Derivations and spectral triples on quantum domains II: Quantum annulus

Science China Mathematics - Continuing our study of spectral triples on quantum domains, we look at unbounded invariant and covariant derivations in the quantum annulus. In particular, we...     

DOSY NMR as a tool for predicting optimal conditions for hydrogel formation: The case of a hyperbranched polyglycidol cross‐linked with boronic acids

This article demonstrates the utility of DOSY NMR for the determination of the optimal conditions for the efficient covalent, reversible cross‐linking of macromolecules in water for hydrogel formation. The studied model system was hyperbranched polyglycidol (HbPGL) containing numerous diol groups in peripheral regions and two types of boronic acids, that is, B(OH)₄^? and benzene‐1,4‐boronic diacid, as cross‐linking agents. Diffusion coefficient changes of a polymer in solution, under the influence of various concentrations of cross‐linking agent and pH, which influences the equilibrium of the reaction between boronic acids and diols, were recorded. These data are consistent with the rheological properties, namely the G′_max(ω) of hydrogels prepared under analogous conditions, from more concentrated solutions of HbPGL. This approach appears to be promising as it facilitates avoiding the loss of a large amount of polymer that is necessary for the elaboration of appropriate conditions for network formation in aqueous media. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2171–2178     

D-bar Operators on Quantum Domains

We study the index problem for the d-bar operators subject to Atiyah- Patodi-Singer boundary conditions on noncommutative disk and annulus.     

Synthesis and EPR Studies of 2′‐Deoxyuridines with Alkynyl,Rodlike Linkages

Sonogashira coupling of diacetyl 5‐ethynyl‐2′‐deoxyuridine with diacetyl 5‐iodo‐2′‐deoxyuridine gave the acylated ethynediyl‐linked 2′‐deoxyuridine dimer ( 3 b ; 63 %), which was deprotected with ammonia/methanol to give ethynediyl‐linked 2′‐deoxyuridines ( 3 a ; 79 %). Treatment of 5‐ethynyl‐2′‐deoxyuridine ( 1 a ) with 5‐iodo‐2′‐deoxyuridine gave the furopyrimidine linked to 2′‐deoxyuridine (78 %). Catalytic oxidative coupling of 1 a (O₂, CuI, Pd/C, N,N‐dimethylformamide) gave butadiynediyl‐linked 2′‐deoxyuridines ( 4 ; 84 %). Double Sonogashira coupling of 5‐iodo‐2′‐deoxyuridine with 1,4‐diethynylbenzene gave 1,4‐phenylenediethynediyl‐bridged 2′‐deoxyuridines ( 5 ; 83 %). Cu‐catalyzed cycloisomerization of dimers 4 and 5 gave their furopyrimidine derivatives. One‐electron addition to 1 a , 3 a , and 4 gave the anion radical, the EPR spectra of which showed that the unpaired electron is largely localized at C6 of one uracil ring (17 G doublet) at 77 K. The EPR spectra of the one‐electron‐oxidized derivatives of ethynediyl‐ and butadiynediyl‐linked uridines 3 a and 4 at 77 K showed that the unpaired electron is delocalized over both rings. Therefore, structures 3 a and 4 provide an efficient electronic link for hole conduction between the uracil rings. However, for the excess electron, an activation barrier prevents coupling to both rings. These dimeric structures could provide a gate that would separate hole transfer from electron transport between strands in DNA systems. In the crystal structure of acylated dimer 3 b , the bases were found in the anti position relative to each other across the ethynyl link, and similar anti conformation was preserved in the derived furopyrimidine–deoxyuridine dinucleoside.     

Synthesis of the Trans and Cis Higher Sugar Allylic Alcohols—Direct Precursors of Dodecoses

Abstract

Reaction of 6,7-dideoxy-l,2:3,4-di-O-isopropylidene-α-D-galacto-hept-6-ynopyranose (3) with 3-O-benzyl-l,2-O-sopropylidene-α-D-xylo-pentodiulose (4) afforded two diastereo-isomeric propargylic alcohols: 5a (n-glycero, R) and 5b (L-glycero, S) in 70% yield and in the 33:67 ratio. Hydrogenalion of 5a and 5b over Pd/BaSO₄ gave cis-allylic alcohols 6a and 6b. Semireduction of the triple bond in 3 with tri-n-butyltin hydride afforded trans-olefin 7 which reacted with 4 yielding two diastereoisomeric trans-allylic alcohols: 8a (D-glycero, R) and 8b (L-glycero, S) in a 74% yield and a 72:28 ratio.     

Hodge numbers of nodal double octics

Let B be a surface of even degree d in P³ with nodes as the only singular points. In [1] Clemens proved that the topology of the small resolution of the double covering of P³ branched along B depends not only on the number of nodes but also on the so-called defect, a non-negative integer describing their configuration.

The aim of this note is to give an elementary proof of the Clemens. result and to present some geometric interpretation of defect.