The random case of Conley's theorem: III. Random semiflow case and Morse decomposition

In the first part of this paper, we generalize the results of the author \cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems. In the second part, by introducing the backward orbit for random semiflow, we are able to decompose invariant random compact set (e.g. global random attractor) into random Morse sets and connecting orbits between them, which generalizes the Morse decomposition of invariant sets originated from Conley \cite{Con} to the random semiflow setting and gives the positive answer to an open problem put forward by Caraballo and Langa \cite{CL}.Comment: 21 pages, no figur

Exploring the key indicators of Social Impact Assessment for Sponge-City PPPs: Sustainable Development Perspective

Sponge city (SPC) is currently being promoted as an initiative under the principle of sustainable development to solve the urban water crisis across China. Moreover, with the introduction of the public-private partnerships (PPPs) in SPC development, the public’s concern regarding SPC PPPs has increased in terms of their more sophisticated outcomes and greater social impacts than general urban development. Thus, to develop an effective set of SIA key indicators for SPC PPPs, this study uses social impact theory (SIT) to explore in greater detail the influencing mechanism for the social impact assessment (SIA) conceptual model proposed in the authors’ previous studies. Confirmatory factor analysis (CFA) was applied to examine whether the hypothesized relationships in the influencing mechanism fit the empirical data and to further consolidate the SIA key indicators. Based on a survey questionnaire and CFA results, a verified and refined SIA framework using 23 key indicators and five corresponding dimensions was proposed, particularly within the context of SPC PPPs. Implications generated from the CFA were discussed to improve the comprehensive performance of sponge city PPPs. These 23 key indicators and the clarification of their relationships to the respective SIA dimensions and to the overall SIA results can be a useful tool for enhancing the social benefits of SPC PPPs. Moreover, this study also provides governments with insights into enabling the low-impact and sustainable development of infrastructure within urban areas

Heavy elements in Galactic and Magellanic Cloud HII regions: recombination-line versus forbidden-line abundances

We have obtained deep optical, long-slit spectrophotometry of the Galactic HII regions M 17, NGC 3576 and of the Magellanic Cloud HII regions 30 Doradus, LMC N11B and SMC N66, recording the optical recombination lines (ORLs) of CII, NII and OII. Temperature-insensitive ORL C2+/O2+ and N2+/O2 ratios are obtained for all nebulae except SMC N66. The ORL C2+/O2+ ratios show remarkable agreement within each galactic system, while also being in agreement with the corresponding CEL ratios. For all five nebulae, the O2+/H+ abundance derived from multiple OII ORLs is found to be higher than the corresponding value derived from the strong [OIII] 4959, 5007A CELs, by factors of 1.8--2.7 for four of the nebulae. The LMC N11B nebula exhibits a more extreme discrepancy factor for the O2+ ion, ~5. Thus these HII regions exhibit ORL/CEL abundance discrepancy factors that are similar to those previously encountered amongst planetary nebulae. Our optical CEL O2+/H+ abundances agree to within 20-30 per cent with published O2+/H+ abundances that were obtained from observations of infrared fine-structure lines. Since the low excitation energies of the latter make them insensitive to variations about typical nebular temperatures, fluctuations in temperature are ruled out as the cause of the observed ORL/CEL O2+ abundance discrepancies. We present evidence that the observed OII ORLs from these HII regions originate from gas of very similar density (<3500 cm-3) to that emitting the observed heavy-element optical and infrared CELs, ruling out models that employ high-density ionized inclusions in order to explain the abundance discrepancy. We consider a scenario whereby much of the heavy-element ORL emission originates from cold (<=500 K) metal-rich ionized regions.Comment: 24 pages; 9 figures; accepted by Monthly Notices of the Royal Astronomical Societ

Gauge theory couplings on anisotropic lattices

The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near the Hamiltonian limit can be used for setting the lattice spacings in real time through analytical continuation, thereby reducing errors in quantum simulations. In this work, we derive perturbative relations between bare and renormalized quantities in Euclidean spacetime at any anisotropy factor - the ratio of spatial to temporal lattice spacings - and in any spatial dimension for U(N) and SU(N). This reduces the required classical preprocessing for quantum simulations. We find less than 10% discrepancy between our perturbative results and those from existing nonperturbative determinations of the anisotropy for SU(2) and U(1) gauge theories. For the discrete groups Z10, Z100 and BI, we perform lattice Monte Carlo simulations to extract anisotropy factors and observe similar agreement with our perturbative results

The topology of U-duality (sub-)groups

We discuss the topology of the symmetry groups appearing in compactified (super-)gravity, and discuss two applications. First, we demonstrate that for 3 dimensional sigma models on a symmetric space G/H with G non-compact and H the maximal compact subgroup of G, the possibility of oxidation to a higher dimensional theory can immediately be deduced from the topology of H. Second, by comparing the actual symmetry groups appearing in maximal supergravities with the subgroups of SL(32,R) and Spin(32), we argue that these groups cannot serve as a local symmetry group for M-theory in a formulation of de Wit-Nicolai type.Comment: 18 pages, LaTeX, 1 figure, 2 table

Soaking up the oil: Biological impacts of dispersants and crude oil on the sponge Halichondria panicea

Used during an oil spill to minimise the formation of an oil slick, dispersants have negative biological effects on marine model organisms. However, no study has investigated the impacts of dispersants on adult sponge individuals. Here, we examine the effects of water accommodated oil fraction (WAF - oil in seawater), chemically enhanced WAF (CEWAF - oil and dispersant in seawater) and Benzo[A]Pyrene on sponge Halichondria panicea at physiological and molecular levels. Sponge clearance rate decreased sharply when exposed to WAF and CEWAF but the oil loading at which the clearance rate was reduced by 50% (ED50) was 39-fold lower in CEWAF than in WAF. Transcriptomic analysis revealed a homogenous molecular response with the greatest number of differentially expressed genes identified in CEWAF samples (1,461 genes). Specifically, genes involved in stress responses were up-regulated. This study presents evidence that the use of dispersants should be considered carefully in areas where sponges are present

Imaging genome abnormalities in cancer research

Increasing attention is focusing on chromosomal and genome structure in cancer research due to the fact that genomic instability plays a principal role in cancer initiation, progression and response to chemotherapeutic agents. The integrity of the genome (including structural, behavioral and functional aspects) of normal and cancer cells can be monitored with direct visualization by using a variety of cutting edge molecular cytogenetic technologies that are now available in the field of cancer research. Examples are presented in this review by grouping these methodologies into four categories visualizing different yet closely related major levels of genome structures. An integrated discussion is also presented on several ongoing projects involving the illustration of mitotic and meiotic chromatin loops; the identification of defective mitotic figures (DMF), a new type of chromosomal aberration capable of monitoring condensation defects in cancer; the establishment of a method that uses Non-Clonal Chromosomal Aberrations (NCCAs) as an index to monitor genomic instability; and the characterization of apoptosis related chromosomal fragmentations caused by drug treatments

Demonstration of a sub‐picosecond x‐ray streak camera

A novel design, magnetically focused, x‐ray streak camera was designed and tested using sub‐20 fs soft‐x‐ray pulses generated by high harmonic emission in a gas. The temporal resolution of the camera was demonstrated to be under 0.9 ps throughout the ultraviolet to soft‐x‐ray wavelength region. Our streak camera represents the fastest x‐ray detector developed to date. © 1996 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69727/2/APPLAB-69-1-133-1.pd

Magnesium isotopic composition of the oceanic mantle and oceanic Mg cycling

© The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 206 (2017): 151-165, doi:10.1016/j.gca.2017.02.016.To constrain the Mg isotopic composition of the oceanic mantle, investigate Mg isotope fractionation of abyssal peridotites during seafloor alteration, and assess Mg budget in the oceans, a suite of 32 abyssal peridotite samples from the Gakkel Ridge and Southwest Indian Ridge (SWIR) was, for the first time, selected for high-precision Mg isotope analyses. Although most of these samples are extensively altered, largely by serpentinization and weathering, primary olivine, diopside and enstatite grains are preserved in some samples. Olivine grains from the least altered samples have δ26Mg varying from −0.30 to −0.12‰ (n = 7), whereas enstatite and diopside have δ26Mg varying from −0.27 to −0.16‰ (n = 7), and from −0.23 to −0.09‰ (n = 6), respectively. Whole-rock δ26Mg values range from −0.24 to 0.03‰ with an average of −0.12 ± 0.13‰ (2SD, n = 32). Strongly serpentinized peridotites have lower average δ26Mg values (δ26Mg = −0.19 ± 0.07‰, 2SD, n = 7) than weathering-dominated ones (δ26Mg = −0.10 ± 0.12‰, 2SD, n = 25). Calculated Mg isotopic compositions of fresh mantle peridotites vary from −0.29 to −0.13‰, beyond the previously reported range of the subcontinental lithospheric mantle (−0.25 ± 0.04‰) and the analytical uncertainty (±0.07‰, 2SD). Our study therefore indicates that the oceanic mantle may have similar but slightly heterogeneous Mg isotopic compositions to that of subcontinental lithospheric mantle. Secondary serpentinization does not fractionate Mg isotopes of abyssal peridotites, whereas low-T weathering and formation of clay can result in the enrichment of heavy Mg isotopes in abyssal peridotites. This study also demonstrates that fluid-rock interaction does not necessarily produce rocks with intermediate Mg isotopic compositions. Magnesium isotopes of the rocks thereafter are dependent on the secondary minerals formed. We also conclude that the release of light Mg isotopes into the ocean during alteration of abyssal peridotites can be an important influx of Mg for the seawater Mg budget. Abyssal peridotites with a heavy Mg isotopic signature can be recycled into the mantle in subduction zones and may thus result in heterogeneous Mg isotopic compositions of the oceanic mantle and heavy Mg isotopic compositions of arc magmas.This study was supported by grants from the National Science Foundation of China (grants 41473038 and 41503010), China Postdoctoral Science Foundation (2015M570145), National Science Foundation (EAR-1056713 and EAR-1340160) and project MOST104 -2745-M-002-001-ASP granted to SLC. Partial support for HJBD was provided by the US National Science Foundation (OCE-1434452)