A cohomological characterization of Leibniz central extensions of Lie algebras

Mainly motivated by Pirashvili's spectral sequences on a Leibniz algebra, a cohomological characterization of Leibniz central extensions of Lie algebras is given. In particular, as applications, we obtain the cohomological version of Gao's main theorem for Kac-Moody algebras and answer a question in an earlier paper by Liu and Hu (2004).

     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

The apolar bilinear form in geometric modeling

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden's identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

     

C_9N_4 as excellent dual electrocatalyst: A first principles study

We perform first principles calculations to investigate the catalytic behavior of C_9 N_4 nanosheet for water splitting.For the pristine C_9 N_4,we find that,at different hydrogen coverages,two H atoms adsorbed on the 12-membered ring and one H atom adsorbed on the 9-membered ring show excellent performance of hydrogen evolution reaction(HER).Tensile strain could improve the catalytic ability of C_9 N_4 and strain can be practically introduced by building C_9 N_4/BiN,and C_9 N_4/GaAs heterojunctions.We demonstrate that the HER performance of heterojunctions is indeed improved compared with that of C_9 N_4 nanosheet.Anchoring transition metal atoms on C_9 N_4 is another strategy to apply strain.It shows that Rh@C_9 N_4 exhibits superior HER property with very low Gibbs free energy change of-30 meV.Under tensile strain within ～2%,Rh@C_9 N_4 could catalyze HER readily.Moreover,the catalyst Rh_9 C_9 N_4 works well for oxygen evolution reaction(OER)with an overpotential of 0.58 V.Our results suggest that Rh@C_9 N_4 is favorable for both HER and OER because of its metallic conductivity,close-zero Gibbs free energy change,and low oneset overpotential.The outstanding performance of C_9 N_4 nanosheet could be attributed to the tunable porous structure and electronic structure compatibility.     

Synthesizing Red Fluorescent Carbon Dots from Rigid Polycyclic Conjugated Molecules: Dual-Mode Sensing and Bioimaging in Biochemical Applications

Red fluorescent carbon dots (R-CDs) are special desirable for biochemical analysis due to good biological compatibility and deep penetration; however, they remain as bottlenecks due to difficulties in expanding the sp² domain, especially those are fused from rigid polycyclic conjugated molecules (RPCMs) with heteroatom substituents due to huge steric hindrance and heteroatom blockage toward graphic lattice. Here, an RPCM with heteroatom substituents, 1,5-diamino-4,8-dihydroxyanthraquinone (DDAQ), based self-doped R-CDs with PL emission at 635 nm is reported. Further investigations reveal that the expanding, hybrid sp² domain with indanthrone tannin structure from DDAQ is mainly responsible for the obtained red fluorescence of R-CDs. Taking advantage of optical properties, R-CDs are considered to construct a colorimetric/fluorescent dual mode sensing array for quantifying trace levels of Fe³⁺ and glyphosate based on the static quenching, and a biomarker for cell imaging. The CD-based sensors exhibit outstanding recovery, high selectivity, and sensitivity, also facilitated dual-mode detection with the naked-eye. The R-CDs have low cytotoxicity, good cell membrane penetration for rapid cell entry, and high resolution, demonstrating their potential for biolabeling and bioanalytic applications.     

双波长高精度红外测温仪

利用双波长红外测温方法,通过黑体红外辐射曲线中双波长等比吸收的原理消除了由于辐射环境中水蒸气等外界吸收原因造成的单波长红外测温仪中的测量误差,实现更稳定的高精度红外测温.该方法绕开了传统红外测温方法中"辐射率修正困难"的问题.同时利用此红外测温仪器改进了金属钨电子逸出功测量实验.     

二重数值积分公式的高精度对偶公式及其应用

给出了计算二重积分的Simpson公式与两点高斯公式的对偶公式的构造过程,得到与之对应的高精度对偶修正解,提高了二重数值积分公式的计算精度,同时给出了二重积分的一种估值方法.最后,应用于几个典型的数值算例,计算结果表明：对偶修正解比对应的数值积分公式及其对偶公式的解有更高的计算精度和更快的收敛速度.     

关于L_p球的几个新不等式和性质(英文)

本文研究了L_p球的相关问题.利用对偶混合体积、球面Radon变换和Fourier变换的方法,获得了关于L_p球的几个新不等式和性质,其中一个不等式与著名的最大切片猜想有关.