Bifurcations on contact manifolds

Consider a 1-parameter compactly supported family of Legendrian submanifolds of the 1-jet bundle of a compact manifold with its natural contact structure and a path of intersection points of the Legendrian family with the 1-jet of a constant function. Since the contact distribution is a symplectic vector bundle, it is possible to assign a Maslov-type index to the intersection path. We show that the non-vanishing of the Maslov intersection index implies that there exists at least one point of bifurcation from the given path of intersection points. This result can be viewed as a kind of analogue in bifurcation theory of the Arnold-Sandon conjecture on intersections of Legendrian submanifols. The proof is based on the technique of generating functions that relates the properties of Hamiltonian diffeomorphisms to the Morse theory of the associated functions.     

Signal suppression/enhancement in high-performance liquid chromatography tandem mass spectrometry

The review discusses the pitfalls of the matrix effect in mass spectrometry detection hyphenated to liquid chromatography separation. Matrix effect heavily influences both qualitative and quantitative analyses, giving rise to suppression or enhancement of the signal. As generally recognised, the predominant cause is the presence of undesired components that co-elute in the chromatographic separation and alter the ionisation process. The interfering species can be components of the sample, compounds released during the pre-treatment/extraction process or reagents added to the mobile phase to improve chromatographic resolution. The different mechanisms proposed in literature to explain the suppression or the enhancement of the signal both in electrospray and atmospheric pressure chemical ionisations are presented and the results observed in the different experimental conditions are compared and discussed. All data together lead to conclude that the chemical properties of the target analyte, the kind of matrix, the matrix to analyte concentration ratio, the extraction process, the chromatographic conditions as well as the kind of the mass spectrometry instrumentation and the ionisation conditions can play a role. Likely all these potential causes act in a synergic way and the final effect observed is hardly due to only one of them. Depending on an unpredictable combination of conditions, signal suppression or enhancement can be observed. The review discusses the matrix effects observed in HPLC–MS and HPLC–MS/MS analysis proposes hypotheses to explain the observed behaviours and proposes methods and strategies to overcome the matrix effects.     

Optimising open porous foam for acoustical and vibrational performance

A computational method for designing optimal arrangements of multilayer noise and vibration treatments in general and porous open cell foam in particular is discussed. The method uses finite element solutions to Biot's equations for poroelastic materials and provides data to evaluate cost functions and gradients. The porous material is parameterised using scaling laws linking the microscopic properties to the classical parameters, i.e. averaged elasticity, flow resistivity and characteristic viscous and thermal lengths. The cost function is either in terms of weight or in terms of the pressure response in a finite cavity, complemented with constraints on the other. However, care must be taken when choosing the cost function, as this will greatly affect the outcome of the optimisation. Observations made during the optimisation process indicate a limited number of minima within the parameter range of interest as well as beneficial continuity around these minima, thus enabling a meaningful optimisation. The results suggest that if alterations of the microscopic properties of the foam are made, the foam may be adapted to specific environmental conditions and thereby achieve improved acoustic behaviour as well as reduced weight.     

Synthesis and characterization of high-molecular-weight syndiotactic amorphous polypropylene

Heterocycle-fused titanium indenyl silylamido dimethyl complexes produce very high molecular weight polypropylene having a prevailingly syndiotactic microstructure with syndiotactic pentad contents rrrr up to 40-55% (sam-PP). The samples are basically amorphous and may slowly develop a low level of crystallinity (16-20%) at room temperature. A structural characterization has shown that sam-PP samples crystallize in disordered modifications of the helical form I of syndiotactic polypropylene (s-PP). The stretching of compression-molded films of sam-PP samples produce oriented crystalline fibers in the trans-planar mesomorphic form of s-PP. The low stereoregularity prevents the formation of the ordered trans-planar form III of s-PP, which instead is obtained in stretched fibers of the highly stereoregular and crystalline s-PP. The trans-planar mesomorphic form, obtained in stretched fibers, in turn transforms into the helical form I upon releasing the tension. The analysis of the mechanical properties has shown that sam-PP samples show good elastic behavior in a large range of deformation with remarkable strength, due to the presence of crystallinity. A comparison with the mechanical properties of less syndiotactic and fully amorphous samples is reported. These fully amorphous samples present lower strength and experience rapid viscous flow of the chains at high deformations and/or by application of stresses for long times. The higher strength in the semicrystalline sam-PP samples makes these materials interesting thermoplastic elastomers showing high toughness and ductility.     

