Delta shock wave for a 3 × 3 hyperbolic system of conservation laws

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. The system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that models viscoelastic fluids. An important issue is that the considered 3×3 system is such that every characteristic field is linearly degenerate. We study theRiemann problemfor this system and under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta shock type solutions are established.     

A fluorescent chemosensor for Cu2+ ions and its application in cell imaging

A new on-off fluorescent probe 1 for Cu²⁺ based on Schiff base compound was designed and synthesized by one-step reaction. The single probe 1 exhibited strong green fluorescence emission. A fluorescence quenching effect and faint color change were observed as soon as the Cu²⁺ was added to the probe system in H₂O/EtOH (v/v = 8:2, HEPES buffer, 0.05 M, pH = 7.4) solution. Other common metal cations did not cause the changes in the fluorescence and color of the probe 1. The optical properties were studied by the fluorescence emission and UV–Vis spectra. Meanwhile, the geometry optimizations of probe 1 and the [1-Cu²⁺] coordination complexes were also carried out by DFT using the Gaussian 09 program, in which the B3LYP function was used. Based on experimental measurement and theoretical analysis, we can know that the combination ratio of the probe and Cu²⁺ is 2:1 and the limit of detection (LOD) is as low as 5.3 × 10^?9 M Besides, the probe 1 was also used to analyze the Cu²⁺ in living cells.     

CoMoO_4晶须材料的制备及烯烃环氧化催化性能研究

利用Co(CH_3COO)_2、氧化钼、钼酸和咪唑为基础原料,在水热条件下成功制备了CoMoO_4晶须材料.通过元素分析、X-射线衍射、傅里叶变换红外光谱以及扫描电子显微镜等手段对材料的结构和形态进行了表征,证明为完整均匀的CoMoO_4晶须.在环辛烯环氧化催化反应中对材料的催化性能进行了测试,结果证明CoMoO_4晶须具有优良的非均相催化性能.     

On the structure vector field of a real hypersurface in complex two-plane Grassmannians

Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.     

Straightforward synthesis of [(2S,4R)-1-cyclohexyl-4-methylpiperidin-2-yl]methanol and [(2S,4R)-1-cyclohexyl-4-methylpiperidin-2-yl](diphenyl)methanol: novel chiral ligands for the catalytic addition of diethylzinc to benzaldehyde to give rise to an extensive turn in the sense of asymmetric induction

Enantiopure [(2S,4R)-1-cyclohexyl-4-methylpiperidin-2-yl]methanol 5a and [(2S,4R)-1-cyclohexyl-4-methylpiperidin-2-yl]-(diphenyl)methanol 5b, new β-amino alcohols based on l-pipecolinic acid (homoproline), have been prepared straightforwardly from rac-alaninol and rac-2-amino-1,1-diphenylpropan-1-ol, respectively. The described route constitutes as a model procedure for the preparation of other related C(4) or/and C(3)-substituted 2-piperidinylmethanols.The new chiral ligands have shown a singular behaviour on the stereocontrol of the benchmark reaction of benzaldehyde and diethylzinc compared with other C(4)-unsubstituted analogues prepared by ourselves from l-pipecolinic acid (compounds 5c, 5d, 5e and 5f). The catalytic activity, the sense of asymmetric induction and the degree of the enantioselectivity depend on the appropriate combination of the substituents on the structural scaffold, but also on the metal-alkoxide involved in the catalysis (zinc or lithium alkoxides). The enantioselective addition of diethylzinc to benzaldehyde mediated by ligands 5a and 5c has been studied with DFT methods. The theoretical evaluation was performed in connection with a working hypothesis based on the different loadings of cis- and trans-catalysts in the reaction medium.     

Hopf bifurcation direction of a delayed bacteria-immunity system with quorum sensing mechanism

Considering the mechanism of quorum sensing, we formulate a bacteria-immunity model to describe the competition between bacteria and immune cells on the basis of Zhang’s model (see [9] for more details). A time delay is introduced to characterize the time in which bacteria receive signal molecules and then combat with immune cells. In the sequel, the length of delay which preserves the stability of the positive equilibrium is estimated, and the existence of Hopf bifurcation when the delay crosses through a critical value is investigated. Further, by using the normal form theory and center manifold theory, the explicit formulae are calculated which determine the stability, the direction and the period of bifurcating periodical solutions. Finally, numerical simulations are employed to verify the mathematical conclusions.     

Annihilators for Harmonic Differential Forms Via Clifford Analysis

In this paper we describe completely the annihilators of harmonic differential forms into the Clifford analysis approach.