一个包含Smarandache函数的方程

对于任意正整数n,我们用S(n)表示Smarandache函数,即S(n)=min{m:n|m!}.本文的主要目的是运用初等方法研究方程∑_(d|n)S(d)=n的可解性,并给出它的所有正整数解.     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

Synthesis of cellulose carbamate by supercritical CO2-assisted impregnation: Structure and rheological properties

Cellulose carbamate, an environmentally friendly material presents an interesting alternative to petroleum-based polymers because of its renewable, biodegradable, biocompatible nature and its solubility in conventional solvents. In synthesis process of cellulose carbamate, urea was firstly impregnated into the cellulose pulp by supercritical CO₂(scCO₂), followed by the esterification of cellulose. The structure of cellulose carbamate was characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffractometry (XRD) and scanning electron microscopy (SEM). The rheological properties of these cellulose carbamates in 9% sodium hydroxide solution were investigated, using a range of the nitrogen content, concentrations and shear rates.     

Image Displaying Method of Ground-Based Millimeter Wave Radiometric Imaging System

The image displaying methods used in a millimeter wave radiometric imaging system have great influence on its imaging quality. In order to obtain high quality millimeter wave radiometric images, intensive studies on the image displaying methods are needed. This paper describes the image displaying method of Ground-based 8mm Millimeter Wave Radiometric Imaging (GMWRI) system and compares two different image displaying methods. The experimental results prove the unequal size element arc displaying method fits GMWRI system better.     

Synthesis of grafted poly(p‐phenyleneethynylene) with energy donor–acceptor architecture via atom transfer radical polymerization: Towards nonaggregating and hole‐facilitating light‐emitting material

In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007     

Electroless deposition of open-end Cu nanotube arrays

Cu nanotube arrays were fabricated by electroless deposition using porous anodic aluminium oxide membranes as templates. This was accomplished by a four-step procedure, i.e. pore-wall modification, polishing treatment, sensitization-activation and electroless deposition. The as-synthesized Cu nanotubes possess controllable inner diameter and open ends.     

Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface

An experimental study was performed to understand the nucleate boiling heat transfer of water–CuO nanoparticles suspension (nanofluids) at different operating pressures and different nanoparticle mass concentrations. The experimental apparatus is a miniature flat heat pipe (MFHP) with micro-grooved heat transfer surface of its evaporator. The experimental results indicate that the operating pressure has great influence on the nucleate boiling characteristics in the MFHP evaporator. The heat transfer coefficient and the critical heat flux (CHF) of nanofluids increase greatly with decreasing pressure as compared with those of water. The heat transfer coefficient and the CHF of nanofluids can increase about 25% and 50%, respectively, at atmospheric pressure whereas about 100% and 150%, respectively, at the pressure of 7.4 kPa. Nanoparticle mass concentration also has significant influence on the boiling heat transfer and the CHF of nanofluids. The heat transfer coefficient and the CHF increase slowly with the increase of the nanoparticle mass concentration at low concentration conditions. However, when the nanoparticle mass concentration is over 1.0 wt%, the CHF enhancement is close to a constant number and the heat transfer coefficient deteriorates. There exists an optimum mass concentration for nanofluids which corresponds to the maximum heat transfer enhancement and this optimum mass concentration is 1.0 wt% at all test pressures. The experiment confirmed that the boiling heat transfer characteristics of the MFHP evaporator can evidently be strengthened by using water/CuO nanofluids.     

Synthesis and light emitting properties of polyacetylenes having pendent fluorene groups

Five novel fluorene‐containing polymers, poly[(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA1 ), poly[(1‐pentyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene) ( PFA2 ), poly[1‐decyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA3 ), poly[1‐phenyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA4 ), and poly[1‐(3,4‐difluorophenyl)‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA5 ) were synthesized by the polymerization of the corresponding fluorene‐substituted acetylenic monomers ( M1–M5), using WCl₆, MoCl_5, and TaCl₅ as catalysts and n‐Bu₄Sn as a cocatalyst. The synthesized polymers were thermally stable and readily soluble in common organic solvents. The degradation temperatures for a 5% weight loss of the polymers were ∼352–503 °C under nitrogen. PFA1–PFA5 show emission peaks from 402 to 590 nm. Besides, their electroluminescent properties were studied in heterostructure light‐emitting diodes (LEDs), using PFA2–PFA5 as an emitting layer. The PFA5 device revealed an orange‐red emission peak at 602 nm with a maximum luminescence of 923 cd/m² at 8 V. A device with the ITO/PEDOT/ a mixture of PFA2 (98 wt %) and PFA5 (2 wt %)/Ca/Al showed near white emission. Its maximum luminance and current efficiency are 450 cd/m² at 15 V and 1.3 cd/A, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 519–531, 2006     

Chemically modified proton‐conducting membranes based on sulfonated polyimides: Improved water stability and fuel‐cell performance

A series of branched/crosslinked sulfonated polyimide (B/C‐SPI) membranes were prepared and evaluated as proton‐conducting ionomers based on the new concept of in situ crosslinking from sulfonated polyimide (SPI) oligomers and triamine monomers. Chemical branching and crosslinking in SPI oligomers with 1,3,5‐tris(4‐aminophenoxy)benzene as a crosslinker gave the polymer membranes very good water stability and mechanical properties under an accelerated aging treatment in water at 130 °C, despite their high ion‐exchange capacity (2.2–2.6 mequiv g^?1). The resulting polymer electrolytes displayed high proton conductivities of 0.2–0.3 S cm^?1 at 120 °C in water and reasonably high conductivities of 0.02–0.03 S cm^?1 at 50% relative humidity. In a single H₂/O₂ fuel‐cell system at 90 °C, they exhibited high fuel‐cell performances comparable to those of Nafion 112. The B/C‐SPI membranes also displayed good performances in a direct methanol fuel cell with methanol concentrations as high as 50 wt % that were superior to those of Nafion 112. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3751–3762, 2006