In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal $L^2$ extension problem on open Riemann surfaces with weights may not be subharmonic.

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.

Mach reflection subjected to the influence of an upstream shock wave from the same side is studied here. This situation occurs when two incident shock waves induced by a double wedge reflect at the same point of the reflecting surface and when the downstream incident shock wave is stronger than the upstream one. A shock polar analysis is used to show that this configuration produces an inverted Mach stem and a type IV shock interference between the Mach stem and the upstream shock wave. This shock interference produces a jet that divides the flow stream downstream of the Mach stem into two ducts with different sonic throats, thus complicating the mechanism by which the Mach stem size is determined. A transition analysis shows that the Mach reflection of the downstream shock wave is promoted by the upstream one. Computational fluid dynamics is used to assess the flow pattern anticipated by shock polar analysis and demonstrates how the heights of Mach stem and jet depend on the inflow Mach number and wedge turning angle.

Ketosis is a metabolic disease of dairy cows often characterized by high concentrations of ketone bodies and fatty acids, but low milk protein and milk production. The Janus kinase 2 (JAK2)-signal transducer and activator of transcription 5 (STAT5) and the mechanistic target of rapamycin (mTOR) signaling pathways are central for the regulation of milk protein synthesis. The effect of high levels of fatty acids on these pathways and β-casein synthesis are unknown in dairy cows with clinical ketosis. Mammary gland tissue and blood samples were collected from healthy (n = 15) and clinically-ketotic (n = 15) cows. In addition, bovine mammary epithelial cells (BMEC) were treated with fatty acids, methionine (Met) or prolactin (PRL), respectively. In vivo, the serum concentration of fatty acids was greater (P > 0.05) and the percentage of milk protein (P > 0.05) was lower in cows with clinical ketosis. The JAK2-STAT5 and mTOR signaling pathways were inhibited and the abundance of β-casein was lower in mammary tissue of cows with clinical ketosis (P > 0.05). In vitro, high levels of fatty acids inhibited the JAK2-STAT5 and mTOR signaling pathways (P > 0.05) and further decreased the β-casein synthesis (P > 0.05) in BMEC. Methionine or PRL treatment, as positive regulators, activated the JAK2-STAT5 and mTOR signaling pathways to increase the β-casein synthesis. Importantly, the high concentration of fatty acids attenuated the positive effect of Met or PRL on mTOR, JAK2-STAT5 pathways and the abundance of β-casein (P > 0.05). Overall, these data indicate that the high concentrations of fatty acids that reach the mammary cells during clinical ketosis inhibit mTOR and JAK2-STAT5 signaling pathways, and further suppress β-casein synthesis.

Mach reflection in steady supersonic flow with two incident shock waves that reflect at the same point on the reflecting surface has been studied recently. Under some conditions we have pre-Mach reflection, where the first incident shock wave produces Mach reflection, the reflected shock wave of which intersects the second incident shock wave, leading to a type I shock interference structure. In this study, we find that a critical condition exists to have a double solution of this shock interference, i.e. we may either have type I interference or type II interference. However, numerical simulation shows that, for inverted Mach reflection, the double solution domain is below the theoretical one and for usual Mach reflection, the double solution domain is above the theoretical one. This discrepancy is found to be due to secondary Mach waves on the initial segment of the slipline of the Mach reflection, thus demonstrating for the first time a case where the transition criterion is modified by secondary Mach waves developed over the primary flow structure.

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

The high-cycle fatigue (HCF) behavior is significantly affected by surface roughness, especially for high strength metal FV520B-I. However, with surface roughness effect, neither the fatigue property, nor the high-cycle fatigue life model about FV520B-I with surface roughness has been reported. In this paper, designed fatigue experiment using the specimen with different surface roughness is presented to study the effectiveness of the roughness to the fatigue. The observations of the fatigue crack initiation sites and the crack propagation. Then the high cycle fatigue behavior of FV520B-I affected by surface roughness is analyzed. The existing very-high-cycle fatigue life model is not well-fit for high-cycle fatigue model of FV520B-I. A NEW high-cycle fatigue life prediction model of FV520B-I, taking surface roughness as a main effective variable is proposed. The model is built up by a comprehensive use of experimental data and the traditional fatigue modeling theory. The new finding between the fatigue strength coefficient and stress amplitude, with surface roughness, is adopted, leading to a NEW modified life prediction model. Study on fatigue model of FV520B-I with surface roughness is a very beneficial effort in fatigue theory and fatigue engineering development.

