Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

黄绿色葡萄石的矿物学特征及谱学研究

葡萄石可以以板状、片状、葡萄状、肾状、放射状或块状集合体的形式产出,因其美丽的外观和特殊的晶体结构,近年来受到了学者的广泛关注。本文通过电子探针、粉晶X射线衍射仪、傅里叶变换红外光谱仪、显微拉曼光谱仪、紫外可见分光光度计等仪器对黄绿色葡萄石的成分、结构及谱学特征进行了分析与探讨。葡萄石的主要致色元素为Fe,且Fe³⁺经常取代Al³⁺占据八面体配位,Fe²⁺经常取代Ca²⁺存在于空隙中。电子探针数据表明:Fe与Al的含量变化整体呈现负相关关系,Fe与Ca的含量变化也整体呈现负相关关系,Fe含量相对较高的样品其黄绿色调加深。XRD图谱和拉曼光谱的结果表明:在葡萄石中绿帘石以包裹体的形式存在。红外光谱和拉曼光谱表明葡萄石中存在硅氧四面体和铝氧八面体两种架构,紫外可见吸收光谱揭示了葡萄石的致色机理。本文对葡萄石的矿物学特征及谱学特征进行系统分析,为后续葡萄石的进一步研究提供思路与实验数据。     

非线性玻尔兹曼方程的傅里叶谱方法

玻尔兹曼方程作为空气动理学中最基本的方程之一,是连接微观牛顿力学和宏观连续介质力学的重要桥梁.该方程描述了一个由大量粒子组成的复杂系统的非平衡态时间演化:除了基本的输运项,其最重要的特性是粒子间的相互碰撞由一个高维,非局部且非线性的积分算子来描述,从而给玻尔兹曼方程的数值求解带来非常大的挑战.在过去的二十年间,基于傅里叶级数的谱方法成为了数值求解玻尔兹曼方程的一种很受欢迎且有效的确定性算法.这主要归功于谱方法的高精度及它可以被快速傅里叶变换加速的特质.本文将回顾玻尔兹曼方程的傅里叶谱方法,具体包括方法的导出,稳定性和收敛性分析,快速算法,以及在一大类基于碰撞的空气动理学方程中的推广.     

Deciphering the Structure and Chemical Composition of Drug Nanocarriers: From Bulk Approaches to Individual Nanoparticle Characterization

Drug nanocarriers (NCs) with sizes usually below 200 nm are gaining increasing interest in the treatment of severe diseases such as cancer and infections. Characterization methods to investigate the morphology and physicochemical properties of multifunctional NCs are key in their optimization and in the study of their in vitro and in vivo fate. Whereas a variety of methods has been developed to characterize “bulk” NCs in suspension, the scope of this review is to describe the different approaches for the NC characterization on an individual basis, for which fewer techniques are available. The accent is put on methods devoid of labelling, which could lead to artefacts. For each characterization method, the principles and approaches to analyze the data are presented in an accessible manner. Aspects related to sample preparation to avoid artefacts are indicated, and emphasis is put on examples of applications. NC characterization on an individual basis allows gaining invaluable information in terms of quality control, on: i) NC localization and fate in biological samples; ii) NC morphology and crystallinity; iii) distribution of the NC components (drugs, shells), and iv) quantification of NCs’ chemical composition. The individual characterization approaches are expected to gain increasing interest in the near future.     

紫色球杆菌视紫红质光谱特性的机器学习研究

近年来，机器学习等人工智能技术被应用于蛋白质工程，其在蛋白质结构、功能预测、催化活性等研究中具有独特优势。在未知蛋白质结构的情况下，将蛋白质序列和功能特性与机器学习相结合，基于序列-活性关系（innovative sequence-activity relationship，ISAR）算法，将蛋白质氨基酸序列数字化，用快速傅里叶变换（fast four transform，FFT）进行预处理，再进行偏最小二乘回归建模，可在数据集较少情况下拟合得到最佳模型。通过机器学习对紫色球杆菌视紫红质（gloeobacter violaceus rhodopsin，GR）的突变体蛋白质氨基酸序列与光谱最大吸收波长进行建模，获得了最佳模型。用最佳索引LEVM760106建模得到的确定系数R² 为0.944，均方误差E为11.64。用小波变换进行的预处理，其R² 虽也约为0.944，但E大于11.64，不及FFT进行的预处理。方法较好地解决了蛋白质序列与功能特性之间的数学建模问题，在蛋白质工程中可为预测更优的突变体提供支持。     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

