrine of this school and the teachings of the late Platonic School as well as its further modifications. These modifications serve as the prototype of the contemporary claims of the mathematicity of the Universe. Secondly, two lines of Penrose’s arguments in support of his unique position on the ontology of the mathematical structures will be presented: (1) their existence independent of the physical world in the atemporal Platonic realm of pure mathematics and (2) the mathematical structures as the patterns governing the workings of the physical Universe. In the third step, a separate line of arguments will be surveyed that Penrose advances in support of the thesis that the complex numbers seem to suit these patterns with exceptional adequacy. Finally, the appropriateness of designation Penrose as a complex Pythagorean will be assessed with the special emphasis on the suddle threshold between his unique position and that of the adherents of the mathematicity of the Universe

Thickness-dependence of the electronic properties in V2O3 thin films

High quality vanadium sesquioxide V2O3 films (170-1100 {\AA}) were grown using the pulsed laser deposition technique on (0001)-oriented sapphire substrates, and the effects of film thickness on the lattice strain and electronic properties were examined. X-ray diffraction indicates that there is an in-plane compressive lattice parameter (a), close to -3.5% with respect to the substrate and an out-of-plane tensile lattice parameter (c) . The thin film samples display metallic character between 2-300 K, and no metal-to-insulator transition is observed. At low temperature, the V2O3 films behave as a strongly correlated metal, and the resistivity (\rho) follows the equation \rho =\rho_0 + A T^2, where A is the transport coefficient in a Fermi liquid. Typical values of A have been calculated to be 0.14 \mu\Omega cm K^{-2}, which is in agreement with the coefficient reported for V2O3 single crystals under high pressure. Moreover, a strong temperature-dependence of the Hall resistance confirms the electronic correlations of these V2O3 thin films samples.Comment: 4 pages, 4 figure