Preparation and electric property of PA/PVDF blend for energy storage material

This paper selected typical polar polymers which are polyvinylidene fluoride (PVDF) and polyamide (PA) to prepare PA/PVDF blend for energy storage material. Three kinds of PA (PA6, PA66 and PA11) with representative characters were chosen as the main research polymers for blending with PVDF. The electrical properties of three kinds of all-polymeric blends were tested and the microstructure was characterized by X-ray diffractometer (XRD), Fourier transform infrared instrument (FTIR), Scanning electron microscope (SEM) and Differential scanning calorimetry (DSC). Our finding suggests that the created high-ε polymeric blends represent a novel type of material that is easy to process. In addition, the dielectric constant and breakdown strength of PA/PVDFs are relatively high so that it can be applied to electronic components.     

Inequalities and solution of an operator equation

In this work, we prove several important inequalities, and investigate the solution of an operator equation by means of the fixed point index in the theory of topological degree. For operator equations with different boundary conditions, the same conclusion is obtained. Meanwhile, the famous Rothe’s Theorem is generalized. Finally, an example is given to show the application of Theorem 3.     

Solvent-free Synthesis of Flowable Carbon Clusters with Customizable Size and Tunable Optical Performance

We propose a rapid and solvent-flee route for synthesizing luminous carbon clusters by controlling carbonization of polyethylene glycol （PEG）. This approach does not involve solvents yet uses the precursor itself as suspend- ing medium, thus features mild and green chemistry, and also enables the formation of uniform-sized carbon clus- ters, of which the diameter can be easily tuned from 0.7 to 3.5 nm via control of reaction time. In term of the di- mension, the resultants are denoted as sub-nano carbon clusters （SNCs） and carbon dots （CDs）, respectively. Bene- fiting from surface anchored PEG segments, both of the two show favorable flowability at room temperature and excellent solubility in aqueous and organic solvents. Comparison of their optical performances and structures re- veals that they share the same chromophores. Particularly, the SNCs demonstrate robust photo- and pH-stable pho- toluminescence and can be directly applied to cell-imaging regarding to its prominent biocompatibility. Moreover, its quantum yield （5.5%）, which is approximately 3 times higher than that of CDs （1.5%）, can be dramatically en- hanced to 18.8% by facile chemical reduction. We anticipate that these PEG derivatives marked with easy synthesis, controllable optical performances and excellent physical properties will be highly appealing in future applications.     

Calculations of random fixed point index

In this paper, we prove an important inequality and investigate some new calculating problems of random fixed point index, and generalize famous theorem by means of the theory of random fixed point index.     

Eigenvalues of the buckling problem of arbitrary order and of the polyharmonic operator on Ricci flat manifolds

In this paper, we study eigenvalues of the buckling problem of arbitrary order and of the polyharmonic operator on bounded domains in Ricci flat manifolds supporting a special function and obtain universal bounds on the (k+1)$(k+1)$th eigenvalue in terms of the first k eigenvalues independent of the domains.     

Closed geodesics and volume growth of open manifolds with sectional curvature bounded from below

In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov＇s theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant.     

半序概率度量空间中φ-μ-混合单调算子方程组的解(英文)

在半序概率度量空间中,引入φ-μ-混合单调算子的概念.同时,构建一些新的条件,并采用半序技巧和分布函数的性质获得了φ-μ-混合单调算子方程组的解.