Quotient morphisms, compositions, and Fredholm index

In this paper we define a composition between two quotient morphisms and prove a multiplication formula for the index of the composition of two Fredholm quotient morphisms. Using this formula and the fact that any linear relation can be seen as a quotient morphism, we obtain a multiplication formula for the index of the composition of two Fredholm linear relations.     

Quaternionic Cayley transform revisited

A Cayley type transform in the context of quaternions (previously introduced by the author) is revisited. A simplified definition is given and shorter proofs are exhibited. As new results, the range of this transform restricted to a class of unbounded normal operators is described, and an application to a moment problem with constraints is given. The extension problem to normal operators in this new context is also revisited.     

Dimensional stability in truncated moment problems

An approach to truncated moment problems is developed, via the Riesz functional and an assumed dimensional stability of its associated Hilbert spaces. Although equivalent to a concept of “flatness” introduced by R. Curto and L. Fialkow, the dimensional stability discussed in this paper has a different geometric aspect and leads to statements parallel to those of the quoted authors, as well as to some newer ones, obtained by simpler arguments. A stability equation, giving a local characterization of the dimensional stability, is also presented.     

A Uniform Ergodic Theorem for Commuting Semigroups

The existence of the limit, in the uniform topology, of theaverages of a finite family of commuting strongly continuoussemigroups of bounded linear operators in a Banach space ischaracterised in terms of infinitesimal generators.     

Heterocyclic organoboron compounds—XVI : Chelated compounds with α,β-unsaturated β-aminoketones

The reaction of β-aminoenones 4 with diphenylborinic acid or 2-alkoxy-1,3,2-benzodioxaborole affords chelated compounds whose UV, IR and NMR spectra are discussed.     

The Künneth formula for Hilbert complexes

A variant of the Künneth formula for tensor products of Fredholm complexes of Hilbert spaces is given.     

Systematic determination of ion score cutoffs based on calculated false positive rates: application for identifying ubiquitinated proteins by tandem mass spectrometry

We report a simple approach for determining ion score cutoffs that permit the confident identification of ubiquitinated proteins by tandem mass spectrometry (MS/MS). Initial experiments involving the analysis of gel bands containing multi-Ubiquitin chains with quadrupole time-of-flight and quadrupole ion trap mass spectrometers revealed that standard ion score cutoffs used for database searching were not sufficiently stringent. We also found that false positive and false negative rates (FPR and FNR) varied significantly depending on the cutoff scores used and that appropriate cutoffs could only be determined following a systematic evaluation of false positive rates. When standard cutoff scores were used for the analysis of complex mixtures of ubiquitinated proteins, unacceptably high FPR were observed. Finally, we found that FPR for ubiquitinated proteins are affected by the size of the protein database that is searched. These observations may be applicable for the study of other post-translational modifications.