Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Nehari函数族的偏差性质与拟共形延拓

研究某一Nehari函数族的偏差性质,得到这类函数族的H?lder连续性及若干偏差定理,同时讨论了该函数类的拟共形延拓问题,并给出拟共形延拓的复伸张估计,推广了杨宗信等人相应的结论.     

第32届江苏省化学竞赛选拔赛有机化学试题解析*

利用有机化学基础知识和理论对第32届江苏省化学竞赛选拔赛试题有机化学部分进行详细解析,为指导老师和参赛学生提供参考。     

Synergistic antibacterial effects of ultrasound and thyme essential oils nanoemulsion against Escherichia coli O157:H7

Essential oil nanoemulsions have been proven to have stronger antimicrobial effects compared to the essential oil alone or coarse emulsion. Sonoporation could be the promising candidate to trigger a synergistic effect with thyme essential oil nanoemulsion (TEON) and produce a more effective antibacterial efficacy. Therefore, in this study, the bactericidal effects of ultrasound (US) in combination with TEON treatments against Escherichia coli (E. coli) O157:H7 were investigated. The remarkable synergistic effects of US (20 kHz, 255 W/cm², 9 min) and TEON (0.375 mg/mL) treatments at 22 °C reduced E. coli O157:H7 populations by 7.42 ± 0.27 log CFU/mL.The morphological changes of cells exposed to different treatments were observed by scanning electron microscopy and transmission electron microscopy. The results showed that the synergistic effects of the ultrasound and TEON treatments altered the morphology and interior microstructure of organism cells. Laser scanning confocal microscopy (LSCM) images revealed that the combination treatments of ultrasound and TEON altered the permeability of cell membranes, and this affected the integrity of E. coli O157:H7 cells. This was further indicated by the high amounts of nucleic acids and proteins released from these cells following treatment.The results from this study illustrated the mechanisms of the synergistic effects of sonoporation and TEON treatments and provided valuable information for their potential in food pasteurization.     

Investigation of stability,consistency, and oil oxidation of emulsion filled gel prepared by inulin and rice bran oil using ultrasonic radiation

Inulin, rice bran oil and rosemary essential oil were used to produce high quality emulsion filled gel (EFG) using ultrasonic radiation. Response surface methodology was used to investigate the effects of oil content, inulin content and power of ultrasound on the stability and consistency of prepared EFG. The process conditions were optimized by conducting experiments at five different levels. Second order polynomial response surface equations were developed indicating the effect of variables on EFG stability and consistency. The oil content of 18%; inulin content of 44.6%; and power of ultrasound of 256 W were found to be the optimum conditions to achieve the best EFG stability and consistency. Microstructure and rheological properties of prepared EFG were investigated. Oil oxidation as a result of using ultrasonic radiation was also investigated. The increase of oxidation products and the decrease of total phenolic compounds as well as radical scavenging activity of antioxidant compounds showed the damaging effect of ultrasound on the oil quality of EFG.     

Classification of extensions of torus algebra II

We use extension theory and algebraic methods to give a complete characterization of extensions of torus algebra by stable Cuntz algebras,and prove certain classification theorems of these extension algebras.     

The trigonometric triangle

A procedure is presented by which the integration of a function such as cos ⁿ (x) or sin ⁿ (x) with n = 1, 2, 3, 4 … is facilitated.     

Essential and continuous spectrum of symmetric difference equations

Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation.