Sharp Hardy inequalities involving distance functions from submanifolds of Riemannian manifolds

We establish various Hardy inequalities involving the distance function from submanifolds of Riemannian manifolds, where the natural weights are expressed in terms of bounds of the mean curvature of the submanifold and sectional/Ricci curvature of the ambient Riemannian manifold. Our approach is based on subtle Heintze-Karcher-type Laplace comparisons of the distance function and on a D'Ambrosio-Dipierro-type weak divergence formula for suitable vector fields, providing Barbatis-Filippas-Tertikas-type Hardy inequalities in the curved setting. Under very mild assumptions, we also establish the sharpness and non-existence of extremal functions within the Hardy inequalities and - depending on the geometry of the ambient manifold - their extensibility to various function spaces. Several examples are provided by showing the applicability of our approach; in particular, well-known Hardy inequalities appear as limit cases of our new inequalities.Comment: 40 page

Cracking Characteristics and Mechanism of Internal Components of Large-Span Shield Tunnel

With the ever-increasing number of large-span shield tunneling projects and the extended operational time, their distinctive internal component issues are becoming more pronounced and exhibiting unique characteristics. In order to reveal the cracking mechanism of concrete on the top of the middle partition wall, based on a large-span shield tunnel section of Nanjing Metro, the crack mode, distribution characteristics, and cracking process of concrete inside tunnel structure were studied by combined field investigation and extended finite element analysis. The results showed that: (1) there were 96 cracks of concrete on the top of the middle partition wall in the interval. Based on the propagation path, number, and shape of cracks, they could be divided into type I, II, III, Y, and Z, with type-Y and type-Z being subtypes of type-I. (2) The crack started at the opposite side of horizontal differential displacement of the flue plate. The development curves of the length and end width of type-I and type-II cracks showed the significant characteristics of three stages. The relationship between crack end width and length was nonlinear, showing that 250 and 225 mm, respectively, were the critical crack lengths growing with the rapid growth of the end width of type-I and type-II cracks. (3) In type-II cracks, the propagation curves of two cracks under the same working condition were consistent, and the spacing of plate joints greatly influenced the length and slope of each stage of the curve. For type-III cracks, the first crack propagation process was basically consistent with type-I and type-II cracks, and the propagation of the other two cracks had obvious brittle characteristics

Concentrations of Four Major Air Pollutants among Ecological Functional Zones in Shenyang, Northeast China

Air pollution is a critical urban environmental issue in China; however, the relationships between air pollutants and ecological functional zones in urban areas are poorly understood. Therefore, we analyzed the spatiotemporal characteristics of four major air pollutants (particulate matter less than or equal to 2.5 µm (PM2.5) and 10 µm (PM10) in diameter, SO2, and NO2) concentrations over five ecological functional zones in Shenyang, Liaoning Province, at hourly, seasonal, and annual scales using data collected from 11 monitoring stations over 2 years. We further assessed the relationships between these pollutants and meteorological conditions and land-use types at the local scale. Peaks in PM, SO2, and NO2 concentrations occurred at 08:00–09:00 and 23:00 in all five zones. Daytime PM concentrations were highest in the industrial zone, and those of SO2 and NO2 were highest in residential areas. All four air pollutants reached their highest concentrations in winter and lowest in summer. The highest mean seasonal PM concentrations were found in the industrial zone, and the highest SO2 and NO2 concentrations were found in residential areas. The mean annual PM and SO2 concentrations decreased in 2017 in all zones, while that of NO2 increased in all zones excluding the cultural zone. The natural reserve zone had the lowest concentrations of all pollutants at all temporal scales. Pollutant concentrations of PM2.5, PM10, SO2, and NO2 were correlated with visibility, and their correlation coefficients are 0.675, 0.579, 0.475, and 0.477. Land coverage with buildings and natural vegetation negatively and positively influence air pollutant concentrations, respectively

Characteristics of Turbulence and Aerosol Optical and Radiative Properties during Haze–Fog Episodes in Shenyang, Northeast China

