Difference Cochains and Reidemeister Traces

The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps,and find out a relation involving these two invariants.As an application,an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex,including spherical manifolds is obtained.     

Some new results on permutation polynomials over finite fields

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete permutation polynomials are presented, one of which confirms a conjecture proposed by Wu et al. (Sci China Math 58:2081–2094, 2015). Furthermore, we give two classes of permutation trinomial, and make some progress on a conjecture about the differential uniformity of power permutation polynomials proposed by Blondeau et al. (Int J Inf Coding Theory 1:149–170, 2010).     

Quasideterminant solutions of the extended noncommutative Kadomtsev–Petviashvili hierarchy

We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.     

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

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A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations

This paper presents a volume integral equation method for an electromagnetic scattering problem for three-dimensional Maxwell's equations in the presence of a biperiodic, anisotropic, and possibly discontinuous dielectric scatterer. Such scattering problem can be reformulated as a strongly singular volume integral equation (i.e., integral operators that fail to be weakly singular). In this paper, we firstly prove that the strongly singular volume integral equation satisfies a Gårding-type estimate in standard Sobolev spaces. Secondly, we rigorously analyze a spectral Galerkin method for solving the scattering problem. This method relies on the periodization technique of Gennadi Vainikko that allows us to efficiently evaluate the periodized integral operators on trigonometric polynomials using the fast Fourier transform (FFT). The main advantage of the method is its simple implementation that avoids for instance the need to compute quasiperiodic Green's functions. We prove that the numerical solution of the spectral Galerkin method applied to the periodized integral equation converges quasioptimally to the solution of the scattering problem. Some numerical examples are provided for examining the performance of the method.     

Prussian blue–gold nanoparticles-ionic liquid functionalized reduced graphene oxide nanocomposite as label for ultrasensitive electrochemical immunoassay of alpha-fetoprotein

In this work, poly(diallyldimethylammonium chloride) (PDDA) protected Prussian blue/gold nanoparticles/ionic liquid functionalized reduced graphene oxide (IL-rGO-Au-PDDA-PB) nanocomposite was fabricated. The resulting nanocomposite exhibited high biocompatibility, conductivity and catalytic activity. To assess the performance of the nanocomposite, a sensitive sandwich-type immunosensor was constructed for detecting alpha-fetoprotein (AFP). Greatly enhanced sensitivity for this immunosensor was based on triple signal amplification strategies. Firstly, IL-rGO modified electrode was used as biosensor platform to capture a large amount of antibody due to its increased surface area, thus amplifying the detection response. Secondly, a large number of Au-PDDA-PB was conjugated on the surface of IL-rGO, which meant the enrichment of the signal and the more immobilization of label antibody. Finally, the catalytic reaction between H₂O₂ and the IL-rGO-Au-PDDA-PB nanocomposite further enhanced the signal response. The signals increased linearly with AFP concentrations in the range of 0.01–100 ng mL⁻¹. The detection limit for AFP was 4.6 pg mL⁻¹. The immunosensor showed high sensitivity, excellent selectivity and good stability. Moreover, the immunosensor was applied to the analysis of AFP in serum sample with satisfactory result.     

染料敏化太阳能电池中具有不同电子给体的吩噻嗪类有机光敏染科的理论研究

采用密度泛函理论和含时密度泛函理论方法计算了2个吩噻嗪类染料及其吸附到TiO2上后分子的基态和激发态光物理性质与热力学参数.结果表明,电子给体的改变虽未明显改变染料的光谱性质(垂直跃迁能和振子强度),但可以改变分子的前线轨道能级,进而影响染料分子的激子结合能Eb及激发态电子注入到半导体TiO2中的驱动力△Gint的大小...     

过渡金属脒配合物的合成与应用研究进展

脒及其衍生物是一类具有广泛而良好生物活性的有机物,也是重要的有机合成中间体.脒作为一类良好的配体,具有多种成键类型,所生成的脒过渡会属配合物也具有很多特殊性质与重要用途.本文主要综述了脒配合物合成方法的进展及其性能与应用.其中腈胺加成"一锅"法制备脒配合物的有效性和方便性.不但可以利用过渡金属诱导有机腈与胺耦合成眯,而...     

基于冠心病心肌缺血血瘀证小型猪血清核磁共振代谢组学的研究

通过左冠状动脉前降支放置Ameriod环制备冠心病慢性心肌缺血动物模型,并结合冠脉造影等方法确立中医血瘀证证候,采用现代核磁共振(NMR)和模式识别技术,分析冠心病心肌缺血血瘀证模型与假手术组小型猪4星期血清的共振氢谱,及相应代谢物谱群的变化,开展中医血瘀证候学的研究.结果显示,该方法制备的模型4星期后确立为稳定的冠心...