In this paper we put forward the definition of particular subsets on a unital C∗-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order relation defined on the spectrum of the algebra, which satisfies a compatibility condition with the topology (complete separateness). We prove that this space/algebra correspondence is a dual equivalence of categories, which generalizes the Gelfand–Naimark duality. Thus we can expect that general isocones could serve to define a notion of “noncommutative ordered spaces”. We also explore some basic algebraic constructions involving isocones, and classify those which are defined in M2(C). 相似文献
Numerical approximation of the five-equation two-phase flow of Kapila et al. [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002–3024] is examined. This model has shown excellent capabilities for the numerical resolution of interfaces separating compressible fluids as well as wave propagation in compressible mixtures [A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics 202(2) (2005) 664–698; R. Abgrall, V. Perrier, Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flows, SIAM Journal of Multiscale and Modeling and Simulation (5) (2006) 84–115; F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214–2248]. However, its numerical approximation poses some serious difficulties. Among them, the non-monotonic behavior of the sound speed causes inaccuracies in wave’s transmission across interfaces. Moreover, volume fraction variation across acoustic waves results in difficulties for the Riemann problem resolution, and in particular for the derivation of approximate solvers. Volume fraction positivity in the presence of shocks or strong expansion waves is another issue resulting in lack of robustness. To circumvent these difficulties, the pressure equilibrium assumption is relaxed and a pressure non-equilibrium model is developed. It results in a single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms. It fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them. This formulation considerably simplifies numerical resolution. Following a strategy developed previously for another flow model [R. Saurel, R. Abgrall, A multiphase Godunov method for multifluid and multiphase flows, Journal of Computational Physics 150 (1999) 425–467], the hyperbolic part is first solved without relaxation terms with a simple, fast and robust algorithm, valid for unstructured meshes. Second, stiff relaxation terms are solved with a Newton method that also guarantees positivity and robustness. The algorithm and model are compared to exact solutions of the Euler equations as well as solutions of the five-equation model under extreme flow conditions, for interface computation and cavitating flows involving dynamics appearance of interfaces. In order to deal with correct dynamic of shock waves propagating through multiphase mixtures, the artificial heat exchange method of Petitpas et al. [F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214–2248] is adapted to the present formulation. 相似文献
Molecular switches : Highly efficient acido‐ and photoswitchable frequency doublers (see scheme) based on the indolinooxazolidine core are studied by means of hyper‐Rayleigh experiments and quantum‐chemical calculations.
The high content in nutrients of freshwater outflows induces highly productive and buoyant plumes spreading over marine waters (MW). As a consequence, the growth of organisms developing in these low‐salinity waters (LSW) might be potentially affected by UV‐R (280–400 nm). This study investigated the penetration of UV‐R and its impact on net community production (NCP) and bacterial protein (BPROTS) and DNA (BDNAS) synthesis in mesotrophic‐LSW formed from the Rhône River and in oligotrophic MW of the Northwestern Mediterranean Sea (Gulf of Lions) in May 2006. High concentrations of chlorophyll a (up to 8 μg L?1) measured in the LSW (<37.8 psu, 0–10 m) were the main factor influencing the diffuse attenuation coefficients (Kd) of both UV‐R and photosynthetically active radiation (PAR). The mean ratio of the Kd measured between the LSW and the MW increased with wavelength from 2.4 at 305 nm to 2.9 at 380 nm and 3.1 for PAR indicating more similarity in the UV region. NCP was severely inhibited by UV‐R at the surface of the LSW, whereas no effect was measured in the surrounding MW. In contrast, BPROTS and BDNAS were affected deeper by UV‐R in the MW (up to 8 m depth) compared to the LSW where inhibition was only observed at the surface. Differences in response of bacteria in LSW and MW are largely explained by differences in UV‐R transparency; however, transplant experiments indicate that bacterial assemblages from the MW were also more sensitive to UV‐R than those present in the LSW. We also observed that higher activity of bacteria after nutrient additions increased their sensitivity to UV‐R during the day, but favored their recovery during the night incubation period for both LSW and MW. Results suggest that riverine and nutrient inputs may alter the effects of UV‐R on microbial activity by attenuating the UV‐R penetration and by modifying the physiology of bacteria. 相似文献
We evaluated the role of nitrate (NO3?) as a potential photosensitizer and the bacterial responses to dissolved organic matter (DOM) phototransformation from coastal waters in the northwestern Mediterranean Sea. In spring, without any addition of NO3?, the exposure of 0.2 μm filtered seawater (DOM-solution) to natural solar radiation (i.e. Full Sun [FS], including photosynthetically available [PAR: 400–700 nm], ultraviolet-A [UVAR: 315–400 nm] and ultraviolet-B [UVBR: 280–315 nm] radiations) stimulated bacterial production (BP) and abundance (BA) in natural assemblages (0.8 μm filtered seawater) by 80 and 20% as compared to unexposed (Dark) DOM-solutions, respectively. This stimulation resulted primarily from the exposure to PAR. When NO3? (30 μM) was added to DOM-solution before irradiation, BP and BA increased by 150 and 65% in FS compared to Dark, respectively, due to both PAR and UVBR. By contrast, in summer, the exposure of DOM-solution caused a decrease in BP by 30% but an increase in BA by 23% in FS compared to Dark, regardless of the NO3? addition before irradiation. The inhibition of BP resulted mainly from UVAR, whereas the stimulation of BA resulted from PAR. These results suggest contrasting effects along seasons of solar radiation and NO3? on DOM bioavailability, depending on its initial chemical composition. 相似文献
Product detection studies of CN reactions with ethene and propene are conducted at room temperature (4 Torr, 533.3 Pa) using multiplexed time-resolved mass spectrometry with tunable synchrotron photoionization. Photoionization efficiency curves, i.e., the ion signal as a function of photon energy, are used to determine the products and distinguish isomers. Both reactions proceed predominantly via CN addition to the π orbital of the olefin. For CN + ethene, cyanoethene (C2H3CN) is detected as the sole product in agreement with recent studies on this reaction. Multiple products are identified for the CN + propene reaction with 75(±15)% of the detected products in the form of cyanoethene from a CH3 elimination channel and 25(±15)% forming different isomers of C4H5N via H elimination. The C4H5N comprises 57(±15)% 1-cyanopropene, 43(±15)% 2-cyanopropene and <15% 3-cyanopropene. No evidence of direct H abstraction or indirect HCN formation is detected for either reaction. The results have relevance to the molecular weight growth chemistry on Saturn's largest moon Titan, where the formation of small unsaturated nitriles are proposed to be key steps in the early chemical stages of haze formation. 相似文献