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1.
Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients
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Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
2.
Minoru Koyama Dr. Takafumi Kawakami Dr. Takashi Okazoe Prof. Dr. Kyoko Nozaki 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(46):10913-10917
Methacrylic esters, represented by methyl methacrylate (MMA), are widely used as commodity chemicals. Here, the one-pot synthesis of methacrylic esters from acetone, a haloform and alcohols in the presence of an organic base is described. Using DBU as the organic base for the reaction of acetone, chloroform and methanol in acetonitrile afforded MMA in 66 % yield. When the solvent was replaced by benzonitrile, the product MMA was successfully purified by distillation. Applicability of this process to various alcohols was also investigated to show ethyl, phenyl, CF3CH2, and n-C6F13CH2CH2 esters were obtained in moderate yields. The use of bromoform instead of chloroform resulted in the improvement of the yield, for example, methyl and n-C6F13CH2CH2 esters up to 81 and 70 %, respectively. The reaction with deuterated starting materials acetone-d6 and MeOH-d4, with DBU in acetonitrile afforded deuterated MMA (MMA-d8) in 70 % yield. 相似文献
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Higher-order implicit strong numerical schemes for stochastic differential equations 总被引:2,自引:0,他引:2
Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined. 相似文献
7.
聚乙烯单晶的退火效应 总被引:1,自引:1,他引:1
用混合晶红外光谱法和SAXS、DSC和LAM等方法研究了聚乙烯单晶在75℃、90℃和105℃退火前后的结构变化,发现在90℃以下和105℃以上退火,遵循不同的退火机制 相似文献
8.
G. R. Sudhakaran R. L. Bhattacharjee J. C. Sarker L. H. Johnston 《International Journal of Infrared and Millimeter Waves》1986,7(12):1903-1911
A submillimeter laser Stark spectrum has been observed for fully deuterated Methyl Chloride (CD3Cl) with the 337 m line of the HCN laser up to Stark fields of about 54000 V/cm. The spectra were taken for both Parallel and Perpendicular Polarizations and the multiplet transitions were identified as JK=42K41K in the ground vibrational state. Three families with K=12, 13 and 14 have been identified and their zero field frequencies have been given with improved accuracy over those calculated from available molecular constants. 相似文献
9.
Peiguang Zhou H. L. Frisch 《Journal of polymer science. Part A, Polymer chemistry》1992,30(12):2577-2585
We have synthesized and characterized the graft copolymer of polymethyl methacrylate (PMMA)-graft-polycarbonate urethane (PCU) (designated PMMA-g-PCU) and the fully gelled mutually crosslinked network composed of both PMMA and PCU (designated as PMMA-PCU-N). Unlike the previously synthesized one phase PCU/PMMA simultaneous interpenetrating polymer networks (IPN's), both of these new materials exhibited two distinct Tg's (from DSC and DMA studies) at all compositions which we have studied. The two-phase nature of the graft and network polymer was confirmed by TEM with domain sizes smaller than those found in the blends of the linear PCU and PMMA chains. In comparison with the corresponding IPN's, the PMMA-g-PCU and the PMMA-PCU-N were thermally less stable and had a lower ultimate strength. © 1992 John Wiley & Sons, Inc. 相似文献
10.
Shih-Jien Sun Teh-Chou Chang 《Journal of polymer science. Part A, Polymer chemistry》1993,31(11):2711-2719
Four series of fully aromatic thermotropic liquid crystalline polycarbonates were prepared by melt polycondensation from various novel phenylene diphenyl dicarbonates with monomers, such as hydroquinone, methylhydroquinone, chlorohydroquinone, resorcinol, bisphenol A, 4,4′-dihydroxydiphenylsulfone, or phenylhydroquinone, respectively. The thermotropic liquid crystalline properties were studied by polarizing microscope with a heating stage, differential scanning calorimeter (DSC), and wide-angle x-ray diffraction (WAXD). It was found that the nonlinearity of the carbonate group was compensated by resorcinol (1,3-phenylene unit), a bent shape unit. Nematic melts were found for the resulting polycarbonates. © 1993 John Wiley & Sons, Inc. 相似文献