The Fractional Derivatives of a Fractal Function

The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.     

Existence and convergence of solutions of singular boundary value problems for second order ordinary differential equations and applications

In this paper,we consider the singular boundary value problems for second order quasilinear ordinary differential equations and prove existence and convergence on second order perturbation terms.The result is applied to solve the Riemann problem for 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathematical area.     

Three-component assembly of conjugated enyne scaffolds via E-selective olefination of ynals

Benefited by the accessible ynamido-lithium intermediates Ib from a Cu-catalyzed azide-alkyne cycloaddition in the presence of stoichiometric amounts of LiOH, a mild and flexible three-component route to conjugated enyne scaffolds was successfully achieved via a formal E-selective olefination strategy.     

Multiplicity of solutions for Kirchhoff type equations involving critical Sobolev exponents in high dimension

In this paper, we study the following Kirchhoff‐type elliptic problem where is a bounded domain with smooth boundary ?Ω, a,b,λ,μ > 0 and 1 < q < 2^?=2N/(N ? 2). When N = 4, we obtain that there is a ground state solution to the problem for q∈(2,4) by using a variational methods constrained on the Nehari manifold and also show the problem possesses infinitely many negative energy solutions for q∈(1,2) by applying usual Krasnoselskii genus theory. In addition, we admit that there is a positive solution to the equations for N≥5 under some suitable conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluation of Multiple Corona Reactor Modes and the Application in Odor Removal

Effects of multiple corona reactor modes on pulse characteristics, energy transfer efficiency, and odor (H₂S and NH₃) removal were investigated experimentally by the wire-plate corona reactor(s). The removal efficiency of H₂S was only 91% and the energy consumption was 16.1 Wh m⁻³ by the single mode with a gas-flow rate of 23 m³ h⁻¹ and an initial concentration of 200 mg m⁻³. At the same experimental conditions, almost 100% removal efficiency was achieved and the energy consumption was only 12.8 and 14.9 Wh m⁻³ by the series and parallel modes. In the case of 50 mg m⁻³ NH₃ removal at the same gas-flow rate, the removal efficiencies with the single mode, the series and parallel modes were 64, 92 and 70%, respectively. The energy requirement did not increase at the same residence time under the experimental conditions of the single mode with a gas-flow rate of 11.5 m³ h⁻¹ and the series or parallel mode with a gas-flow rate of 23.0 m³ h⁻¹. The experimental results indicate that the series and parallel modes are effective in saving energy consumption, improving removal ability and efficiency, especially for the series mode.     

Boron content dependance of magnetoimpedance in Fe91−xZr5BxNb4 alloys

A systematic investigation of the influence of B content on the magnetoimpedance (MI) effect in melt-spun Fe_91−xZr₅B_xNb₄ (FZBN, 0 ? x ? 30) ribbons has been performed within a frequency range, f ∼ 310-1110 kHz and under a varying dc magnetic field (H_dc) up to 70 Oe. The MI effect is not observed in the sample with x ? 5 but within the range 8 ? x ? 30. A distinct MI effect has been observed with a maximum change of 180% at around 1.1 MHz in the sample with x = 20, coincident with a saturation magnetic field of 66 Oe and a field sensitivity of about 7%/Oe. Magnetic measurements reveal that the MI effect and B content dependence of the effect are closely related to coercivity of the FZBN alloy series, except for the sample with 20 at.%. The drastic MI ratio observed in the sample with x = 20 is ascribed to its special microstructure. The mechanism of the MI effect in FZBN alloys and of the significant MI value appearing at a B content of x = 20 is discussed in this paper.     

Inhomogeneity of composition in near‐stoichiometric LiNbO3 single crystal grown from Li rich melt

A near‐stoichiometric LiNbO₃ single crystal has been grown by the Czochralski technique from a melt of 58.5 mol% Li₂O. Its composition homogeneity was assessed by measuring the UV absorption edge. It was found that the maximum composition difference is about 0.03 mol% in the radial direction and 0.05 mol% in the axial direction. Differential scanning calorimetry (DSC) analysis was performed on the powder from the synthesized raw material and the frozen melt after crystal growth. The analytical results indicate that, during crystal growth, the magnitude of lithium volatilization from the melt surface is more than the degree of segregation from the crystal. The volatilized lithium diffuses into the crystal to compensate for the lithium segregation in the LiNbO₃ crystal. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vertical Bridgman growth and characterization of large ZnGeP2 single crystals

The growth of ZnGeP₂ crystals by seeded Vertical Bridgman method was studied. High-quality near-stoichiometric ZnGeP₂ single crystals obtained were of 20–30 mm in diameter and 90–120 mm in length. By selection of the seed crystallographic orientation the single crystal ingots without cracks and twins were grown, as shown by X-ray diffraction. The infrared transmission property of the ZnGeP₂ crystals was studied by the calculated optical absorption coefficient spectra. The results showed that after thermal annealing of the crystals the optical absorption coefficient was ～0.10 cm^?1 at 2.05 μm, and ～0.01 cm^?1 at 3–8 μm. The rocking curves patterns of the (4 0 0) reflection demonstrated that the as-grown single crystals possessed a good structural quality. The composition of the crystals was close to the ideal stoichiometry ratio of 1:1:2. The low-loss typical ZnGeP₂ samples of 6 mm×6 mm×15 mm in sizes were cut from the annealed ingots for optical parametric oscillation experiments. The output power of 3.2 W was obtained at 3–5 μm when the incident pumping power of 2.05 μm laser was 9.4 W, and the corresponding slope efficiency and the conversion efficiency were 44% and 34%, respectively.     

Crystallisation and performance characteristics of high‐temperature annealed electroless Ni‐W‐P coatings

Electroless deposition of Ni–P based alloys is a well‐known commercial process that has numerous applications because of their excellent anticorrosive and wear properties. However, for some special occasions, like the components for gas making furnaces in chemical fertiliser industry, the coatings must be reinforced to withstand short‐term high temperatures between 600 °C and 700 °C as well as light erosive wear. Therefore, co‐deposition of high melting point metallic element, W, has been considered as a preferred choice. In the present study, two Ni–W–P alloy coatings were deposited on mild steel panels from different alkaline baths. The microstructures of the annealed coatings were characterised by quantitative XRD, XPS and SEM/EDS analysis techniques and their microhardness, friction and wear behaviour, corrosion mechanism as well as microstrain and residual stress are discussed in comparison with the as‐plated state. The results indicate that the hardness mainly depends on the volume fraction and crystallite size of Ni₃P phase; the uniform corrosion in sulfuric acid solution is closely related to the ratio of I_Ni/I_Ni3P as well as grain size. The wear mechanism of the high‐temperature annealed coating is dominated by abrasive wear, but the wear in the early stages started from mild adhesive wear caused by adhesion between the friction couples. Electroless deposited Ni‐W‐P alloys with high phosphorus present relatively good properties, including hardness, wear and corrosion resistance when 700 °C is applied for annealing process.