The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Polyoxygenated dihydropyrano[2,3-c]pyrrole-4,5-dione derivatives from the marine mangrove-derived endophytic fungus Penicillium brocae MA-231 and their antimicrobial activity

A new polyoxygenated dihydropyrano[2,3-c]pyrrole-4,5-dione derivative, pyranonigrin F (1), together with a related known compound, pyranonigrin A (2), were isolated and identified from Penicillium brocae MA-231, an endophytic fungus obtained from the fresh tissue of the marine mangrove plant Avicennia marina. The structures of these metabolites were determined based on comprehensive spectral interpretation and the absolute configuration of compound 1 was established by X-ray crystallographic analysis. Compounds 1, and 2 showed potent activity against a broad spectrum of human-, aqua-, and plant-pathogens.     

Effects of ultrasound treatment on the morphological characteristics,structures and emulsifying properties of genipin cross-linked myofibrillar protein

Genipin is a natural crosslinker that improves the functional properties of proteins by modifying its structures. This study aimed to investigate the effects of sonication on the emulsifying properties of different genipin concentration-induced myofibrillar protein (MP) cross-linking. The structural characteristics, solubility, emulsifying properties, and rheological properties of genipin-induced MP crosslinking without sonication (Native), sonication before crosslinking (UMP), and sonication after crosslinking (MPU) treatments were determined, and the interaction between genipin and MP were estimated by molecular docking. The results demonstrated that hydrogen bond might be the main forces for genipin binding to the MP, and 0.5 μM/mg genipin was a desirable concentration for protein cross-linking to improve MP emulsion stability. Ultrasound treatment before and after crosslinking were better than Native treatment to improve the emulsifying stability index (ESI) of MP. Among the three treatment groups at the 0.5 μM/mg genipin treatment, the MPU treatment group showed the smallest size, most uniform protein particle distribution, and the highest ESI (59.89%). Additionally, the highest α-helix (41.96%) in the MPU + G5 group may be conducive to the formation of a stable and multilayer oil–water interface. Furthermore, the free groups, solubility, and protein exposure extent of the MPU groups were higher than those of UMP and Native groups. Therefore, this work suggests that the treatment of cross-linking followed by ultrasound (MPU) could be a desirable approach for improving the emulsifying stability of MP.     

二次纳流电喷雾电离耦合超高分辨质谱检测人体呼出气中相对高分子量化合物

二次电喷雾电离源耦合超高分辨质谱(SESI-UHRMS)有望检出人体呼出气中分子量大于300的相对高分子量化合物,这些化合物的发现将有助于更准确地理解呼出气中挥发性有机化合物(VOCs)的来源、产生机制以及SESI源电离机理,更好地实现SESI-UHRMS的转化应用.本研究自组装nanoSESI源(尚无商业产品)耦合四极杆-静电场轨道阱质谱(最高质量分辨率1.2×10~5),考察了该装置对健康人体呼出气中分子量为300~500化合物的检出情况.结果表明,所搭建的nanoSESI-UHRMS装置检测人体呼出气的重现性好、灵敏度高,可检出数十种分子量为300~500的化合物.根据这些化合物在单次呼气过程中信号强度随时间变化的趋势,推断其来源分别为内源性和外源性;各化合物的元素组成主要包括C,H,N和O,环-双键当量(RDB)的均值为(4.5±3.1),表明检出的化合物可能为醛酮或不饱和脂肪酸,容易在SESI源中被电离.本研究初步验证了自组建nanoSESI-UHRMS检测人体呼出气中相对高分子量化合物的可行性,为后续进一步开展方法应用奠定了基础.