有限循环群的Fuzzy子群的等价类数

有限循环群G的F子群可以有无数个．但是．若当两个F子群的水平集构成的集合相等就称其等价的话，那么其等价类数是有限的。通过研究群的合成群列、商群列以及数的因数列和极大因数列找出了有限循环群的极大F子群和F子群的等价类数的求解公式．并给出二者之间的关系式．     

Novel,biodegradable, functional poly(ester‐carbonate)s by copolymerization of trans‐4‐hydroxy‐L‐proline with cyclic carbonate bearing a pendent carboxylic group

Water‐soluble poly(ester‐carbonate) having pendent amino and carboxylic groups on the main‐chain carbon is reported for the first time. This article describes the melt ring‐opening/condensation reaction of trans‐4‐hydroxy‐N‐benzyloxycarbonyl‐L ‐proline (N‐CBz‐Hpr) with 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) at a wide range of molar fractions. The influence of reaction conditions such as catalyst concentration, polymerization time, and temperature on the number average molecular weight (M_n) and molecular weight distribution (M_w/M_n) of the copolymers was investigated. The polymerizations were carried out in bulk at 110 °C with 3 wt % stannous octoate as a catalyst for 16 h. The poly(ester‐carbonate)s obtained were characterized by Fourier transform infrared spectroscopy, ¹H NMR, differential scanning calorimetry, and gel permeation chromatography. The copolymers synthesized exhibited moderate molecular weights (M_n = 6000–14,700 g mol^?1) with reasonable molecular weight distributions (M_w/M_n = 1.11–2.23). The values of the glass‐transition temperature (T_g) of the copolymers depended on the molar fractions of cyclic carbonate. When the MBC content decreased from 76 to 12 mol %, the T_g increased from 16 to 48 °C. The relationship between the poly(N‐CBz‐Hpr‐co‐MBC) T_g and the compositions was in approximation with the Fox equation. In vitro degradation of these poly(N‐CBz‐Hpr‐co‐MBC)s was evaluated from weight‐loss measurements and the change of M_n and M_w/M_n. Debenzylation of 3 by catalytic hydrogenation led to the corresponding linear poly(ester‐carbonate), 4 , with pendent amino and carboxylic groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2303–2312, 2004     

Reversible nonlinear conduction in high‐density polyethylene/acetylene carbon black composites at various ambient temperatures

The reversible nonlinear conduction (RNC) in of high‐density polyethylene/acetylene carbon black composites with different degrees of crosslinking was studied above room temperature and below the melting point of high‐density polyethylene (HDPE). The experimental current density‐electric field strength curves can be overlapped onto a master curve, suggesting that the microscopic mechanisms for the appearance of RNC exist regardless of the ambient temperature and the crosslinking degree of the HDPE matrix. The relationship between the crossover current density and the linear conductivity can be explained in the framework of the dynamic random‐resistor‐network model. According to these results, two electron‐tunneling models are suggested to interpret the microscopic conduction behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1212–1217, 2004     

Synthesis and characterization of polyaniline/graphite conducting nanocomposites

A new method for the synthesis of exfoliated graphite and polyaniline (PANI)/graphite nanocomposites was developed. Exfoliated graphite nanosheets were prepared through the microwave irradiation and sonication of synthesized expandable graphite. The nanocomposites were fabricated via the in situ polymerization of the monomer at the presence of graphite nanosheets. The as-synthesized graphite nanosheets and PANI/graphite nanocomposite materials were characterized with Fourier transform infrared spectroscopy, scanning electron microscopy, transmission electron microscopy, and thermogravimetric analysis (TGA). The conductivity of the PANI/graphite nanocomposites was dramatically increased over that of pure PANI. TGA indicated that the incorporation of graphite greatly improved the thermal stability of PANI. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1972–1978, 2004     

Control of self‐organized low‐dimensional morphology in poly(styrene‐b‐4vinylpyridine)/polystyrene blend thin films

