左右手系材料界面处全反射行为的特性

基于电磁场理论，推导了左右手系材料界面处发生全反射时的物理特性，分析了相位变化情况.提出利用左右手系材料构成周期性结构，观测全反射时介质中隐失波干涉的实验设想，并从理论上计算了干涉条纹的分布. 关键词： 左手材料 负折射率 全反射 隐失波     

SYNTHESIS AND PROPERTIES OF ANILING ANILING AND 0-AMINOBENZENESULFONIC ACID COPOLYMER*

Poly(aniline- co-o-aminobenzenesulfonic acid) (PAOABSA) as a water soluble conducting polymerwas synthesized by chemical polymerization. The productivity and the room-temperature conductivity of thecopolymer were measured as a function of the reaction conditions, such as reaction temperature, the ratio ofoxidant to monomer and the degree of sulfonation defined as the ratio of sulfur to nitrogen atoms(S/N). Themain results obtained are summarized as follows : (1) lower reaction temperature (at about 0℃) is favorablefor the enhancement of the room-temperature conductivity of the copolymer; (2) higher content of oxidant isunfavorable for increasing the room-temperature conductivity of the copolymer; (3) both productivity androom-temperature conductivity of the copolymer decrease with increase of the degree of sulfonation whichwas always lower than 0.5 even an excess of o-aminobenzenesulfonic acid was added, probably because thereactivity ratio of aniline (γ=2.99± 0.05) is much higher than that of o-aminobenzenesulfonic acid (γ_2 = 0.06±0.02) estimated by using Fineman-Ross method and least square method.     

Vertically Grown Few-Layer MoS2 Nanosheets on Hierarchical Carbon Nanocages for Pseudocapacitive Lithium Storage with Ultrahigh-Rate Capability and Long-Term Recyclability

Molybdenum disulfide (MoS₂) is an intensively studied anode material for lithium-ion batteries (LIBs) owing to its high theoretical capacity, but it is still confronted by severe challenges of unsatisfactory rate capability and cycle life. Herein, few-layer MoS₂ nanosheets, vertically grown on hierarchical carbon nanocages (hCNC) by a facile hydrothermal method, introduce pseudocapacitive lithium storage owing to the highly exposed MoS₂ basal planes, enhanced conductivity, and facilitated electrolyte access arising from good hybridization with hCNC. Thus, the optimized MoS₂/hCNC exhibits reversible capacities of 1670 mAh g⁻¹ at 0.1 A g⁻¹ after 50 cycles, 621 mAh g⁻¹ at 5.0 A g⁻¹ after 500 cycles, and 196 mAh g⁻¹ at 50 A g⁻¹ after 2500 cycles, which are among the best for MoS₂-based anode materials. The specific power and specific energy, which can reach 16.1 kW and 252.8 Wh after 3000 cycles, respectively, indicate great potential in high-power and long-life LIBs. These findings suggest a promising strategy for exploring advanced anode materials with high reversible capacity, high-rate capability, and long-term recyclability.     

Perfect matchings extend to two or more hamiltonian cycles in hypercubes

Kreweras conjectured that every perfect matching of a hypercube $Q_n$ for $n\ge 2$ can be extended to a hamiltonian cycle of $Q_n$. Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of $Q_n$ for $n\ge 2$ can be extended to two or more hamiltonian cycles of $Q_n$. In this paper, we prove that every perfect matching of $Q_n$ for $n\ge 4$ can be extended to at least $2^{2^{n?4}}$ different hamiltonian cycles of $Q_n$.     

Phase transition layers with boundary intersection for an inhomogeneous Allen–Cahn equation

We consider the nonlinear problem of inhomogeneous Allen–Cahn equation

${?}^2\mathrm{\Delta }u+V(y)u(1?u^2)=0\text{in}\mathrm{\Omega },\frac{?u}{?\nu }=0\text{on}?\mathrm{\Omega },$

where Ω is a bounded domain in ${\mathbb{R}}^2$ with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on $\overline{\mathrm{\Omega }}$. Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional ${\int }_{\mathrm{\Gamma }}{V}^{1/2}$. We can prove that there exists a solution $u_{?}$ such that: as $?\to 0$, $u_{?}$ approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ.     

Pricing Derivatives under a Markov Skeleton Process

In this paper, it is assumed that the underlying is a Markov skeleton process (abbreviated MSP): this process can be better reflecting the instability of the financial market. Using the properties of Markov skeleton process, the characteristic function of the price process is given, combined with fast Fourier transform (FFT) method, the pricing formula of derivatives under the Markov skeleton process is given. The results of this paper can be applied to price other financial derivatives, and it enriching the pricing theory of financial derivatives.     

Exploring Microstructures and Interphase Properties of Surface- Grafted Diblock Copolymers in a Homopolymer Melt by Self-Consistent Field Theory Simulations

Polymeric self-consistent field theory is used to investigate microstructures and interphase properties of diblock copolymers grafted onto solid surfaces in a homopolymer melt. The calculations show that the grafted diblock copolymers can self-assemble into hemispherical microstructures at low grafting densities of the diblock copolymers. The morphology transforms into hemicylinder-like and sandwich-like lamellar microstructures with an increase in the chain-grafting density. The effective thickness of the grafted block layer and the interphase width between the homopolymer melt and the grafted copolymers strongly depend on the physicochemical parameters of the system, such as the composition of the grafted copolymer, the chemical incompatibility between the different components, the length ratio of grafted copolymer to homopolymer, and the grafting density of the diblock copolymers. In addition, the above computational results of microphase-separated structures and interphase properties are qualitatively compared with our previous experimental observations. The comparison indicates that our theoretical results not only reproduce the general feature of the experimental observations, but also elucidate the internal structural information and complement the findings in the region of high grafting densities of diblock copolymers.     

Predicting Polymorphism of Electrospun Polyvinylidene Fluoride Membranes by Their Morphologies

Although electrospinning of polyvinylidene fluoride (PVDF) has been studied for more than 10 years, the crystalline phase differentiation of the electrospun mats is still normally through the combination of different characterization techniques, and the relationship between polymorphism and morphology of the fibers in electrospun PVDF membranes has never been reported. Here, we show their close relationships by conducting room-temperature electrospinning experiments on various polymer/solvent systems. The electrospun membranes full of bead-free fibers have a very high fraction of β-phase, F(β), over 90%, and high orientation, whereas the membranes comprising beads and/or a large number of beaded fibers most often result in a low fraction of β-phase (F(β) normally below 50%) and low orientation. On the other hand, electrospun membranes consisting of both bead-free fibers and a very limited number of beaded fibers showed a medium high fraction of β-phase, F(β) more than 70% but less than 90%. These findings suggest the feasibility of intuitively predicting the crystalline phase of electrospun PVDF membranes directly by their morphologies, which is obviously simple, inexpensive and convenient for future investigations.