Equivalent Conditions for Ω-Inverse Limit Stability

Recently we obtained sufficient conditions for an endomorphism to be -inverse limit stable. That is, if an endomorphism f satisfies weak Axiom A and the no-cycles condition, then f is -inverse limit stable. In this paper we give alternative conditions for -inverse limit stability. The following are equivalent: (a) f satisfies weak Axiom A and the no-cycles condition; (b) the chain recurrent set is prehyperbolic; and (c) the closure of the set of -limit points of f, L ⁺(f), is prehyperbolic with no cycles.     

PM2.5 in China： Measurements,sources, visibility and health effects,and mitigation

Concern over the health effects of fine particles in the ambient environment led the U.S. Environmental Protection Agency to develop the first standard for PM2.5 （particulate matter less than 2.5 μm） in 1997. The Particle Technology Laboratory at the University of Minnesota has helped to establish the PM2.5 standard by developing many instruments and samplers to perform atmospheric measurements. In this paper, we review various aspects of PM2.5, including its measurement, source apportionment, visibility and health effects, and mitigation. We focus on PM2.s studies in China and where appropriate, compare them with those obtained in the U.S. Based on accurate PM2.5 sampling, chemical analysis, and source apportionment models, the major PM2.5 sources in China have been identified to be coal combustion, motor vehicle emissions, and industrial sources. Atmospheric visibility has been found to correlate well with PM2.s concentration. Sulfate, ammonium, and nitrate carried by PM2.s, commonly found in coal burning and vehicle emissions, are the dominant contributors to regional haze in China. Short-term exposure to PM2.s is strongly associated with the increased risk of morbidity and mortality from cardiovascular and respiratory diseases in China. The strategy for PMzs mitigation must be based on reducing the pollutants from the two primary sources of coal-fired power plants and vehicle emissions. Although conventional Particulate Emission Control Devices （PECD） such as electrostatic precipitators in Chinese coal-fired power plants are generally effective for large particles, most of them may not have high collection efficiency of PM2.5. Baghouse filtration is gradually incorporated into the PECD to increase the PM2.5 collection efficiency. By adopting stringent vehicle emissions standard such as Euro 5 and 6, the emissions from vehicles can be gradually reduced over the years. An integrative approach, from collaboration among academia, government, and industries, can effectively manage and mitigate the PM2.s p     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials III: Diffusion,thermal diffusion,and thermal conductivity in a binary,rigid-sphere,gas mixture

The Chapman–Enskog solutions of the Boltzmann equation provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper (I), for simple, rigid-sphere gases (i.e. single-component, monatomic gases) we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error and, in a second paper (II), we have extended our initial simple gas work to modeling the viscosity in a binary, rigid-sphere, gas mixture. In this latter paper we reported an extensive set of order 60 results which are believed to constitute the best currently available benchmark viscosity values for binary, rigid-sphere, gas mixtures. It is our purpose in this paper to similarly report the results of our investigation of relatively high-order (order 70), standard, Sonine polynomial expansions for the diffusion- and thermal conductivity-related Chapman–Enskog solutions for binary gas mixtures of rigid-sphere molecules. We note that in this work, as in our previous work, we have retained the full dependence of the solution on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals. For rigid-sphere gases, all of the relevant omega integrals needed for these solutions are analytically evaluated and, thus, results to any desired precision can be obtained. The values of the transport coefficients obtained using Sonine polynomial expansions for the Chapman–Enskog solutions converge and, therefore, the exact diffusion and thermal conductivity solutions to a given degree of convergence can be determined with certainty by expanding to sufficiently high an order. We have used Mathematica® for its versatility in permitting both symbolic and high-precision computations. Our results also establish confidence in the results reported recently by other authors who used direct numerical techniques to solve the relevant Chapman–Enskog equations. While in all of the direct numerical methods more-or-less full calculations need to be carried out with each variation in molecular parameters, our work has utilized explicit, general expressions for the necessary matrix elements that retain the complete parametric dependence of the problem and, thus, only a matrix inversion at the final step is needed as a parameter is varied. This work also indicates how similar results may be obtained for more realistic intermolecular potential models and how other gas-mixture problems may also be addressed with some additional effort.     

Stable Configurations in Superconductivity: Uniqueness, Multiplicity, and Vortex‐Nucleation

. We find new stable solutions of the Ginzburg‐Landau equation for high κ superconductors with exterior magnetic field h _ex. First, we prove the uniqueness of the Meissner‐type solution. Then, we prove, in the case of a disc domain, the coexistence of branches of solutions with n vortices of degree one, for any n not too high and for a certain range of h _ex; and describe these branches. Finally, we give an estimate on the nucleation energy barrier, to pass continuously from a vortexless configuration to a configuration with a centered vortex. (Accepted October 29, 1998)     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials II: Viscosity in a binary,rigid-sphere,gas mixture

