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.     

Electrochemical Monitoring of Methotrexate Anticancer Drug in Human Blood Serum by Using in situ Solvothermal Synthesized Fe3O4/ITO Electrode

Here, we reported on a one‐step fabrication of magnetite Fe₃O₄ nanoparticles/indium tin oxide (ITO) electrode based on the direct growing of Fe₃O₄ nanoparticles on the ITO surface by using a solvothermal process. The modified electrode was used as electrochemical methotrexate (MTX) biosensor with high sensitivity based on cyclic voltammetry and square wave voltammetry techniques. The results demonstrated a linear relationship between the MTX concentration and its oxidation current peak over a wide range from 10^?5 to 10^?14 mole/L with a limit of detection of 0.4×10^?15 M based on the square wave voltammetry (SWV) technique. In addition, Fe₃O₄/ITO electrode showed a good capability for measuring very low concentrations of MTX drug dissolved in human serum solution. Also, Fe₃O₄/ITO electrode was used for detecting MTX in blood serum samples collected from patients after their treatment with MTX. The prepared electrode showed the higher sensitivity that higher than the Viva‐E instrument, which opens the door for developing a cheap, simple and higher sensitive MTX sensor.     

Highly Sensitive AdSV Method for Fe(III) Determination in Presence of Solochrome Violet RS on Renewable Amalgam Film Electrode

The new DP AdSV method for high sensitive Fe(III) determination in the presence of Solochrome Violet RS was developed. The use of an innovative renewable amalgam film electrode Hg(Ag)FE allowed to obtain high sensitivity and significantly minimize the mercury consumption. The best results were obtained for surface area of Hg(Ag)FE equal to 11.8 mm². Instrumental parameters were optimized. The optimal results were obtained using differential pulse technique for the following values: sampling and waiting time ts=tw=10 ms, step potential Es=5 mV, pulse amplitude ΔE=50 mV. Measurements were conducted in 0.05 M acetate buffer (pH 5.6), the concentration of SVRS was equal to 5 μM. Deposition step was carried out at the potential ?400 mV for 20 s. Calculated detection limit for 40 s preconcentration time was equal to 1.4 nM (78 ng L^?1). The influence of the common in environment, organic and inorganic interferences was studied. The developed method for Fe(III) determination was successfully applied and validated by investigation of certified reference material SPS‐SW2 Batch 118 and recovery of Fe(III) from various spiked samples as snow, tap water and bottom sediments. The repeatability (for 50 nM of Fe(III)) of the developed method expressed as CV was equal 3.1 % (n=5).     

The double deflating technique for irreducible singular M-matrix algebraic Riccati equations in the critical case

As is known, Alternating-Directional Doubling Algorithm (ADDA) is quadratically convergent for computing the minimal nonnegative solution of an irreducible singular M-matrix algebraic Riccati equation (MARE) in the noncritical case or a nonsingular MARE, but ADDA is only linearly convergent in the critical case. The drawback can be overcome by deflating techniques for an irreducible singular MARE so that the speed of quadratic convergence is still preserved in the critical case and accelerated in the noncritical case. In this paper, we proposed an improved deflating technique to accelerate further the convergence speed – the double deflating technique for an irreducible singular MARE in the critical case. We proved that ADDA is quadratically convergent instead of linearly when it is applied to the deflated algebraic Riccati equation (ARE) obtained by a double deflating technique. We also showed that the double deflating technique is better than the deflating technique from the perspective of dimension of the deflated ARE. Numerical experiments are provided to illustrate that our double deflating technique is effective.     

次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

Precise Synthesis of Poly(thioester)s with Diverse Structures by Copolymerization of Cyclic Thioanhydrides and Episulfides Mediated by Organic Ammonium Salts

The precise synthesis of poly(thioester)s with diverse structures is still a significant challenge in the polymeric materials field. Herein, we report a novel approach to the synthesis of well‐defined poly(thioester)s by the controlled alternating copolymerization of cyclic thioanhydrides and episulfides induced by simple organic ammonium salts. Both the cation and anion have strong effects on the copolymerization. [PPN]OAc ([PPN]=bis(triphenylphosphine)iminium) with a bulky cation was proven to be efficient in initiating this polymerization, yielding poly(thioester)s with a completely alternating structure, controlled molecular weight, and narrow polydispersity. The poly(thioester) obtained from succinic thioanhydride and propylene sulfide is a typical semicrystalline material, possessing a high refractive index of up to 1.78. Because it uses readily available monomers, this method is expected to open up a new route to poly(thioester)s with diverse structures and properties.     

