A numerical resolution of the Gelfand-Levitan equation

The Gelfand-Levitan equation is the main equation in inverse scatterring theory; a new numerical method for solving this equation is presented, based on a predictor-corrector scheme.     

On the Exact Controllability of the Wave Equation with Interior and Boundary Controls

The exact controllability of the wave equation in a bounded domain of Rⁿ, with controls on a part of the boundary and in the interior, is studied. Feedback laws are established.     

Effect of amino acids on the interaction between cobalamin(II) and dehydroascorbic acid

The kinetics of the reaction between one-electron-reduced cobalamin (cobalamin(II), Cb(II)) and the two-electron-oxidized form of vitamin C (dehydroascorbic acid, DHA) with amino acids in an acidic medium is studied by conventional UV–Vis spectroscopy. It is shown that the oxidation of Cbl(II) by dehydroascorbic acid proceeds only in the presence of sulfur-containing amino acids (cysteine, acetylcysteine). A proposed reaction mechanism includes the step of amino acid coordination on the Co(II)-center through the sulfur atom, along with that of the interaction between this complex and DHA molecules, which results in the formation of ascorbyl radical and the corresponding Co(III) thiolate complex.     

Weighted Bounds for Multilinear Square Functions

Let \(\vec {P}=(p_{1},\dotsc ,p_{m})\) with 1 < p ₁, …, p _m < ∞, 1/p ₁+?+1/p _m =1/p and \(\vec {w}=(w_{1},\dotsc ,w_{m})\in A_{\vec {P}}\). In this paper, we investigate the weighted bounds with dependence on aperture α for multilinear square functions \(S_{\alpha ,\psi }(\vec {f})\). We show that

$$\|S_{\alpha,\psi}(\vec{f})\|_{L^{p}(\nu_{\vec{w}})} \leq C_{n,m,\psi,\vec{P}} \alpha^{mn}[\vec{w}]_{A_{\vec{P}}}^{\max(\frac{1}{2},\tfrac{p_{1}^{\prime}}{p},\dotsc,\tfrac{p_{m}^{\prime}}{p})} \prod\limits_{i=1}^{m} \|f_{i}\|_{L^{p_{i}}(w_{i})}. $$

This result extends the result in the linear case which was obtained by Lerner in 2014. Our proof is based on the local mean oscillation technique presented firstly to find the weighted bounds for Calderón–Zygmund operators. This method helps us avoiding intrinsic square functions in the proof of our main result.     

Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains

Consider the nonlinear parabolic equation in the form

$$\begin{aligned} u_t-\mathrm{div}{\mathbf {a}}(D u,x,t)=\mathrm{div}\,(|F|^{p-2}F) \quad \text {in} \quad \Omega \times (0,T), \end{aligned}$$

where \(T>0\) and \(\Omega \) is a Reifenberg domain. We suppose that the nonlinearity \({\mathbf {a}}(\xi ,x,t)\) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity \({\mathbf {a}}(\xi ,x,t)\) and to more general setting of Lorentz spaces.

     

二维接力-HOHAHA和NOE差谱法测定甙类化合物的结构

该文提出一种新的二维接力-HOHAHA实验方法.研究结果表明,该方法可用于从高度重迭的谱图中分离出各个糖体的¹H NMR信号,并且与NOE差谱实验相结合可以用于测定甙类化合物中糖体间和糖体与甙元间的连接位置.本方法以¹H NMR为基础,故其灵敏度比以¹³C NMR为基础的甙化位移方法高得多.     

Synthesis of poly-β-(α-benzyl-L-aspartate) from L-aspartic β-lactam benzyl ester (3(R)-benzoxycarbonyl-2-azetidinone)

A study on the anionic-assisted polymerization of L-aspartic β-lactam benzyl ester in solution has been carried out in order to prepare an improved poly-β-(α-benzyl-L-aspartate). We have found that both imide formation (with appreciable racemization) and size of the resulting polymers are highly dependent on the nature of reaction medium. A high molecular weight poly-β-aspartate without detectable branching could thus be obtained by using solvents with low polarity. The mechanism of side reactions is discussed.     

Instance Segmentation of Multiple Myeloma Cells Using Deep-Wise Data Augmentation and Mask R-CNN

Multiple myeloma is a condition of cancer in the bone marrow that can lead to dysfunction of the body and fatal expression in the patient. Manual microscopic analysis of abnormal plasma cells, also known as multiple myeloma cells, is one of the most commonly used diagnostic methods for multiple myeloma. However, as it is a manual process, it consumes too much effort and time. Besides, it has a higher chance of human errors. This paper presents a computer-aided detection and segmentation of myeloma cells from microscopic images of the bone marrow aspiration. Two major contributions are presented in this paper. First, different Mask R-CNN models using different images, including original microscopic images, contrast-enhanced images and stained cell images, are developed to perform instance segmentation of multiple myeloma cells. As a second contribution, a deep-wise augmentation, a deep learning-based data augmentation method, is applied to increase the performance of Mask R-CNN models. Based on the experimental findings, the Mask R-CNN model using contrast-enhanced images combined with the proposed deep-wise data augmentation provides a superior performance compared to other models. It achieves a mean precision of 0.9973, mean recall of 0.8631, and mean intersection over union (IOU) of 0.9062.