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper (I), for simple, rigid-sphere gases (i.e. single-component, monatomic gases) we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are error free. It is our purpose in this paper to report the results of our investigation of relatively high-order, standard, Sonine polynomial expansions for the viscosity-related Chapman–Enskog solutions for binary gas mixtures of rigid-sphere molecules. We note that in this work we have retained the full dependence of the solution on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals. For rigid-sphere gases, all of the relevant omega integrals needed for these solutions are analytically evaluated and, thus, results to any desired precision can be obtained. The values of viscosity obtained using Sonine polynomial expansions for the Chapman–Enskog solutions converge monotonically from below and, therefore, the exact viscosity solution to a given degree of convergence can be determined with certainty by expanding to sufficiently high an order. We have used Mathematica® for its versatility in permitting both symbolic and high precision computations. Our results also establish confidence in the results reported recently by other authors who used direct numerical techniques to solve the relevant Chapman–Enskog equations. While in all of the direct numerical methods more-or-less full calculations need to be carried out with each variation in molecular parameters, our work utilizes explicit, general expressions for the necessary matrix elements that retain the complete parametric dependence of the problem and, thus, only a matrix inversion at the final step is needed as a parameter is varied. This work also indicates how similar results may be obtained for more realistic intermolecular potential models and how other gas-mixture problems may also be addressed with some additional effort.     

Liquid film characterization in horizontal,annular, two-phase,gas–liquid flow using time-resolved laser-induced fluorescence

A non-intrusive optical technique was developed to provide time-resolved longitudinal and cross-sectional images of the liquid film in horizontal annular pipe flow of air and water, revealing the interfacial wave behavior. Quantitative information on the liquid film dynamics was extracted from the time-resolved images. The planar laser-induced fluorescence technique was utilized to allow for optical separation of the light emitted by the film from that scattered by the air–water interface. The visualization test section was fabricated from a tube presenting nearly the same refractive index as water, which allowed the visualization of the liquid film at regions very close to the pipe wall. Longitudinal images of the liquid film were captured using a high-frame-rate digital video camera synchronized with a high-repetition-rate laser. An image processing algorithm was developed to automatically detect the position of the air–water interface in each image frame. The thickness of the liquid film was measured at two axial stations in each processed image frame, providing time history records of the film thickness at two different positions. Wave frequency information was obtained by analyzing the time-dependent signals of film thickness for each of the two axial positions recorded. Wave velocities were measured by cross-correlating the amplitude signals from the two axial positions. For the film cross-section observations, two high-speed digital video cameras were used in a stereoscopic arrangement. Comparisons with results from different techniques available in literature indicate that the technique developed presents equivalent accuracy in measuring the liquid film properties. Time-resolved images of longitudinal and cross-section views of the film were recorded, which constitute valuable information provided by the technique implemented.     

Epidemiological characterization of congenital heart disease in São Miguel Island, Azores, Portugal

OBJECTIVES: This study aimed to characterize the prevalence of congenital heart disease (CHD) in children born alive in S?o Miguel island from January 1992 to December 2001. METHODS: Based on the Azorean Registry of CHD, which includes complete clinical and personal information, 189 patients were diagnosed. RESULTS: During this 10-year period, the average prevalence of CHD is 9.16 per 1,000 live births (range 4.77-12.75). The most frequent cardiac malformations found were: ventricular septal defect (38.1%), atrial septal defect (12.2%) and patent ductus arteriosus (11.6%). Until now, four familial clusters were identified, representing a total of 13 patients. CONCLUSIONS: This first epidemiological study of CHD in the Azorean population reveals evidence for familial aggregation, which is of great interest for understanding the genes involved in these complex pathologies.     

Stabilität einer in zylindrischen Gleitlagern laufenden,unwuchtfreien Welle

Zusammenfassung Das Problem der sogenannten Lagerinstabilität wurde rechnerisch untersucht. Als Vorbereitung wurde der Schmiermitteldruck und die Feder- und Dämpfungskonstanten des Schmierfilms berechnet. Die lineare Stabilitätsrechnung ergab, daß die Größe des Breitenverhältnisses die Stabilitätsgrenzkurve nur wenig, die Anfahrkurve jedoch stark beeinflußt. Wie man aus dem Verlauf der Grenzkurven ersieht, muß man bei der Stabilisierung eines instabilen Gleichgewichtes zwei Fälle unterscheiden: Beim leicht belasteten Lager ist das Lagerspiel r zu verkleinern und die Eigenfrequenz _k der Welle zu erhöhen, beim schwer belasteten Lager ist die Zähigkeit und die Lagerbreite B zu verkleinern und das Lagerspiel r zu vergrößern. Die nichtlineare Bahnberechnung ergab: Auch wenn nach linearer Rechnung das Gleichgewicht stabil ist, kann bei höheren Drehzahlen eine hinreichend große Anfangsstörung Instabilität hervorrufen. Die Bahnkurven werden bei Instabilität mit wachsender Amplitude mehr und mehr kreisförmig. Dabei stellt sich bei Drehzahlen unter 2 _k die Halbdrehfrequenzschwingung mit einer endlichen Rotoramplitude ein, während bei Drehzahlen über 2 _k die Eigenfrequenzschwingung entsteht, deren Amplitude unaufhörlich anwächst. Dieses Anwachsen beruht auf einer durch den Schmiermitteldruck bedingten Energiezufuhr. Soll also in Wirklichkeit die Amplitude endlich bleiben, so muß eine äußere Dämpfung auf die Welle wirken. Für einen einfachen Dämpfungsansatz wurde daher abschließend die stationäre, kreisförmige Wellenschwingung berechnet, wobei sich wiederum die Halbdrehfrequenz- und die Eigenfrequenzschwingung ergaben. Für große Werte des Parameters / nimmt danach die Rotoramplitude mit der Drehzahl zu, für kleine /-Werte nimmt sie dagegen nach Überschreiten eines Maximums wieder ab. In diesem Falle läßt sich die Rotoramplitude auch durch ein Verkleinern des Parameters / vermindern. Die bisher bekannten Versuchsergebnisse scheinen die Rechenergebnisse zu bestätigen.Gekürzte Fassung der Dissertation an der T.H. Karlsruhe, 1962; Referent: Prof. Dr.-Ing. K. Kollmann; Korreferent: Prof. Dr. K. Nickel und Prof. Dr. F. Weidenhammer; insbesondere Herrn Professor Kollmann danke ich herzlich für die Anregung und großzügige Förderung der Arbeit.     

