关于完全完备分配格上矩阵相对于特征值的特征向量

借助于伪补和矩阵的幂序列研究了完全完备分配格上矩阵相对于特征值的特征向量的计算方法,利用特征向量的性质证明了最大特征向量的计算公式,并给出了一般特征向量的计算方法.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

Study on the reaction mechanism between Pb3O4 and Si in stored silicon delay composition

Journal of Thermal Analysis and Calorimetry - The thermogravimetric techniques and differential thermal analysis have been employed in this work to analyze the macro-reactions mechanism of the...     

Core–shell CeO2 micro/nanospheres prepared by microwave-assisted solvothermal process as high-stability anodes for Li-ion batteries

Journal of Solid State Electrochemistry - Core–shell CeO2 micro/nanospheres are prepared via microwave-assisted solvothermal process followed by calcination in air. The reaction time is only...     

Solvent replacement to thermo‐responsive nanoparticles from long‐subchain hyperbranched PSt grafted with PNIPAM for encapsulation

Long‐subchain hyperbranched polystyrene (lsc‐hp PSt) with uniform subchain length was obtained through copper‐catalyzed azide‐alkyne cycloaddition click chemistry from seesaw macromonomer of PSt having one alkynyl group anchored at the chain centre and two azido group attached to both chain ends [alkynyl‐(PSt‐N₃)₂]. After precipitation fraction, different portions of lsc‐hp PSt having narrow overall molecular weight distribution were obtained for further grafting with alkynyl‐capped poly(N‐isopropylacrylamide) (alkynyl‐PNIPAM), which was obtained via single‐electron transfer living radical polymerization of NIPAM with propargyl 2‐bromoisobutyrate as the initiator and grafted onto the peripheral azido groups of lsc‐hp PSt via click chemistry. Thus, amphiphilic lsc‐hp PSt grafted with PNIPAM chains (lsc‐hp PSt‐g‐PNIPAM) was obtained and would have star‐like conformation in tetrahydrofuran (THF). By replacing THF with water, lsc‐hp PSt‐g‐PNIPAM was dissolved at molecular level in aqueous solution due to the hydrophilicity of PNIPAM and exhibited thermal induced shrinkage of PNIPAM arms. The water‐insoluble lsc‐hp PSt would collapse densely and could be served as a reservoir to absorb hydrophobic chemicals in aqueous solution. The influence of overall molecular weight of lsc‐hp PSt on the absorption of pyrene was studied. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Conjugated polymer‐functionalized graphite oxide sheets thin films for enhanced photovoltaic properties of polymer solar cells

In this study, the maleimide‐thiophene copolymer‐functionalized graphite oxide sheets (PTM21‐GOS) and carbon nanotubes (PTM21‐CNT) were developed for polymer solar cell (PSC) applications. The grafting of PTM21‐OH onto the CNT and GO sheets was confirmed using FTIR spectroscopy. PTM21‐CNT and PTM21‐GOS exhibited excellent dispersal behavior in organic solvents. Better thermal stability was observed for PTM21‐CNT and PTM21‐GOS as compared with that for PTM21‐OH. In addition, the optical band gaps of PTM21‐GOS and PTM21‐CNT were lower than that of PTM21‐OH. We incorporated PTM21‐GOS and PTM21‐CNT individually into poly(3‐hexylthiophene) (P3HT)/[6,6]‐phenyl‐C₆₁‐butyric acid methyl ester (PCBM) blends for use as photoconversion layers of PSCs. Good distributional homogeneity was observed for PTM21‐GOS or PTM21‐CNT in the P3HT/PCBM blend film. The UV–vis absorption peaks of the blend films red‐shifted slightly upon increasing the content of PTM21‐GOS or PTM21‐CNT. The band gap energies and LUMO/HOMO energy levels of the P3HT/PTM21‐GOS and P3HT/PTM21‐CNT blend films were slightly lower than those of the P3HT film. The conjugated polymer‐functionalized PTM21‐GOS and PTM21‐CNT behaved as efficient electron acceptors and as charge‐transport assisters when incorporated into the photoactive layers of the PSCs. PV performance of the PSCs was enhanced after incorporating PTM21‐GOS or PTM21‐CNT in the P3HT/PCBM blend. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Rhodium-Catalyzed Addition of Aryl Boronic Acids to 2,2-Disubstituted Malononitriles

β-Ketonitriles bearing a quaternary carbon at the 2-position were prepared through Rh-catalyzed addition of aryl boronic acids to 2,2-disubstituted malononitriles. In contrast to the previously described transnitrilative cyanation of aryl boronic acids with dialkylmalononitriles, the present reaction avoids retro-Thorpe collapse of the intermediate addition product through the use of a milder base. The reaction was amenable to a variety of aryl boronic acids and disubstituted malononitriles, providing a diverse array of β-ketonitriles. The products could be further derivatized to valuable chiral α,α-disubstituted-β-aminonitriles through addition reactions to the corresponding N-tert-butanesulfinyl imines.     

Observation of capillary discharge Ne-like Ar 46.9?nm laser with pre-pulse and main-pulse delay time in the domain of 2–130?μs

We demonstrated the lasing of Ne-like Ar 46.9?nm pumped by capillary discharge with the delay time between pre-pulse and main-pulse ranging from 2 to 130???s. Results show that the laser output reduced significantly when the delay time is much longer than 12???s. The temporal evolution of spontaneous radiation emitted from pre-ionized plasma implies that the observed reduction of the laser output is caused by the axial non-uniformity of pre-ionized plasma density and the decrease of pre-ionized plasma density.     

Cerium (IV) ammonium nitrate (CAN)-mediated regioselective synthesis and anticancer activity of 6-substituted 5,8-dimethoxy-1,4-naphthoquinone

6-Substituted 5,8-O-dimethyl-1,4-naphthoquinones (6-DMNQ), the promising anticancer scaffolds, were selectively generated by oxidative demethylation of 2-substituted 1,4,5,8-tetramethoxynaphthalenes with CAN in EtOAc/H₂O in comparatively high yields. An interesting finding was that apart from the reported electron-withdrawing effects of substituents on position 2 of naphthalene ring, regioselective synthesis of 6-DMNQ was largely dependent on the steric effects in CAN-mediated oxidation. The selective cytotoxicities of 6-DMNQ from the in vitro cell-based assays were exhibited between the cancer cells and normal cells. Moreover, most of sulfur-containing 6-DMNQ derivatives displayed better anticancer activities than the corresponding oxygen-containing ones, which could provide an available strategy for the design of 6-DMNQ derivatives as potential anticancer agents.