This study aimed to explore whether the presence of a Y chromosome azoospermia factor (AZF) microdeletion confers any adverse effect on embryonic development and clinical outcomes after intracytoplasmic sperm injection (ICSI) treatment. Fifty-seven patients with AZF microdeletion were included in the present study and 114 oligozoospermia and azoospermia patients without AZF microdeletion were recruited as controls. Both AZF and control groups were further divided into subgroups based upon the methods of semen collection: the AZF-testicular sperm extraction subgroup (AZF-TESE, n = 14), the AZF-ejaculation subgroup (AZF-EJA, n = 43), the control-TESE subgroup (n = 28) and the control-EJA subgroup (n = 86). Clinical data were analyzed in the two groups and four subgroups respectively. A retrospective case–control study was performed. A significantly lower fertilization rate (69.27 versus 75.70%, P = 0.000) and cleavage rate (89.55 versus 94.39%, P = 0.000) was found in AZF group compared with the control group. Furthermore, in AZF-TESE subgroup, the fertilization rate (67.54 versus 74.25%, P = 0.037) and cleavage rate (88.96 versus 94.79%, P = 0.022) were significantly lower than in the control-TESE subgroup; similarly, the fertilization rate (69.85 versus 75.85%, P = 0.004) and cleavage rate (89.36 versus 94.26%, P = 0.002) in AZF-EJA subgroup were significantly lower than in the control-EJA subgroup; however, the fertilization rate and cleavage rate in AZF-TESE (control-TESE) subgroup was similar to that in the AZF-EJA (control-EJA) subgroup. The other clinical outcomes were comparable between four subgroups (P > 0.05). Therefore, sperm from patients with AZF microdeletion, obtained either by ejaculation or TESE, may have lower fertilization and cleavage rates, but seem to have comparable clinical outcomes to those from patients without AZF microdeletion.

Autonomous docking is a focus of research in the field of self-assembly robots. Navigation is a significant stage in the process of autonomous docking between two robotic modules; it determines the efficiency of docking and even the success and failure of the docking task. In most cases, it is too difficult to simultaneously satisfy both linear and angular displacement constraints in a single dynamic numerical computation process. In the present paper, the navigation process is divided into two stages: first, the angular displacement constraint is satisfied, and then the linear displacement condition is fulfilled. In this way, the constraints are loosened and the difficulty of numerical computation is thereby effectively reduced. This two-stage docking navigation model is the main contribution of the present work. By taking the non-holonomic nature of the navigation behavior into consideration, both kinematic and dynamic analyses are performed, and the voltage data of the DC motors required by the two-stage docking navigation are obtained. Finally, docking navigation experiments are completed on a self-assembly modular robot named Sambot. It is verified that the present two-stage strategy is effective in controlling the docking navigation process.

Background: The aim of the current study was to investigate the associations between family characteristics and depressive symptoms, and provide new evidence and recommendations for prevention and intervention in the depressive symptoms of older adults.

Methods: The study was a cross-sectional survey conducted door-to-door, utilizing a sample of 1,317 individuals aged 60 years and above in rural China. The five family characteristic variables recorded were: living with spouse, living with descendant, support of family members, self-reported family economic status in the previous year, and family-related negative life events that occurred anytime in the past with a continuous psychological effect during the past 12 months. Gender, age, years of schooling, and self-rated physical health status were taken as potential confounders. Univariable and multivariable logistic regression models were used to examine independent effects on depressive symptoms.

Results: In addition to the potential confounders, only family-related negative life events, support of family members, and self-reported family economic status had significant effects on depressive symptoms in older adults. Experiencing a family-related negative life event was the most significant variable (OR = 11.70, 95% CI: 7.72–17.73), the second was support of family members (OR = 6.93, 95% CI: 3.26–14.70), while family economic status was less important than support of family members (OR = 2.38, 95% CI: 1.08–5.25).

Conclusion: This study, from the perspective of family characteristics on depressive symptoms in older adults, showed a strong correlation between being exposed to harmful family environments and depressive symptoms among the elderly. Efforts to address family risk factors and strengthen family cohesiveness deserve a higher priority, given the importance of these factors, compared with other efforts such as promoting economic development.

The current work describes the simple solution process of ball-chain polycrystalline Fe nanofibers with aspect ratios (λ) and diameters (D) of over 1−65 and 30−95 nm. Static magnetic and microwave electromagnetic property studies demonstrated that such properties strongly depend on the λ and D of the Fe nanofibers. As the λ and D increase, the U-shape of the saturation magnetization (Ms) reaches a maximum of 180.0 emu·g−1, owing to the cooperative action of nanoeffects and magnetic interactions, whereas the coercivity (Hc) gradually increases due to aspect ratio variations. In contrast, the change in trends of the permittivity (ε′, ε″) and the dielectric loss (tgδE) are represented as an inverted U-shape; the permeability (μ′, μ″) and magnetic loss (tgδM) increase at low-frequency ranges and decrease at high frequency ranges. Stronger absorption and broader bandwidths of Fe nanofibers compared with Fe nanoparticles are ascribed to higher dielectric losses. The prepared Fe nanofibers have high potential in light-weight and broad bandwidth microwave absorbing applications.

In the present work, Fe3O4 nanospheres, sponges, and urchins were prepared. Investigation of static magnetic and microwave electromagnetic (EM) characteristics of polymorphic Fe3O4 nanomaterials showed that morphology plays a crucial role in determining the resulting properties. Compared with Fe3O4 nanospheres and urchins, enhanced saturation magnetization and coercivity were observed in Fe3O4 sponges composed of ordered nanofibers. Enhancement of saturation magnetization and coercivity are associated with increased magnetic interactions and shape anisotropy, respectively. The Fe3O4 sponges and urchins produced reflection loss (RL) values of −35.77 dB at 8.0 GHz and −43.23 dB at 16.8 GHz, respectively. The excellent microwave absorption performance is ascribed to their unique morphologies. Such morphologies resulted in reinforced EM parameters and multiresonant behavior.