The characteristics of turbulence in the planetary boundary layer (PBL) and the aerosol optical and radiative properties during haze and haze–fog mixed episodes on 22–27 January 2021, in Shenyang, a provincial city in Northeast China, were analyzed using meteorological and aerosol observations. During the haze episode, the hourly mean PM2.5 concentration reached a maximum of 337 µg m−3 and visibility decreased to 1.6 km. The PM2.5 concentration decreased gradually during the haze–fog mixed episode as a result of the scavenging effects of fog, but visibility mostly remained below 1 km owing to high ambient relative humidity (>90%). During the haze–fog mixed episode, an increasing proportion of PM2.5 led to a higher ratio of the backward to the total scattering coefficient. As fog occurred, downward shortwave radiation arriving at the surface was significantly reduced, and upward longwave radiation increased and almost equaled the downward longwave radiation, which can be used as a good indicator for distinguishing haze and fog. Mechanical turbulence was weak during both episodes, and latent heat flux varied within a wider range during the haze–fog mixed episode. The PBL dynamic structure affected the vertical distribution of aerosols/fog droplets. Aerosol-rich layers appeared at altitudes below 0.5 km and above 0.6 km during the haze episode. The elevated aerosol layer was related to the aerosol transport from upstream polluted areas caused by strong upper-level turbulence, and it began to mix vertically after sunrise because of convective turbulence. Aerosols and fog droplets were mostly trapped in a shallower PBL with a height of 0.2–0.4 km during the haze–fog mixed episode because of weaker turbulence

Characteristics of Turbulence and Aerosol Optical and Radiative Properties during Haze–Fog Episodes in Shenyang, Northeast China

The characteristics of turbulence in the planetary boundary layer (PBL) and the aerosol optical and radiative properties during haze and haze–fog mixed episodes on 22–27 January 2021, in Shenyang, a provincial city in Northeast China, were analyzed using meteorological and aerosol observations. During the haze episode, the hourly mean PM2.5 concentration reached a maximum of 337 µg m−3 and visibility decreased to 1.6 km. The PM2.5 concentration decreased gradually during the haze–fog mixed episode as a result of the scavenging effects of fog, but visibility mostly remained below 1 km owing to high ambient relative humidity (>90%). During the haze–fog mixed episode, an increasing proportion of PM2.5 led to a higher ratio of the backward to the total scattering coefficient. As fog occurred, downward shortwave radiation arriving at the surface was significantly reduced, and upward longwave radiation increased and almost equaled the downward longwave radiation, which can be used as a good indicator for distinguishing haze and fog. Mechanical turbulence was weak during both episodes, and latent heat flux varied within a wider range during the haze–fog mixed episode. The PBL dynamic structure affected the vertical distribution of aerosols/fog droplets. Aerosol-rich layers appeared at altitudes below 0.5 km and above 0.6 km during the haze episode. The elevated aerosol layer was related to the aerosol transport from upstream polluted areas caused by strong upper-level turbulence, and it began to mix vertically after sunrise because of convective turbulence. Aerosols and fog droplets were mostly trapped in a shallower PBL with a height of 0.2–0.4 km during the haze–fog mixed episode because of weaker turbulence

“Colorless-to-black” electrochromic and AIE-active polyamides: An effective strategy for the highest-contrast electrofluorochromism

Electrofluorochromic (EFC) materials have gained extensive attention owing to their interesting modulations of fluorescence by an electric stimulus. However, the limited performances, especially the low fluorescence on/off contrast, significantly hampered their further applications. Herein, we design a new strategy to achieve high-contrast electrofluorochromism by combinations of “colorless-to-black” electrochromism and highly fluorescent AIE activity. Given the effective fluorescence quenching effect and high solid-state fluorescence, a fluorescence contrast of 838 is realized, to the best of our knowledge, the highest reported so far. Furthermore, to explore the structure-property relationships, we also separated the E/Z isomers of tetraphenylethylene (TPE) and studied the properties of the three electroactive/fluorescent polymers (11TPE-PA, E-12TPE-PA, and Z-12TPE-PA) derived from different TPE derivatives and isomers. The three branches of polymers all exhibited AIE-active and “colorless-to-black” electrochromic (EC) properties. In addition to the ultrahigh fluorescence contrast, Z-12TPE-PA also integrated high electrochromic contrast (Δ% T = 92%), short response time (0.6 s/0.3 s), and excellent switching stability (300 cycles), paving the way for the applications in various electronic applications. The study will provide novel insights into the future design and development of high-performance EC/EFC materials

