Quantization of the Space of Conformal Blocks

We consider the discrete Knizhnik–Zamolodchikov connection (qKZ) associated to gl(N), defined in terms of rational R-matrices. We prove that under certain resonance conditions, the qKZ connection has a non-trivial invariant subbundle which we call the subbundle of quantized conformal blocks. The subbundle is given explicitly by algebraic equations in terms of the Yangian Y(gl(N)) action. The subbundle is a deformation of the subbundle of conformal blocks in CFT. The proof is based on an identity in the algebra with two generators x,y and defining relation xy=yx+yy.     

Structure and properties of sequentially polymerized propylene-b-[ethylene-co-propylene]-b-propylene copolymers

The structure and properties of presumed block copolymers of polypropylene (PP) with ethylene-propylene random copolymers (EPR), i.e., PP-EPR and PP-EPR-PP, have been investigated by viscometry, transmission electron microscopy, dynamic mechanical analysis, differential scanning calorimetry, gel permeation chromatography, wide-angle x-ray diffraction, and other techniques testing various mechanical properties. PP-EPR and PP-EPR-PP were synthesized using δ-TiCl₃-Et₂-AlCl as a catalyst system. The results indicate that the intrinisic viscosity of these polymers increases with each block-building step, whereas the intrinsic viscosity of those prepared by chain transfer reaction (strong chain-transfer reagent hydrogen was introduced between block-building steps during polymerization) hardly changes with the reaction time. Compared with PP/EPR blends, PP-EPR-PP block copolymers have lower PP and polyethylene crystallinity, and lower melting and crystallization temperatures of crystalline EPR. Two relaxation peaks of PP and EPR appear in the dynamic spectra of blends. They merge into a very broad relaxation peak with block sequence products of the same composition, indicating good compatibility between PP and EPR in the presence of block copolymers. Varying the PP and EPR content affects the crystallinity, density, and morphological structure of the products, which in turn affects the tensile strength and elongation at break. Because of their superior mechanical properties, sequential polymerization products containing PP-EPR and PP-EPR-PP block copolymers may have potential as compatibilizing agents for isotactic polypropylene and polyethylene blends or as potential heat-resistant thermoplastic elastomers.     

Quasi-Symmetric Designs with Good Blocks and Intersection Number One

We show that a quasi-symmetric design with intersection numbers 1 and y > 1 and a good block belongs to one of three types: (a) it has the same parameters as PG ₂(4, q), the design of points and planes in projective 4-space; (b) it is the 2-(23, 7, 21) Witt design; (c) its parameters may be written v = 1 + (( – 1) + 1)(y – 1) and k = 1 + (y – 1), where is an integer and > y 5, and the design induced on a good block is a 2-(k, y, 1) design. No design of type (c) is known; moreover, for large ranges of the parameters, it cannot exist for arithmetic reasons concerning the parameters. We show also that PG ₂(4, q) is the only design of type (a) in which all blocks are good.     

A lower bound for the pitman efficiency of Friedman type tests

An expression for the sharp lower bound for the efficiency of any Friedman type test with respect to the Friedman type test with optimal scores under weak model restrictions is given and calculated explicitely for the classical Friedman test.     

Synthesis of modular building blocks using glycosyl phosphate donors for the construction of asymmetric N-glycans

Glycosyl phosphates are known as versatile donors for the synthesis of complex oligosaccharides both chemically and enzymatically. Herein, we report the stereoselective construction of modular building blocks for the synthesis of N-glycan using glycosyl phosphates as donors. We have synthesized four trisaccharide building blocks with orthogonal protecting groups, namely, Manβ2GlcNAc(OAc)₃β6GlcNAc (9), Manβ2GlcNAc-β6GlcNAc(OAc)₃ (15), Manβ2GlcNAc(OAc)₃β4GlcNAc (18) and Manβ2GlcNAcβ4GlcNAc(OAc) (22) for further selective elongation using glycosyltransferases. The glycosylation reaction using glycosyl phosphate was found to be high yielding with shorter reaction time. Initially, The phthalimide protected glucosamine donor was exploited to ensure the formation of β-glycosidic linkage and later converted to the N-acetyl group before the enzymatic synthesis. The selective deprotection of O-benzyl group was performed prior to enzymatic synthesis to avoid its negative interference.     

