Reverse mathematics,well-quasi-orders,and Noetherian spaces

A quasi-order Q induces two natural quasi-orders on \({\mathcal{P}(Q)}\), but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on \({\mathcal{P}(Q)}\) preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on \({\mathcal{P}(Q)}\) are Noetherian, which means that they contain no infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) \({\mathcal{P}(Q)}\) is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA₀ over RCA₀. To state these theorems in RCA₀ we introduce a new framework for dealing with second-countable topological spaces.     

Rethinking polyhedrality for lindenstrauss spaces

We present a Lindenstrauss space with an extreme point that does not contain a subspace linearly isometric to c. This example disproves a result stated by Zippin in a paper published in 1969 and it shows that some classical characterizations of polyhedral Lindenstrauss spaces, based on Zippin’s result, are false, whereas some others remain unproven; then we provide a correct proof for those characterizations. Finally, we also disprove a characterization of polyhedral Lindenstrauss spaces given by Lazar, in terms of the compact norm-preserving extension of compact operators, and we give an equivalent condition for a Banach space X to satisfy this property.     

An investigation on the nature of the peptide at m/z 904, overexpressed in plasma of patients with colorectal cancer and familial adenomatous polyposis

In an investigation devoted to the search for plasma markers for colorectal cancer (CRC), carried out by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, a series of overexpressed peptides were identified in the plasma of patients. Among them the peptide with molecular weight 903 Da was the most abundant one, with a mean +/- (SD) relative abundance of 37 +/- 17% and a frequency over 60%. Interestingly, also in plasma samples of ten subjects affected by familial adenomatous polyposis (FAP), the peptide with molecular weight 903 was overexpressed. In this investigation, MALDI/MS/MS experiments were carried out on the ion at m/z 904 detected in the MALDI mass spectra of CRC and FAP patients. The data analysis by SwissProt.2007.01.09 indicates that this peptide is due to the sequence RPPGFSPF, found in the kininogen-1 precursor, which is an alpha-2-thiol proteinase inhibitor. In the case of subjects affected by a particular FAP syndrome, the MALDI/MS/MS spectra were quite different from those obtained from CRC and FAP patients. In fact, two sequences have been evidenced: RPPGFSPF belonging to kininogen-1 precursor, and PRKSSSSR belonging to Forkhead box protein 01A.     

Geometry and Conformation of Thietanium Ions from Diffraction Data and Ab Initio Calculations

Four‐membered ring thiosulfonium ions may be obtained quantitatively and under mild conditions by anionotropic rearrangement of C‐(tert‐butyl)‐substituted thiiranium ion precursors. Thus, t‐4‐(tert‐butyl)‐r‐1,2,2,c‐3‐tetramethylthietanium tetrafluoroborate or hexachloroantimonate ( 2a or 2b , resp.) were formed from thiiranium ion 1 . The thietanium salts 2a and 2b were characterized by X‐ray crystal‐structure analysis. Their cation geometry was also optimized by ab initio calculations at the RHF/6‐31G*//RHF/6‐31G* level, as were those of its stereoisomer 3 and of the unsubstituted S‐methylthietanium ion 5 . Comparison of 2 , 3 , and 5 with 4 – the only other thietanium ion studied by XRD, where the C‐atoms of the thioniacyclobutane ring are part of a trinorbornane skeleton – indicates that, in these systems, relief from substituent overcrowding is easily achieved by a folding of the four‐membered ring along the line connecting the two opposite C‐atoms. The corresponding ring‐deformation normal mode has a calculated frequency as low as 109 cm⁻¹ in ion 5 , to be compared with a frequency of 138 cm⁻¹ in methylcyclobutane. For thietanium ion 2 , the frequencies of the two normal modes involving such ring deformation have calculated values of 61 and 85 cm⁻¹.     

Solvent Trapping during Large Volume Injection with an Early Vapor Exit,Part 2: Chromatographic Results and Conclusions

Solvent trapping reconcentrates volatile components after injection or on-line transfer of large volumes. When an early vapor exit is used, typically after a 5–10 m × 0.53 mm i.d. uncoated precolumn, the solvent trapping process differs from that described previously. The visual experiments and the conclusions drawn therefrom, as described in a previous paper, are supplemented with chromatographic results. They show that even hexane can be quantitatively analyzed in 250 μl of a pentane solution. Injection of a volume of 250 μl by vaporizer/precolumn solvent splitting was used in the analysis of gasoline in drinking water. Conditions for the transfer of a 1000 μl volume can easily be adjusted through detection of the front end of the flooded zone by a thermocouple mounted on the outer wall of the precolumn.     

Surface-controlled spatially heterogeneous physical properties of a supramolecular gel with homogeneous chemical composition

Controlling supramolecular self-assembly across multiple length scales to prepare gels with localised properties is challenging. Most strategies concentrate on fabricating gels with heterogeneous components, where localised properties are generated by the stimuli-responsive component. Here, as an alternative approach, we use a spiropyran-modified surface that can be patterned with light. We show that light-induced differences in surface chemistry can direct the bulk assembly of a low molecular weight gelator, 2-NapAV, meaning that mechanical gel properties can be controlled by the surface on which the gel is grown. Using grazing incidence X-ray diffraction and grazing incidence small angle X-ray scattering, we demonstrate that the origin of the different gel properties relates to differences in the architectures of the gels. This provides a new method to prepare a single domain (i.e., chemically homogeneous) hydrogel with locally controlled (i.e., mechanically heterogeneous) properties.

A mechanical pattern is created in a hydrogel film by pre-patterning the underlying surface chemistry. This allows spatial variation of the viscous component of the gel, controlling dissipative forces in the gel film without altering gel chemistry.     

Solvent effects in the reaction of 2-thiophenesulfonyl chloride with aniline

The second order rate constants k₂ and the activation parameters for the reaction of 2-thiophenesulfonyl chloride with aniline together with solution enthalpies of the reactants have been measured in methanol, ethanol, 2-propanol, acetonitrile and acetone. The reaction rates are slower in dipolar aprotic solvents than in protic ones due to a remarkable activation negative entropy. The rate constants k₂ are correlated with empirical solvent polarity parameters. The data seem in accord with a S_AN reaction mechanism.