In-source fragmentation and analysis of polysaccharides by capillary electrophoresis/mass spectrometry

In order to develop a robust and easy-to-use technique for characterization of bacterial polysaccharides, a pseudo-hydrolysis strategy was investigated. Based on in-source collision-induced dissociation, polysaccharide molecular ions were fragmented within the orifice-skimmer region of an electrospray ionization (ESI) mass spectrometer. The fragment ions thus generated were then analyzed similarly to the conventional ESI mass spectrometry approach. MS/MS scanning was applied to obtain product-ion spectra of the primary fragments for sequencing. To further improve the sensitivity and separation of polysaccharides from other components in the samples, a pressure-assisted capillary electrophoresis/mass spectrometry (CE/MS) system was employed. Using bacterial polysaccharides as model compounds, the mass spectra obtained for polysaccharide repeating units generated through chemical hydrolysis and in-source fragmentation were directly compared, both in positive and negative ion modes. With the additional separation of impurities provided by CE, the success of this technique has been demonstrated for structural analysis of O-chain polysaccharides (O-PS) and capsular polysaccharides (CPS). In-source fragmentation was applied to promote the formation of structurally relevant repeating units of heterogeneous CPS that would remain undetected using conventional ESI conditions. This approach was proven to be particularly useful for probing the subtle structural differences in monosaccharide composition and functionalities arising across bacterial serotypes.     

Structure and properties of ZnS nanoclusters

Earlier studies have shown that the most stable structures for (ZnS)n clusters with n = 10-47 are hollow polyhedral clusters ("bubbles"). We report a detailed study of larger clusters, where n = 50, 60, 70, and 80, for which onionlike or "double bubble" structures are predicted. We report calculations of the vibrational spectra and the electronic structure of bubble and double bubble clusters, which may assist in their experimental identification.     

Diiron-aminocarbyne complexes with amine or imine ligands: C-N coupling between imine and aminocarbyne ligands promoted by tolylacetylide addition to [Fe2{μ-CN(Me)R}(μ-CO)(CO)(NHCPh2)(Cp)2][SO3CF3]

A terminally coordinated CO ligand in the complexes [Fe₂{μ-CN(Me)R}(μ-CO)(CO)₂(Cp)₂][SO₃CF₃] (R = Me, 1a; R = Xyl, 1b; Xyl = 2,6-Me₂C₆H₃), is readily displaced by primary and secondary amines (L), in the presence of Me₃NO, affording the complexes [Fe₂{μ-CN(Me)R}(μ-CO)(CO)(L)(Cp)₂][SO₃CF₃] (R = Me, L = NH₂Et, 4a; R = Xyl, L = NH₂Et, 4b; R = Me, L = NH₂Prⁱ, 5a; R = Xyl, L = NH₂Prⁱ, 5b; R = Xyl, L = NH₂C₆H₁₁, 6; R = Xyl, L = NH₂Ph, 7; R = Xyl, L = NH₃, 8; R = Me, L = NHMe₂, 9a; R = Xyl, L = NHMe₂, 9b; R = Xyl, = NH(CH₂)₅, 10). In the absence of Me₃NO, NH₂Et gives addition at the CO ligand of 1b, yielding [Fe₂{μ-CN(Me)(Xyl)}(μ-CO)(CO){C(O)NHEt}(Cp)₂] (11). Carbonyl replacement is also observed in the reaction of 1a-b with pyridine and benzophenone imine, affording [Fe₂{μ-CN(Me)R}(μ-CO)(CO)(L)(Cp)₂][SO₃CF₃] (R = Me, L = Py, 12a; R = Xyl, L = Py, 12b; R = Me, L = HNCPh₂, 13a; R = Xyl, L = HNCPh₂, 13b). The imino complex 13b reacts with p-tolylacetylide leading to the formation of the μ-vinylidene-diaminocarbene compound [Fe₂{μ-η¹:η²- CC(Tol)C(Ph)₂N(H)CN(Me)(Xyl){(μ-CO)(CO)(Cp₂)] (15) which has been studied by X-ray diffraction.