We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided.
Quercetin has been reported to suppress protein glycation or the formation of advanced glycation end-products (AGEs), but the inhibition mechanism related to protein structure and glycation sites and the influence on physicochemical properties remain unclear. The aim of the current research was to investigate the mechanism of quercetin against glycation with BSA-fructose as model by spectroscopic and spectrometric techniques. Changes in physicochemical properties were evaluated by antioxidant activity and emulsifying properties. The results indicated that quercetin dose-dependently inhibited the glycation of BSA by attenuating the alteration of conformational structure and microenvironment induced by glycation. It could also suppress the cross-linking or aggregation of glycated BSA, which reflected in the decreased molecular weight determined by SDS-PAGE and MALDI-TOF. Nanoliquid chromatography coupled to Q-Exactive tandem mass spectrometry analysis revealed the mapping of 20, 23, 19, and 19 glycation sites in glycated BSA with 0, 0.5, 1.5, and 3.0 mM quercetin, respectively. Quercetin changed the glycation sites of BSA, but it could not reduce the number greatly. In addition, quercetin reduced the antioxidant ability and increased the emulsifying properties of BSA, while negligible efficiency was observed on the antioxidant activity and emulsifying activity index of glycated BSA.
A robust one-step synthetic strategy for ynamide with cheap and easily available stock chemicals vinyl dichlorides and electron deficient amides as the starting material is described. In the absence of transition-metal catalyst, the reaction proceeds under mild reaction conditions in open air and thus rendering a convenient operation. This strategy is not only suitable for both terminal and internal ynamide synthesis but also amenable for large-scale preparation. Broad substrate scopes with respect to vinyl dichloride as well as electron-deficient amide were observed.
Abstract:The energy transition and dissipation of atomic-scale friction are investigated using the one-dimensional Prandtl-Tomlinson model. A systematic study of the factors influencing the energy dissipation is conducted, indicating that the energy that accumulated during the stick stage does not always dissipate completely during stick-slip motion. We adopt the energy-dissipation ratio (EDR) to describe the relationship between the energy dissipated permanently in the system and the conservative reversible energy that can be reintroduced to the driving system after the slip process. The EDR can change continuously from 100% to 0, covering the stick-slip, intermediate, and smooth-sliding regimes, depending on various factors such as the stiffness, potential-energy corrugation, damping coefficient, sliding velocity, and the temperature of the system. Among these, the parameter η, which depends on both the surface potential and the lateral stiffness, is proven in this paper to have the most significant impact on the EDR. According to η-T phase diagrams of the EDR, the smooth-sliding superlubricity and thermolubricity are found to be unified with regard to the energy dissipation and transition. An analytical formulation for the EDR that can be used to quantitatively predict the amount of energy dissipation is derived from a lateral-force curve.
In this paper, the gravitational deflection of a relativistic massive neutral particle in the Schwarzschild-de Sitter spacetime is studied via the Rindler–Ishak method in the weak-field limit. When the initial velocity $$v_0$$
v
0
of the particle tends to the speed of light, the result is consistent with that obtained in the previous work for the light-bending case. Our result is reduced to the Schwarzschild deflection angle of massive particles up to the second order, if the contributions from the cosmological constant $$\varLambda $$
Λ
are dropped. The observable correctional effects due to the deviation of $$v_0$$
v
0
from light speed on the $$\varLambda $$
Λ
-induced contributions to the deflection angle of light are also analyzed.
An efficient palladium-catalyzed Suzuki coupling of 1,1-diarylmethyl-trimethylammonium triflates with arylboronic acids is reported. This reaction offers a novel approach to triarylmethane derivatives in good to excellent yields with the palladium-catalyzed C-N bond cleavage as the key feature. Broad substrate scope regarding both reaction partners are observed. Moreover, reactive functional groups such as vinyl and formyl groups are conserved in this transformation.
Let α > 0 and let µ be a bounded Radon measure on the interval (−1, 1). We are interested in the equation −(|x| 2α u ) + u = µ on (−1, 1) with boundary condition u(−1) = u(1) = 0. We identify an appropriate concept of solution for this equation, and we establish some existence and uniqueness results. The cases 0 < α < 1 and α ≥ 1 must be considered separately. We also study the limiting behavior of two different approximation schemes: one is the elliptic regularization and the other is to approximate a measure µ by a sequence of L ∞ -functions.
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