时间反转聚焦在组织中形成损伤的数值建模

为考察基于时间反转方法的高强度聚焦超声治疗在预设目标点处的组织损伤情况,使用三维有限差分算法求解Westervelt方程,建立非线性声波传播数值模型,采用97阵元相控阵结合虚拟源的时间反转方法进行超声聚焦,分析其形成的声场和热场,并考察目标点偏离轴线时的组织损伤形成规律。结果表明随着目标点偏轴距离的增大,声压旁瓣开始增多。旁瓣的温升较低,不足以形成组织损伤。时间反转方法可用于多点聚焦,在一定的范围内,形成多点目标损伤而不产生额外的周围组织损伤。同时多点聚焦可以形成一个较大的损伤区域,减少超声治疗时间。     

Relaxations and approximations of chance constraints under finite distributions

Optimization problems with constraints involving stochastic parameters that are required to be satisfied with a prespecified probability threshold arise in numerous applications. Such chance constrained optimization problems involve the dual challenges of stochasticity and nonconvexity. In the setting of a finite distribution of the stochastic parameters, an optimization problem with linear chance constraints can be formulated as a mixed integer linear program (MILP). The natural MILP formulation has a weak relaxation bound and is quite difficult to solve. In this paper, we review some recent results on improving the relaxation bounds and constructing approximate solutions for MILP formulations of chance constraints. We also discuss a recently introduced bicriteria approximation algorithm for covering type chance constrained problems. This algorithm uses a relaxation to construct a solution whose (constraint violation) risk level may be larger than the pre-specified threshold, but is within a constant factor of it, and whose objective value is also within a constant factor of the true optimal value. Finally, we present some new results that improve on the bicriteria approximation factors in the finite scenario setting and shed light on the effect of strong relaxations on the approximation ratios.     

Distributionally robust simple integer recourse

The simple integer recourse (SIR) function of a decision variable is the expectation of the integer round-up of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two-stage stochastic linear programming. Structural properties and approximations of SIR functions have been extensively studied in the seminal works of van der Vlerk and coauthors. We study a distributionally robust SIR function (DR-SIR) that considers the worst-case expectation over a given family of distributions. Under the assumption that the distribution family is specified by its mean and support, we derive a closed form analytical expression for the DR-SIR function. We also show that this nonconvex DR-SIR function can be represented using a mixed-integer second-order conic program.     

求解隐式差分方程的加速迭代并行算法

1、引言 近年来,求解抛物型方程的有限差分并行迭代算法有了较大发展．针对稳定性好且难于并行化的隐式差分方程,文第一次提出了构造分段隐式的思想,建立了分段显-隐式（ASE-Ⅰ）方法和交替分段Crank-Nicolson（ASC-N）方法,实现了分而治之原则,     

含呋喃环生物基聚酰胺的合成

随着环境保护和化石资源问题的日益严峻,开发基于可再生生物质资源的生物基高分子材料,成为未来的发展趋势。作为最具有价值的生物基平台化合物之一,呋喃二甲酸及其衍生物可用于制造精细化学品和高分子材料。近年来,通过熔融聚合、溶液聚合、界面缩聚和固相缩聚等方法,将呋喃二甲酸及其衍生物与二元胺反应,制备出不同结构的生物基聚酰胺的均聚物和共聚物。本文从单体、聚合方法、聚合物结构和性能等方面,对含呋喃环生物基聚酰胺的合成作一总结,同时对这一领域的前景和挑战进行了探讨。     

Preparation and characterization of phosphorylated graphene oxide grafted with poly(L‐lactide) and its effect on the crystallization,rheological behavior,and performance of poly (lactic acid)

Phosphorylated graphene oxide (PGO) was prepared by using phosphoric acid as functional reagent, and PGO was grafted with poly(L‐lactide) (PGO‐PLLA) by ring‐opening polymerization of L‐lactide as monomer under nano‐ZnO catalyst. The results of the orthogonal analysis showed the optimum reaction conditions to be as follows: the reaction temperature of 170°C, reaction time of 14 hours, the mass ratio of PGO of 10 wt%, and the mass of nano‐ZnO of 1 wt%. PGO‐PLLA was characterized by fourier transform infrared spectroscopy, gel permeation chromatography, and X‐ray photoelectron spectroscopy, which demonstrated that the PLLA molecular chains were successfully grafted onto the surface of PGO. Poly (lactic acid)/PGO‐PLLA nanocomposites (PLA/PGO‐PLLA) were prepared by melt intercalation. Mechanical test and fracture scanning electron microscopy showed that PGO‐PLLA (0.3 wt%) improved impact strength of PLA by 52.19%, which resulted in ductile fractures surface of PLA/PGO‐PLLA. Microcalorimetry and thermal degradation kinetics proved that PGO‐PLLA improved the thermal stability of PLA. Polarized optical microscopy and differential scanning calorimetry confirmed that PGO‐PLLA increased crystallization rate and spherulite kernel density of PLA, and crystallinity of PLA/PGO‐PLLA reached to 22.05%. Rheological behavior proved that PGO‐PLLA increased the self‐lubricity of PLA. Enzymatic degradation results illustrated that PGO‐PLLA had some inhibition for the biodegradability of PLA based nanocomposites.     

Transition‐Metal‐Free Hydrogen Autotransfer: Diastereoselective N‐Alkylation of Amines with Racemic Alcohols

A practical method for the synthesis of α‐chiral amines by alkylation of amines with alcohols in the absence of any transition‐metal catalysts has been developed. Under the co‐catalysis of a ketone and NaOH, racemic secondary alcohols reacted with Ellman's chiral tert‐butanesulfinamide by a hydrogen autotransfer process to afford chiral amines with high diastereoselectivities (up to >99:1). Broad substrate scope and up to a 10 gram scale production of chiral amines were demonstrated. The method was applied to the synthesis of chiral deuterium‐labelled amines with high deuterium incorporation and optical purity, including examples of chiral deuterated drugs. The configuration of amine products is found to be determined solely by the configuration of the chiral tert‐butanesulfinamide regardless of that of alcohols, and this is corroborated by DFT calculations. Further mechanistic studies showed that the reaction is initiated by the ketone catalyst and involves a transition state similar to that proposed for the Meerwein–Ponndorf–Verley (MPV) reduction, and importantly, it is the interaction of the sodium cation of the base with both the nitrogen and oxygen atoms of the sulfinamide moiety that makes feasible, and determines the diastereoselectivity of, the reaction.     

The effect of low temperature AlN interlayers on the growth of GaN epilayer on Si (111) by MOCVD

Low temperature (LT) AlN interlayers were used to effectively reduce the tension stress and micro-cracks on the surface of the GaN epilayer grown on Si (111) substrate. Optical Microscopy (OM), Atomic Force Microscopy (AFM), Surface Electron Microscopy (SEM) and X-Ray Diffraction (XRD) were employed to characterize these samples grown by metal-organic chemical vapor deposition (MOCVD). In addition, wet etching method was used to evaluate the defect of the GaN epilayer. The results demonstrate that the morphology and crystalline properties of the GaN epilayer strongly depend on the thickness, interlayer number and growth temperature of the LT AlN interlayer. With the optimized LT AlN interlayer structures, high quality GaN epilayers with a low crack density can be obtained.     

分数次多线性交换子在Herz空间上的有界性

本文先建立了一个向量值多线性交换子的有界性,并由它证明了分数次极大多线性交换子在Lp(Rn)(p＞1)及Herz空间上的有界性,借助于后者,我们证明了一类多线性交换子在Herz空间上的有界性.