HUA’S THEOREM WITH FIVE ALMOSTE QUAL PRIME VARIABLES

§1. IntroductionIn the additive theory of prime numbers, one studies the representation of positive in-tegers by powers of primes. For the quadratic case, Hua [1] proved that each large integercongruent to 5 modulo 24 can be written as the sum of ?ve squ…     

Synthesis of side‐chain liquid‐crystalline homopolymers and triblock copolymers with p‐methoxyazobenzene moieties and poly(ethylene glycol) as coil segments by atom transfer radical polymerization and their thermotropic phase behavior

A series of side‐chain liquid‐crystalline (LC) homopolymers of poly[6‐(4‐methoxy‐4′‐oxy‐azobenzene) hexyl methacrylate] with different degrees of polymerization were synthesized by atom transfer radical polymerization (ATRP), which were prepared with a wide range of number‐average molecular weights from 5.1 × 10³ to 20.6 × 10³ with narrow polydispersities of around 1.17. Thermal investigation showed that the homopolymers exhibit two mesophases, a smectic phase, and a nematic phase, and the phase‐transition temperatures of the homopolymers increase clearly with increasing molecular weights. A series of novel LC coil triblock copolymers with narrow polydispersities was synthesized by ATRP, and their thermotropic phase behavior was investigated with differential scanning calorimetry and polarized optical microscopy. The LC coil triblocks were designed to have an LC conformation of poly[6‐(4‐methoxy‐4′‐oxy‐azobenzene) hexyl methacrylate] with a wide range of molecular weights from 3.5 × 10³ to 1.7 × 10⁴ and the coil conformation of poly(ethylene glycol) (PEG) (number‐average molecular weight: 6000 or 12,000) segment. Their characterization was investigated with ¹H NMR, Fourier transform infrared spectra, and gel permeation chromatography. Triblock copolymers exhibited a crystalline phase, a smectic phase, and a nematic phase. The phase‐transition temperatures from the smectic to nematic phase and from the nematic to isotropic phase increased, and the crystallization of PEG depressed with increasing molecular weight of the LC block. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2854–2864, 2003     

Synthesis and characterization of 6‐ and 12‐arm star polymers by nitroxide‐mediated radical polymerization of St and MA from dendritic TIPNO‐based hexafunctional and dodecafunctional macroinitiators

Dendritic multifunctional macroinitiators having six and 12 TIPNO‐based alkoxyamines, TIPNO‐6 and TIPNO‐12 , were synthesized and used in the living radical polymerization of styrene (St), methyl acrylate (MA), N,N‐dimethylacrylamide (DMAAm), and isoprene (IP). The polymerizations of St initiated with TIPNO‐6 gave 6‐arm star polymers with narrow polydispersities of 1.14–1.18. In the polymerizations of MA initiated with TIPNO‐6 and TIPNO‐12 , the influences of added TIPNO on the polydispersity indexes (PDIs) of the resulting star polymers were first investigated, and this led to the successful formation of poly(MA) star polymers with narrow polydispersities (1.10–1.18). Moreover, the polymerizations of DMAAm and IP from TIPNO‐6 in the presence or absence of TIPNO were briefly investigated. The benzyl ether bonds of the poly(St) and poly(MA) star polymers were cleaved by treating with Me₃SiI or Pd/C, and the resulting arm's parts were analyzed with SEC. The PDIs of the resulting arm parts were low (1.19–1.23), and the M_ns agreed with the M_n,theor, indicating that the poly(St) and poly(MA) star polymers had well‐controlled arms. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4364–4376, 2007     

Rigid nitronyl-nitroxide-labelled anchoring molecules: syntheses, structural and magnetic investigations

The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety.     

Block copolymers of acrylic acid and butyl acrylate prepared by reversible addition–fragmentation chain transfer polymerization: Synthesis,characterization, and use in emulsion polymerization

Amphiphilic block copolymers of poly(acrylic acid‐b‐butyl acrylate) were prepared by reversible addition–fragmentation chain transfer polymerization in a one‐pot reaction. These copolymers were characterized by NMR, static and dynamic light scattering, tensiometry, and size exclusion chromatography. The aggregation characteristics of the copolymers corresponded to those theoretically predicted for a star micelle. In a butyl acrylate and methyl methacrylate emulsion polymerization, low amounts of these copolymers could stabilize latices with solid contents up to 50%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 684–698, 2003     

Synthesis and characterization of poly(methyl methacrylate)‐block‐poly(methylphenylsilane)‐ block‐poly(methyl methacrylate) by atom transfer radical polymerization

ABA block copolymers of methyl methacrylate and methylphenylsilane were synthesized with a methodology based on atom transfer radical polymerization (ATRP). The reaction of samples of α,ω‐dihalopoly(methylphenylsilane) with 2‐hydroxyethyl‐2‐methyl‐2‐bromoproprionate gave suitable macroinitiators for the ATRP of methyl methacrylate. The latter procedure was carried out at 95 °C in a xylene solution with CuBr and 2,2‐bipyridine as the initiating system. The rate of the polymerization was first‐order with respect to monomer conversion. The block copolymers were characterized with ¹H NMR and ¹³C NMR spectroscopy and size exclusion chromatography, and differential scanning calorimetry was used to obtain preliminary evidence of phase separation in the copolymer products. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 30–40, 2003     

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亚细胞器诱导的2,4,6-三硝基甲苯阴离子自由基的ESR研究

本文在无氧条件下利用ESR分别观察了肝脏和晶状体的微粒体及线粒体酶在NADPH存在下还原三硝基甲苯(TNT)的过程,检测到参数为g=2.0048±0.0005,A_对位~N=1.215mT,A~N=0.800±0.010mT,A~H=0.122±0.0206mT的自由基信号,并通过电子计算机对ESR谱的模拟证明该自由基信号为TNT硝基阴离子自由基,根据其超精细分裂常数认为,其不配对电子的电子云密度主要分布在对位硝基上。     

γ辐射引发淀粉目由基衰减的动力学研究

用ESR方法研究了红薯淀粉在γ射线预辐照下,产生的淀粉自由基特性及其室温下的自由基衰减动力学反应。结果表明在室温条件下,淀粉自由基的相对浓度随辐射剂量的增大而增加。自由基相对浓度的室温衰减用二级反应动力学处理,求得了衰减速率常数和淀粉自由基反应的半衰期。