中红外光谱结合向量夹角直接定量三氯蔗糖

多组分复杂体系的红外光谱由于成分多样、谱带严重重叠、背景干扰等导致谱图特征减弱，且体系中的红外光谱往往不是各组分光谱的简单叠加，需要借助于化学计量学技术以实现解析。基于朗伯-比尔定律（Lambert-Beer law）并且随着衰减全反射（ATR）技术取样普及，结合偏最小二乘回归法（PLS）、人工神经网络（artificial neural network, ANN）等化学计量法将数据进行累积、特征提取以及校正建模等工作解决红外光谱中严重重叠和非线性等问题，再采用二次测量定量分析已初步具有应用成效，而有效增强信息量表达，降低背景、噪声干扰，减少复杂的计算过程，进而保证定量分析结果的可靠性，则成为研究的主要方向。通过讨论光通道和背景对光谱强度变化的影响，结合向量角度转换提出一种新的近似线性定量方法。经初步理论计算，发现多组分混合物与该混合物中待测组分的相对含量二者间的向量夹角值存在一定的关系，而该关系并不受批次制样的影响，进一步通过高斯曲线模拟混合信号，充分说明选择合适的波长范围，二者在一定范围内存在线性相关性，相关性不受测量条件变化的影响。采用KBr压片法，向待测样品中逐步加入待测组分得到混合样本，分别得到待测组分光谱与混合样本光谱信号，先将其进行一阶求导，消除加性误差后，再将其转化为空间向量角度，消除批次制样中光程差异，再以百分比定义待测物样品的含量，所得到混合样的夹角值与其中所含参照品含量成简单线性关系，即以计算结果夹角值与含量作标准曲线，实现定量分析。本测量方法用于三氯蔗糖（Sucralose, TGS）与三氯蔗糖-6-乙酸酯（4,1,6-trichloro sucrose-6-acetate, TGS-6-A）二者进行一定比例混合（双组分体系），以及TGS-6-A的脱酰产物（多组分体系）中的TGS的含量定量分析，在两种体系中定量均得到令人满意的结果，所建立标准曲线的相关系数r均达到0.995 0以上，相对误差均低于8.0%，所建立的分析方法对利用中红外透射光谱分析研究多组分样品具有重要的参考价值。     

DNA interaction,cytotoxicity and molecular structure of cobalt complex of 4‐amino‐N‐(6‐chloropyridazin‐3‐yl)benzene sulfonamide in the presence of secondary ligand pyridine

Novel cobalt complex of 4‐amino‐N‐(6‐chloropyridazin‐3‐yl)benzene sulfonamide (sulfachloropyridazine) has been synthesized and characterized by elemental analysis, FT‐IR spectroscopy and magnetic susceptibility (VSM). Cobalt complex of Sulfachloropyridazine (Co‐SCP) crystallized in monoclinic space group P2₁/n with Z = 4. The structure is solved by direct method and refined to R = 0.099 for 4720 reflections with I ?4σ(I). The results of FT‐IR spectra suggest the binding of cobalt atom to the sulfonamide ligand which is in agreement with the crystal structure determination. In crystal structure, molecule is linked via, C‐H … π, C‐Cl … π and π … π intermolecular interactions. The computational studies like the optimization energy and root means square deviation compare with single crystal structure, frontier molecular orbital (Homo‐Lumo energy) and binding energy of the Co‐SCP has been carried out using DFT/B3LYP level of theory in gaseous phase. Hirshfeld surfaces and the 2D‐fingerprint analysis are performed to study the nature of interactions and their measurable contributions towards crystal packing. The interaction of the complex with DNA is investigated using viscosity measurement and absorption titration studies. The result shows the complex bind to DNA with intercalative mode with high DNA‐binding constant (K_b). Also, in vivo and in vitro cytotoxic studies are performed using S. pombe cells and brine shrimp lethality bioassay. DNA‐cleavage study shows better cleaving ability of the complex.     

The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.