The invariant of the stiffness filter function with the weight filter function of the power function form

Based on the independent, continuous and mapping (ICM) method and homogenization method, a research model is constructed to propose and deduce a theorem and corollary from the invariant between the weight filter function and the corresponding stiffness filter function of the form of power function. The efficiency in searching for optimum solution will be raised via the choice of rational filter functions, so the above mentioned results are very important to the further study of structural topology optimization.     

Undersampled Windowed Exponentials and Their Applications

We characterize the completeness and frame/basis property of a union of under-sampled windowed exponentials of the form

$$ {\mathcal{F}}(g): =\bigl\{ e^{2\pi i n x}: n\ge 0\bigr\} \cup \bigl\{ g(x)e^{2\pi i nx}: n< 0\bigr\} $$

for \(L^{2}[-1/2,1/2]\) by the spectra of the Toeplitz operators with the symbol \(g\). Using this characterization, we classify all real-valued functions \(g\) such that \({\mathcal{F}}(g)\) is complete or forms a frame/basis. Conversely, we use the classical non-harmonic Fourier series theory to determine all \(\xi \) such that the Toeplitz operators with the symbol \(e^{2\pi i \xi x}\) is injective or invertible. These results demonstrate an elegant interaction between frame theory of windowed exponentials and Toeplitz operators. Finally, we use our results to answer some open questions in dynamical sampling, and derivative samplings on Paley-Wiener spaces of bandlimited functions.

     

Effects of ultrasonic field on structure evolution of Ni film electrodeposited by bubble template method for hydrogen evolution electrocatalysis

Journal of Solid State Electrochemistry - Self-supporting porous Ni film with uniform honeycomb-like micropores and a thickness of up to 66&nbsp;μm is electrodeposited by dynamic hydrogen...     

Correlations between microstructure of α‐row nuclei and polymorphism of shear‐induced iPP/carbon fiber cylindrite

Herein, we reported the formation mechanism of hybrid crystalline (cylindrite) in isotactic polypropylene (iPP)/carbon fiber (CF) via pulling a CF within the iPP melt. The α‐row nuclei layer closely attached to the surface of CF acts as a self‐nucleation site, rather than a heterogeneous nucleation one, to grow cylindrites. As a result, the polymorphic feature of iPP/CF cylindrite is significantly influenced by the microstructure of α‐row nuclei. With decreasing crystallization temperature (T_c), the polymorphic cylindrite changes from pure α‐form to mixed α‐/β‐form and to β‐rich form. The main characteristics of this change include: (a) the outlines of α‐row nuclei layer correspond to wave‐like, saw‐like, and straight lines; (b) the orientation level of iPP molecules in the α‐row nuclei layer become higher; (c) the α‐lamellae rearrange from loose to compact; and (d) the distance between the growth sites of β‐sectors and the surface of CF is evidently longer than in the case of α‐sectors. Moreover, this study provides a guideline for developing the interfacial enhanced iPP/CF composites through manipulation of polymorphic structure in cylindrites. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 368–377     

Chiral aminocyclopentene-based cycloaddition strategies to bicyclic [3.3.0] rings

Two cycloaddition methods were applied to chiral protected aminocyclopentenes 2 and 9 and provided novel bicyclic products 3 and 4 in good yields. The explanation for the observed stereochemistry was based on the sterically encumbered β-face forcing the cycloadditions to occur on the α-face of the cyclopentene ring. The stereochemistry of 4 was confirmed by X-ray of the fumarate salt 10 and showed the trans-relationship between the newly formed ring and the chiral –NHBoc group.     

