Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point

In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.     

Preparation of Functionalized Imidazolium Salts under Microwave Irradiation

A direct alkylation of a substituted imidazole to prepare the corresponding functionalized ionic liquid has been developed in excellent yields under microwave irradiation.     

Cholesteric induction power of β-galactose derivatives

Galactose derivatives were explored as chiral dopants, effective for inducing chiral nematic liquid crystal (LC) phases. Galactose bearing O-isopropylidene substituents at the C3 and C4 and butoxybiphenyl substituents at the C2 and C6 positions exhibits a high helical twisting power (HTP) value of ?74.4 μm^?1. Such a high HTP value for the galactose derivative is attributed to (1) linkage of the C3 and C4 carbons with the O-isopropylidene substituent, which places the C2 and C6 substitutes in a skew arrangement at a large angle and (2) enhancement of the affinity with the host nematic LCs by incorporating aromatic substituents at the C2 and C6 positions that are similar to those in the host.     

A bird nest-like manganese dioxide and its application as electrode in supercapacitors

A novel bird nest-like nanostructured MnO2(BNNS-MnO2) was prepared by a facile and cost-effective strategy. Their structures and morphologies were characterized by field emission scanning electron microscopy, transmission electron microscopy and powder X-ray diffraction. Capacitive behaviors were investigated by cyclic voltammetry and galvanostatic charge-discharge. The obtained nano-MnO2 possesses a well designed loose-assembled hierarchical nanoarchitecture with an appropriate crystallinity which gives rise to excellent performances as an electrode material for supercapacitors. A maximum specific capacitance of 917 F/g has been obtained at a current density of 5 mA/cm2 in 6 mol/L KOH aqueous solution, and a specific capacitance of 210 F/g has been maintained for 500 cycles. As the low cost of MnSO4 and KCr2O7 and the low reaction temperature, the present method avoids the requirements for complicated operations, time/energy-consuming and expensive reagents, and perhaps is ready for the industrialization of nano-MnO2 production.     

(R)-3-乙酸奎宁环基酯的合成

分别以(R)-3-奎宁环醇与乙酸乙酯的酯交换法和(R)-3-奎宁环醇与乙酸酐的乙酸酐法合成了(R)-3-乙酸奎宁环基酯。通过考察原料摩尔比、催化剂用量、反应时间对产品收率的影响探索了合适的合成工艺。结果表明,乙酸酐法得到的产品收率远远高于酯交换法得到的产品收率,收率最高可达86.1%。     

Zigzag defect-free alignment of surface stabilized ferroelectric liquid crystal cells with a polyimide irradiated by polarized UV light

Zigzag defect-free surface stabilized ferroelectric liquid crystal (SSFLC) cells were prepared using a photodegradable polyimide (PI) having a cyclobutane ring in the backbone. The PI layers were irradiated by polarized ultraviolet light (PUVL) at normal incidence to the surface, and characterized by UV and FTIR spectroscopy. The anisotropy originates from preferential cleavage of PI chains oriented parallel to the polarization direction of the irradiating PUVL. After the polarized UV light irradiation, the PI surface was much flatter than that after rubbing, but it induced a similar order parameter of dye-doped nematic LC molecules to that for a rubbed cell. Alignment of both the FLC molecules and the layer structure is important in SSFLC. After 40 min irradiation, the FLC molecules were well aligned homogeneously, and the FLC cells showed a uniform texture without zigzag defects which also indicates a well aligned layer structure. Zigzag defect-free alignment may result from the flatter surface, the much smaller and more constant pretilt angles, and the bigger cone angle than those achieved by rubbing.     

Liquid crystalline behaviour of hydrogen-bonded complexes of alkoxycinnamic acids with octyloxystilbazole

Hydrogen-bonded liquid crystalline complexes have been obtained through 1:1 (molar ratio) complexation of 4-n-alkoxycinnamic acids (nCNA: n = 4, 8, 10, 12, where n is the number of carbons in the alkyloxy chain) and trans-4-octyloxystilbazole (8Sz). These hydrogen-bonded complexes (nCNA8Sz) form stable mesophases. The mesomorphic range was extended by the mixing of complexes. Hexatic modification of smectic B (SmB_h), smectic C (SmC), smectic A (SmA), and nematic mesophases of these complexes were determined by a combination of X-ray diffraction and polarizing optical microscopy. Transitions between the various smectic phases were deduced from the temperature-dependent layer spacing of nCNA8Sz. The layer spacing of these complexes in the SmB_h and SmA phases gradually increased with increasing alkoxy chain length. The favouring of smectic phases in these complexes is believed to originate from the increment of polarity of the mesogen by intermolecular H-bonding.