On the Impossibility, in Some Cases, of the Leray�CHopf Condition for Energy Estimates

Current proofs of time independent energy bounds for solutions of the time dependent Navier–Stokes equations, and of bounds for the Dirichlet norms of steady solutions, are dependent upon the construction of an extension of the prescribed boundary values into the domain that satisfies the inequality (1.1) below, for a value of κ less than the kinematic viscosity. It is known from the papers of Leray (J Math Pure Appl 12:1–82, 1993), Hopf (Math Ann 117:764–775, 1941) and Finn (Acta Math 105:197–244, 1961) that such a construction is always possible if the net flux of the boundary values across each individual component of the boundary is zero. On the other hand, the nonexistence of such an extension, for small values of κ, has been shown by Takeshita (Pac J Math 157:151–158, 1993) for any two or three-dimensional annular domain, when the boundary values have a net inflow toward the origin across each component of the boundary. Here, we prove a similar result for boundary values that have a net outflow away from the origin across each component of the boundary. The proof utilizes a class of test functions that can detect and measure deformation. It appears likely that much of our reasoning can be applied to other multiply connected domains.     

Ricci flow and nonlinear reaction�Cdiffusion systems in?biology, chemistry, and?physics

This paper proposes the Ricci?Cflow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction?Cdiffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a conjecture that any kind of reaction?Cdiffusion processes in biology, chemistry, and physics can be modeled by the combined geometric?Cdiffusion system. In order to demonstrate the validity of this hypothesis, we review a number of popular nonlinear reaction?Cdiffusion systems and try to show that they can all be subsumed by the presented geometric framework of the Ricci flow.     

Well-Posedness, Instabilities, and Bifurcation Results for the Flow in a Rotating Hele�CShaw Cell

We study the radial movement of an incompressible fluid located in a Hele–Shaw cell rotating at a constant angular velocity in the horizontal plane. Within an analytic framework, local existence and uniqueness of solutions is proved, and it is shown that the unique rotationally invariant equilibrium of the flow is unstable. There are, however, other time-independent solutions: using surface tension as a bifurcation parameter we establish the existence of global bifurcation branches consisting of stationary fingering patterns. The same results can be obtained by fixing the surface tension while varying the angular velocity. Finally, it is shown that the equilibria on a global bifurcation branch converge to a circle as the surface tension tends to infinity, provided they stay suitably bounded.     

Characteristics of elemental carbon and organic carbon in PM10 during spring and autumn in Chongqing, China

PM10 （particulate matter with aerodynamic diameter less than 10 μm） samples were collected simultaneously at nine urban sites and one urban background site during two intensive observation campaigns in 2006. Concentrations of elemental carbon （EC） and organic carbon （OC） in PM10 were analyzed using an element analyzer. The characteristics regarding spatial and seasonal distribution patterns of OC and EC concentrations and their contributions to PM10 mass, as well as correlation between OC and EC, were investigated in detail. The average OC and EC concentrations for urban sites were 57.5 ± 20.8 and 8.3 ± 3.9 μg/m^3, respectively, both being around three times higher than those for urban background site. As a whole, EC concentrations did not show distinct seasonal variations, though OC concentrations were generally higher in autumn than in spring. For urban sites, total carbonaceous aerosol （TCA） accounted for 33.2% in spring and 35.0% in autumn of PM10 mass. The OC and EC concentrations were found significantly correlated to each other both in spring and in autumn, implying the existence of similar emission sources such as coal combustion. The OC/EC ratios generally exceeded 2.0, indicating the presence of secondary organic carbon （SOC）, whose estimated concentration for urban Chongqing was 26.7 and 39.4μg/m^3, accounting for 48.9 and 61.9% of the total OC observed in the samples, in spring and in autumn, respectively.