Inheritance of hyper-duality in imprimitive Bose–Mesner algebras

We prove the following result concerning the inheritance of hyper-duality by block and quotient Bose–Mesner algebras associated with a hyper-dual pair of imprimitive Bose–Mesner algebras. Let and denote Bose–Mesner algebras. Suppose there is a hyper-duality ψ from the subconstituent algebra of with respect to p to the subconstituent algebra of with respect to . Also suppose that is imprimitive with respect to a subset of Hadamard idempotents, so is dual imprimitive with respect to the subset of primitive idempotents, where is the formal duality associated with ψ. Let denote the block Bose–Mesner algebra of on the block containing p, and let denote the quotient Bose–Mesner algebra of with respect to . Then there is a hyper-duality from the subconstituent algebra of with respect to p to the subconstituent algebra of with respect to .     

Discrete behavior of Seshadri constants on surfaces

Working over , we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this result is of practical value, which we demonstrate by giving significantly improved explicit lower bounds for Seshadri constants on and new results about ample divisors on blow ups of at general points.     

Multiple weak supramolecular interactions stabilize a surprisingly twisted As2L3 assembly

A combined crystallographic, DFT and NMR spectroscopic study of a flexible As(2)(3) assembly reveals temperature dependent conformational behavior in solution and a highly asymmetric structure stabilized by As-pi and edge-to-face aromatic interactions.     

'Lock and key' control of optical properties in a push-pull system

We report the modulation of the absorbance of a flavin push-pull derivative through specific recognition by a complementary diamidopyridine (DAP), shifting the flavin intramolecular charge transfer band by approximately 30 nm.     

Tuneable pseudorotaxane formation between a biotin-avidin bioconjugate and CBPQT4+

A biotinylated 1,5-dialkoxynaphthalene derivative has been shown to have the ability to bind strongly to avidin and thus act as an artificial binding site for cyclobis(paraquat-p-phenylene) thereby facilitating the formation of a tuneable pseudorotaxane-based bioconjugate.     

Highly dispersed clay-polyolefin nanocomposites free of compatibilizers, via the in situ polymerization of alpha-olefins by clay-supported catalysts

In situ polymerization by certain transition metal catalysts supported on and activated by acid-treated montmorillonite produces well-dispersed clay-polyolefin nanocomposites, without requiring either organic surfactants to be present in the clay phase or modification of the polyolefin structure.     

Synthesis and reactivity of bis(imido) uranium(VI) cyclopentadienyl complexes

The bis(imido) uranium(VI)-C(5)H(5) and -C(5)Me(5) complexes (C(5)H(5))(2)U(N(t)Bu)(2), (C(5)Me(5))(2)U(N(t)Bu)(2), (C(5)H(5))U(N(t)Bu)(2)(I)(dmpe), and (C(5)H(5))(2)U(N(t)Bu)(2)(dmpe) can be synthesized from reactions between U(N(t)Bu)(2)(I)(2)(L)(x) (L=THF, x=2; L=dmpe, x=1) and Na(C(5)R(5)) (R=H, Me); these complexes represent the first structurally characterized C(5)H(5)-compounds of uranium(VI) and they further highlight the differences between UO(2)(2+) and the bis(imido) fragment.