Some results about zero‐cycles on abelian and semi‐abelian varieties

In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration of Suslin's singular homology group, , such that the successive quotients are isomorphic to a certain Somekawa K‐group.     

Antimicrobial loading into and release from poly(ethylene glycol)/poly(acrylic acid) semi‐interpenetrating hydrogels

Electrostatic interactions within a semi‐interpenetrating network (semi‐IPN) gel can control the postsynthesis loading, long‐term retention, and subsequent release of small‐molecule cationic antibiotics. Here, electrostatic charge is introduced into an otherwise neutral gel [poly(ethylene glycol) (PEG)] by physically entrapping high‐molecular‐weight poly(acrylic acid) (PAA). The network structure is characterized by small‐angle neutron scattering. PEG/PAA semi‐IPN gels absorb over 40 times more antibiotic than PAA‐free PEG gels. Subsequent soaking in physiological buffer (pH 7.4; 0.15 M NaCl) releases the loaded antibiotics for periods as long as 30 days. The loaded gels elute antibiotics with diffusivities of 4.46 × 10^?8 cm²/s (amikacin) and 2.08 × 10^?8 cm²/s (colistin), which are two orders of magnitude less than those in pure PEG gels where diffusion is controlled purely by gel tortuosity. The release and hindered diffusion can be understood based on the partial shielding of the charged groups within the loaded gel, and they have a significant effect on the antimicrobial properties of these gels. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 64–72     

Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions

By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls

For 1‐D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be realized in a shorter time by means of additional internal controls acting on suitably small space‐time domains. On the other hand, using a perturbation method, the exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with zero eigenvalues can be realized by additional internal controls to the part of equations corresponding to zero eigenvalues. Furthermore, by adding suitable internal controls to all the equations on suitable domains, the exact controllability of nodal profile for systems with zero eigenvalues can be realized in a shorter time.     

The Expanded Genetic Alphabet

All biological information, since the last common ancestor of all life on Earth, has been encoded by a genetic alphabet consisting of only four nucleotides that form two base pairs. Long‐standing efforts to develop two synthetic nucleotides that form a third, unnatural base pair (UBP) have recently yielded three promising candidates, one based on alternative hydrogen bonding, and two based on hydrophobic and packing forces. All three of these UBPs are replicated and transcribed with remarkable efficiency and fidelity, and the latter two thus demonstrate that hydrogen bonding is not unique in its ability to underlie the storage and retrieval of genetic information. This Review highlights these recent developments as well as the applications enabled by the UBPs, including the expansion of the evolution process to include new functionality and the creation of semi‐synthetic life that stores increased information.     

时滞对结构振动半主动控制效果的影响

应用磁流变阻尼器对结构振动进行控制，采用最优控制原理设计了控制器，给出在地震激励下结构半主动控制的仿真计算。研究了时滞对结构振动半主动控制效果的影响。数值结果表明：本文设计的半主动控制策略可有效地减小结构的振动响应，时滞对磁流变半主动控制效果随着时滞的增大而变差，但时滞不会导致该反馈控制系统的失稳。     

A novel synthetic strategy for preparing semi‐aromatic components modified polyamide 6 polymer

In this work, a novel synthetic path for preparing semi‐armotic components modified polyamide 6 was developed by caprolactam as solvent of purified terephthalic acid and 1,6‐hexanediamine. First, the ring opening reaction and poly‐addition of caprolactam were initiated by 1,6‐hexanediamine to generate a prepolymer containing amino groups in both ends, then followed by the poly‐condensation reaction with purified terephthalic acid, a long chain copolymer was produced, which the reaction time was reduced by 4 h compared with conventional hydrolytic ring‐opening polymerization of pure caprolactam. By varying the ratio of terephthalic acid and 1,6‐hexanediamine, a series of copolymers with different number average molecular weight and physical properties were prepared. Analytical results showed that the conversion percentage of caprolactam is significantly increased by the proposed method. Furthermore, this new copolymers exhibited excellent transparence and high decomposition temperature. Besides, the copolymers with average molecular weight ≥15,000 present good mechanical properties, making it a potentially useful application in plastics, textile yarn, and membranes. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 959–967     

The use of Sinc‐collocation method for solving Falkner–Skan boundary‐layer equation

The MHD Falkner–Skan equation arises in the study of laminar boundary layers exhibiting similarity on the semi‐infinite domain. The proposed approach is equipped by the orthogonal Sinc functions that have perfect properties. This method solves the problem on the semi‐infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, the governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by the Sinc‐collocation method. It is shown that the Sinc‐collocation method converges to the solution at an exponential rate. Copyright © 2010 John Wiley & Sons, Ltd.     

Issue Information

An integrated finite element method (FEM) is proposed to simulate incompressible two‐phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2‐iso‐Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic‐type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi‐implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1‐integrated FEM coupled with the semi‐implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.