Liouville Theorems for Generalized Harmonic Functions

Each nonzero solution of the stationary Schrödinger equation u(x)–c(r)u(x)=0 in R ⁿ with a nonnegative radial potential c(r) must have certain minimal growth at infinity. If r ² c(r)=O(1), r, then a solution having power growth at infinity, is a generalized harmonic polynomial.     

Sets that force recurrence

We characterize those subsets of the positive integers with the property that, whenever a point in a dynamical system enters a compact set along , contains a recurrent point. We do the same for uniform recurrence.

     

New weighted Rogers-Ramanujan partition theorems and their implications

This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi's celebrated triple product identity for theta functions, Sylvester's famous refinement of Euler's theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts (mod 6), and a set of three theorems involving partitions into parts (mod 7), .

     

Crystal structure of a squalene cyclase in complex with the potential anticholesteremic drug Ro48-8071

Squalene-hopene cyclase (SHC) catalyzes the conversion of squalene into pentacyclic compounds. It is the prokaryotic counterpart of the eukaryotic oxidosqualene cyclase (OSC) that catalyzes the steroid scaffold formation. Because of clear sequence homology, SHC can serve as a model for OSC, which is an attractive target for anticholesteremic drugs. We have established the crystal structure of SHC complexed with Ro48-8071, a potent inhibitor of OSC and therefore of cholesterol biosynthesis. Ro48-8071 is bound in the active-center cavity of SHC and extends into the channel that connects the cavity with the membrane. The binding site of Ro48-8071 is largely identical with the expected site of squalene; it differs from a previous model based on photoaffinity labeling. The knowledge of the inhibitor binding mode in SHC is likely to help develop more potent inhibitors for OSC.     

Fusion and planarization of a quinoidal porphyrin dimer

The crystal structure, near-infrared spectrum and electrochemistry of a quinoidal triply-linked porphyrin dimer are compared with those of its singly-linked precursor; fusing the two porphyrins planarizes the pi-system and reduces the optical HOMO-LUMO gap while increasing the gap between the first oxidation and reduction potentials.     

Mixed-anion complexes with a bipyrazolyl ligand. A new entry to a realm of three-dimensional five-connected coordination topologies

Cross-linking of corrugated square grid coordination layers by anionic bridging groups generates five-connected coordination networks; the 3D topologies of mixed-anion cobalt(II) and nickel(II) complexes with a tetramethyl-substituted 4,4'-bipyrazolyl ligand are supported by mu-SO4(2-) functions and exist as neutral or cationic five-connected arrays involving additional terminal (NCS-) or non-coordinated (NO3-, ClO4-) groups.     

Complexation of small molecules by open-ended resorcarene hosts

[structure: see text] Sterically hindered tetraaminomethylated resorcarenes form inclusion complexes in CDCl(3) with acetonitrile and acetaldehyde, which are kinetically stable on the NMR time scale at 233 K.