具有变时滞和马尔可夫切换的随机递归神经网络的弱收敛(英文)

本文研究了具有变时滞和马尔可夫切换的随机递归神经网络的弱收敛,通过运用Lyapunov函数、随机分析技巧和推广了的Halanay不等式,得到了上述模型为弱收敛的充分性条件,并且我们揭示了对上述递归神经网络模型所确定的segment过程的转移概率的极限分布是此模型的解过程的唯一的遍历不变概率测度.此外,我们还给出了例子和数值模拟来说明我们结论的正确性.     

一个2+1维可积方程的代数几何解

该文从1+1维的孤子方程出发,构造出一个2+1维在Lax意义下可积的方程.接着这个2+1维可积方程被分解为可解的常微分方程.随后引入超椭圆Riemann曲面和Abel-Jacobi坐标把流进行了拉直.再利用Riemannθ函数给出了这个2+1维方程的代数几何解.     

正项级数敛散性新的根式判别法

基于几何级数的敛散性和比较判别法,给出判断正项级数敛散性的一个新的根式判别法,并举例说明其应用.     

Commuting Toeplitz operators on the hardy space of the polydisk

In this paper, we show that two Toeplitz operators T_f and T_g on the Hardy space of the polydisk can commute if and only if the Berezin transform of the commutator [T_f, T_g] is n-harmonic.     

Amarusine A,a new dioxaspiro[4.4]nonane derivative with a butyrolactone ring from Pleioblastus amarus

Amarusine A (1), a new polyketide derivative possessing an unusual dioxaspiro[4.4]nonane derivative with a butyrolactone ring, was isolated from the leaves of Pleioblastus amarus. The structure and absolute stereochemistry of compound 1 were rigorously determined using UV, IR, HRESIMS, and 1D and 2D NMR techniques and by comparing experimental and calculated electronic circular dichroism (ECD) spectra. Amarusine A (1) exhibits a good antioxidant activity for scavenging the DPPH radical. A possible biosynthetic pathway was postulated.     

Investigating the effects of side chain length on the AIE properties of water-soluble TPE derivatives

The emissive properties of fluorophores in aggregated state are important for the development of bio-sensors or bio-imaging reagents. So three water-soluble TPE derivatives with different lengths of side chains have been synthesized and we investigated the effects of side chains on aggregation-induced emission (AIE) properties in the aggregated states. The results indicate that side chains on the fluorophores play a pivotal role in their emission in aggregated state mediated by heparin or solid state, because the coplanarity of these TPE derivatives was affected by side chains. The rates of radiative decay k_f and non-radiative decay k_nr have been obtained through the quantum yields and lifetime, and a larger k_f and smaller k_nr were present for compound TPE-C4N, suggesting that the aggregated TPE-C4N should posses the most remarkable fluorescent property.     

Highly unsaturated pyranone derivatives from the basidiomycete Junghuhnianitida

Four new highly unsaturated pyranone derivatives A–D (1–4), together with one known compound 5 (−)-nitidon were isolated from cultures of the fungus Junghuhnianitida. Planar structures of the new compounds were elucidated on the basis of extensive NMR spectroscopic and mass spectrometric analyses. Absolute configurations of the new compounds were determined on the basis of biosynthetic considerations and quantum chemistry theory. Compound 1 exhibited almost the same cytotoxic activities as cis-platin.     

Tuning Structural Topologies of Two Cadmium(II) Coordination Polymers via Isomeric Dipyridyl Ligands: Syntheses,Crystal Structures,and Luminescent Properties

Abstract. Two new coordination polymers {[Cd₂(BDC)₂(3‐bpmp)(H₂O)₂] · 2H₂O}_n ( 1 ) and [Cd₂(BDC)₂(4‐bpmp)]_n ( 2 ) [H₂BDC = 5‐hydroxy‐isophthalic acid, 3‐bpmp = 1,4‐bis(3‐pyridylmethy)piperazine, and 4‐bpmp = 1,4‐bis(4‐pyridylmethy) piperazine] were synthesized via hydrothermal synthesis, and further characterized by IR spectroscopy, elemental analysis, XRD, and X‐ray crystallography. Complex 1 shows a two‐dimensional (4,4) sql topology and complex 2 features an 8‐connected hex topology. Moreover, the luminescent properties of complexes 1 and 2 were investigated in the solid state at room temperature.     

C?H Functionalization/Asymmetric Michael Addition Cascade Enabled by Relay Catalysis: Metal Carbenoid Used for C?C Bond Formation

A combination of either ruthenium(II) or rhodium(II) complexes and quinine‐derived squaramide enables 3‐diazooxindoles, indoles, and nitroalkenes to undergo highly efficient asymmetric three‐component reactions, thus affording optically active 3,3′‐bis(indole)s through a consecutive C C bond‐forming sequence, which turned out to be applicable to the facile total synthesis of (−)‐folicanthine.