Simplicial Girth and Pure Resolutions

Generalizing the notion of the girth of a graph, a sequence of simplicial girths is assigned to each simplicial complex. Given a simplicial girth, lower bounds on higher simplicial girths are proven. When a simplicial girth is given and the Stanley–Reisner ring has a pure resolution, upper bounds on the number of vertices are proven.     

Simple Access to Highly Functional Bicyclic γ‐ and δ‐Lactams: Origins of Chirality Transfer to Contiguous Tertiary/Quaternary Stereocenters Assessed by DFT

This paper describes the synthesis of both polysubstituted oxazolo‐pyrrolidinones and ‐piperidinones by a domino process. The methodology is based on the reaction between hydroxyl halogenoamides and Michael acceptors, which leads efficiently to bicyclic lactams. The process is compatible with unsymmetrical electron‐withdrawing groups on the Michael acceptor, which allows the formation of two contiguous and fully controlled tertiary and quaternary stereocenters. In the case of tetrasubstituted Michael acceptors, two adjacent quaternary stereocenters are formed in good yield. Starting from (R)‐phenylglycinol derived amides results in the formation of enantioenriched bicyclic lactams in low to good yields and with high levels of stereoselectivity, thus greatly increasing the scope and interest of this strategy. The origins of chirality transfer and diastereoselectivity were studied by DFT calculations and have been attributed to a kinetic control in one of the last two steps of the reaction sequence. This selectivity is dependent upon both the substituents on the Michael acceptor and the sodium cation chelation.     

Structural phase transitions in the relaxor ferroelectric Pb2Bi4Ti5O18

The relaxor ferroelectric Pb₂Bi₄Ti₅O₁₈ has been studied by Rietveld refinement of powder neutron diffraction data collected at temperatures of 100, 250 and 400 °C. Our refinements are compatible with the ‘average’ crystal structure of Pb₂Bi₄Ti₅O₁₈ undergoing the phase transition sequence F2mm→I4mm→I4/mmm as a function of increasing temperature, with the latter phase being observed above the known ferroelectric Curie temperature, T_m, and the intermediate phase consistent with a previously observed dielectric anomaly around 207 °C. The results are, however, in conflict with both observation of a symmetry lowering (to space group B2eb) in the lowest temperature phase, observed by electron diffraction, and also with electrical property measurements, which suggest both a- and c-axis polarisation up to T_m. Nevertheless, these crystallographic results are consistent with the observation of relaxor behaviour in this material, and underline the importance of considering ‘long-range’ versus ‘local’ structural effects in relaxor materials.     

Bounding Betti numbers of bipartite graph ideals

We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs.     

The effect of self-equilibrating stresses on the natural frequencies of a free-free rectangular plate

A rectangular plate supported with all edges free vibrates in both torsional and flexural modes. A self-equilibrating stress system, induced by running a weld on the longitudinal centre-line, reduces the natural frequencies of the plate. The effect is more marked in the torsional than in the flexural modes. It becomes less significant with increase in frequency.The paper describes an experimental and theoretical study of this effect and seeks to suggest a physical interpretation of the phenomenon.     

Synthesis and NKT cell stimulating properties of fluorophore- and biotin-appended 6"-amino-6"-deoxy-galactosylceramides

Alpha-galactosylceramides are potent stimulators of human T cells. Stimulation occurs through binding of the glycolipids by CD1d, presentation to T cells, and formation of a CD1d-glycolipid-T cell receptor complex. To facilitate the elucidation of the structural features of glycolipids necessary for T cell stimulation, alpha-galactosylceramides have been prepared with small molecules appended at the C6 position of the sugar. The appended molecules do not significantly influence the abilities of the glycolipids to stimulate T cells. [reaction: see text]     

The NMR spectra of porphyrins. 27—proton NMR spectra of chlorophyll-a and pheophytin-a

The 500 MHz proton NMR spectra of chlorophyll-a in several non-aggregating solvents, at high dilution, are given and that of pheophytin-a in CDCl₃ at 360 MHz and at high dilution is reported. Under these conditions, the dispersion is such that separate resonances are observed and can be assigned for all protons in the molecules, except P-5 to P-15 in phytyl side-chain. The complex spin systems of the C-7 propionic ester side-chains, and of the P-1/P-2 fragment, are analysed and the couplings obtained are interpreted in terms of possible conformations of the side-chain.     

Highly efficient P-N nickel(II) complexes for the dimerisation of ethylene

New P-N ligands featuring a phosphino group and an iminophosphorane moiety were successfully employed in the nickel-catalysed dimerisation of ethylene.