一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Chiral phase transition and equation of state in chiral imbalance

The chiral phase transition and equation of state are studied within a novel self-consistent mean-field approximation of the two-flavor Nambu-Jona-Lasinio model. In this newly developed model, modifications to the chemical μ and chiral chemical \begin{document}$\mu_5$\end{document} potentials are naturally included by introducing vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian. In the proper-time scheme, the chiral phase transition is a crossover in the \begin{document}$T-\mu$\end{document} plane. However, when \begin{document}$\mu_5$\end{document} is incorporated, our study demonstrates that a first order phase transition may emerge. Furthermore, the chiral imbalance will soften the equation of state of quark matter. The mass-radius relationship and tidal deformability of quark stars are calculated. The maximum mass and radius decrease as \begin{document}$\mu_5$\end{document} increases. Our study also indicates that the vector and axial-vector channels exhibit an opposite influence on the equation of state.     

Selective Catalytic Isomerization of β-Pinene Oxide to Perillyl Alcohol Enhanced by Protic Tetraimidazolium Nitrate

A series of tetraimidazolium salts with different anions was prepared and applied in the isomerization of β-pinene oxide. After examining the activity of different catalysts, a remarkable enhancement of the selectivity of perillyl alcohol (47 %) was obtained over [PEimi][HNO₃]₄ under mild reaction conditions and using DMSO as the solvent. Furthermore, noncovalent interactions between solvent molecules and the catalyst were found by FT-IR spectroscopy and confirmed by computational chemistry. The homogeneous catalyst showed excellent stability and was reused up to six times without significant loss.     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Aryl Boronic Acid Catalysed Dehydrative Substitution of Benzylic Alcohols for C−O Bond Formation

A combination of pentafluorophenylboronic acid and oxalic acid catalyses the dehydrative substitution of benzylic alcohols with a second alcohol to form new C−O bonds. This method has been applied to the intermolecular substitution of benzylic alcohols to form symmetrical ethers, intramolecular cyclisations of diols to form aryl-substituted tetrahydrofuran and tetrahydropyran derivatives, and intermolecular crossed-etherification reactions between two different alcohols. Mechanistic control experiments have identified a potential catalytic intermediate formed between the aryl boronic acid and oxalic acid.     

Dimeric Manganese-Catalyzed Hydroarylation and Hydroalkenylation of Unsaturated Amides

An unprecedented Mn(I)-catalyzed selective hydroarylation and hydroalkenylation of unsaturated amides with commercially available organic boronic acids is reported. Alkenyl boronic acids have been successfully employed for the first time in Mn(I)-catalyzed carbon–carbon bond formation. A wide array of β-alkenylated amide products can be obtained in moderate to good yields, which offers practical access to five- and six-membered lactams. This protocol has predictable regio- and chemoselectivity, excellent functional group compatibility and ease of operation in air, representing a significant step-forward towards manganese-catalyzed C−C coupling.