矩阵方程AX=B的中心对称定秩解及其最佳逼近

本文研究了矩阵方程AX=B的中心对称解.利用矩阵对的广义奇异值分解和广义逆矩阵,获得了该方程有中心对称解的充要条件以及有解时,最大秩解、最小秩解的一般表达式,并讨论了中心对称最小秩解集合中与给定矩阵的最佳逼近解.     

The long‐term extreme price risk measure of portfolio in inventory financing: An application to dynamic impawn rate interval

Different from the short‐term risk measure for traditional financial assets (stocks, bonds, etc.), the key to illiquid inventory portfolio traded in the over‐the‐counter markets is to estimate the long‐term extreme price risk with time varying volatility. In this article, a new long‐term extreme price risk (value at risk and conditional value at risk) measure method for inventory portfolio and an application to dynamic impawn rate interval are proposed. To realize this, we first establish AutoRegressive Moving Average‐Exponential Generalized Autoregressive Conditional Heteroskedasticity‐Extreme Value Theory model and multivariatet‐Copula to depict the autocorrelation, fat tails, and volatility clustering of returns of inventories and the nonlinear dependence structure of inventories. Furthermore, we obtain the long‐term extreme price risk with time varying volatility via Monte Carlo simulation instead of square‐root‐of time rule. The results show that, first, benefits from risk diversification is significant; second, long‐term extreme price risk measure of inventory portfolio via Monte Carlo method outperforms the square‐root‐of time rule; the last is that the dynamic rate interval based on the long‐term price risk is superior to the crude rules of thumb in terms of reducing efficiency loss and improving risk coverage. In summary, this article provides a new quantitative framework for managing the risk of portfolio in inventory financing practice for banks constrained by risk limitation. © 2014 Wiley Periodicals, Inc. Complexity 20: 17–34, 2015     

1,3-Diyne chemistry: synthesis and derivations

Conjugated diynes have attracted more and more attention not only for their unique rod like structures and wide existence in nature product, but also the abundant properties and derivations of them. Although oxidative dimerization of alkynes or Cadiot–Chodkiewicz reactions were the main pathway and have achieved great success in the synthesis of diynes, oxidative cross coupling, FBW rearrangement as well as diyne metathesis emerged rapidly recently. Moreover, diynes could be precursors of basic heterocycles, which represented an emerging research area. This Letter will cover the recent progresses in the synthesis and further derivations of diynes.     

Synthesis and application of moisture-stable methallylsilanated phosphorylcholine as a surface modifier

New methallylsilanated phosphorylcholine (MASPCs) were synthesized via a copper-catalyzed ‘click’ reaction and demonstrated excellent moisture stability. Hydroxylated silicon compounds, silanol, and silica were grafted or modified by MASPCs in the presence of triflic acid (TfOH) and they possessed a good grafting efficiency and high loading rate.     

Practical and Highly Selective C?H Functionalization of Structurally Diverse Ethers

A trityl ion mediated C H functionalization of ethers with a wide range of nucleophiles at ambient temperature has been developed. The reaction displays high chemoselectivity and good functional group tolerance. The protocol also exhibits excellent regio‐ and diastereoselectivities for the unsymmetric ethers, thus stereoselectively generating highly functionalized disubstituted 2,5‐trans tetrahydrofurans (THF), 2,6‐trans tetrahydropyrans (THP), 2,6‐trans dihydropyrans (DHP), and 1,3‐trans isochromans, and highlighting the capacity of the protocol in complex molecule synthesis.     

Phosphine-catalyzed [4+2] cycloaddition of sulfamate-derived cyclic imines with allenoates: synthesis of sulfamate-fused tetrahydropyridines

Using n-PrPPh₂ as the nucleophilic catalyst, the [4+2] cycloaddition reaction of the sulfamate-derived cyclic imines with allenoates works efficiently to yield various sulfamate-fused tetrahydropyridines in high yields with excellent diastereoselectivities. Using amino acid-based bifunctional phosphine as chiral catalyst, an asymmetric [4+2] cycloaddition reaction was achieved, giving chiral sulfamate-fused tetrahydropyridines in high yields with good enantiomeric excesses.     

Novel cytotoxic nine-membered macrocyclic polysulfur cembranoid lactones from the soft coral Sinularia sp.

One novel nine-membered macrocyclic polysulfur cembranoid lactone, sinulariaoid A (1); three new multioxygenated cembranoids, sinulariaoid B (2), sinulariaoid C (3), sinulariaoid D (4); and four known cembranoids, capilloloid (5), dihydrosinularin (6), sinularin (7), and dihydrosinuflexolide (8) were isolated from the soft coral Sinularia sp. collected off of Sanya Bay in the South China Sea. Their stereochemical structures were determined on the basis of extensive spectroscopic methods, including single crystal X-ray diffraction analysis. Sinulariaoid A (1) is the first reported nine-membered macrocyclic polysulfur cembranoid from soft coral. The cytotoxic activities of compounds 1–8 were determined in four human cancer cell lines (HepG2, HepG2/ADM, MCF-7, and MCF-7/ADM). Of these, sinulariaoid A (1) exhibited the most potent anticancer activity in vitro, and its cytotoxicity in HepG2/ADM was more potent than in the other three cell lines. Furthermore, it was found that sinulariaoid A (1) induced apoptosis, and its selective toxicity toward HepG2/ADM cells was not related to P-glycoproteins.     

Neuroprotective glucosides of magnolol and honokiol from microbial-specific glycosylation

Thirteen new glucosides (1–13) of magnolol and honokiol were obtained from specific O-glycosylation by two filamentous fungi, Cunninghamella echinulata AS 3.3400 and Rhizopus japonicus ZW-4. The glucosides' structures were determined on the basis of extensive spectroscopic (HRESIMS, 1D and 2D NMR, and CD) analyses and a chemical method. C. echinulata appeared to transfer a glucosyl moiety to 2-OH of magnolol and honokiol, whereas R. japonicus preferred to regio-specifically transfer a glucosyl moiety to 4′-OH when honokiol was as the substrate. In addition, hydroxylation by C. echinulata and specific 6″-O-acylation of the introduced glucosyl moiety by R. japonicus were observed as minor reactions. Bioassay results indicated that glucosides 1–12 together with magnolol and honokiol at 10 μM attenuated the glutamate-induced toxicity in SK-N-SH cells to levels comparable to the results for MK-801, a positive control. However, the water-solubility of major glucosylated products (1, 8, and 11) increased greatly.