Coastal eutrophication and hypoxia remain a persistent environmental crisis despite the great efforts to reduce nutrient loading and mitigate associated environmental damages. Symptoms of this crisis have appeared to spread rapidly, reaching developing countries in Asia with emergences in Southern America and Africa. The pace of changes and the underlying drivers remain not so clear. To address the gap, we review the up-to-date status and mechanisms of eutrophication and hypoxia in global coastal oceans, upon which we examine the trajectories of changes over the 40 years or longer in six model coastal systems with varying socio-economic development statuses and different levels and histories of eutrophication. Although these coastal systems share common features of eutrophication, site-specific characteristics are also substantial, depending on the regional environmental setting and level of social-economic development along with policy implementation and management. Nevertheless, ecosystem recovery generally needs greater reduction in pressures compared to that initiated degradation and becomes less feasible to achieve past norms with a longer time anthropogenic pressures on the ecosystems. While the qualitative causality between drivers and consequences is well established, quantitative attribution of these drivers to eutrophication and hypoxia remains difficult especially when we consider the social economic drivers because the changes in coastal ecosystems are subject to multiple influences and the cause–effect relationship is often non-linear. Such relationships are further complicated by climate changes that have been accelerating over the past few decades. The knowledge gaps that limit our quantitative and mechanistic understanding of the human-coastal ocean nexus are identified, which is essential for science-based policy making. Recognizing lessons from past management practices, we advocate for a better, more efficient indexing system of coastal eutrophication and an advanced regional earth system modeling framework with optimal modules of human dimensions to facilitate the development and evaluation of effective policy and restoration actions.

We consider the boundary Hardy–Hénon equation

\[ -\Delta u=(1-|x|)^{\alpha} u^{p},\ \ x\in B_1(0), \]

$B_1(0)\subset \mathbb {R}^{N}$

$(N\geq 3)$

$1$

$0$

$p>0$

$\alpha \in \mathbb {R}$

$0< p<({N+2})/({N-2})$

$\alpha \leq -2$

$p>1$

$\alpha >-2$

$1< p<({N+2})/({N-2})$

$0< p\leq 1$

$\alpha \leq -2$

$0< p<1$

$\alpha >-2$

A novel type of alumina (Al2O3)-doped molybdenum (Mo) alloy sheet was prepared by a hydrothermal method and a subsequent powder metallurgy process. Then the characterization of α-Al2O3 was investigated using high-resolution transmission electron microscopy as the research focus. The tensile strength of the Al2O3-doped Mo sheet is 43–85% higher than that of the pure Mo sheet, a very obvious reinforcement effect. The sub-micron and nanometer-scale Al2O3 particles can increase the recrystallization temperature by hindering grain boundary migration and improve the tensile strength by effectively blocking the motion of the dislocations. The Al2O3 particles have a good bond with the Mo matrix and there exists an amorphous transition layer at the interface between Al2O3 particles and the Mo matrix in the as-rolled sheet. The sub-structure of α-Al2O3 is characterized by a number of nanograins in the $\left[ {2\bar{2}1} \right]$ direction. Lastly, a new computer-based method for indexing diffraction patterns of the hexagonal system is introduced, with 16 types of diffraction patterns of α-Al2O3 indexed.

Associations of folic acid supplementation with risk of preterm birth (PTB) and small-for-gestational-age (SGA) birth were unclear for the Chinese populations. The aim of the present study was to investigate the associations in a large Chinese prospective cohort study: the Jiaxing Birth Cohort. In the Jiaxing Birth Cohort, 240 954 pregnant women visited local clinics or hospitals within their first trimester in Southeast China during 1999–2012. Information on anthropometric parameters, folic acid supplementation and other maternal characteristics were collected by in-person interviews during their first visit. Pregnancy outcomes were recorded during the follow-up of these participants. Multinomial logistic regression was used to examine the association of folic acid supplementation with pregnancy outcomes. The prevalence of folic acid supplementation was 24·9 % in the cohort. The prevalence of PTB and SGA birth was 3·48 and 9·2 %, respectively. Pre-conceptional folic acid supplementation was associated with 8 % lower risk of PTB (relative risk (RR) 0·92; 95 % CI 0·85, 1·00; P=0·04) and 19 % lower risk of SGA birth (RR 0·81; 95 % CI 0·70, 0·95; P=0·008), compared with non-users. Higher frequency of pre-conceptional folic acid use was associated with lower risk of PTB (Ptrend=0·032) and SGA birth (Ptrend=0·046). No significant association between post-conceptional initiation of folic acid supplementation and either outcome was observed. In conclusion, the present study suggests an association between pre-conceptional, but not post-conceptional, folic acid supplementation and lower risk of PTB and SGA birth in the Jiaxing Birth Cohort. Further research in other cohorts of large sample size is needed to replicate these findings.

In this short note, we present a sharp upper bound for the perturbation of eigenvalues of a singular diagonalizable matrix given by Stanley C. Eisenstat [3].

Dragonfly eye beads are considered to be the earliest types of glass objects in China, and in the past have been considered as evidence of culture interaction or trade between West and East Asia. In this article, synchrotron radiation microcomputed tomography and μ-probe energy dispersive X-ray fluorescence were used to determine the chemical composition, microstructure, and manufacturing technology of four dragonfly eye beads, excavated from a Chu tomb at the Shenmingpu site, Henan Province, China, dated stylistically to the Middle and Late Warring State Period (475 bc–221 bc). First, a nondestructive method was used to differentiate the material types including faience (glazed quartz), frit, glazed pottery (clay ceramic), and glass. Three beads were identified as faience and one bead as glazed pottery. The glaze recipe includes quartz, saltpeter, plant ash, and various copper, and is classified as belonging to the K2O-CaO-SiO2 glass system, which indicates that these beads were not imported from the West. Based on computed tomography slices, the manufacturing technology of the faience eye beads appears to include the use of an inner core, molding technology, and the direct application glazing method. These manufacturing features are consistent with the techniques used in China during this same time period for bronze mold-casting, proto-porcelain, and glass.

For any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.

Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if Ad denotes the generalized Drazin inverse of a bounded linear operator A on an arbitrary complex Banach space, then in some special cases (A + B)d is computed in terms of Ad and Bd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.

The purpose of this paper is to derive an integral representation of the Drazin inverse of an element of a Banach algebra in a more general situation than previously obtained by the second author, and to give an application to the Moore–Penrose inverse in a $C^*$-algebra.

AMS 2000 Mathematics subject classification:Primary 46H05; 46L05

We study the perturbation of the generalized Drazin inverse for the elements of Banach algebras and bounded linear operators on Banach space. This work, among other things, extends the results obtained by the second author and Guorong Wang on the Drazin inverse for matrices.