Towards a world‐sheet description of doubled geometry in string theory

Starting from a sigma‐model for a doubled target‐space geometry, we show that the number of target‐space dimensions can be reduced by half through a gauging procedure. We apply this formalism to a class of backgrounds relevant for double field theory, and illustrate how choosing different gaugings leads to string‐theory configurations T‐dual to each other. We furthermore discuss that given a conformal doubled theory, the reduced theories are conformal as well. As an example we consider the three‐dimensional WZW model and show that the only possible reduced backgrounds are the cigar and trumpet CFTs in two dimensions, which are indeed T‐dual to each other.     

Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

Die Änderung der Wärme- und Stoffübergangskoeffizienten beim gleichzeitigen Wärme- und Stoffübergang

The values of sensible and latent heat and of the resulting energy flow through laminar boundary layer have been developed for the four possible combinations of the directions of heat- and mass flows. When the values of heat- and mass flows are used with the correct sign according to the definitions of Fourier's law and Pick's law, the changes of heat transfer- and mass transfer coefficients can be described by one equation alone for all cases. The equations are extended in that way that they are valid for arbitrary cases of countercurrent diffusing mass flows — not only for the well known case of Stefan diffusion.     

Axial anomalies of Lifshitz fermions

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z = 3 which is minimally coupled to geometry in 3+1 space‐time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the η‐invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non‐relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Hořava–Lifshitz theory and find that the index is non‐zero provided that the space‐time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2) × U(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Hořava–Lifshitz theory arising at λ = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non‐relativistic quantum field theories are also discussed.     

Tandem nitrosation/cycloaddition of heterocyclic enamines using nitrolic acids

The reaction of alkylidenepyrrolidines with nitrolic acids gives rise to the formation of novel 3,7a-disubstituted (1,2,4-oxadiazol-5-yl)-5,6,7,7a-tetrahydropyrrolo[1,2-d][1,2,4]oxadiazoles. A plausible mechanism for this reaction is proposed, which features nitrosation of the enamine by the nitrous acid that is liberated from the nitrolic acid.     

Novel and Stereospecific Synthesis of (2S)‐3‐(2,4,5‐Trifluorophenyl)propane‐1,2‐diol from D‐Mannitol

A stereospecific synthesis of (2S)‐3‐(2,4,5‐trifluorophenyl)propane‐1,2‐diol from D ‐mannitol has been developed. The reaction of 2,3‐O‐isopropylidene‐D ‐glyceraldehyde with 2,4,5‐trifluorophenylmagnesium bromide gave [(4R)‐2,2‐dimethyl‐1,3‐dioxolan‐4‐yl](2,4,5‐trifluorophenyl)methanol in 65% yield as a mixture of diastereoisomers (1 : 1). The Ph₃P catalyzed reaction of the latter with C₂Cl₆ followed by reduction with Pd/C‐catalyzed hydrogenation gave (2S)‐3‐(2,4,5‐trifluorophenyl)propane‐1,2‐diol with >99% ee and 65% yield.     

Synthesis of novel PPARα/γ dual agonists as potential drugs for the treatment of the metabolic syndrome and diabetes type II designed using a new de novo design program PROTOBUILD

Peroxisome proliferator activated receptors (PPARs) have been shown to have critical roles in fatty acid oxidation, triglyceride synthesis, and lipid metabolism - making them an important target in drug discovery. Here we describe the in silico design, synthesis and in vitro characterisation of a novel series of 2,5-disubstituted indoles as PPARα/γ dual agonists. PPAR activation assays are performed with known agonists diazabenzene (WY14.643), aminopyridine (BRL49653) and bisaryl (L165.041), as positive controls. All the indole compounds synthesized are found to be active PPARα and PPARγ agonists, with particular efficacy from those with 2-naphthylmethyl substitution. This is a useful demonstration of a new de novo design methodology implemented by the protobuild program and its ability to rapidly produce novel modulators for a well characterized drug target.