代数κ-拟-A类算子的Weyl定理

若T或T~*是无穷维可分的Hilbert空间H上的代数κ-拟-A类算子,则Weyl定理对任意的f∈H(σ(T))成立,其中H(σ(T))为σ(T)的开邻域上解析函数的全体.若T~*是代数κ-拟-A类算子,则a-Weyl定理对f(T)成立。还证明了若T或T~*是代数κ-拟-A类算子,则Weyl谱与本质近似点谱的谱映射定理对f(T)成立.     

静态球对称黑洞热力学与爱因斯坦场方程

建立在广义相对论基础上的黑洞理论与热力学定律之间有着深刻的内在联系.具体考虑球对称黑洞,研究表明通过史瓦西黑洞和Reissner-Nordstrom黑洞在其视界附近的爱因斯坦场方程可以直接得到对应的黑洞热力学第一定律.这揭示了爱因斯坦引力场方程与黑洞热力学的关系,表明了在广义相对论理论框架下黑洞热力学规律的必然性.     

Electronic and optical properties of 3N-doped graphdiyne/MoS2 heterostructures tuned by biaxial strain and external electric field

The construction of van der Waals (vdW) heterostructures by stacking different two-dimensional layered materials have been recognised as an effective strategy to obtain the desired properties. The 3N-doped graphdiyne (N-GY) has been successfully synthesized in the laboratory. It could be assembled into a supercapacitor and can be used for tensile energy storage. However, the flat band and wide forbidden bands could hinder its application of N-GY layer in optoelectronic and nanoelectronic devices. In order to extend the application of N-GY layer in electronic devices, MoS₂ was selected to construct an N-GY/MoS₂ heterostructure due to its good electronic and optical properties. The N-GY/MoS₂ heterostructure has an optical absorption range from the visible to ultraviolet with a absorption coefficient of 10⁵ cm^-1. The N-GY/MoS₂ heterostructure exhibits a type-Ⅱ band alignment allows the electron-hole to be located on N-GY and MoS₂ respectively, which can further reduce the electron-hole complexation to increase exciton lifetime. The power conversion efficiency of N-GY/MoS₂ heterostructure is up to 17.77%, indicating it is a promising candidate material for solar cells. In addition, the external electric field and biaxial strain could effectively tune the electronic structure. Our results provide a theoretical support for the design and application of N-GY/MoS₂ vdW heterostructures in semiconductor sensors and photovoltaic devices.     

Hemin-Promoted Direct C−H Thiolation in the Synthesis of Diaryl Sulfides

Diaryl sulfides are a class of important synthetic chemical units. Herein, we report a new method for direct preparation of diphenyl sulfides using P-toluenesulfonyl chloride as an effective thiophenyl radical precursor with assistance from Hemin. Various substituted anisoles and benzenesulfonyl chlorides are well tolerated, resulting in moderate to good yields of diaryl sulfides. The potential of the proposed method is validated by good yields obtained in gram scale reactions.     

Residue Theorem and Theta Function Identities

In this paper we will use the residue theorem of elliptic functions to prove some theta function identities of Ramanujan. We also derive some new identities by this method.     

Three kinds of horizon-like hypersurface of a uniformly accelerating, non-stationary charged black hole

Three kinds of horizon-like hypersurface of a uniformly rectilinearly accelerating, non-stationary charged black hole: event horizon, apparent horizon and time-like limit surface are studied. The result is that the event horizon is apart from the time-like limit surface and the apparent horizon in the case where the black hole is charged, uniformly accelerating and its mass is varying (evaporating and accreting). Some other new results are also given. Project supported by the National Natural Science Foundation of China.     

NIR light-induced tumor phototherapy using ICG delivery system based on platelet-membrane-camouflaged hollow bismuth selenide nanoparticles

Near-infrared (NIR) light-triggered photothermal therapy (PTT) is a promising treatment strategy for treating cancer. The combination of nanotechnology and NIR has been widely applied. However, the therapeutic efficacy of the drug-delivery system depends on their ability to avoid phagocytosis of endothelial system, cross the biological barriers, prolong circulation life, localize and rapidly release the therapeutic at target sites. In this work, we designed a platelet membrane (PM)-camouflaged hollow mesoporous bismuth selenide nanoparticles (BS NPs) loading with indocyanine green (ICG) (PM@BS-ICG NPs) to achieve the above advantages. PM-coating has active tumor-targeting ability which could prevent drug leakage and provide drug long circulation, causing drug delivery systems to accumulate in tumor sites effectively. Moreover, as a type of the photothermal sensitizers, BS NPs are used as the inner cores to improve ICG stability and are served as scaffolds to enhance the hardness of this drug delivery system. For one hand, the thermal vibration of BS NPs under NIR laser irradiation causes tumor inhibition through hyperthermia. For another hand, this hyperthermia process could damage PM and let ICG rapid release from PM@BS-ICG NPs. The in vitro and in vivo results showed that this biomimetic nano-drug delivery system exhibits obvious antitumor activity which has good application prospect.     

An Expansion Formula for q-Series and Applications

In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers–Fine identity, the nonterminating ₆₅ summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.     

钫原子磁偶极超精细结构常数及其同位素的磁偶极矩的理论计算

应用基于B样条基组的相对论耦合簇理论方法,计算了~(212)Fr原子的n S (n=7—12), n P (n=7—12)和n D (n=6—11)态的磁偶极超精细结构常数.与精确实验值的比较说明这套理论方法能精确计算出磁偶极超精细结构常数,其中7P态的磁偶极超精细常数的理论值与实验值之间的差异小于1%.在忽略场移效应对Fr原子7P态超精细结构常数的影响下,通过结合实验值进一步定出了~(207-213,220-228)Fr核磁偶极矩μ,这些值与已有的测量值具有非常好的一致性.本文报道了12S, n P (n=9—12)和n D (n=10—11)态的磁偶极超精细结构常数.