Role of moving planes and moving spheres following Dupin cyclides

We provide explicit representations of three moving planes that form a μ-basis for a standard Dupin cyclide. We also show how to compute μ-bases for Dupin cyclides in general position and orientation from their implicit equations. In addition, we describe the role of moving planes and moving spheres in bridging between the implicit and rational parametric representations of these cyclides.     

The effect of different lattice sites substitution on photoluminescence characteristics of Eu2+/Ce3+ doped M5(ZO4)3X

The empirical formula of Van Uitert is applied to calculating the emission wavelengths of haloapatite and silicon apatite phosphors doped with Eu²⁺/Ce³⁺. The relationship between emission wavelengths and occupied lattice sites of Eu²⁺/Ce³⁺ is discussed in haloapatite crystal. For phosphors of haloapatite and silicon apatite doped with Eu²⁺, the emission bands of the long-wave region are interpreted reasonably. Phosphors Sr₅(PO₄)₂SiO₄ doped with Eu²⁺/Ce³⁺ are synthesized by high temperature solid state reaction under two different atmospheres, the spectral characteristics of Eu²⁺/Ce³⁺ occupying different lattice sites are studied. The luminescent materials Sr₅(PO₄)₂SiO₄ doped with Eu²⁺/Ce³⁺ are promising blue-green phosphors for application in white-LEDs.     

Implicit Runge–Kutta methods based on Radau quadrature formula

Using W-transformation of Hairer and Wanner, high-order implicit Runge–Kutta methods based on Radau quadrature are studied. Methods constructed and presented include and extend the existing RadauIA, IB, IIA, IIB type RK methods. 2- and 3-stage general Radau RK methods with two parameters (δ, γ) are constructed. The RK methods with five parameters (α, β, γ, δ, τ), which include both Radau and Lobatto type methods, will be discussed at last.     

A fast numerical algorithm for solving nearly penta-diagonal linear systems

In this paper, we present a fast numerical algorithm for solving nearly penta-diagonal linear systems and show that the computational cost is less than those of three algorithms in El-Mikkawy and Rahmo, [Symbolic algorithm for inverting cyclic penta-diagonal matrices recursively–Derivation and implementation, Comput. Math. Appl. 59 (2010), pp. 1386–1396], Lv and Le [A note on solving nearly penta-diagonal linear systems, Appl. Math. Comput. 204 (2008), pp. 707–712] and Neossi Nguetchue and Abelman [A computational algorithm for solving nearly penta-diagonal linear systems, Appl. Math. Comput. 203 (2008), pp. 629–634.]. In addition, an efficient way of evaluating the determinant of a nearly penta-diagonal matrix is also discussed. The algorithm is suited for implementation using computer algebra systems (CAS) such as MATLAB, MACSYMA and MAPLE. Some numerical examples are given in order to illustrate the efficiency of our algorithm.     

对《自承式给水钢管跨越结构设计规程》中最大组合折算应力的探讨

对《自承式给水钢管跨越结构设计规程》中强度计算的最大组合折算应力计算公式进行了深入探讨,并提出了完善和修改建议。此外,还对《规程》附录中折管、拱管计算实例中的一些计算步骤与实际不符之处提出了建议。希望对该规程的应用和进一步的修编提供有价值的参考。     

A simple and sensitive aptasensor with rolling circle amplification for viable Cronobacter sakazakii detection in powdered infant formula

Cronobacter sakazakii is a foodborne, emerging opportunistic pathogen that causes severe bacteremia, necrotizing enterocolitis, and sepsis with a mortality rate of up to 80%. In this study, we developed a simple and sensitive fluorescent turn-off aptasensor with rolling circle amplification assay for viable C. sakazakii detection in powdered infant formula. The results showed that the proposed aptasensor has good performance and specificity for detecting viable C. sakazakii in pure culture and powdered infant formula samples within 3 h. Under the optimal reaction conditions, there is a linear relationship between fluorescent intensity at 490 nm and logarithmic concentration of C. sakazakii in the range of 2.7 × 10⁵ to 2.7 × 10² cfu/mL, with a limit of detection of 2.7 × 10² cfu/mL in pure culture. The proposed aptasensor achieved a recovery of 104 to 111% in pure culture, and 96 to 107% in spiked powdered infant formula samples. The proposed aptasensor does not require complicated DNA extraction steps or antibodies, and can be performed at 37°C, making it a convenient and sensitive strategy for C. sakazakii detection.     

泰勒公式在不等式中的应用

泰勒公式在高等数学中应用广泛.在简单介绍泰勒公式的基础上，通过具体实例，将泰勒公式（包含佩亚诺型余项、拉格朗日型余项）应用于高阶不等式的证明中，最后对证明步骤及注意事项进行相应分析，以便为学生学习泰勒公式提供参考。     

United friction resistance in open channel flows

It is now over half a century since Keulegan conducted his open channel flow experiments.Over the past decades,many empirical formulae were proposed based on his results,however,there is still not a combined expression to describe the effects of friction over all hydraulic regions in open channel flows.Therefore,in this letter,based on the analysis of the implicit model and the logarithmic matching method,the results of Keulegan(for authentic experiment data are no longer available,here we adopt the analytical solutions given by Dou)are rescaled into one monotone curve by combining the Reynolds number and the relative roughness of the river bed.A united expression that could cover the entire turbulence regions and be validated with Dou’s analytical solutions is suggested to estimate the friction factor throughout the turbulent region in open channel flows,with higher accuracy than that of the previous formulas.     

Consumer confidence in the safety of milk and infant milk formula in China

A series of food safety incidents related to domestically produced dairy in China harmed consumer confidence and caused a dramatic decrease in dairy consumption from 2008 to 2010. Compared with previous studies that mainly assessed consumer confidence in food or dairy in general, this study focused on 2 specific dairy products, milk and infant milk formula (IMF). Based on data from 934 Chinese consumers, confidence in the safety of milk and IMF was measured by using a multi-item scale with 2 dimensions—optimism and pessimism. We found that Chinese consumers were optimistic about the safety of milk and IMF but, at the same time, were concerned about the risks related to milk and IMF. Chinese consumers have less confidence in IMF than in milk. Structural equation modeling indicated that consumer trust in manufacturers and third parties in the dairy supply chain and confidence in other foods, such as meat and fish, can foster consumer confidence in the safety of milk and IMF, while the extent of recall of the melamine infant formula incident in 2008 and trait worry exert negative effects. In addition, consumers with more children or less family income are likely to be more confident in domestically produced IMF. These insights into consumer confidence and its determinants can assist dairy supply chains and regulatory institutions in formulating effective risk communication strategies to strengthen consumer confidence.     

Methodology for spectral emissivity measurement by means of single color pyrometer

The application of non-intrusive optical devices, such as infrared pyrometers able to measure the temperature of surfaces, makes possible the evaluation of emissivity curve of the tested materials at different temperature values. In this paper the authors propose a methodology for the spectral emissivity measurement by means of a single color pyrometer providing a semi-empirical formula, obtained experimentally at CIRA’s laboratory. The semi-empirical formula allows to know the actual emissivity value of the sample’s surface for whatever emissivity value set up on the pyrometer. The agreement between the experimental emissivity and the emissivity predicted by semi-empirical formula was verified.