Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.     

A higher-order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions

We propose a hybrid numerical scheme to discretize a class of singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions on an equidistributed grid. The hybrid difference scheme is developed by using a modified backward difference scheme in time, a combination of the cubic spline and exponential spline difference scheme in space. The proposed scheme uses a cubic spline difference scheme for the discretization of robin-boundary conditions. For the time discretization of the problem, we use the standard uniform mesh while a layer adapted equidistributed grid is generated for the spatial discretization. By equidistributing a curvature-based monitor function, the spatial adaptive grid is able to capture the presence of parabolic boundary layers without using any prior information about the solution. Parameter uniform error estimates are derived to illustrate an optimal convergence of first-order in time and second-order in space for the proposed discretization. The accuracy of the proposed scheme is confirmed by the numerical experiments that underpin the theoretical analysis.     

一般超图的张量谱性质

将一致超图的逆Perron值的概念推广到了一般超图上,并证明了超图G连通的充要条件为其逆Perron值大于0。同时给出了一般超图G的二分宽度、等周数、离心率基于逆Perron值的一些下界。最后,讨论了张量的可奇染色问题,得到非负对称弱不可约张量A可奇染色的充要条件为A的拉普拉斯张量和无符号拉普拉斯张量有相同的的谱。     

Nutritional potential of edible Russula species from Alédjo Wildlife Reserve (AWR)

In order to contribute to the valorisation of wild fungi whose nutritional potential, although considerable, is not sufficiently known in some countries such as Togo, a study has been carried out on Russula species. The diversity of Russula species from Alédjo Wildlife Reserve has been assessed using a focused inventory in woodlands dominated by Isoberlinia doka Craib & Stapf, Isoberlinia tomentosa (Harms) Craib & Stapf, Monotes kerstingii Gilg, Uapaca togoensis Pax and gallery forests dominated by Berlinia grandiflora (Vahl) Hutch & Dalz and Uapaca guineensis Müll. Ethnomycological surveys have been carried out among Tém and Kabyè, two riparian ethnic groups that are mainly represented. Biochemical analyses have been carried out using the AOAC method. Fifteen (15) taxa of edible Russula species are commonly used by Tém and Kabyè people living along the Alédjo Wildlife Reserve among which thirteen (13) taxa have been identified up to species level. R. oleifera is eaten by all interviewed people in both sociolinguistic groups (Fr = 100%) followed by R. compressa (Fr = 92.31%), R. ochrocephala (Fr = 87.18%) among Tém people and R. ochrocephala (Fr = 91.67%), R. compressa (Fr = 83.33%) among Kabyè people. Five (05) new species of edible Russula have been identified for the first time in Togo. The Russula species analysed have been rich in macronutrients with contents ranging from 2.88 g/100 g of dw for fat to 65.83 g/100 g of dw for total carbohydrates. In addition, these Russula species have shown a relatively high mineral content with contents ranging from 405.70 mg/100 g of dw for Ca to 2784 mg/100 g of dw for K. Furthermore, the results have revealed that Russula species analysed are a source of energy with 309.50 Kcal/100 g of dw. The edible Russula species analysed can thus contribute to food security in Togo.     

熔盐电化学还原二氧化碳制备碳材料研究进展北大核心CSCD

二氧化碳浓度持续升高导致的温室效应已在全球范围内引发极端天气、冰川融化等一系列生态环境问题。为降低二氧化碳含量,改善气候变暖带来的恶劣影响,研发高效、绿色、安全的二氧化碳处理技术,促进碳资源循环可持续发展刻不容缓。熔盐离子液体作为一种良好的电化学转化介质,为二氧化碳还原提供了一条极具应用前景的技术路线。综述了国内外近几年高温熔盐中二氧化碳的捕获与电化学还原的研究,简述了熔盐电沉积碳的电化学机理和热力学机制,对不同形貌高附加值碳材料:无定形碳、碳球和碳纳米管的制备进行了总结,最后对未来发展方向做出展望。     

QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

IntroductionIn applications, it is commonly considered that the phenomena of cavity formation,growth and run-through of adjacent cavities occur in materials as precursors to failure. Thesephenomena are mainly due to instability of materials. On the other …     

Rotationally Symmetric Deformations of Partially Loaded Annular Elastic Membranes Without Wrinkling

This paper investigates axisymmetric deformations of curved annular membranes subjected to a partially vanishing vertical surface load and to radial edge loads or displacements. The frame of the membrane model we deal with is the nonlinear small-strain theory. The determination of the principal stresses reduces to the solution of a single nonlinear second order ODE. Analysis becomes explicit on the unloaded membrane part while the loaded part is treated by methods which have been previously developed. In particular, the ranges of those stress and displacement boundary data are determined which admit for wrinkle-free solutions only, i.e. for solutions governed by a nonnegative radial and circumferential stress component. For such a tensile state, a curved membrane flattens out on the unloaded portions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Paradoxical Bending Behavior of Shearable Nonlinearly Elastic Rods

In nonlinear elasticity the exact geometry of deformation is combined with general constitutive relations. This allows a very sophisticated interaction of deformations in different material directions. Based on the Cosserat theory for planar deformations of nonlinearly elastic rods we demonstrate some paradoxical bending effects caused by a nontrivial interaction of extension, flexure, and shear. The analytical results are illustrated by numerical examples.     

A SINGULAR VALUE DECOMPOSITION BASED TRUNCATION ALGORITHM IN SOLVING THE STRUCTURAL DAMAGE EQUATIONS

The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods.Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.     

双周期圆截面纤维复合材料平面问题的解析法

结合双准周期Riemann边值问题理论与Eshelby等效夹杂原理，为双周期圆截面纤维复合材 料平面问题发展了一个实用有效的解析方法，获得了问题的全场级数解并与有限元结果进行 了比较. 该方法为非均匀材料的力学性质分析和复合材料等新材料的微结构设计提供了 一个有效的计算工具，也可用来评估有限元等数值与近似方法的精度.