A new method for numerical differentiation based on direct and inverse problems of partial differential equations

In this paper, we mainly study a numerical differentiation problem which aims to approximate the second order derivative of a single variable function from its noise data. By transforming the problem into a combination of direct and inverse problems of partial differential equations (heat conduction equations), a new method that we call the PDEs-based numerical differentiation method is proposed. By means of the finite element method and the Tikhonov regularization, implementations of the proposed PDEs-based method are presented with a posterior strategy for choosing regularization parameters. Numerical results show that the PDEs-based numerical differentiation method is highly feasible and stable with respect to data noise.     

Optimum step-stress accelerated degradation test for Wiener degradation process under constraints

To assess a product's reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.     

Inverse screening of Simvastatin kinase targets from glioblastoma druggable kinome

The statin drug Simvastatin is a HMG-CoA reductase inhibitor that has been widely used to lower blood lipid. However, the drug is clinically observed to reposition a significant suppressing potency on glioblastoma (GBM) by unexpectedly targeting diverse kinase pathways involved in GBM tumorigensis. Here, an inverse screening strategy is described to discover potential kinase targets of Simvastatin. Various human protein kinases implicated in GBM are enriched to define a druggable kinome; the binding behavior of Simvastatin to the kinome is profiled systematically via an integrative computational approach, from which most kinases have only low or moderate binding potency to Simvastatin, while only few are identified as promising kinase hits. It is revealed that Simvastatin can potentially interact with certain known targets or key regulators of GBM such as ErbB, c-Src and FGFR signaling pathways, but exhibit low affinity to the well-established GBM target of PI3K/Akt/mTOR pathway. Further assays determine that Simvastatin can inhibit kinase hits EGFR, MET, SRC and HER2 at nanomolar level, which are comparable with those of cognate kinase inhibitors. Structural analyses reveal that the sophisticated T790 M gatekeeper mutation can considerably reduce Simvastatin sensitivity to EGFR by inducing the ligand change between different binding modes.     

SOURCE TERM IDENTIFICATION WITH DISCONTINUOUS DUAL RECIPROCITY APPROXIMATION AND QUASI-NEWTON METHOD FROM BOUNDARY OBSERVATIONS

This paper deals with discontinuous dual reciprocity boundary element method for solving an inverse source problem.The aim of this work is to determine the source term in elliptic equations for nonhomogenous anisotropic media,where some additional boundary measurements are required.An equivalent formulation to the primary inverse problem is established based on the minimization of a functional cost,where a regularization term is employed to eliminate the oscillations of the noisy data.Moreover,an efficient algorithm is presented and tested for some numerical examples.     

平面波超声成像中的波束合成方法研究进展

平面波成像通过单次全孔径发射-接收即可获取整幅图像,将成像帧频显著地提升至1000帧/秒以上.然而,平面波成像过程中发射的非聚焦波束将导致回波信号信噪比降低,进而使图像的分辨率和对比度变差.通过多角度相干复合成像技术可以改善平面波成像的图像质量,但是会以牺牲帧频为代价.因此研究人员们开始将新型波束合成技术引入平面波成像...     

二烯丙基二甲基氯化铵—丙烯酰胺反相乳液聚合的动力学特征研究

采用油酸失水山梨醇酯（ＳＰＡＮ）－壬基酚聚氧化乙烯醚（ＯＰ）复合乳化剂与Ｋ２Ｓ２Ｏ８－Ｎａ２ＳＯ３氧化还原引发剂，进行二烯丙基二甲基氯化铵－丙烯酰胺反相乳液共聚合，测得单体的竞聚率为γＤＡＤＭＡＣ＝０．１４±０．１１，γＡＭ＝５．０５±０．６６；在单体浓度为２５─４５％，引发剂浓度０．０６—０．１％，乳化剂浓度为５—９％，聚合温度３０３Ｋ条件下，得到了共聚反应动力学方程：Ｒｐ＝ｋ［Ｍ］０．６８［Ｉ］１．３１［Ｅ］０．７３，文中对上述结果做了解释．     

反相气相色谱表征可溶性聚酰亚胺的表面性质

采用反相气相色谱技术,将正己烷、正庚烷、正辛烷、正壬烷作为非极性分子探针,乙醚、丙酮、三氯甲烷作为极性分子探针在50℃、60℃、70℃和80℃条件下测定了可溶性聚酰亚胺HQDPA-DMMDA的表面色散自由能与表面Lewis酸碱性质.HQDPA-DMMDA在50℃、60℃、70℃和80℃的表面色散自由能分别为34.37、31.80、29.50和27.64 mJ/m2,自由能随温度的升高而线性降低.实验发现,HQDPA-DMMDA为弱的Lewis两性聚合物材料,其Lewis酸常数Ka为0.4115,碱常数Kb为0.5812.     

亲水性含环氧基磁性聚合物微球的制备与性能表征

选择甲酰胺作磁性Fe3O4微晶的分散剂,通过设计反相悬浮聚合体系,合成了粒径分布窄、球状亲水性含环氧基磁性聚合物(MGM).利用扫描电子显微镜(SEM)、红外光谱(FT-IR)、X射线粉末衍射仪(XRD)、振动样品磁强计(VSM)和低温N2吸附以及化学分析方法对聚合物进行了性能表征.结果表明,合成的MGM呈球形,且粒度分布较窄,粒径为0.13~0.28 mm的粒子占91%;甲酰胺分散Fe3O4,微晶表面的亲水性进一步增强,单体甲基丙烯酸缩水甘油酯和N,N′-亚甲基双丙烯酰胺交联共聚生成的胶粒能够包埋Fe3O4微晶形成胶核,胶核聚集形成均匀、稳定的MGM微球.MGM中Fe3O4含量为6.17%时,比饱和磁化强度σs达6.5 emu/g;其比表面积、平均孔径和孔容分别为117.6 m2/g,15.6 nm和0.46 cm3/g,表面环氧基团含量为0.53 mmol/g.MGM借助自身的活性环氧基团在十分温和的条件下共价偶联青霉素酰化酶(penicillin G acylase EC 3.5.1.11,简称PGA),制备的固定化酶在37℃下催化水解青霉素G钾生成6-氨基青霉烷酸(6-APA)的表观活性达502IU/g,并且在使用过程中没有出现磁聚集现象.     

An error-free algorithm to solve a linear system of polynomial equations

The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors.     

Inverse Scattering Problem for the Schrödinger Operator with External Yang–Mills Potentials in Two Dimensions at Fixed Energy

ABSTRACT

We consider the Schrödinger equation in ?², with external Yang–Mills potentials that decay exponentially as |x| → ∞. We prove that the scattering amplitude at fixed positive energy determines the potentials uniquely modulo a gauge transformation, assuming that potentials are small.