Approximation and Markov moment problem on concrete spaces

Polynomial approximation results on unbounded subsets of \(R^n\) are discussed. By applying these results, one obtains characterizations of the existence of the solutions of the multidimensional vector valued moment problems in terms of quadratic mappings. Two other applications related to the Markov moment problem are considered. The main ingredients of the proofs are the extension of linear operator’s results, with two constraints. All sections contain statements using Hahn–Banach principle or its generalizations, as well as natural order relations on function or operator spaces. One solves the difficulty created by the existence of positive polynomials that are not sums of squares in several dimensions.     

Über die Invarianten von Linienelementen und die projektive Geometrie der Kurvengewebe

Ohne ZusammenfassungNach einem am 8. Jänner 1941 in Hamburg gehaltenen Vortrag. Mit 3 Figuren im Text     

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10–20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4–5.2 kJ/mol and a correlation coefficient (R²) of 0.77–0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD?=?3–8 kJ/mol and R²?=?0.1–0.9), but the results were improved compared to previous studies of this system with similar methods.     

The bovine basic pancreatic trypsin inhibitor (Kunitz inhibitor): a milestone protein

The pancreatic Kunitz inhibitor, also known as aprotinin, bovine basic pancreatic trypsin inhibitor (BPTI), and trypsin-kallikrein inhibitor, is one of the most extensively studied globular proteins. It has proved to be a particularly attractive and powerful tool for studying protein conformation as well as molecular bases of protein/protein interaction(s) and (macro)molecular recognition. BPTI has a relatively broad specificity, inhibiting trypsin- as well as chymotrypsin- and elastase-like serine (pro)enzymes endowed with very different primary specificity. BPTI reacts rapidly with serine proteases to form stable complexes, but the enzyme: inhibitor complex formation may involve several intermediates corresponding to discrete reaction steps. Moreover, BPTI inhibits the nitric oxide synthase type-I and -II action and impairs K+ transport by Ca2+-activated K+ channels. Clinically, the use of BPTI in selected surgical interventions, such as cardiopulmonary surgery and orthotopic liver transplantation, is advised, as it significantly reduces hemorrhagic complications and thus blood-transfusion requirements. Here, the structural, inhibition, and bio-medical aspects of BPTI are reported.     

Una generalizzazione del birapporto sopra un anello

We generalize to the case of the projective line over a (not necessarily commutative) ring the well-know theorem on the bijective maps preserving a given cross-ratio.

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Ricerca finanziata con fondi R.S. 40% del M.P.I.