Selective Decrosslinking in Liquid Crystal Polymer Actuators for Optical Reconfiguration of Origami and Light‐Fueled Locomotion

The ability to optically reconfigure an existing actuator of a liquid crystal polymer network (LCN) so that it can display a new actuation behavior or function is highly desired in developing materials for soft robotics applications. Demonstrated here is a powerful approach relying on selective polymer chain decrosslinking in a LCN actuator with uniaxial LC alignment. Using an anthracene‐containing LCN, spatially controlled optical decrosslinking can be realized through photocleavage of anthracene dimers under 254 nm UV light, which alters the distribution of actuation (crosslinked) and non‐actuation (decrosslinked) domains and thus determines the actuation behavior upon order‐disorder phase transitions. Based on this mechanism, a single actuator having a flat shape can be reconfigured in an on‐demand manner to exhibit reversible shape transformation such as self‐folding into origami three‐dimensional structures. Moreover, using a dye‐doped LCN actuator, a light‐fueled microwalker can be optically reconfigured to adopt different locomotion behaviors, changing from moving in the laser scanning direction to moving in the opposite direction.     

One‐Step Labeling of Collagen Hydrogels with Polydopamine and Manganese Porphyrin for Non‐Invasive Scaffold Tracking on Magnetic Resonance Imaging

Biomaterial scaffolds are the cornerstone to supporting 3D tissue growth. Optimized scaffold design is critical to successful regeneration, and this optimization requires accurate knowledge of the scaffold's interaction with living tissue in the dynamic in vivo milieu. Unfortunately, non‐invasive methods that can probe scaffolds in the intact living subject are largely underexplored, with imaging‐based assessment relying on either imaging cells seeded on the scaffold or imaging scaffolds that have been chemically altered. In this work, the authors develop a broadly applicable magnetic resonance imaging (MRI) method to image scaffolds directly. A positive‐contrast “bright” manganese porphyrin (MnP) agent for labeling scaffolds is used to achieve high sensitivity and specificity, and polydopamine, a biologically derived universal adhesive, is employed for adhering the MnP. The technique was optimized in vitro on a prototypic collagen gel, and in vivo assessment was performed in rats. The results demonstrate superior in vivo scaffold visualization and the potential for quantitative tracking of degradation over time. Designed with ease of synthesis in mind and general applicability for the continuing expansion of available biomaterials, the proposed method will allow tissue engineers to assess and fine‐tune the in vivo behavior of their scaffolds for optimal regeneration.     

Nanocrystalline cellulose/fluorinated polyacrylate latex via RAFT‐mediated surfactant‐free emulsion polymerization and its application as waterborne textile finishing agent

A simple method for nanocrystalline cellulose (NCC)/fluorinated polyacrylate was developed by RAFT‐mediated surfactant‐free emulsion polymerization, in which the nanocomposites formed a core‐shell spherical morphology. The influence of the content of NCC‐g‐(PAA‐b‐PHFBA) (AA was acrylic acid, HFBA was hexafluorobutyl acrylate) on the properties of latex and film were systematically studied. The monomer conversion, the tensile strength, and water–oil repellency of film increased first and then decreased, the latex particle size decreased first and then decreased, when the content of NCC‐g‐(PAA‐b‐PHFBA) increased from 1 to 6 wt %. Elongation at break and thermal stability distinctly decreased when the content of NCC‐g‐(PAA‐b‐PHFBA) gradually increased. XPS showed that the fluorine‐containing groups well concentrated at the film–air interfaces during the annealing process. SEM analysis revealed that the treated fiber had a rugged surface, and the treated fabric had an excellent water repellency. In addition, this green grafting method in water offered a new perspective for the fabrication of exceptional NCC‐based nanocomposites with NCC as the core and also helped to promote the potential applicability of NCC in a range of multipurpose applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1305–1314