Flame‐retardant and mechanical properties of phenolic foams toughened with polyethylene glycol phosphates

Three kinds of polyethylene glycol phosphates (PEGPs) toughening agents were synthesized by esterification of phosphorus pentoxide (P₂O₅) with polyethylene glycol and characterized by Fourier transform infrared spectra and ³¹P nuclear magnetic resonance. A series of lightweight phenolic foams toughened with different loadings of PEGPs were prepared. Optical microscopy results show that the addition of PEGPs with small molecular weight PEG improves the structural homogeneity of phenolic foams obviously. The flame retardancy of toughened phenolic foams was evaluated by using UL 94, limiting oxygen index, and cone calorimeter. The results indicate that the incorporation of PEGPs not only increases the toughness of phenolic foams but also improves their flame retardancy. Moreover, the thermal stability of PEGPs and the toughened foams was investigated by thermogravimetric analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

A UFLC‐MS/MS method with a switching ionization mode for simultaneous quantitation of polygalaxanthone III,four ginsenosides and tumulosic acid in rat plasma: application to a comparative pharmacokinetic study in normal and Alzheimer's disease rats

A fast, sensitive and reliable ultra fast liquid chromatography‐tandem mass spectrometry (UFLC‐MS/MS) method has been developed and validated for simultaneous quantitation of polygalaxanthone III (POL), ginsenoside Rb1 (GRb1), ginsenoside Rd (GRd), ginsenoside Re (GRe), ginsenoside Rg1 (GRg1) and tumulosic acid (TUM) in rat plasma after oral administration of Kai‐Xin‐San, which plays an important role for the treatment of Alzheimer's disease (AD). The plasma samples were extracted by liquid–liquid extraction using ethyl acetate–isopropanol (1:1, v/v) with salidrdoside as internal standard (IS). Good chromatographic separation was achieved using gradient elution with the mobile phase consisting of methanol and 0.01% acetic acid in water. The tandem mass spectrometric detection was performed in multiple reaction monitoring mode on 4000Q UFLC‐MS/MS system with turbo ion spray source in a negative and positive switching ionization mode. The lower limits of quantification were 0.2–1.5 ng/ml for all the analytes. Both intra‐day and inter‐day precision and accuracy of analytes were well within acceptance criteria (±15%). The mean absolute extraction recoveries of analytes and IS from rat plasma were all more than 60.0%. The validated method has been successfully applied to comparing pharmacokinetic profiles of analytes in normal and AD rat plasma. The results indicated that no significant differences in pharmacokinetic parameters of GRe, GRg1 and TUM were observed between the two groups, while the absorption of POL and GRd in AD group were significantly higher than those in normal group; moreover, the GRb1 absorbed more rapidly in model group. The different characters of pharmacokinetics might be caused by pharmacological effects of the analytes. Copyright © 2013 John Wiley & Sons, Ltd.     

Thermogravimetry study of the pyrolytic characteristics and kinetics of macro-algae Macrocystis pyrifera residue

Macrocystis pyrifera is one important marine macro-algae, while its residues produced by industrial alginate extraction is a hot potato. To figure out whether its residue is suitable for pyrolysis for biofuel, the pyrolytic characteristics and kinetics of macro-algae M. pyrifera residue was investigated using thermogravimetric method from 50 to 800 °C in an inert argon atmosphere at different heating rates of 5, 10, 20, and 30 °C min^?1. The activation energy and pre-exponential factor was calculated by Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose, and Popescu methods, and the kinetic mechanism was deduced by Popescu method. The results showed that the primary devolatilization stage of M. pyrifera residue can be described by Jander function $ \left(\left[ {1 - \left( {1 - \alpha } \right)^{1/3} } \right]^{2}\right) $ . The average activation energy of M. pyrifera residue was 222.4 kJ mol^?1. The results suggested that the experimental results and kinetic parameters provided useful information for the design of pyrolytic processing system using M. pyrifera residue as feedstock.     

复合酶酶解假酸浆黄酮苷抗氧化性研究

本文研究了复合酶酶解前后假酸浆提取物的抗氧化活性能力,并采用薄层色谱法(TLC)对酶解产物中总黄酮进行了分离,利用高效液相色谱-质谱联用技术对其鉴定分析。通过对DPPH自由基、羟自由基及超氧阴离子自由基清除能力实验,酶解液抗氧化性能显著高于假酸浆提取液;酶解液的薄层及HPLC-MS法初步鉴定出假酸浆中含有桑色素、二氢槲皮素和儿茶素三种黄酮。