Lp空间Kantorovich-Vertesi算子逼近的Jackson型估计

考虑了Kantorovich-Vertesi有理插值型算子L^*n,s（f,X,x）对L^p[-1,1]（1≤p≤∞）空间函数逼近的Jackson型估计。并获得了如下逼近阶：‖L^*n,s(f,X,x)-f(x)‖L^p[-1,1]≤Cp,sw(f,1/n 2)L^p[-1,1] （s＞2）。     

Autocorrelation of Random Matrix Polynomials

 We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly the autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions. Received: 1 August 2002 / Accepted: 25 December 2002 Published online: 7 May 2003 Communicated by P. Sarnak     

The First Molecular Main Group Metal Species Containing Interstitial Hydride

Lithium cages containing hydride: The reaction of tBuLi with Me(2)AlN(2-Pyr)Ph in toluene gave [Li(8)(H){N(2-Pyr)Ph}(6)](+)[Li(Me(2)AltBu(2))(2)](-), whose cation is the first molecular main group metal species to contain interstitial hydride (the cluster core is shown in the picture). Treatment of the reaction mixture with THF gave the neutral hydride Li(7)(H)[N(2-Pyr)Ph](6), which has a capped octahedral (Li(+))(7) cluster core. 2-Pyr=2-pyridyl.     

Monodisperse Dual‐Functional Upconversion Nanoparticles Enabled Near‐Infrared Organolead Halide Perovskite Solar Cells

Extending the spectral absorption of organolead halide perovskite solar cells from visible into near‐infrared (NIR) range renders the minimization of non‐absorption loss of solar photons with improved energy alignment. Herein, we report on, for the first time, a viable strategy of capitalizing on judiciously synthesized monodisperse NaYF₄:Yb/Er upconversion nanoparticles (UCNPs) as the mesoporous electrode for CH₃NH₃PbI₃ perovskite solar cells and more importantly confer perovskite solar cells to be operative under NIR light. Uniform NaYF₄:Yb/Er UCNPs are first crafted by employing rationally designed double hydrophilic star‐like poly(acrylic acid)‐block‐poly(ethylene oxide) (PAA‐b‐PEO) diblock copolymer as nanoreactor, imparting the solubility of UCNPs and the tunability of film porosity during the manufacturing process. The subsequent incorporation of NaYF₄:Yb/Er UCNPs as the mesoporous electrode led to a high efficiency of 17.8 %, which was further increased to 18.1 % upon NIR irradiation. The in situ integration of upconversion materials as functional components of perovskite solar cells offers the expanded flexibility for engineering the device architecture and broadening the solar spectral use.