非线性不适定问题一种双循环的牛顿型迭代格式

本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。     

Epoxy resin containing polyphenylsilsesquioxane: Preparation,morphology, and thermomechanical properties

Polyphenylsilsesquioxane (PPSQ) was incorporated into an epoxy resin to prepare organic–inorganic composites, and two strategies were adopted to afford composites with different morphologies. Phase separation induced by polymerization occurred in the physical blending system. However, nanostructured composites were obtained when a catalytic amount of aluminum triacetylacetonate was added to mediate the reaction between PPSQ and diglycidyl ether of bisphenol A (DGEBA). The intercomponent reaction significantly suppressed the phase separation on the micrometer scale. Organic–inorganic composites with different morphologies displayed quite different thermomechanical properties. Both differential scanning calorimetry and dynamic mechanical analysis showed that the nanostructured composites possessed higher glass‐transition temperatures than the phase‐separated composites with the same loading of PPSQ, although the intercomponent reaction between PPSQ and DGEBA reduced the crosslinking density of the epoxy matrix. This result was ascribed to the presence of nanosized PPSQ domains in the nanostructured composites, which acted as physical crosslinking sites and thus reinforced the epoxy networks. The nanoreinforcement of the PPSQ domains afforded the enhanced dynamic storage modulus for the nanostructured composites in comparison with the phase‐separated composites with a PPSQ concentration less than 15 wt %. In terms of thermogravimetric analysis, the organic–inorganic composites displayed improved thermal stability and flame retardancy. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1093–1105, 2006     

Physically cross‐linked networks of POSS‐capped poly(acrylate amide)s: Synthesis,morphologies, and shape memory behavior

In this work, we synthesized a novel organic–inorganic semitelechelic polymer from polyhedral oligomeric silsesquioxane (POSS) and poly(acrylate amide) (PAA) via reversible addition‐fragmentation chain transfer (RAFT) polymerization. The organic–inorganic semitelechelic polymers have been characterized by means of nuclear magnetic resonance spectroscopy, thermal gravimetric analysis, and dynamic mechanical thermal analysis. It was found that capping POSS groups to the single ends of PAA chains caused a series of significant changes in the morphologies and thermomechanical properties of the polymer. The organic–inorganic semitelechelics were microphase‐separated; the POSS microdomains were formed via the POSS–POSS interactions. In a selective solvent (e.g., methanol), the organic–inorganic semitelechelics can be self‐assembled into the micelle‐like nanoobjects. Compared to plain PAA, the POSS‐capped PAAs significantly displayed improved surface hydrophobicity as evidenced by the measurements of static contact angles and surface atomic force microscopy. More importantly, the organic–inorganic semitelechelics displayed typical shape memory properties, which was in marked contrast to plain PAA. The shape memory behavior is attributable to the formation of the physically cross‐linked networks from the combination of the POSS–POSS interactions with the intermolecular hydrogen‐bonding interactions in the organic–inorganic semitelechelics. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 587–600     

Poly(N-isopropylacrylamide)-block-poly(acrylic acid) hydrogels: synthesis and rapid thermoresponsive properties

In this contribution, we reported the synthesis of poly(N-isopropylacrylamide)-block-poly(acrylic acid) (PNIPAAm-b-PAA) copolymer networks via sequential reversible addition-fragmentation chain transfer (RAFT) polymerization. The PNIPAAm-b-PAA block copolymer networks were characterized by means of Fourier transform infrared spectroscopy (FTIR) and small angle X-ray scattering (SAXS). The volume phase transition (VPT) temperatures of the PNIPAAm-b-PAA hydrogels were measured by means of micro-differential scanning calorimetry (micro-DSC). It was found that the block copolymer hydrogels displayed the VPT temperatures lower than the control PNIPAAm hydrogel. Compared to the control PNIPAAm hydrogel, the deswelling and reswelling properties of the block copolymer hydrogels were significantly improved. The improved thermoresponsive properties of the PNIPAAm-b-PAA hydrogels have been interpreted on the basis of the formation of the architecture of the block copolymer networks.     

