In this paper, we are concerned with a class of reflected stochastic differential equations (reflected SDEs) with non-Lipschitzian
coefficients. Under the same coefficients assumptions as Fang and Zhang [Probab. Theory Relat. Fields, 2005, 132(3): 356–390]
for a class of SDEs, we establish the pathwise uniqueness for the reflected SDEs. Furthermore, a strong comparison theorem
is proved for the reflected SDEs in a one-dimensional case.
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With aggressive scaling down of feature sizes in VLSI fabrication, process variation has become a critical issue in designs. We show that two necessary conditions for the ldquomaxrdquo operation are actually not satisfied in the moment matching based statistical timing analysis approaches. We propose two correlation-aware block-based statistical timing analysis approaches that keep these necessary conditions, and show that our approaches always achieve the lower bound and the upper bound on the timing yield. Our approach combining with moment-matching based statistical static timing analysis (SSTA) approaches can efficiently estimate the maximal possible errors of moment-matching-based SSTA approaches. 相似文献
The oxidation behaviors of LiH under a high purity argon atmosphere, an argon atmosphere with some O2 and H2O impurities, and ambient air at both room and high temperatures, are investigated using a variety of analytical instruments including X-ray diffractometry, thermogravimetry, mass spectrometry, scanning electron microscopy, and specific surface area analysis. The oxidation behaviors of the ball-milled LiH under different atmospheres are also studied and compared with those without ball milling. It is shown that no oxidation of LiH occurs under a high-purity argon atmosphere. However, oxidation of LiH takes place when the argon atmosphere contains some H2O and O2 impurities. At temperatures higher than approximately 55 degrees C, oxidation of LiH proceeds via the reaction of LiH + 1/4 O2 = 1/2 Li2O + 1/2 H2, whereas at room temperature oxidation of LiH is likely caused by the simultaneous reactions of LiH + H2O = LiOH + H2 and LiH + 1/2 O2 = LiOH. The oxidation behavior of LiH in ambient air with a 27% relative humidity can be well described by the Johnson-Mehl-Avrami equation. Furthermore, the ball-milled LiH oxidizes faster than the unmilled one, which is due to the finer particle size and larger surface area of the ball-milled powder. 相似文献
The Catellani reaction is known as a powerful strategy for the expeditious synthesis of highly substituted arenes and benzo‐fused rings, which are usually difficult to access through traditional cross‐coupling strategies. It utilizes the synergistic interplay of palladium and norbornene catalysis to facilitate sequential ortho C?H functionalization and ipso termination of aryl halides in a single operation. In classical Catellani‐type reactions, aryl halides are mainly used as the substrates, and a Pd0 catalyst is required to initiate the reaction. Nevertheless, recent advances showcase that Catellani‐type reactions can also be initiated by a PdII catalyst with different starting materials instead of aryl halides via different reaction mechanisms and under different conditions. This emerging concept of PdII/norbornene cooperative catalysis has significantly advanced Catellani‐type reactions, thus enabling future developments of this field. In this Minireview, PdII‐initiated Catellani‐type reactions and their application in the synthesis of bioactive molecules are summarized. 相似文献
The synthesis of fully conjugated sp2‐carbon covalent organic frameworks (COF) is extremely challenging given the difficulty of the formation of very stable carbon‐carbon double bonds (‐C=C‐). Here, we report the successful preparation of a 2D COF (TP‐COF) based on triazine as central planar units bridged by sp2‐carbon linkers through the ‐C=C‐ condensation reaction. High‐resolution‐transmission electron microscopy (HRTEM) clearly confirmed the tessellated hexagonal pore structure with a pore center‐to‐center distance of 2 nm. Powder X‐ray diffraction (PXRD) together with structural simulations revealed an AA stacking mode of the obtained layered structure. TP‐COF turned out to be an excellent semiconductor material with a LUMO energy of ?3.23 eV and a band gap of 2.36 eV. Excitingly, this novel sp2‐carbon conjugated TP‐COF exhibited unprecedented coenzyme regeneration efficiency and can significantly boost the coenzyme‐assisted synthesis of l ‐glutamate to a record‐breaking 97 % yield within 12 minutes. 相似文献
Clay adsorbents are considered an inexpensive and readily available solution for removing heavy metals, including cadmium, from the environment to reduce pollution. In this study, thiol-modified bentonite (SH-Bent) was prepared by grafting cysteamine hydrochloride onto natural bentonite (Bent). The effects of pH, equilibrium contact time, and temperature on the adsorption–desorption behavior of Cd2+ were studied, and adsorption isotherm models were applied to examine the adsorption behavior of SH-bent. SH-Bent demonstrated better performance and stability for Cd2+ adsorption than Bent. SH-Bent exhibited an enhanced adsorption capacity for Cd2+ at equilibrium of 49.3 mg/g at pH 6, 120 min, and 303 K, which was 42-fold higher than that of Bent under the same conditions. An investigation of the desorption behavior of Cd2+ adsorbed on Bent and SH-Bent in simulated acid rain revealed that SH-Bent has high stability, with a desorption rate of 5.73% at pH 4.5, 60 min, and 303 K, which was much lower than that demonstrated by Bent under the same conditions (45.68%). The Langmuir equation was the best-fitted adsorption isotherm model, closely followed by the Freundlich, Tempkin, and Dubinin–Radushkevich models. A significant difference in diffusion was observed between the two types of clay according to the intraparticle diffusion model. The adsorption–desorption processes of SH-Bent and Bent fit the pseudo-second-order model best among the five kinetic models examined. The information provided in this study can be used to apply thiol-modified clay for wastewater treatment or for the removal of cadmium from soil.