Inf‐sup stability of Petrov‐Galerkin immersed finite element methods for one‐dimensional elliptic interface problems

In this article, we analyze the Petrov‐Galerkin immersed finite element method (PG‐IFEM) when applied to one‐dimensional elliptic interface problems. In the PG‐IFEM (T. Hou, X. Wu and Y. Zhang, Commun. Math. Sci., 2 (2004), 185‐205, and S. Hou and X. Liu, J. Comput. Phys., 202 (2005), 411‐445), the classic immersed finite element (IFE) space was taken as the trial space while the conforming linear finite element space was taken as the test space. We first prove the inf‐sup condition of the PG‐IFEM and then show the optimal error estimate in the energy norm. We also show the optimal estimate of the condition number of the stiffness matrix. The results are extended to two dimensional problems in a special case.     

A new constructive method for solving singular integral equations

In this paper, a new method for the approximate solution of linear singular integral equations defined on smooth closed curves is proposed and justified.     

一类拟线性抛物型方程广义解的Hlder连续性

考虑如下拟线性抛物型方程ｕｔ－ｄｉｖＡ（ｘ，ｔ，ｕ，ｕ）＋Ｂ（ｘ，ｔ，ｕ，ｕ）＝０在Ａ，Ｂ满足很一般的结构条件下证明了它的广义解在Ｑ＝Ｇ×（０，Ｔ）上的局部Ｈｌｄｅｒ连续性     

二元凸函数的判别条件

给出了二元凸函数的定义,导出了二元凸函数的判别条件,该判别条件由二元函数的二阶导数给出.用二元凸函数的判别条件和半正定的(半负定)矩阵的性质,得到了二元二次多项式凸性的简单判别形式.     

基于PHM的舰艇装备视情维修技术研究

针对PHM技术在舰艇装备视情维修中的应用需求,在分析剩余寿命预测机理的基础上,为解决舰艇装备历史数据少、状态变化普遍表现为非线性等难题,建立基于粒子滤波的多步剩余寿命预测模型,通过仿真表明：随着时间的推移剩余寿命PDF图变狭窄,剩余寿命预测误差逐渐降低,证明了预测方法的有效性。在此基础上,考虑装备维修费用最低为目标,建立以费用最低为目标的预防性维修时间确定模型,使得单位时间内的平均维修费用最低,并通过采用建立的基于粒子滤波的多步剩余寿命预测模型,最终确定了最优预防性维修时间,为装备保障人员拟订精确维修保障计划提供依据,也为舰艇装备开展视情维修奠定基础。     

Multifractal formalism for self-similar measures with weak separation condition

For any self-similar measure μ on satisfying the weak separation condition, we show that there exists an open ball U₀ with μ(U₀)>0 such that the distribution of μ, restricted on U₀, is controlled by the products of a family of non-negative matrices, and hence μ|_U0 satisfies a kind of quasi-product property. Furthermore, the multifractal formalism for μ|_U0 is valid on the whole range of dimension spectrum, regardless of whether there are phase transitions. Moreover the dimension spectra of μ and μ|_U0 coincide for q0. This result unifies and improves many of the recent works on the multifractal structure of self-similar measures with overlaps.     

The Behavior of Solutions of Multidimensional Aggregation Equations with Mildly Singular Interaction Kernels

The authors consider the multidimensional aggregation equation tp-div（p K＊ ρ） = 0 in which the radially symmetric attractive interaction kernel has a mild singularity at the origin （Lipschitz or better）, and review recent results on this problem concerning well-posedness of nonnegative solutions and finite time blowup in multiple space dimensions depending on the behavior of the kernel at the origin. The problem with bounded initial data, data in L^p ∩ L^1, and measure solutions are also considered.     

Stochastic partial functional differential equations with locally monotone coefficients,locally Lipschitz non-linearity and delay

In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results.     

Aqueous microwave-assisted DMAP catalyzed synthesis of β-phosphonomalonates and 2-amino-4H-chromen-4-ylphosphonates via a domino Knoevenagel-phospha-Michael reaction

An aqueous microwave (mw)-assisted DMAP catalyzed one-pot highly efficient route to synthesize β-phosphonomalonates and 2-amino-4H-chromen-4-yl phosphonates has been demonstrated via the domino Knoevenagel-phospha-Michael reaction of aryl aldehyde/salicylaldehyde, malononitrile/ethyl cyanoacetate and alkyl phosphite ester. Optimization of reaction conditions were performed by using conventional and microwave synthetic approaches. This conversion proceeded smoothly to deliver the desired product in good to excellent yields (75–95%) in a short reaction time (10–12 min). The present methodology is very simple, environmentally benign, high yielding and has very well demonstrated the synergistic effect of water and microwaves.     

Microbial desulfurization of waste latex rubber with Alicyclobacillus sp.

A microbe with desulfurizing capability, Alicyclobacillus sp., was selected to recycle waste latex rubber (WLR). The growth characteristics of the microorganism and the technical conditions in the co-culture desulfurization process were studied. The desulfurization effect of Alicyclobacillus sp. on the WLR was characterized, and the mechanism for the microbial desulfurization of WLR was tentatively explored. The results showed that adding 5% (w/v) WLR into medium had little effect on the growth of Alicyclobacillus sp. The surfactant polysorbate 80 (Tween 80) had a toxic effect on Alicyclobacillus sp., but the growth of the microbe was vigorous if the proper technique was used: the mixing of WLR with Tween 80, followed by the addition of the mixture into the culture media. With the increase of desulfurization time, the swelling value of desulfurizated waste latex rubber (DWLR) increased, but the crosslink density decreased. After co-culture desulfurization for 8–10 days, a DWLR with good desulfurization effect was obtained. The mechanical properties of natural rubber (NR)/DWLR composite improved significantly over those of NR/WLR composite. XPS and FTIR results revealed that Alicyclobacillus sp. could break the crosslinked sulfur bonds and oxidize them to sulfones groups. The increase of O element content on the surface of DWLR was confirmed by water contact angle measurements. The relationship between the crosslink density and sol fraction of DWLR with different desulfurization times agreed with the Horikx equation, an indication that the microorganisms could break the crosslinked sulfur bonds on the surface of WLR, but leaving the main chains intact.