环氧树脂/聚碳酸酯固化共混物的结构及性能

相结构;酯交换反应;力学性能;环氧树脂/聚碳酸酯固化共混物的结构及性能     

Hyperbranched block copolymer from AB2 macromonomer: Synthesis and its reaction‐induced microphase separation in epoxy thermosets

In this contribution, we reported the synthesis of a hyperbranched block copolymer composed of poly(ε‐caprolactone) (PCL) and polystyrene (PS) subchains. Toward this end, we first synthesized an α‐alkynyl‐ and ω,ω′‐diazido‐terminated PCL‐b‐(PS)₂ macromonomer via the combination of ring‐opening polymerization and atom transfer radical polymerization. By the use of this AB₂ macromonomer, the hyperbranched block copolymer (h‐[PCL‐b‐(PS)₂]) was synthesized via a copper‐catalyzed Huisgen 1,3‐dipolar cycloaddition (i.e., click reaction) polymerization. The hyperbranched block copolymer was characterized by means of ¹H nuclear magnetic resonance spectroscopy and gel permeation chromatography. Both differential scanning calorimetry and atomic force microscopy showed that the hyperbranched block copolymer was microphase‐separated in bulk. While this hyperbranched block copolymer was incorporated into epoxy, the nanostructured thermosets were successfully obtained; the formation of the nanophases in epoxy followed reaction‐induced microphase separation mechanism as evidenced by atomic force microscopy, small angle X‐ray scattering, and dynamic mechanical thermal analysis. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 368–380     

Microphase separation in polybenzoxazine thermosets containing benzoxazine-terminated poly(ethylene oxide) telechelics

Benzoxazine-terminated poly(ethylene oxide) telechelics (Ba-terminated PEO) was synthesized and incorporated into polybenzoxazine to obtain the nanostructured thermosets. The morphology of the thermosets was investigated by means of atomic force microscopy (AFM), small angle X-ray scattering (SAXS) and dynamic mechanical analysis (DMA). The formation of the nanophase structures in the thermosetting composites was addressed on the basis of the mechanism of reaction-induced microphase separation (RIMPS), which was in marked contrast to the case of the binary thermosetting blends of polybenzoxazine with hydroxyl-terminated poly(ethylene oxide). The occurrence of RIMPS resulted from the copolymerization reaction of the end groups of Ba-terminated PEO telechelics with the precursor of thermosetting matrix (i.e., benzoxazine), which suppressed the occurrence of the macroscopic phase separation. It was found that the formation of the nanostructures has a significant effect on the melting behavior of PEO in the thermosets, thermal transition properties of the PBZ thermosets.     

Supramolecular inclusion complexation of polyhedral oligomeric silsesquioxane capped poly(ε‐caprolactone) with α‐cyclodextrin

Supramolecular inclusion complexes (ICs) involving polyhedral oligomeric silsesquioxane (POSS) capped poly(?‐caprolactone) (PCL) and α‐cyclodextrin (α‐CD) were investigated. POSS‐terminated PCLs with various molecular weights were prepared via the ring‐opening polymerization of ?‐caprolactone (CL) with 3‐hydroxypropylheptaphenyl POSS as an initiator. Because of the presence of the bulky silsesquioxane terminal group, the inclusion complexation between α‐CD and the POSS‐capped PCL was carried out only with a single end of a PCL chain threading inside the cavity of α‐CD, which allowed the evaluation of the effect of the POSS terminal groups on the efficiency of the inclusion complexation. The X‐ray diffraction results indicated that the organic–inorganic ICs had a channel‐type crystalline structure. The stoichiometry of the organic–inorganic ICs was quite dependent on the molecular weights of the POSS‐capped PCLs. With moderate molecular weights of the POSS‐capped PCLs (e.g., M_n =3860 or 9880), the stoichiometry was 1:1 mol/mol (CL unit/α‐CD), which was close to the literature value based on the inclusion complexation of α‐CD with normal linear PCL chains with comparable molecular weights. When the PCL chains were shorter (e.g., for the POSS‐capped PCL of M_n = 1720 or 2490), the efficiency of the inclusion complexation decreased. The decreased efficiency of the inclusion complexation could be attributed to the lower mobility of the bulky POSS group, which restricted the motion of the PCL chain attached to the silsesquioxane cage. This effect was pronounced with the decreasing length of the PCL chains. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1247–1259, 2007     

Douglis代数意义下的超复函数空间上的Tn算子及其性质

In this paper, some properties of Tⁿ operator for hypercomplex space are studied.     

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Rayleigh-Taylor (R-T) instability is known as the fundamental mechanism of equatorial plasma bubbles (EPBs). However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows: if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments are designed to validate the sufficient conditions. The results agree with the derived sufficient conditions.