Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems

   Abstract. There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete point set or tiling, defined through a primitive substitution system, given that it is pure point diffractive? Our basic objects are Delone multisets and tilings, which are self-replicating under a primitive substitution system of affine mappings with a common expansive map Q . Our first result gives a partial answer to a question of Lagarias and Wang: we characterize repetitive substitution Delone multisets that can be represented by substitution tilings using a concept of ``legal cluster.' This allows us to move freely between both types of objects. Our main result is that for lattice substitution multiset systems (in arbitrary dimensions), being a regular model set is not only sufficient for having pure point spectrum—a known fact—but is also necessary. This completes a circle of equivalences relating pure point dynamical and diffraction spectra, modular coincidence, and model sets for lattice substitution systems begun by the first two authors of this paper.     

Synthesis of potential prodrug systems for reductive activation. Prodrugs for anti-angiogenic isoflavones and VEGF receptor tyrosine kinase inhibitory oxindoles

A number of potential prodrug systems for reductive activation have been investigated. The prodrug systems chosen for the study were the 2-nitrophenylacetyl, 3-methyl-3-(3,6-dimethyl-1,4-benzoquinon-2-yl)butanoyl and 4-nitrobenzyl groups, readily attached to acidic OH or NH groups in drug molecules, and released upon bioreductive activation. The drug molecules studied were the naturally occurring isoflavone biochanin A, an inhibitor of VEGF-induced angiogenesis, and the pyrrolylmethylidenyl oxindole SU5416 (semaxanib) and its 6-hydroxy derivative, inhibitors of VEGF receptor tyrosine kinase. Following coupling the prodrug system to the drug, the compounds were evaluated chemically and biologically. Under chemical reducing conditions, the 3-methyl-3-(3,6-dimethyl-1,4-benzoquinon-2-yl)butanoic acid based prodrugs appear to fragment the most efficiently, followed by the 2-nitrophenylacetate esters with the 4-nitrobenzyl ethers being the least efficient. The potentially pro-anti-angiogenic compounds were also assayed for their ability to block VEGF-induced angiogenesis in HUVECS in comparison to the free agents. Control compounds that cannot be activated under bioreductive conditions are less potent than the free drug, whereas many of the potential prodrugs not only exhibit a dose response, but appear at least equipotent with the free drug.     

Die Bestimmung der Hydrolyse

Ohne Zusammenfassung     

Die Darstellung einer genauen Normals?ure

Ohne Zusammenfassung     

Recent Trends in Enzyme Immobilization—Concepts for Expanding the Biocatalysis Toolbox

Enzymes have been exploited by humans for thousands of years in brewing and baking, but it is only recently that biocatalysis has become a mainstream technology for synthesis. Today, enzymes are used extensively in the manufacturing of pharmaceuticals, food, fine chemicals, flavors, fragrances and other products. Enzyme immobilization technology has also developed in parallel as a means of increasing enzyme performance and reducing process costs. The aim of this review is to present and discuss some of the more recent promising technical developments in enzyme immobilization, including the supports used, methods of fabrication, and their application in synthesis. The review highlights new support technologies such as the use of well-established polysaccharides in novel ways, the use of magnetic particles, DNA, renewable materials and hybrid organic–inorganic supports. The review also addresses how immobilization is being integrated into developing biocatalytic technology, for example in flow biocatalysis, the use of 3D printing and multi-enzymatic cascade reactions.     

Biosynthesis inspired Diels-Alder route to pyridines: synthesis of the 2,3-dithiazolylpyridine core of the thiopeptide antibiotics

Reaction of serine derived 1-alkoxy-2-azadienes with dehydroalanine derived dienophiles results in Diels-Alder reaction and aromatisation to give 2,3,6-trisubstituted pyridines, thereby establishing the viability of the proposed biosynthetic route to the pyridine ring of the thiopeptide antibiotics originally proposed by Bycroft and Gowland.     

Chiral N-Acetyl Selone-Promoted Aldol Reactions

The chiral oxazolidineselone functionality was found to be an excellent partner in the stereospecific acetate aldol reaction with aldehydes via the titanium enolates. Good stereocontrol was obtained as determined by NMR spectroscopy. The oxazolidineselone also provided a straightforward way to establish the stereopurity of the coupling reaction through ⁷⁷Se NMR spectroscopy.     

On ranks of quadratic twists of a Mordell curve

The Ramanujan Journal - In this article, we consider the quadratic twists of the Mordell curve $$E:y^2=x^3-1$$ . For a square-free integer k, the quadratic twist of E is given by...