关于一类复合幂级数展开式的收敛性定理

本文研究了一类复合型幂级数展开式,证明了一个收敛性定理并举例说明其应用.在注记中指出了可进一步研究的问题.     

Preparation of enediyne-crosslinked networks and their reactivity under thermal and mechanical conditions

The COGEF technique (COnstrained Geometries simulating External Force) was used to investigate the effects of macroscopic forces on cyclic enediynes, which can undergo Bergman Cyclization (BC). Because the forces needed to activate BC were found to be less than the forces needed for chain scission in polymer backbones, the calculations suggest that enediynes are potentially useful mechanophores. Three enediynes studied computationally were synthesized. The thermal BC reactions for these compounds were studied by DSC and found to be consistent with the predicted thermal sensitivity based on known substituent effects. However, upon incorporation of the enediynes into a polymer matrix as crosslinks, no definitive mechanical activation was observed, and conclusions about the stress-sensitivity of enediynes were unable to be drawn. Model studies suggest that insufficient force was applied to the crosslinks for mechanical activation to be observable by DSC.     

Eine neue Form von Verbrennungsr?hren

Ohne Zusammenfassung     

Nachweis und Bestimmung von Stickstoff

Ohne Zusammenfassung     

Solubility behavior of amphiphilic block and random copolymers based on 2‐ethyl‐2‐oxazoline and 2‐nonyl‐2‐oxazoline in binary water–ethanol mixtures

The solution properties of random and block copolymers based on 2‐ethyl‐2‐oxazoline (EtOx) and 2‐nonyl‐2‐oxazoline (NonOx) were investigated in binary solvent mixtures ranging from pure water to pure ethanol. The solubility phase diagrams for the random and block copolymers revealed solubility (after heating), insolubility, dispersions, micellization as well as lower critical solution temperature (LCST) and upper critical solution temperature behavior. The random and block copolymers containing over 60 mol % pNonOx were found to be solubilized in ethanol upon heating, whereas the dissolution temperature of the block copolymers was found to be much higher than for the random copolymers due to the higher extent of crystallinity. Furthermore, the block copolymer containing 10 mol % pNonOx exhibited a LCST in aqueous solution at 68.7 °C, whereas the LCST for the random copolymer was found to be only 20.8 °C based on the formation of hydrophobic microdomains in the block copolymer. The random copolymer displayed a small increase in LCST up to a solvent mixture of 9 wt % EtOH, whereas further increase of ethanol led to a decrease in LCST, which is probably due to the “water‐breaking” effect causing an increased attraction between ethanol and the hydrophobic part of the copolymer. In addition, the EtOx‐NonOx block copolymers revealed the formation of micelles and dynamic light scattering demonstrated that the micellar size is increasing with increasing the ethanol content due to the enhanced solubility of EtOx. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 515–522, 2009     

Benzothiazines in synthesis. Eight-membered ring formation in an intramolecular Friedel-Crafts reaction

Treatment of certain benzothiazines bearing allylic bromides side chains with indium tribromide resulted in the formation of eight-membered rings in addition to the expected six-membered rings.     

The robertson-taussky inequality revisited

Let a positive definite Hermitian matrix HεMⁿ(C) be decomposed as H=A + iB, with A, B ε M_nm(R). We give two new proofs of the inequality det H ≤ det A (with equality iff B = 0. each of which vields something futher. One exhibits majorization between the eigenvalues of A and H the other allows proof of the permanental analog per H≥per A.     

Compatibility studies of blends of polycarbonate and poly(ethylene terephthalate)

Blends of bisphenol-A polyarbonate (PC) and poly(ethylene terephthalate) (PET) has been investigated by differential scanning calorimetry and scanning electron microscopy. Blends were prepared by screw extrusion and solution casting with weight fractions of PC in the blends varying from 0.90 to 0.10. From the measured glass transition temperature (T_g) and apparent weight fractions of PC and PET dissolved in each phase, it appears that PET dissolves more in the PC-rich phase than does the PC in the PET-rich phase. The composition-dependent values of the Flory–Huggins polymer–polymer–interaction parameter were determined and found to be from 0.054 to 0.037 for extruded blends at 275°C and from 0.058 to 0.040 for solution casting at 25°C. The interaction parameter decreases with increasing PET concentration. This result is consistent with the values of the T_gs, the microscopy study, and the measured extrudate swell ratios which show that compatibility increases more in the PET-rich compositions than in the PC-rich compositions. The PC–PET blends are not microscopically miscible for all the blend compositions.