Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Synthesis,Characterisation and Crystal Structures of Two Bi‐oxadiazole Derivatives Featuring the Trifluoromethyl Group

The synthesis, characterisation, and crystal structure determination of the closely related compounds 3,3′‐bi‐(5‐trifluoromethyl‐1,2,4‐oxadiazole) and 5,5′‐bi‐(2‐ trifluoromethyl‐1,3,4‐oxadiazole) are reported. These two compounds are known for their bioactivity; however, in this study they serve as model compounds to evaluate the suitability of the heterocyclic oxadiazole ring system for energetic materials when the fluorine atoms in the exocyclic CF₃ groups are substituted successively by nitro groups. Quantum chemical calculations for the bi‐1,3,4‐ oxadiazole derivatives with difluoronitromethyl, fluorodinitromethyl, and trinitromethyl groups have been carried out and predict promising energetic performances for both explosive and propulsive applications.     

Columnar Liquid‐Crystalline Dinaphthoperylenetetracarboxdiimides

Although the double Friedel–Crafts acylation of arenes with ethyl chloroglyoxylate is hindered by the strongly deactivating effect of the first‐entering glyoxylic substituent, the double reaction is successful with the reactive arene perylene under long reaction times and with concomitant ester hydrolysis. The reaction is regiospecific, giving the 3,9‐regioisomer exclusively. This perylenylenediglyoxylic acid is condensed first with o‐bromophenylacetic acid and then with α‐branched alkylamines to yield the title compounds. Whilst the corresponding tetraalkyl esters only show monotropic mesophases, these diimides show enantiotropic columnar mesophases that can be maintained at room temperature if racemically branched alkyl chains of moderate size are used. A palladium‐induced C?C bond migration during the build‐up of the arene system leads to an isomeric side product of reduced symmetry that can be isolated by aggregation‐controlled chromatographic separation. The HOMO and LUMO energies of the title compounds are considerably higher than those of established perylenetetracarboxdiimides.     

Highly fluorescent polycaprolactones decorated with di(thiophene‐2‐yl)‐diketopyrrolopyrrole: A covalent strategy of tuning fluorescence properties in solid states

Well‐defined 1,4‐diketo‐3,6‐di(thiophen‐2‐yl)pyrrolo[3,4‐c]pyrrole (DTDPP) labeled polycaprolactones (PCL) with different chain lengths were synthesized and characterized. The effect of polymer chain lengths on the optical properties of DTDPP in solid states was studied by UV‐Vis absorption spectroscopy as well as steady‐state and dynamic fluorescence spectroscopies. Our results indicate that when the PCL side chain is extended to a certain length, the intermolecular aggregation of DTDPP units can be reduced significantly due to segregation effect of PCL. This approach offers a new facile strategy to address the common problem of aggregation‐caused quenching existing in organic fluorophores. These highly fluorescent biodegradable PCL polymers may find broad biomedical applications such as fluorescence‐based bioimaging and tissue engineering. © 2015 Wiley Periodicals, Inc. J. Polym. Sci. Part A: Polym. Chem. 2015 , 53, 1032–1042     

Synthesis of diblock copolymers by combination of organocatalyzed ring‐opening polymerization and atom transfer radical polymerization using trichloroethanol as a bifunctional initiator

This study reports an application of trichloroethanol (TCE) as a bifunctional initiator for the synthesis of block copolymers (BCPs) by organocatalyzed ring‐opening polymerization (OROP) and atom transfer radical polymerization (ATRP). TCE was employed to synthesize a low dispersity poly (valerolactone) macroinitiator, which was subsequently used for the ATRP of tert‐butyl methacrylate. While it is known that TCE can serve as an initiator in ATRP, the ability to induce polymerization under OROP is reported for the first time. The formation of well‐defined BCPs was confirmed by gel permeation chromatography and ¹H NMR. Computational studies were performed to obtain a molecular‐level understanding of the ring‐opening polymerization mechanism involving TCE as initiator. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 563–569     

Synthesis of poly(ω‐pentadecalactone)‐b‐poly(acrylate) diblock copolymers via a combination of enzymatic ring‐opening and RAFT polymerization techniques

Herein the first reported preparation of diblock copolymers of the polyethylene‐like polyester poly(ω‐pentadecalactone) (PPDL) via a combination of enzymatic ring‐opening polymerization (eROP) and reversible addition‐fragmentation chain‐transfer (RAFT) polymerization techniques is described. PPDL was synthesized via eROP using Novozyme 435 as a catalyst and a bifunctional initiator/chain transfer agent (CTA) appropriate for the eROP of ω‐pentadecalactone (PDL) and RAFT polymerization of acrylic and styrenic monomers. Chain growth of the PPDL macro‐CTA was performed to prepare acrylic and styrenic diblock copolymers of PPDL, and demonstrates a facile, metal‐free, and “greener” alternative to preparing acrylic diblock copolymers of polyethylene (PE). Diblock copolymer architecture was substantiated via analysis of ¹H NMR spectroscopic, UV‐GPC chromatographic, DSC onset crystallization (T_c), and MALDI‐ToF mass spectrometric data. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3326–3335     

17β-雄甾醇-[3,2-b]-吲哚的合成

以表雄酮为原料,经羟基氧化、羰基保护、还原、Fischer吲哚环化等反应合成了17-β-醇-雄甾-[3,2-b]-吲哚(5),总收率43.2%,其结构经1H NMR,IR和MS确证。生物活性初步测试结果表明:与雄诺龙相比,5对淡色库蚊的杀虫活性显著提高,在浓度为400 mg·L-1时,杀虫率为41.5%。