"Magic" numbers in Smale's 7th problem

Smale's 7-th problem concerns N-point configurations on the 2-dim sphere which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the pairs in a configuration; here, r is the chordal distance between the points forming a pair. More generally, V_0(r) may be replaced by the standardized Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to 0, and the sphere may be replaced by other compact manifolds. This paper inquires into the concavity of the map from the integers N>1 into the minimal average standardized Riesz pair-energies v_s(N) of the N-point configurations on the 2-sphere for various real s. It is known that v_s(N) is strictly increasing for each real s, and for s<2 also bounded above, hence "overall concave." It is (easily) proved that v_{-2}(N) is even locally strictly concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental data of putatively minimal average Riesz pair-energies v_s^x(N) for s in {-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally strictly concave, while v_s^x(N) is not always locally strictly concave for s in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific empirical set of integers). It is found that the empirical map C^{x}_+(s), with s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The integers in C^{x}_+(0) are few and far between, forming a curious sequence of numbers, reminiscent of the "magic numbers" in nuclear physics. It is conjectured that the "magic numbers" in Smale's 7-th problem are associated with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised version, to appear in J. Stat. Phys. under the different title: `Optimal N point configurations on the sphere: "Magic" numbers and Smale's 7th problem

Effects on the maternofetal unit of the rabbit model after substitution of the amniotic fluid with perfluorocarbons

Objectives: Exchanging amniotic fluid (AF) with perfluorocarbon (PFC) may serve as a medium for fetoscopic surgery. This study evaluates the distribution and physiologic effects of intraamniotic PFC as a medium for fetoscopy. Methods: Fetuses of 17 pregnant rabbits underwent either exchange of the AF with PFC, electrolyte solution (ES), or control. The quality of vision during fetoscopy was assessed in AF and PFC. After 6 h, we determined the distribution of PFC in the maternofetal unit. Results: Quality of vision during fetoscopy was better in PFC than with AF. There was no difference in fetal survival between the study groups. PFC was demonstrated on X-ray in the pharynx of 4 fetuses, and the esophagus in 1. Conclusions: PFC provided an ideal medium for fetoscopy without fetal compromise. Copyright (c) 2005 S. Karger AG, Basel

New and practical mathematical model of membrane fouling in an aerobic submerged membrane bioreactor

© 2017 Elsevier Ltd This study aimed to develop a practical semi-empirical mathematical model of membrane fouling that accounts for cake formation on the membrane and its pore blocking as the major processes of membrane fouling. In the developed model, the concentration of mixed liquor suspended solid is used as a lumped parameter to describe the formation of cake layer including the biofilm. The new model considers the combined effect of aeration and backwash on the foulants’ detachment from the membrane. New exponential coefficients are also included in the model to describe the exponential increase of transmembrane pressure that typically occurs after the initial stage of an MBR operation. The model was validated using experimental data obtained from a lab-scale aerobic sponge-submerged membrane bioreactor (MBR), and the simulation of the model agreed well with the experimental findings

A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment

Micropollutants are emerging as a new challenge to the scientific community. This review provides a summary of the recent occurrence of micropollutants in the aquatic environment including sewage, surface water, groundwater and drinking water. The discharge of treated effluent from WWTPs is a major pathway for the introduction of micropollutants to surface water. WWTPs act as primary barriers against the spread of micropollutants. WWTP removal efficiency of the selected micropollutants in 14 countries/regions depicts compound-specific variation in removal, ranging from 12.5 to 100%. Advanced treatment processes, such as activated carbon adsorption, advanced oxidation processes, nanofiltration, reverse osmosis, and membrane bioreactors can achieve higher and more consistent micropollutant removal. However, regardless of what technology is employed, the removal of micropollutants depends on physico-chemical properties of micropollutants and treatment conditions. The evaluation of micropollutant removal from municipal wastewater should cover a series of aspects from sources to end uses. After the release of micropollutants, a better understanding and modeling of their fate in surface water is essential for effectively predicting their impacts on the receiving environment. © 2013 Elsevier B.V

Effects of hyperoxia on 18F-fluoro-misonidazole brain uptake and tissue oxygen tension following middle cerebral artery occlusion in rodents: Pilot studies.