Concise synthesis of Bacillusanthracis exosporium tetrasaccharide via two-stage activation of allyl glycosyl donor strategy

A highly efficient glycosylation protocol recently developed in our laboratory has been utilized in the short synthesis of the tetrasaccharide 1, an antigen important to the development of carbohydrate-based diagnostic tools and vaccines against anthrax. The protocol employs allyl glycosides as building blocks and improves the overall synthetic efficiency.     

Aza-Heterocyclic Building Blocks with In-Ring CF2-Fragment

Modern organic chemistry is a titan supporting and reinforcing pharmaceutical, agricultural, food and material science products. Over the past decades, the organic compounds market has been evolving to meet all the research demands. In this regard, medicinal chemistry is especially dependent on available chemical space as subtle tuning of the molecule structure is required to create a drug with relevant physicochemical properties and a remarkable activity profile. The recent rapid evolution of synthetic methodology to deploy fluorine has brought fluorinated compounds to the spotlight of MedChem community. And now unique properties of fluorine still keep fascinating more and more as its justified installation into a molecular framework has a beneficial impact on membrane permeability, lipophilicity, metabolic stability, pharmacokinetic properties, conformation, pK_a, etc. The backward influence of medicinal chemistry on organic synthesis has also changed the landscape of the latter towards new fluorinated topologies as well. Such complex relationships create a flexible and ever-changing ecosystem. Given that MedChem investigations strongly lean on the ability to reach suitable building blocks and the existence of reliable synthetic methods in this review we collected advances in the chemistry of respectful, but still enigmatic gem-difluorinated aza-heterocyclic building blocks.     

Enantioselective Synthesis with Lithium/(−)-Sparteine Carbanion Pairs

“Chiral carbanions”—that is, enentiomerically enriched lithium–carbanion pairs in which the carbanionic center carries the chiral information—were regarded until recently as “exotic species.” In the past ten years it has become clear that they can, in fact, play a meaningful role in enantioselective synthesis, since substitution for lithium occurs here stereospecifically, usually with retention of configuration. They are also more readily and commonly accessible than was originally assumed. The trick lies in the use of lithium cations with chiral ligands, whether in the form of alkyllithium species used as bases in kinetically controlled, enantiotopically discriminating deprotonation, or in thermodynamically controlled equilibration in configurationally labile epimeric ion pairs. The lupine alkaloid (?)-sparteine has shown itself admirably suited as a chiral bidentate ligand, and its efficiency and breadth of application are so far unsurpassed. This contribution constitutes an overview of the preparation of chiral reagents, convering primarily “umpoled” synthons such as homoenolates. 1-oxyalkanides with a broad pattern of substitution, and α-aminobenzyl anions.     

Diethyl Fluoronitromethylphosphonate: Synthesis and Application in Nucleophilic Fluoroalkyl Additions

Diethyl fluoronitromethylphosphonate ( 3 ), a previously unknown compound, was synthesized by electrophilic fluorination of diethyl nitromethylphosphonate with Selectfluor. Base‐induced decomposition of 3 was studied by NMR spectroscopy, which identified diethyl fluorophosphate and fluoronitromethane as the main decomposition products. C?H acidities [pK_a values in dimethyl sulfoxide (DMSO)] of 3 , 1‐fluoro‐1‐phenylsulfonylmethanephosphonate ( 1 ; McCarthy’s reagent), tetraethyl fluoromethylenebisphosphonate ( 2 ), and some nonfluorinated phosphonates were computed, and a good correlation between calculated and experimental pK_a values was found. The calculated C?H acidities increased in the sequence 2 < 1 < 3 . Diethyl fluoronitromethylphosphonate ( 3 ) was applied in the Horner–Wadsworth–Emmons reaction with aldehydes and trifluoromethyl ketones to provide new 1‐fluoro‐1‐nitroalkenes with good to high stereoselectivities. Alkylation of 3 was successful only with iodomethane, however, conjugate additions of 3 to Michael acceptors such as α,β‐unsaturated carbonyl compounds, sulfones, and nitro compounds allowed access to variously modified diethyl 1‐fluoro‐1‐nitrophosphonates.     

Synthesis of 3,3-disubstituted oxetane building blocks

The synthesis of two different sets of 3,3-disubstituted oxetane building blocks is described. These molecules can be usefully incorporated in more complex structures to modulate their metabolic and physicochemical properties. The synthetic pathways are general and could be exploited for the synthesis of many other related derivatives.