A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.     

disjoint cycles containing specified independent vertices

Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ₂(G)n+k-1. Let v₁,…,v_k be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C₁,…,C_k with v_iV(C_i) for all 1ik.Then G has k vertex-disjoint cycles such that

(i) for all 1ik.

(ii) , and

(iii) At least k-1 of the k cycles are triangles.

The condition of degree sum σ₂(G)n+k-1 is sharp.

Preparation and properties of electroless Ni-P-SiO2 composite coatings

Dispersible SiO₂ nanoparticles were co-deposited with electroless Ni-P coating onto AISI-1045 steel substrates in the absence of any surfactants in plating bath. The resulting Ni-P/nano-SiO₂ composite coatings were heat-treated for 1 h at 200 °C, 400 °C, and 600 °C, respectively. The hardness and wear resistance of the heat-treated composite coatings were measured. Moreover, the structural changes of the composite coatings before and after heat treatment were investigated by means of X-ray diffraction (XRD), while their elemental composition and morphology were analyzed using an energy dispersive spectrometer (EDS) and a scanning electron microscope (SEM). Results show that co-deposited SiO₂ particles contributed to increase the hardness and wear resistance of electroless Ni-P coating, and the composite coating heat-treated at about 400 °C had the maximum hardness and wear resistance.     

Functional Ag porous films prepared by electrospinning

Face-centered cubic Ag porous films have been prepared directly from the heat treatment of AgNO₃-doped poly(vinyl alcohol) (PVA) electrospun nanofibers. Using Rhodamine B (RB) as the probing molecule, the surface-enhanced Raman scattering (SERS) effect of Ag porous films was demonstrated. The antibacterial activity of Ag porous films was also studied in this work. The propagation and biological activity of yeast cells were effectively inhibited by Ag porous films. These functional Ag porous films were expected to be applied in many fields, such as catalysis, diagnostics, sensors and antibacterial, etc.     

The analysis of a novel 3-D autonomous system and circuit implementation

This Letter presents a new three-dimensional autonomous system with four quadratic terms. The system with five equilibrium points has complex chaotic dynamics behaviors. It can generate many different single chaotic attractors and double coexisting chaotic attractors over a large range of parameters. We observe that these chaotic attractors were rarely reported in previous work. The complex dynamical behaviors of the system are further investigated by means of phase portraits, Lyapunov exponents spectrum, Lyapunov dimension, dissipativeness of system, bifurcation diagram and Poincaré map. The physical circuit experimental results of the chaotic attractors show agreement with numerical simulations. More importantly, the analysis of frequency spectrum shows that the novel system has a broad frequency bandwidth, which is very desirable for engineering applications such as secure communications.     

Bayesian analysis of loss reserving using dynamic models with generalized beta distribution

A Bayesian approach is presented in order to model long tail loss reserving data using the generalized beta distribution of the second kind (GB2) with dynamic mean functions and mixture model representation. The proposed GB2 distribution provides a flexible probability density function, which nests various distributions with light and heavy tails, to facilitate accurate loss reserving in insurance applications. Extending the mean functions to include the state space and threshold models provides a dynamic approach to allow for irregular claims behaviors and legislative change which may occur during the claims settlement period. The mixture of GB2 distributions is proposed as a mean of modeling the unobserved heterogeneity which arises from the incidence of very large claims in the loss reserving data. It is shown through both simulation study and forecasting that model parameters are estimated with high accuracy.     

Rainbow Connection Number, Bridges and Radius

Let G be a connected graph. The notion of rainbow connection number rc(G) of a graph G was introduced by Chartrand et al. (Math Bohem 133:85–98, 2008). Basavaraju et al. (arXiv:1011.0620v1 [math.CO], 2010) proved that for every bridgeless graph G with radius r, ${rc(G)\leq r(r+2)}$ and the bound is tight. In this paper, we show that for a connected graph G with radius r and center vertex u, if we let D ^r  = {u}, then G has r?1 connected dominating sets ${ D^{r-1}, D^{r-2},\ldots, D^{1}}$ such that ${D^{r} \subset D^{r-1} \subset D^{r-2} \cdots\subset D^{1} \subset D^{0}=V(G)}$ and ${rc(G)\leq \sum_{i=1}^{r} \max \{2i+1,b_i\}}$ , where b _i is the number of bridges in E[D ⁱ , N(D ⁱ )] for ${1\leq i \leq r}$ . From the result, we can get that if ${b_i\leq 2i+1}$ for all ${1\leq i\leq r}$ , then ${rc(G)\leq \sum_{i=1}^{r}(2i+1)= r(r+2)}$ ; if b _i  > 2i + 1 for all ${1\leq i\leq r}$ , then ${rc(G)= \sum_{i=1}^{r}b_i}$ , the number of bridges of G. This generalizes the result of Basavaraju et al. In addition, an example is given to show that there exist infinitely graphs with bridges whose rc(G) is only dependent on the radius of G, and another example is given to show that there exist infinitely graphs with bridges whose rc(G) is only dependent on the number of bridges in G.     

近红外、中红外和拉曼光谱法测定商品农药制剂中溴氰菊酯的含量

利用近红外、中红外和拉曼光谱法定量分析了商品农药制剂中有效成分溴氰菊酯的含量,采用偏最小二乘法(partial least squares,PLS)建立溴氰菊酯的定量模型并进行了优化,用独立检验集对模型适应性进行评价。近红外和中红外法溴氰菊酯定量模型的相关系数和定标标准差分别是0.9999,0.022和0.9996,0.056,两种方法的定量效果接近;拉曼法溴氰菊酯定量模型的相关系数是0.9967,定标标准差是0.172,预测精度不如近红外和中红外高。MIR-ATR,NIR和Raman方法均能满足现场检测农药质量的需要,对生产企业的连续在线检测、监督部门进行农药质量控制和农产品安全具有重要意义。     

靶丸X射线数字图像的轮廓分析及功率谱评价

针对多层靶丸X射线数字图像的成像原理和轮廓边缘进行了理论分析;推导了由靶丸边缘特征点确定靶丸圆心和半径的精确最小二乘拟合算法;对于不同类型(阶跃状或屋顶状)的靶丸图像边缘,采用均化二阶微分算法或径向吸收强度最小二乘洛伦兹型拟合寻峰算法获取亚像素精度的靶丸圆周轮廓边缘数据;应用快速傅里叶变换算法对靶丸圆周轮廓数据进行分析,获得了靶丸表面外轮廓或内轮廓模数-功率谱特征曲线。