Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C¹⁺ conjugacy classes of C^1+H Cantor exchange systems that are C^1+H fixed points of renormalization and (ii) C¹⁺ conjugacy classes of C^1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, we prove that there is no C^1+α Cantor exchange system, with bounded geometry, that is a C^1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set.     

Universal properties of maps of the circle with ɛ-singularities

Following the work of Collet, Eckmann, and Lanford on the Feigenbaum conjecture, we study the structure of the renormalization transformation introduced in [12] upon maps of the circle with critical points of the formx|x|^?.     

Efficient Demethylation of Methyl Esters with Anhydrous Trifluoroacetic Acid

Trifluoroacetic acid (TFA) is an effective reagent for the demethylation of methyl esters under anhydrous conditions, affording the parent acids and methyl trifluoroacetate.     

About a class of nonlinear oscillators with amplitude-independent frequency

This work is concerned with nonlinear oscillators that have a fixed, amplitude-independent frequency. This characteristic, known as isochronicity/isochrony, is achieved by establishing the equivalence between the Lagrangian of the simple harmonic oscillator and the Lagrangian of conservative oscillators with a position-dependent coefficient of the kinetic energy, which can stem from their mass that changes with the displacement or the geometry of motion. Conditions under which such systems have an isochronous center in the origin are discussed. General expressions for the potential energy, equation of motion as well as solutions for a phase trajectory and time response are provided. A few illustrative examples accompanied with numerical verifications are also presented.     

On homology modeling of the M2 muscarinic acetylcholine receptor subtype

Twelve homology models of the human M₂ muscarinic receptor using different sets of templates have been designed using the Prime program or the modeller program and compared to crystallographic structure (PDB:3UON). The best models were obtained using single template of the closest published structure, the M₃ muscarinic receptor (PDB:4DAJ). Adding more (structurally distant) templates led to worse models. Data document a key role of the template in homology modeling. The models differ substantially. The quality checks built into the programs do not correlate with the RMSDs to the crystallographic structure and cannot be used to select the best model. Re-docking of the antagonists present in crystallographic structure and relative binding energy estimation by calculating MM/GBSA in Prime and the binding energy function in YASARA suggested it could be possible to evaluate the quality of the orthosteric binding site based on the prediction of relative binding energies. Although estimation of relative binding energies distinguishes between relatively good and bad models it does not indicate the best one. On the other hand, visual inspection of the models for known features and knowledge-based analysis of the intramolecular interactions allows an experimenter to select overall best models manually.