The enantioselective Friedel—Crafts reaction of 1-naphthols with isatins and subsequent treatment of the products with ethyl iodide gives compounds (IV) with good to high enantioselectivities.
The enantioselective Friedel—Crafts reaction of 1-naphthols with isatins and subsequent treatment of the products with ethyl iodide gives compounds (IV) with good to high enantioselectivities.
A suitable treatment method for decentralized sewage remediation in drinking water protection source zones of rural areas in Beijing is concerned in this *** anaerobic biological treatment process,it has the lowest co...
A suitable treatment method for decentralized sewage remediation in drinking water protection source zones of rural areas in Beijing is concerned in this *** anaerobic biological treatment process,it has the lowest construction and operating costs,but its treatment effect is *** MBR process has the feature of high operating cost, complicated operation and membrane's short-lived *** aerobic biological treatment process,the effluent still can not attain the discharge standard.A transformed treatment process -‘A/O + the quartz sand filtration + activated carbon adsorption', with a satisfied treatment effect,is proposed in this paper.
We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in Hs\documentclass[12pt]{mini...
We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in Hs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>{s}$$\end{document} Sobolev space. We find the well/ill-posedness separation at regularity s=d-12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s=\frac{d-1}{2}$$\end{document}, strictly 12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document}-derivative higher than the scaling-invariant index s=d-22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s=\frac{d-2}{2}$$\end{document}, the usually expected separation point.
In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equation ut - u(xxt) + 4u(m)u(x) = 3u(x)u(xx...
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In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equation ut - u(xxt) + 4u(m)u(x) = 3u(x)u(xx) + uu(xxx). The parameter condition under which peakons, compactons and periodic cusp wave solutions exist is given. The numerical simulation results show the consistence with the theoretical analysis at the same time. (C) 2006 Elsevier B.V. All rights reserved.
By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equation m(t) + c(0)u(x) + um(x) + 2mu(x) = -yu(xxx) with m = u - alpha(2)u(xx), alpha not equal 0, co, gamma are constant, whi...
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By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equation m(t) + c(0)u(x) + um(x) + 2mu(x) = -yu(xxx) with m = u - alpha(2)u(xx), alpha not equal 0, co, gamma are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time. (c) 2005 Elsevier Ltd. All rights reserved.
We study the differences of two consecutive eigenvalues lambda i - lambda i - 1 , i up to 2 g - 2, for the Laplacian on hyperbolic surfaces of genus g , and show that the supremum of such spectral gaps over the moduli...
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We study the differences of two consecutive eigenvalues lambda i - lambda i - 1 , i up to 2 g - 2, for the Laplacian on hyperbolic surfaces of genus g , and show that the supremum of such spectral gaps over the moduli space has infimum limit at least 4 1 as the genus goes to infinity. A min-max principle for eigenvalues on degenerating hyperbolic surfaces is also established.
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