Chebyshev diagrams for two-bridge knots

We show that every two-bridge knot K of crossing number N admits a polynomial parametrization x = T ₃(t), y = T _b (t), z = C(t), where T _k (t) are the Chebyshev polynomials and b + deg C = 3N. If C(t) = T _c (t) is a Chebyshev polynomial, we call such a knot a harmonic knot. We give the classification of harmonic knots for a ≤ 3. Most results are derived from continued fractions and their matrix representations.     

Synthesis of α-trifluoromethyl-α-amino-β-sulfone hydroxamates: novel nanomolar inhibitors of matrix metalloproteinases

The racemic α-trifluoromethyl-α-amino-β-sulfone hydroxamates 1 were synthesized by means of a nucleophilic addition of sulfur-stabilized carbanions to a N-Cbz imine of trifluoropyruvate (4). The free amino derivative 1a was the most potent inhibitor of both MMP-3 (stromelysin-1) and MMP-9 (gelatinase-B), showing an IC₅₀ = 14 nM and 1 nM, respectively, and excellent selectivity versus MMP-1 (>5000-fold difference in inhibitory capacity). The N-Me derivative 1b was the most selective for MMP-3 with respect to MMP-9 (62-fold difference).     

Novel highly potent, structurally simple γ-trifluoromethyl γ-sulfone hydroxamate inhibitor of stromelysin-1 (MMP-3)

The γ-trifluoromethyl γ-sulfone hydroxamate 1 was synthesized both in racemic and enantiomerically pure forms by means of a thia-Michael reaction of p-methoxythiophenol on achiral and chiral 3,3,3-trifluorocrotonoyl Michael acceptors. The (R)-1 enantiomer was the most potent inhibitor of MMP-3 (stromelysin-1), showing an IC₅₀ = 3.2 nM, as well as the most selective with respect to MMP-9 (65-fold).     

An estimate of maximum ground surface motion for non zero surface velocityEstimation du mouvement sismique maximal à la surface du sol pour une celerite d'ondes non nulle en surface

The increasing need for probability seismic hazard assessment (PSHA) of critical facilities sometimes leads to unrealistic earthquake scenarios with very high induced ground motions. From a physical standpoint these high motions cannot exist because of the limiting resistance capacity of the soil strata through which the seismic waves travel. A simple analytical model is proposed to bound the maximum ground surface acceleration that any soil deposit can transfer. This model is an extension to non zero ground surface velocity of a previously presented model. To cite this article: A. Pecker, C. R. Mecanique 332 (2004).     

An estimate of maximum ground surface motionEstimation du mouvement sismique maximal à la surface du sol

The increasing need for probability seismic hazard assessment (PSHA) of critical facilities sometimes leads to unrealistic earthquake scenarios with very high induced ground motions. From a physical standpoint these high motions cannot exist because of the limiting resistance capacity of the soil strata through which the seismic waves travel. A simple analytical model is proposed to estimate a bound to the maximum ground surface acceleration that any soil deposit can transfer. To cite this article: A. Pecker, C. R. Mecanique 331 (2003).     

Stickstoffbestimmung

Ohne Zusammenfassung     

Poncelet’s theorem and billiard knots

Let D be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in D. This proves a conjecture of Lamm and gives a new proof of a conjecture of Jones and Przytycki. We use Jacobi??s proof of Poncelet??s theorem by means of elliptic functions.     

Cosmological implications of anomalous redshifts—A possible working hypothesis

An analysis of the most recent experimental data shows that the isotropic and universal proportionality of redshift to distance, predicted for all distant objects by the expanding universe model, cannot be regarded as an established fact at the present stage of experimental knowledge. An interpretation of the conflicting data is given in terms of interactions between nonzero-mass photons and light scalar bosons. This leads to a new, static, Einstein-type hierarchical model of the universe, where the cosmological redshift results essentially from a tired-light effect.     

Ein photoelektrisches (direkt anzeigendes) Polarimeter

Ohne Zusammenfassung