超广义Burgers方程族的非线性可积耦合及其Bargmann对称约束

基于李超代数,构造了超广义Burgers方程族的非线性可积耦合,并且利用超级恒等式得到了它的超Hamilton结构.此外,该文计算出超广义Burgers方程族的非线性可积耦合的Bargmann对称约束.     

Influence of the Thiophene Ring on the Molecular Order of Structurally Simple π-Conjugated Smectogens: 13C NMR Study

Structurally simple rod-like π-conjugated mesogens with thiophene directly connected to phenyl, biphenyl, and fluorenone rings with terminal chains are synthesized respectively. The occurrence of smectic A/smectic C phases is concurred by a hot-stage optical polarising microscope (HOPM), differential scanning calorimetry (DSC), and X-ray diffraction (XRD). The static 1D and 2D ¹³C nuclear magnetic resonance (NMR) studies in the liquid crystalline phase are carried out to find the alignment-induced chemical shifts (AIS) and ¹³C−¹H dipolar couplings. The orientational order parameters of the mesogens determined from ¹³C−¹H dipolar couplings disclose that the long axis is not only collinear to the C3−C4 bond of the thiophene ring but also for the local axes of phenyl and biphenyl rings. For fluorenone-based mesogen, the molecular biaxiality is found to be high owing to the increased breadth of the molecule. The study unveils that the orientation of thiophene and the phenyl rings is similar in the current mesogens in stark contrast to mesogens, where thiophene is connected to phenyl rings through linking groups.