Polymer 4D printing: Advanced shape-change and beyond

4D printing is an exciting branch of additive manufacturing. It relies on established 3D printing techniques to fabricate objects in much the same way. However, structures which fall into the 4D printed category have the ability to change with time, hence the “extra dimension.” The common perception of 4D printed objects is that of macroscopic single-material structures limited to point-to-point shape change only, in response to either heat or water. However, in the area of polymer 4D printing, recent advancements challenge this understanding. A host of new polymeric materials have been designed which display a variety of wonderful effects brought about by unconventional stimuli, and advanced additive manufacturing techniques have been developed to accommodate them. As a result, the horizons of polymer 4D printing have been broadened beyond what was initially thought possible. In this review, we showcase the many studies which evolve the very definition of polymer 4D printing, and reveal emerging areas of research integral to its advancement.     

Insights into MWCNTs/polyimide nanocomposites: from synthesis to application as free-standing flexible electrodes in low-cost micro-supercapacitors

In the pursuit to enlarge the library of polyimide materials for energy applications, new polyimide/MWCNTs composite films have been developed by MWCNTs-assisted polycondensation reaction of a hydroxyl and triphenylmethane-containing diamine with benzophenone tetracarboxylic dianhydride targeting to highlight their electrical storage capability as flexible electrodes in micro-supercapacitors (mSCs). The Fourier-transform infrared spectroscopy, proton nuclear magnetic resonance, UV–vis, fluorescence, and Raman spectroscopies were used to demonstrate the evolution of interfacial interactions between MWCNTs and the precursors (diamine monomer and intermediate polyamidic acid) and polyimide matrix that proved to be the origin of MWCNTs homogeneous dispersion. Thus, composite films incorporating 1, 3, 5, and 10 w.t.% MWCNTs were obtained and thoroughly investigated with regard to their morphology, mechanical behavior, thermal stability, and electrical conductivity. The electrochemical performance of these composites was first analyzed in a classical three-electrode cell by cyclic voltammetry and galvanostatic charge-discharge in both aqueous and organic electrolyte systems. By far, the best electrical storage capacity was obtained with the composite polyimide film containing 10% MWCNTs that was further used as both active material and current collector in a flexible symmetric mSC realized by a straightforward and low-cost procedure. In the attempt to better exploit the advantages of this composite film, it was layered with a graphite-containing paint and tested as an electrode in a flexible mSC, which provided satisfactory results. To our knowledge, this is the first report on the electrical charge storage capability of a polyimide/MWCNTs free-standing film as a flexible electrode in mSCs, which do not require time- and resource-consuming processing steps.     

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.     

The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

One-pot,one-step,and selective terpolymerization of ethylene oxide,propylene oxide,and COS to copoly(thioether)s with tunable thermal properties

Facile construction of sulfur-rich polymers using readily available raw chemicals is an area aggressively pursued but challenging. Herein we use common feedstocks of ethylene oxide (EO), propylene oxide (PO), and carbonyl sulfide (COS) to synthesize copoly(thioether)s which are traditionally produced from unpleasant and difficult to store episulfides. In this protocol, the EO/COS coupling selectively generates a pure poly(ethylene sulfide) (PES) with melting temperature (T_m) values up to 172°C and high yields up to 98%. The EO/PO/COS terpolymerization leads to the incorporation of soft poly(propylene sulfide) (PPS) and hard PES segments together, affording a random PES-co-PPS copoly(thioether) with the complete consumption of EO and PO. Additionally, by simply varying the EO/PO feeding ratio, the obtained copoly(thioether)s possess tunable thermal properties, T_m values in the range of 76–144°C, and excellent solubility. These copolymerizations are conducted in one-pot/one-step at industrially favored reaction temperatures of 100–120°C using catalysts of common organic bases, suggesting a facile and practical manner. Especially, the copoly(thioether) exhibits high refractive indices up to 1.68 owing to its high sulfur content, suggesting a broad application prospect in optical materials.     

Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

基于GA_XGBoost模型的大学生科研能力预测问题研究

科学评价大学生科研创新能力对我国科研水平的提高具有重要意义.采用机器学习模型来预测大学生科研能力可以起到良好的效果,提出一种GAXGBoost模型来实现对大学生的科研能力预测.此模型是以Xgboost算法为基础,然后充分利用遗传算法的全局搜索能力自动搜索Xgboost最优超参数,避免了人为经验调参不准确的缺陷,最后采用精英选择策略以此确保每一轮都是最佳的进化结果.通过分析表明,所采用的GAXGBoost模型在大学生科研能力预测的结果中具有很高的精度,将此模型与Logistic Regression、Random Forest、SVM等模型进行对比,GAXGBoost模型的预测精度最高.