Let M be a compact convex hypersurface of class C2, which is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere. 相似文献
The influence of the length of the cation alkyl chain on the dispersibility by ultrasonic treatment of TiO2 nanopowders in hydrophilic imidazolium-based room temperature ionic liquids was studied for the first time by dynamic light scattering and advanced rheology. TiO2 nanopowders had been synthesized by chemical vapor synthesis (CVS) under varied conditions leading to two different materials. A commercial nanopowder had been used for comparison. Characterizations had been done using transmission electron microscopy, X-ray diffraction, nitrogen adsorption with BET analysis, and FT-IR spectroscopy. Primary particle sizes were about 6 and 8 nm for the CVS-based and 26 nm for the commercial materials. The particle size distribution in the dispersion was strongly influenced by the length of the cation alkyl chain for all the investigated powders with different structural characteristics and concentrations in the dispersion. It was found that an increase of the alkyl chain length was beneficial, leading to a narrowing of the particle size distribution and a decrease of the agglomerate size in dispersion. The smallest average nanoparticle sizes in dispersion were around 30 nm. Additionally, the surface functionality of the nanoparticles, the concentration of the solid material in the liquid, and the period of ultrasonic treatment control the dispersion quality, especially in the case of the ionic liquids with the shorter alkyl chain. The influence of the nanopowders characteristics on their dispersibility decreases considerably with increasing cation alkyl chain length. The results indicate that ionic liquids with adapted structure are candidates as absorber media for nanoparticles synthesized in gas phase processes to obtain liquid dispersions directly without redispergation. 相似文献
Solid electrolytes which possess excellent lithium-ion conductivity and chemical compatibility with electrode materials are necessary for the commercialization of all-solid-state lithium batteries. However, a single solid electrolyte meeting above requirements is difficult. Consequently, the composite electrolytes have attracted more attention. In this paper, Li6PS5Cl–xLi6.5La3Zr1.5Ta0.5O12 (LLZTO) (x = 0, 2.5 wt%, 5 wt%, 10 wt%) composite electrolytes are prepared by a simple planetary grinding process. It has been found that adding an appropriate amount of LLZTO can increase the lithium-ion conductivity. At 30 °C, the lithium-ion conductivity increases from 2.6 × 10−4 S/cm (Li6PS5Cl) to 5.4 × 10−4 S/cm (Li6PS5Cl-5 wt% LLZTO). Besides, the addition of LLZTO to the Li6PS5Cl can influence the growth rate of the SEI. It has been shown that the SEI growth rate obeys a parabolic rate law, and the growth rates of Li6PS5Cl, Li6PS5Cl-2.5 wt% LLZTO, Li6PS5Cl-5 wt% LLZTO, and Li6PS5Cl-10 wt% LLZTO are 8.62, 3.53, 3.33, and 3.38 Ω/h1/2 at 60 °C, respectively. In lithium plating and stripping experiment, the voltage of symmetrical Li/Li6PS5Cl/Li cell suddenly drops to 0 V after cycling 39 h at 0.103 mA/cm2 (0.097 mAh/cm2). On the contrary, the Li/Li6PS5Cl–xLLZTO (x = 2.5 wt%, 5 wt%, 10 wt%)/Li symmetrical cell exhibits a stable voltage profile over 100 h at the same test conditions. The corresponding interfacial impedance of Li/Li6PS5Cl–xLLZTO (x = 2.5 wt%, 5 wt%, 10 wt%) remains stable after 10, 30, and 50 charge/discharge cycles.
This paper presents the analysis of a discrete-time Geo/G/1 queue with randomized vacations. Using the probability decomposition theory and renewal process, two variants on this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both the cases, recursive solution for queue length distributions at arbitrary, just before a potential arrival, pre-arrival, immediately after potential departure, and outside observer’s observation epochs are obtained. Further, various performance measures such as potential blocking probability, turned-on period, turned-off period, vacation period, expected length of the turned-on circle period, average queue length and sojourn time, etc. have been presented. It is hoped that the results obtained in this paper may provide useful information to designers of telecommunication systems, practitioners, and others. 相似文献
This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a piecewise linear function in time. Then, piecewise quadratic polynomial in space and an efficient method to discretize the memory term of the equation is designed using the moving mesh approach. In each time slice, a simple piecewise constant approximation of the integrand is used, and thus a quadrature is constructed for the memory term. The central finite difference scheme for space and the backward Euler scheme for time are used. The paper proves that the accumulation of the quadrature error is uniformly bounded and that the convergence of the method is second order in space and first order in time. Numerical experiments are carried out to confirm the theoretical predictions. 相似文献
In this paper we implement the moving mesh PDE method for simulating the blowup in reaction–diffusion equations with temporal and spacial nonlinear nonlocal terms. By a time-dependent transformation, the physical equation is written into a Lagrangian form with respect to the computational variables. The time-dependent transformation function satisfies a parabolic partial differential equation — usually called moving mesh PDE (MMPDE). The transformed physical equation and MMPDE are solved alternately by central finite difference method combined with a backward time-stepping scheme. The integration time steps are chosen to be adaptive to the blowup solution by employing a simple and efficient approach. The monitor function in MMPDEs plays a key role in the performance of the moving mesh PDE method. The dominance of equidistribution is utilized to select the monitor functions and a formal analysis is performed to check the principle. A variety of numerical examples show that the blowup profiles can be expressed correctly in the computational coordinates and the blowup rates are determined by the tests. 相似文献
Bioactive glasses are well known for their bone regeneration ability. Sol-gel bioglasses have many advantages comparing to melt derived bioglasses. 3-D scaffold prepared by sol-gel method is a promising substrate material for bone tissue engineering and large scale bone repair. But it is very difficult to produce macroporous sol-gel bioglasses with pores larger than 100 m. In this work, a series sol-gel bioglasses with macropores larger than 100 m are produced by adding PVA particles into the sol as pore former. The texture feature of this material is obtained by nitrogen adsorption/desorption analysis. Pore size distribution is collected by intrusion mercury porosimetry. SEM (Scanning Electron Microscope) was used to observe the pore structure of these samples. In these bioglasses, the diameter of the pore created by pore former vary from 100 to 300 m. In vitro tests were used to evaluate the bioactivity of these sol-gel bioglasses. The samples prepared in this work show satisfactory handle resistance and good bioactivity. 相似文献
Prodrugs that release hydrogen sulfide upon esterase‐mediated cleavage of an ester group followed by lactonization are described herein. By modifying the ester group and thus its susceptibility to esterase, and structural features critical to the lactonization rate, H2S release rates can be tuned. Such prodrugs directly release hydrogen sulfide without the involvement of perthiol species, which are commonly encountered with existing H2S donors. Additionally, such prodrugs can easily be conjugated to another non‐steroidal anti‐inflammatory agent, leading to easy synthesis of hybrid prodrugs. As a biological validation of the H2S prodrugs, the anti‐inflammatory effects of one such prodrug were examined by studying its ability to inhibit LPS‐induced TNF‐α production in RAW 264.7 cells. This type of H2S prodrugs shows great potential as both research tools and therapeutic agents. 相似文献