The surface morphologies of poly(styrene‐b‐4vinylpyridine) (PS‐b‐P4VP) diblock copolymer and homopolystyrene (hPS) binary blend thin films were investigated by atomic force microscopy as a function of total volume fraction of PS (?_PS) in the mixture. It was found that when hPS was added into symmetric PS‐b‐P4VP diblock copolymers, the surface morphology of this diblock copolymer was changed to a certain degree. With ?_PS increasing at first, hPS was solubilized into the corresponding domains of block copolymer and formed cylinders. Moreover, the more solubilized the hPS, the more cylinders exist. However, when the limit was reached, excessive hPS tended to separate from the domains independently instead of solubilizing into the corresponding domains any longer, that is, a macrophase separation occurred. A model describing transitions of these morphologies with an increase in ?_PS is proposed. The effect of composition on the phase morphology of blend films when graphite is used as a substrate is also investigated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3496–3504, 2004     

Detection of Pb2+ using a hydrogel swelling microcantilever sensor.

Hydrogels containing benzo-18-crown-6 were used to modify microcantilevers for measurements of the concentration of Pb2+ in aqueous solutions. These microcantilevers undergo bending deflection upon exposure to solutions containing various Pb2+ concentrations as the result of a swelling of the hydrogels. It was found that a concentration of 10(-6) M Pb2+ can be detected using this technology. Other cations, such as Na+, have no effect on the deflection of this cantilever. The cation K+, which also complexes with benzo-18-crown-6, could interfere with Pb2+ detection, but only at high concentrations (> 10(-4) M).     

A Quantum Chemical Study on Recognition of Nitro-phenols by Calix[n]arenes

A PM3 calculation in vacuum of the inclusion complexation ofo-, m-, p-nitro-phenol with calix[n]arenes is performedsuccessfully. The pathways for inclusion process are describedand the most probable structures of the 1:1 complex are soughtthrough a potential energy scan. The energy differences betweenthe inclusion complexes and the hosts, by calculation, show thatthe most stable complexation is calix[4]-p-nitro phenol andcalix[6]-m-nitro phenol.     

Electrospinning of ultrafine cellulose acetate fibers: Studies of a new solvent system and deacetylation of ultrafine cellulose acetate fibers

Electrospinning of cellulose acetate (CA) in a new solvent system and the deacetylation of the resulting ultrafine CA fibers were investigated. Ultrafine CA fibers (∼2.3 μm) were successfully prepared via electrospinning of CA in a mixed solvent of acetone/water at water contents of 10–15 wt %, and more ultrafine CA fibers (0.46 μm) were produced under basic pH conditions. Ultrafine cellulose fibers were regenerated from the homogeneous deacetylation of ultrafine CA fibers in KOH/ethanol. It was very rapid and completed within 20 min. The crystal structure, thermal properties, and morphology of ultrafine CA fibers were changed according to the degree of deacetylation, finally to those of pure cellulose, but the nonwoven fibrous mat structure was maintained. The activation energy for the deacetylation of ultrafine CA fibers was 10.3 kcal/mol. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 5–11, 2004     

Relationship between the dynamic softening transition and wet sliding friction of elastomer compounds

For properly chosen elastomer compounds, thermorheological characterization is combined with an examination of the variation of the wet sliding friction with temperature. A conceptual argument leads to the assumption that the wet sliding friction should maximize at the energy dissipation peak associated with the dynamic softening transition at a characteristic frequency determined by the sliding speed and the effective smallest surface asperity scale. The dynamic softening transition is characterized with the peak in tan δ/G′ⁿ, where tan δ is the loss tangent, G′ is the elastic modulus, and n is a constant between 0 and 1. The William–Landel–Ferry transform is uncritically applied for extrapolating the position of the peak in tan δ/G′ⁿ at high frequencies. Even based on the criterion of tan δ, the results obtained on a concrete surface indicate that the effective smallest asperity scale is of order of 100 μm. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2467–2478, 2004