Identification of a Lead Candidate in the Search for Carbene‐Stabilised Homoaromatics

The effect of carbenes as Lewis donor groups on the homoaromaticity of mono‐ and bicyclic organic molecules is surveyed. The search for viable carbene‐stabilised homoaromatics resulted in a large amount of rejected candidates as well as nine promising candidates that are further analysed for their homoaromaticity by using a number of metrics. Of these, five appeared to show modest homoaromaticity, whereas another compound showed a level of homoaromaticity comparable with the homotropylium cation benchmark compound. Isoelectronic analogues and constitutional isomers of the lead compound were investigated, however, none of these showed comparable homoaromaticity. The implications of these calculations on the design of donor‐stabilised homoaromatics are discussed.     

Intramolecular N to N acyl migration in conformationally mobile 1′-acyl-1-benzyl-3′,4′-dihydro-1′<Emphasis Type="Italic">H</Emphasis>-spiro[piperidine-4,2′-quinoline] systems promoted by debenzylation conditions (HCOONH<Subscript>4</Subscript>/Pd/C)

We report an efficient and useful synthesis of new attractive spiropiperdine scaffolds 4 based on an intramolecular acyl transfer process in 1′-acyl-1-benzyl-3′,4′-dihydro-1′H-spiro[piperidine-4,2′-quinolines] 3 using simple and mild debenzylation reaction conditions (HCOONH₄/Pd/C). The compounds 3 were prepared by acylating 1-benzyl-4′-methyl-3′,4′-dihydro-1′H-spiro[piperidine-4,2′-quinolines] 2 that are easily available from 1-benzyl-4-piperidone 1. The intramolecular character of this process was proven primarily through a crossover experiment technique. Through an examination of all spectroscopic information (¹H, ¹³C NMR, VT-¹H NMR, and ²D NMR) it was possible to correctly predict amide configurations and piperidine ring conformations of starting and final spiropiperidine compounds.      

Invariant Measures for Cherry Flows

We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.     

Electrical conductivity relaxation in PVOH+LiH2PO4+Al2O3 polymer composites

Low-frequency conductivity measurements have been performed in solid polymer electrolyte composites based on the anhydrous PVOH–LiH₂PO₄–Al₂O₃ system. A typical power law dependency in the real part of the conductivity, at higher frequencies, of the form ω ⁿ is observed, with an exponent n that depends on the alumina content and nearly independent of temperature. An analysis of the frequency dependence of the electrical susceptibility is conducted to obtain relaxation functions of the form exp[?(t/τ) ^β ], with an exponent β?≈?n???1. Correlation times, τ, and parameters characterizing the electrical relaxation in time and frequency domains are compared to show the equivalence of these representations. The anhydrous dc conductivity of the electrolytes increases with increasing lithium salt content, becoming of the order of 10^?5 S/cm for a salt molar fraction of x?=?0.14. This conductivity value increased by about one order of magnitude by addition of nanoporous particles of Al₂O₃. The temperature dependence of the samples conductivity was well described by the Vogel–Tammann–Fulcher’s equation indicating the effect of the polymer chains flexibility on ion migration. Although all membranes exhibited a “universal dynamic response” associated to the random hopping of the mobile carriers, variations in the measured relaxation parameters with alumina content indicate an increase of ionic correlations when adding the nonporous particles to the polyelectrolyte.     

On the use of the photoacoustic technique for the measurement of the thermomechanical properties of semiconductor two-layer systems

The photoacoustic technique is used in semiconductor two-layer systems for the determination of thermal properties and thermal expansion coefficient. The two-layer systems studied were amorphous silicon-glass and Al_0.2Ga_0.8As---GaAs. Our results show that the proposed method is a reliable technique for the characterization of other semiconductor two-layers systems.     

Canonical connections of Finsler metrics and Finslerian connections on Riemannian metrics

A concept of canonical connection of a Finsler metric is developed. Connections that are compatible with Finsler metrics are compared with the canonical connection itself. They are also compared with the corresponding Cartan connection. A necessary and sufficient condition on metric Finsler connections is given for the metric to be Riemannian. This study unearths different ways in which Finsler geometry could be used to generalize the theory of general relativity.     

The emergence of a Kaluza-Klein microgenometry from the invariants of optimally Euclidean Lorentzian spaces

It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω⁰, mod ωⁱ) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian) connections are scrutinized. The fact that (ω^μ, ω₀ ⁱ) is the set of horizontal fundamental 1-forms in the Finslerian fibration implies that it can be used in principle for obtainingcompatible new structures. If the connection is teleparallel, a Kaluza-Klein space (KKS) indeed emerges from (ω^μ, ω₀ ⁱ), endowed ab initio with intertwined tangent and cotangent Clifford algebras. A deeper level of Kähler calculus, i.e., the language of Dirac equations, thus emerges. This makes the existance of an intimate relationship between classical differential geometry and quantum theory become ever more plausible. The issue of a geometric canonical Dirac equation is also raised.