Polymeric Carbon Nitride-based Single Atom Photocatalysts for CO2 Reduction to C1 Products

Photocatalytic CO₂ reduction to C₁ fuels is considered to be an important way for alleviating increasingly serious energy crisis and environmental pollution. Due to the environment-friendly, simple preparation, easy formation of highly-stable metal-nitrogen(M-N_x) coordination bonds, and suitable band structure, polymeric carbon nitride-based single-atom catalysts(C₃N₄-based SACs) are expected to become a potential for CO₂ reduction under visible-light irradiation. In this review, we summarize the recent advancement on C₃N₄-based SACs for photocatalytic CO₂ reduction to C₁ products, including the reaction mechanism for photocatalytic CO₂ reduction to C₁ products, the structure and synthesis methods of C₃N₄-based SACs and their applications toward photocatalytic CO₂ reduction reaction(CO₂RR) for C₁ production. The current challenges and future opportunities of C₃N₄-based SACs for photoreduction of CO₂ are also discussed.     

B(X)上保持约当积的固定点的满射

设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.     

Semi-concurrent vector fields in Finsler geometry

In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold $(M,F)$, admitting a non-constant smooth function f on M such that $\frac{\partial f}{\partial x^i}\frac{\partial g^{ij}}{\partial y^k}=0$?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented.     

High-frequency lengthwise diffraction by the curve separating soft and hard part of the surface

The paper examines the model problem of high-frequency diffraction by a convex surface consisting of two parts. One is soft, the other is hard. The incident wave falls at a small angle to the line which separates soft and hard parts of the surface. The change in the boundary condition provokes the field in the Fock zone to have a rapid transverse variation. This causes a special boundary-layer to be formed. The boundary value problem for the three dimensional parabolic equation is reduced to the Riemann problem solved by the factorization in the form of infinite products containing the zeros of the Airy function and zeros of its derivative. the results of this factorization appear under the sign of double Fourier integral in the representation of the field. Both numerical and asymptotic analysis of this representation is carried out and illustrates the effects of high-frequency diffraction caused by the line of the boundary condition discontinuity.     

有限群共轭类长度的一点注记

假设G=AB是子群A和B的互相置换积。通过A?B中元素的共轭类长度给出了群G的结构，推广了一些最近的结论。