PURPOSE: Mapping brain hypoxia is a major goal for stroke diagnosis, pathophysiology and treatment monitoring. 18F-fluoro-misonidazole (FMISO) positron emission tomography (PET) is the gold standard hypoxia imaging method. Normobaric hyperoxia (NBO) is a promising therapy in acute stroke. In this pilot study, we tested the straightforward hypothesis that NBO would markedly reduce FMISO uptake in ischemic brain in Wistar and spontaneously hypertensive rats (SHRs), two rat strains with distinct vulnerability to brain ischemia, mimicking clinical heterogeneity. METHODS: Thirteen adult male rats were randomized to distal middle cerebral artery occlusion under either 30% O2 or 100% O2. FMISO was administered intravenously and PET data acquired dynamically for 3hrs, after which magnetic resonance imaging (MRI) and tetrazolium chloride (TTC) staining were carried out to map the ischemic lesion. Both FMISO tissue uptake at 2-3hrs and FMISO kinetic rate constants, determined based on previously published kinetic modelling, were obtained for the hypoxic area. In a separate group (n = 9), tissue oxygen partial pressure (PtO2) was measured in the ischemic tissue during both control and NBO conditions. RESULTS: As expected, the FMISO PET, MRI and TTC lesion volumes were much larger in SHRs than Wistar rats in both the control and NBO conditions. NBO did not appear to substantially reduce FMISO lesion size, nor affect the FMISO kinetic rate constants in either strain. Likewise, MRI and TTC lesion volumes were unaffected. The parallel study showed the expected increases in ischemic cortex PtO2 under NBO, although these were small in some SHRs with very low baseline PtO2. CONCLUSIONS: Despite small samples, the apparent lack of marked effects of NBO on FMISO uptake suggests that in permanent ischemia the cellular mechanisms underlying FMISO trapping in hypoxic cells may be disjointed from PtO2. Better understanding of FMISO trapping processes will be important for future applications of FMISO imaging

Removal and fate of micropollutants in a sponge-based moving bed bioreactor

This study investigated the removal of micropollutants using polyurethane sponge as attached-growth carrier. Batch experiments demonstrated that micropollutants could adsorb to non-acclimatized sponge cubes to varying extents. Acclimatized sponge showed significantly enhanced removal of some less hydrophobic compounds (log. D<. 2.5), such as ibuprofen, acetaminophen, naproxen, and estriol, as compared with non-acclimatized sponge. The results for bench-scale sponge-based moving bed bioreactor (MBBR) system elucidated compound-specific variation in removal, ranging from 25.9% (carbamazepine) to 96.8% (β-Estradiol 17-acetate) on average. In the MBBR system, biodegradation served as a major removal pathway for most compounds. However, sorption to sludge phase was also a notable removal mechanism of some persistent micropollutants. Particularly, carbamazepine, ketoprofen and pentachlorophenol were found at high concentrations (7.87, 6.05 and 5.55. μg/g, respectively) on suspended biosolids. As a whole, the effectiveness of MBBR for micropollutant removal was comparable with those of activated sludge processes and MBRs. © 2014 Elsevier Ltd

Effect of hydraulic retention time on the performance of a hybrid moving bed biofilm reactor-membrane bioreactor system for micropollutants removal from municipal wastewater

© 2017 Elsevier Ltd This study evaluated micropollutants removal and membrane fouling behaviour of a hybrid moving bed biofilm reactor-membrane bioreactor (MBBR-MBR) system at four different hydraulic retention times (HRTs) (24, 18, 12 and 6 h). The results revealed that HRT of 18 h was the optimal condition regarding the removal of most selected micropollutants. As the primary removal mechanism in the hybrid system was biodegradation, the attached growth pattern was desirable for enriching slow growing bacteria and developing a diversity of biocoenosis. Thus, the efficient removal of micropollutants was obtained. In terms of membrane fouling propensity analysis, a longer HRT (e.g. HRTs of 24 and 18 h) could significantly mitigate membrane fouling when compared with the shortest HRT of 6 h. Hence, enhanced system performance could be achieved when the MBBR-MBR system was operated at HRT of 18 h

Direct Formation of Supermassive Black Holes via Multi-Scale Gas Inflows in Galaxy Mergers

Observations of distant bright quasars suggest that billion solar mass supermassive black holes (SMBHs) were already in place less than a billion years after the Big Bang. Models in which light black hole seeds form by the collapse of primordial metal-free stars cannot explain their rapid appearance due to inefficient gas accretion. Alternatively, these black holes may form by direct collapse of gas at the center of protogalaxies. However, this requires metal-free gas that does not cool efficiently and thus is not turned into stars, in contrast with the rapid metal enrichment of protogalaxies. Here we use a numerical simulation to show that mergers between massive protogalaxies naturally produce the required central gas accumulation with no need to suppress star formation. Merger-driven gas inflows produce an unstable, massive nuclear gas disk. Within the disk a second gas inflow accumulates more than 100 million solar masses of gas in a sub-parsec scale cloud in one hundred thousand years. The cloud undergoes gravitational collapse, which eventually leads to the formation of a massive black hole. The black hole can grow to a billion solar masses in less than a billion years by accreting gas from the surrounding disk.Comment: 26 pages, 4 Figures, submitted to Nature (includes Supplementary Information

Understanding the power of the prime minister : structure and agency in models of prime ministerial power

Understanding the power of the prime minister is important because of the centrality of the prime minister within the core executive of British government, but existing models of prime ministerial power are unsatisfactory for various reasons. This article makes an original contribution by providing an overview and critique of the dominant models of prime ministerial power, highlighting their largely positivist bent and the related problem of the prevalence of overly parsimonious conceptions of the structural contexts prime ministers face. The central argument the paper makes is that much of the existing literature on prime ministerial power is premised on flawed understandings of the relationship between structure and agency, that this leads to misunderstandings of the real scope of prime ministerial agency, as well as its determinants, and that this can be rectified by adopting a strategic-relational view of structure and agency