Survival of Dipolar Splittings between Equivalent Nuclei in High-Speed MAS-NMR—Interpretation of the 31P Coupling Patterns for Tetraphosphorus Decaoxide

Unexpected splittings in solid-state MAS-NMR spectra can indicate high rather than low local symmetry. A quantitative analysis of the resulting lineshapes provides information about geometry from a different range of space and time averaging than that of X-ray crystallography, as is demonstrated here for tetraphosphorus decaoxide (spectra on the right).     

Curves on normal surfaces

We study locally Cohen-Macaulay space curves lying on normal surfaces. We prove some theorems on the behaviour of the cohomology functions and initial ideals of such space curves, which give a basic distinction between those curves and curves lying on non-normal surfaces.

     

Nd[Al(iPrO)4]3, a novel tetranuclear alkoxide forming merohedrally twinned crystals

The new tetranuclear alkoxide hexa‐μ₂‐isopropoxy‐1:2κ⁴O;1:3κ⁴O;1:4κ⁴O‐hexaisopropoxy‐2κ²O,3κ²O,4κ²O‐trialumin­ium(III)­neodymium(III), [Nd{Al(C₃H₇O)₄}₃], has a metal–oxy­gen NdAl₃O₁₂ core which consists of four metal atoms arranged in an approximately planar triangular geometry. The central Nd atom is six‐coordinated by O atoms and the Al atoms are four‐coordinated by O atoms.     

A New Way of Using Semidefinite Programming with Applications to Linear Equations mod p

We introduce a new method of constructing approximation algorithms for combinatorial optimization problems using semidefinite programming. It consists of expressing each combinatorial object in the original problem as a constellation of vectors in the semidefinite program. When we apply this technique to systems of linear equations mod p with at most two variables in each equation, we can show that the problem is approximable within (1 − κ(p))p, where κ(p) > 0 for all p. Using standard techniques, we also show that it is NP-hard to approximate the problem within a constant ratio, independent of p.     

Selective F MR imaging of 5-fluorouracil and α-fluoro-β-alanine

A ¹⁹F MR chemical shift imaging (CSI) technique is presented which enables selective imaging of the antineoplastic drug 5-fluorouracil (5-FU) and its major catabolite α-fluoro-β-alanine (FBAL). The CSI sequence employs a chemical shift selective (CHESS) saturation pulse to suppress either the 5-FU or the FBAL resonance before the other component of the two-line ¹⁹F MR spectrum is measured. Because the transmitter frequency can always be set to the Larmor frequency of the ¹⁹F resonance to be imaged, this approach yields 5-FU and FBAL MR images free of chemical shift artifacts in read-out and slice-selection direction. In phantom experiments, selective 5-FU and FBAL images with a spatial resolution of 15 × 15 × 20 mm³ (4.5 ml) were obtained in 30 min from a model solution, whose drug and catabolite concentrations were similar to those estimated in the liver of tumor patients undergoing IV chemotherapy with 5-FU. The drug-specific MR imaging technique developed is, therefore, well-suited for the direct and noninvasive monitoring of the up-take and trapping of 5-FU in liver tumors in vivo.