A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.     

Bounds for the perimeter of an ellipse

In this paper, we present several bounds for the perimeter of an ellipse, which improve some well-known results.     

Periodic solutions for second order singular damped differential equations

We study the existence of positive periodic solutions for second order singular damped differential equations by combining the analysis of the sign of Green?s functions for the linear damped equation, together with a nonlinear alternative principle of Leray–Schauder. Recent results in the literature are generalized and significantly improved.     

A multi-stage financial hedging approach for the procurement of manufacturing materials

This paper addresses the problem of mitigating procurement risk that arises from volatile commodity prices by proposing a hedging strategy within a multi-stage time frame. The proposed multi-stage hedging strategy requires a commodity futures position to be correctly initialised and rebalanced with adequate volumes of short/long positions, so as to reduce the volatility in the total procurement cost that would otherwise be generated by varying commodity spot prices. The novelty in the approach is the introduction of the rebalancing of commodity futures position at defined intermediate stages. To obtain an efficient or near optimal multi-stage hedging strategy, a discrete-time stochastic control model (DSCM) is developed. Numerical experiments and Monte Carlo simulation are used to show that the proposed multi-stage hedging strategy compares favourably with the minimal-variance hedge and the one-stage hedge. A close-form optimal solution is also presented for the case when procurement volume and price are independent.     

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.     

A new differential scanning calorimetry based approach for the characterization of peracid resin

Differential scanning calorimetry was used to trace the heat of decomposition of the peracid groups (ΔH_d) in the oxidized EVA-g-AA resin. From the correlation between ΔH_d and the oxidation capacity measured by iodometry, it was found that 35 ± 5 cal of energy evolved per miliequivalent of peracid group decomposed. The ΔH_d values are also useful in finding the optimum condition for oxidation of acid groups and can be used to investigate the distribution of active peracid groups across the matrix. The stability and the activation energy of decomposition of grafted type peracid resin were also studied, where the activation energy of decomposition was calculated to be 13.4 kcal/mol.     

Pd-Based Metallenes for Fuel Cell Reactions

Pd-based metallenes, atomically thin layers composed primarily of under-coordinated Pd atoms, have emerged as the newest members in the family of two-dimensional (2D) nanomaterials. Moreover, the unique physiochemical properties, high intrinsic activity associated with metallenes coupled with the ease of applying chemical modifications result in great potential in catalyst engineering for fuel cell reactions. Especially in recent years, interest in Pd-based metallenes is growing, as evidenced by surge in available literatures. Herein, we have reviewed the recent findings achieved in Pd-based metallenes in fuel cells by highlighting the technologies available for deriving metallenes and manifesting the modification strategies for designing them to better suit the application demand. Moreover, we also discuss the perspective insights of Pd-based metallenes for fuel cells regarding the surfactant-free synthesis method, strain engineering, constructing high-entropy alloy, and so on.     

Products of two 1ϕ1 series and implications

An expansion formula into bivariate formal power series is established that implies, as consequences, three remarkable identities of partial theta functions due to Warnaar (2003), Schilling–Warnaar (2002) and Andrews–Warnaar (2007).     

Synthesis of multi-walled carbon nanotubes using CoMnMgO catalysts through catalytic chemical vapor deposition

The Co Mg O and Co Mn Mg O catalysts are prepared by a co-precipitation method and used as the catalysts for the synthesis of carbon nanotubes（CNTs） through the catalytic chemical vapor deposition（CCVD）. The effects of Mn addition on the carbon yield and structure are investigated. The catalysts are characterized by temperature programmed reduction（TPR） and X-ray diffraction（XRD） techniques, and the synthesized carbon materials are characterized by transmission electron microscopy（TEM） and thermo gravimetric analysis（TG）. TEM measurement indicates that the catalyst Co Mg O enclosed completely in the produced graphite layer results in the deactivation of the catalyst. TG results suggest that the Co Mn Mg O catalyst has a higher selectivity for CNTs than Co Mg O. Meanwhile, different diameters of CNTs are synthesized by Co Mn Mg O catalysts with various amounts of Co content, and the results show that the addition of Mn avoids forming the enclosed catalyst, prevents the formation of amorphous carbon, subsequently promotes the growth of CNTs, and the catalyst with decreased Co content is favorable for the synthesis of CNTs with a narrow diameter distribution.The Co Mn Mg O catalyst with 40% Co content has superior catalytic activity for the growth of carbon nanotubes.     

静水压对立方钙钛矿CsSnX3(X=I, Br, Cl)光电性质的第一性原理探究

全无机无铅卤化物钙钛矿已经成为重要的新一代太阳能电池材料.采用密度泛函理论的第一性原理研究了不同静水压下CsSnX₃(X=I, Br, Cl)材料的晶体结构,电子结构和光学性能,并分析了其内在联系.结果表明施加静水压可使材料中Sn-X键长减小,使原子之间的耦合增强,带隙值减小,且随着卤族元素半径的增大,压力效应越明显;随着压力的增加,材料的吸收系数和复折射率增大,吸收光谱出现红移现象,在可见光区和近红外光区吸收增强.相比CsSnBr₃和CsSnCl₃,CsSnI₃在可见光区吸收最佳且受压力作用影响最小,更适用于钙钛矿太阳能电池材料.