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), .

     

Synthesis of a giant 222 carbon graphite sheet

In this paper we present the synthesis and characterization of the so far largest polycyclic aromatic hydrocarbon (PAH), containing 222 carbon atoms or 37 separate benzene units. First a suitable three-dimensional oligophenylene precursor molecule is built up by a sequence of Diels-Alder and cyclotrimerization reactions and then planarized in the final step by oxidative cyclodehydrogenation to the corresponding hexagonal PAH. Structural proof is based on isotopically resolved MALDI-TOF mass spectra and electronic characteristics are studied by UV/Vis spectroscopy.     

Highly sulfurated heterocycles via dithiiranes and trithietanes as key intermediates

2,2,4,4-Tetramethyl-3-thioxocyclobutanone (8b) easily reacts with gaseous chlorine to yield the stable alpha-chloro sulfenyl chloride 10. The same product was obtained when 8b was treated either with phosphorus pentachloride (PCl(5)) or sulfuryl chloride (SO(2)Cl(2)) in CCl(4) solution. Sulfur dichloride (SCl(2)) reacts with 8b to give the alpha-chloro thiosulfenyl chloride 12 along with an almost equimolar amount of the trisulfide 13b. The less reactive disulfur dichloride (S(2)Cl(2)) was shown to react slowly with 8b and the symmetrical tetrasulfide 15 was found as the exclusive product. The pure thiosulfenyl chloride 12 added to adamantanethione (8c) yielded the unsymmetrical trisulfide 13c. When 12 was treated with thioacetic acid, the acetylated trisulfide 17 was formed in high yield. "Unzipping" reactions with the acetylated disulfide 16 and trisulfide 17 with morpholine in THF at -40 degrees C led to the formation of mixtures of two sulfur-rich heterocycles identified as the pentathiepane 6b and the hexathiepane 7b. A mixture of analogous products was obtained when alpha-chloro sulfenyl chloride 10 was treated with sodium sulfide in anhydrous THF at -40 degrees C. The formation of 6b and 7b is believed to occur via the intermediate dithiirane 1b and/or the isomeric thiosulfine 2b. In the case of 17 the reaction starts probably with the formation of a nonisolable tetrathiane 18b as presented in Scheme 5.     

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.     

Dendritic aliphatic polyethers as high-loading soluble supports for carbonyl compounds and parallel membrane separation techniques

This paper describes the use of dendritic polyglycerol as a new high-loading polymeric support. The soluble polyether skeleton allows the parallel synthesis of small libraries on a large scale (1-5 mmol). Purification of polymer-bound products is easily achieved by a parallel dialysis apparatus, which was developed to separate up to 12 reaction mixtures simultaneously. The terminal 1,2-diol groups of polyglycerol (loading capacity: 4.1 mmol diol/g) can be directly coupled with carbonyl compounds without additional linker groups. At the same time the polyglycerol support acts as a polymeric ketal protecting group. The coupling of the carbonyl compounds occurs in high yields, and effective loading capacities of up to 3.5 mmol of ketone/g can be reached. The obtained polymeric acetals can easily be characterized by standard analytical techniques, such as NMR, IR, UV, and SEC. The versatility of this new polymeric support for solution-phase organic synthesis is demonstrated by two efficient polymer-supported syntheses: nucleophilic substitutions of gamma-chloroketones with amines and Suzuki-coupling on p-bromobenzaldehyde. The acid-catalyzed acetal cleavage with a solid-phase acidic ion-exchange resin in methanol demonstrates the orthogonal use of these soluble polymeric supports with conventional solid-phase reagents. Cleavage of products occurs in high yields, and almost complete recovery (>95%) of the polyglycerol support has been demonstrated after phase separation or ultrafiltration.