Synergistic effect between electroactive tetraphenyl-: P -phenylenediamine and AIE-active tetraphenylethylene for highly integrated electrochromic/electrofluorochromic performances

Switchable fluorescent materials have gained great attention due to their promising applications in sensors, memory devices and displays. However, further progress is hindered by the low fluorescence contrast, modest response speed and inferior long-term cycling stability. Based on a rational design strategy by combining a highly conjugated tetraphenyl-p-phenylenediamine (TPPA) unit and an aggregation induced emission (AIE)-active tetraphenylethylene (TPE) unit, we synthesized a novel diamine "N,N′-bis(4-aminophenyl)-N,N′-di(4-(1,2,2-triphenylethenyl)phenyl)-1,4-phenylenediamine" to construct an electro- and AIE-active polymer. In addition to the high efficiency solid-state fluorescence and the extremely stable redox properties, the resulting polymer TPE-TPPA-PA realized highly integrated emission/color dual-switchable properties, including multistage color-changing, high fluorescence on/off contrast up to 252, impressively rapid response rate (1.3/0.5 s for EC and 0.7/2.1 s for EFC processes) and excellent cycling stability over 10000 s. The demonstrated synergistic effect between stable electroactive TPPA and AIE-active TPE may provide a new pathway for further molecular design to realize high-performance emission/color dual-switchable materials

Pulse Pressure Is Associated with Rapid Cognitive Decline over 4 Years: A Population-Based Cohort Study

Aiming to investigate the relationship between pulse pressure (PP) and cognitive decline, cognitively normal subjects from a community-based longitudinal cohort were followed-up for 4 years. The Mini-Mental State Examination (MMSE) was used to evaluate global cognitive function, and a ≥2-point decrease in the MMSE score from baseline was defined as cognitive decline. Restricted cubic spline, multivariable linear regression and logistic regression were used to investigate the relationship between PP and cognitive decline. A total of 1173 participants completed the follow-up, and 205 (17.5%) met the criteria for cognitive decline. Restricted cubic splines showed no nonlinear relationship between PP and ΔMMSE (Poverall = 0.037, Pnon-linear = 0.289) or cognitive decline (Poverall = 0.003, Pnon-linear = 0.845). Multivariable linear regression analysis showed that PP was positively related to ΔMMSE (b = 0.021, p = 0.020). Multivariable logistic regression analysis showed that PP was positively associated with cognitive decline (OR = 1.020, p = 0.023). A stratified analysis found an association between PP and cognitive decline in participants who were aged ≤65 years, male, and APOEε4 noncarriers and who had school education ≤6 years or hypertension. A sensitivity analysis after propensity-score matching did not alter our findings. These findings highlight that elevated PP is associated with rapid cognitive decline, particularly in males, middle-aged, low-educated, hypertensive individuals and APOEε4 noncarriers

Aggregation-enhanced emission (AEE)-active polyamides with methylsulfonyltriphenylamine units for electrofluorochromic applications

In this work, a series of AEE-active polyamides containing methylsulfonyltriphenylamine units were prepared from a newly synthesized diamine "4,4'-diamine-4"-methylsulfonyltriphenylamine" and three dicarboxylic acids, which were highly soluble in various organic solvents and exhibited outstanding thermostability. The resulting polymer films showed one reversible redox couple along with apparent color changing from colorless to purple. The polymer solutions revealed relatively weak fluorescence with quantum yields in the range of 2.2-26.2%, which could be enhanced by induced aggregation in poor solvents. Furthermore, the bright fluorescence of the solid polymer film could be reversibly tuned by direct electrochemical redox of triphenylamine with a high contrast ratio (I-off/I-on) of 234. Overall, this comprehensive investigation of their interesting electrochromic and electrofluorochromic bifunctional properties not only supplies a deep understanding of the optical essence upon electrical stimuli but also paves the way for their future intelligent applications. (C) 2017 Elsevier Ltd. All rights reserved