A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations

We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties for the analysis is that certain weight averages of the approximated solutions are considered in the discretization and standard energy estimates cannot be applied directly. By introducing a new grid function, which further approximates the solution, and using ideas in some recent studies, we show that the method converges with second-order accuracy in time.     

Synthesis of high-quality single-walled carbon nanotubes by catalytic decomposition of C2H2

High-quality single-walled carbon nanotubes free of defects and amorphous carbon coating have been produced by catalytic decomposition of C2H2 over Fe-Mo/Al2O3 catalyst.     

Composites prepared by penetrating poly(ethylene oxide) chains into mesoporous silica

Mesoporous silica was synthesized by hydrolysis of tetraethylorthosilicate (TEOS, formula Si(OCH₂CH₃)₄) at ambient temperature in a basic ethanol-water solution, with cetyltrimethyl ammonium bromide as a template. It had a surface area of approximately 1,400 m²/g, and an average pore diameter of approximately 40 Å. Portions were blended into three samples of poly(ethylene oxide) (PEO) of varying molecular weights, in the hope of making novel composites by penetrating some of the PEO chains into the silica channels. Differential Scanning Calorimetry (DSC) and X-ray diffraction (XRD) were used to characterize the structures of the PEO/mesoporous silica composites after they were held at 100 °C for up to 30 min. In both experiments, the melting temperature of the PEO decreased and ultimately disappeared. These results suggest that the PEO chains did penetrate into the silica pores, and since they were constrained in the pores, their crystallization was suppressed. This provides an interesting parallel to the disappearance of the glass transition temperatures of polymers constrained in the cavities of zeolites or in the galleries of intercalated clays.     

Electrogenerated Chemiluminescence Ethanol Biosensor Based on Carbon Nanotube‐Titania‐Nafion Composite Film

Mesoporous titania‐Nafion composite doped with carbon nanotube (CNT) has been used for the immobilization of tris(2,2′‐bipyridyl)ruthenium(II) (Ru(bpy)₃²⁺) and alcohol dehydrogenase on an electrode surface to yield a highly sensitive and stable electrogenerated chemiluminescence (ECL) ethanol biosensor. The presence of CNT in the composite film increases not only the sensitivity of the ECL biosensor but also the long‐term stability of the biosensor. The present biosensor responds linearly to ethanol in the wide concentration ranges from 1.0×10^?5 M to 1.0×10^?1 M with a detection limit of 5.0×10^?6 M (S/N=3). The present ECL ethanol biosensor exhibited higher ECL response compared to that obtained with the ECL biosensor based on the corresponding composite without CNT. The present CNT‐based ECL biosensor showed good long‐term stability with 75% of its initial activity retained after 2 weeks of storage in 50 mM phosphate buffer at pH 7.0.     

h-Miura Transformation in the DYh(sl2)k Case

The h-analogue of the Sugawara operater is constructed for the Yangian double with central extension in the sl₂ case.Using the free fields realization of the quantum currents,the h-analogue Miura transformation is obtained.     

Bosonized Vertex Operators Realize Z-F Algebra for Zn Symmetric Belavin R Matrix

From the bosonization of vertex operators for A⁽¹⁾_n－1 face model given by Asai,Jimbo,Miwa and Pugai,using vertex-face correspondence,we obtain bosonized vertex operators for Z_n symmetric Belavin R matrix,which realize the Zamolodchikov-Fadeev algebra for that R matrix.     

Lagrangian Form of the Self-Dual Equations for SU(N) Gauge Fields on Four-Dimensional Euclidean Space

By compactifying the four-dimensional Euclidean space into S₂×S₂ manifold and introducing two topological relevant Wess-Zumino terms to H_n≡SL(n, c)/SU(n) nonlinear sigma model, we construct a Lagrangian form for SU(n) self-dual Yang-Mills field, from which the self-dual equations follow as the Euler-Lagrange equations.     

Multi-Hop Question Generation Using Hierarchical Encoding-Decoding and Context Switch Mechanism

Neural auto-regressive sequence-to-sequence models have been dominant in text generation tasks, especially the question generation task. However, neural generation models suffer from the global and local semantic semantic drift problems. Hence, we propose the hierarchical encoding–decoding mechanism that aims at encoding rich structure information of the input passages and reducing the variance in the decoding phase. In the encoder, we hierarchically encode the input passages according to its structure at four granularity-levels: [word, chunk, sentence, document]-level. Second, we progressively select the context vector from the document-level representations to the word-level representations at each decoding time step. At each time-step in the decoding phase, we progressively select the context vector from the document-level representations to word-level. We also propose the context switch mechanism that enables the decoder to use the context vector from the last step when generating the current word at each time-step.It provides a means of improving the stability of the text generation process during the decoding phase when generating a set of consecutive words. Additionally, we inject syntactic parsing knowledge to enrich the word representations. Experimental results show that our proposed model substantially improves the performance and outperforms previous baselines according to both automatic and human evaluation. Besides, we implement a deep and comprehensive analysis of generated questions based on their types.     

Experimental study on oblique water entry of two tandem spheres with collision effect

Journal of Visualization - In this paper, the hydrodynamic characteristics associated with oblique water entry of two tandem spheres were experimentally investigated using high-speed photography....