Let be a commutative ring containing a primitive $l'$th root $\varepsilon $ of $1$. The infinitesimal q-Schur algebras over form an ascending chain of subalgebras of the q-Schur algebra , which are useful in studying representations of the Frobenius kernel of the associated quantum linear group. Let be the quantized enveloping algebra of $\mathfrak {gl}_n$ over . There is a natural surjective algebra homomorphism $\zeta _{d}$ from to . The map $\zeta _{d}$ restricts to a surjective algebra homomorphism $\zeta _{d,r}$ from to , where is a certain Hopf subalgebra of , which is closely related to Frobenius–Lusztig kernels of . We give the extra defining relations needed to define the infinitesimal q-Schur algebra as a quotient of . The map $\zeta _{d,r}$ induces a surjective algebra homomorphism , where is the modified quantum algebra associated with . We also give a generating set for the kernel of $\dot {\zeta }_{d,r}$. These results can be used to give a classification of irreducible -modules over a field of characteristic p.

In this work, the Riemann–Hilbert (RH) problem is employed to study the multiple high-order pole solutions of the cubic Camassa–Holm (cCH) equation with the term characterizing the effect of linear dispersion under zero boundary conditions and nonzero boundary conditions. Under the reflectionless situation, we generalize the residue theorem and obtain the multiple high-order pole solutions of cCH equation by solving an algebraic system. During the process of establishing the solution of RH problem, to simplify the calculations involving the implicitly expressed of variables (x, t) in the solution, we introduce a new scale (y, t) to ensure the solution of RH problem is explicitly expressed with respect to it. Finally, the exact solutions are obtained for cases involving one high-order pole and N high-order poles.

Fast neutron absorption spectroscopy is widely used in the study of nuclear structure and element analysis. However, due to the traditional neutron source pulse duration being of the order of nanoseconds, it is difficult to obtain a high-resolution absorption spectrum. Thus, we present a method of ultrahigh energy-resolution absorption spectroscopy via a high repetition rate, picosecond duration pulsed neutron source driven by a terawatt laser. The technology of single neutron count is used, which results in easily distinguishing the width of approximately 20 keV at 2 MeV and an asymmetric shape of the neutron absorption peak. The absorption spectroscopy based on a laser neutron source has one order of magnitude higher energy-resolution power than the state-of-the-art traditional neutron sources, which could be of benefit for precisely measuring nuclear structure data.

In [2], Beilinson–Lusztig–MacPherson (BLM) gave a beautiful realization for quantum $\mathfrak {gl}_n$ via a geometric setting of quantum Schur algebras. We introduce the notion of affine Schur superalgebras and use them as a bridge to link the structure and representations of the universal enveloping superalgebra ${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ of the loop algebra $\widehat {\mathfrak {gl}}_{m|n}$ of ${\mathfrak {gl}}_{m|n}$ with those of affine symmetric groups ${\widehat {{\mathfrak S}}_{r}}$ . Then, we give a BLM type realization of ${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ via affine Schur superalgebras.

The first application of the realization of ${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ is to determine the action of ${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ on tensor spaces of the natural representation of $\widehat {\mathfrak {gl}}_{m|n}$ . These results in epimorphisms from $\;{\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ to affine Schur superalgebras so that the bridging relation between representations of ${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ and ${\widehat {{\mathfrak S}}_{r}}$ is established. As a second application, we construct a Kostant type $\mathbb Z$ -form for ${\mathcal U}_{\mathbb Q}(\widehat {\mathfrak {gl}}_{m|n})$ whose images under the epimorphisms above are exactly the integral affine Schur superalgebras. In this way, we obtain essentially the super affine Schur–Weyl duality in arbitrary characteristics.

To assess the relationship between the neutrophil-to-lymphocyte ratio (NLR) and related parameters to the severity of coronavirus disease 2019 (COVID-19) symptoms. Clinical data from 38 COVID-19 patients who were diagnosed, treated and discharged from the Qishan Hospital in Yantai over the period from January to February 2020 were analysed. NLR and procalcitonin (PCT) were determined in the first and fourth weeks after their admission, along with the clinical characteristics and laboratory test results of these patients. Based on results as obtained on the first and fourth weeks after admission, five indices consisting of NLR, white blood cells, neutrophils, lymphocytes (LY) and monocytes (MON) were selected to generate receiver operating characteristic curves, while optimal cutoff values, sensitivities and specificities were obtained according to the Yuden index. Statistically significant differences in neutrophils, LY and the NLR were present in the severe vs. moderate COVID-19 group from the first to the fourth week of their hospitalisation. The cut-off value of NLR for predicting the severity of COVID-19 was 4.425, with a sensitivity of 0.855 and a specificity of 0.979. A statistically significant positive correlation was present between PCT and NLR in the severe group as determined within the first week of admission. NLR can serve as a predictor of COVID-19 disease severity as patients' progress from the first to the fourth week of their hospitalisation. The statistically significant positive correlation between levels of NLR and PCT in severe patients indicated that increases in NLR were accompanied with gradual increases in PCT.

We present a spatiotemporal model of pulse amplification in the double-pass active mirror (AM) geometry. Three types of overlap condition are studied, and the spatiotemporal scaling under the four-pulse overlapping (4PO) condition is fully characterized for the first time, by mapping the temporal and spatial segments of beam to the instantaneous gain windows. Furthermore, the influence of spatiotemporal overlaps on the amplified energy, pulse distortion and intensity profile is unraveled for both AM and zigzag configurations. The model, verified by excellent agreement between the predicted and measured results, can be a powerful tool for designing and optimizing high energy multi-pass solid-state laser amplifiers with AM, zigzag and other geometries.

We divide the corrosion products on ancient bronzes into two categories, i.e., "inward growth" and “outward growth” corrosions. Several selected Chinese ancient bronzes with the "inward growth” corrosion are studied; and their chemical compositions, microstructures and morphologies are characterized systematically. According to the results, it is found that the “inward growth” corrosion can be further divided into three types, i.e., "noble patina", "noble-like patina" and "lamellar peeling patina". We propose that the growth mechanism of the “inward growth” corrosion is that the corrosion initiates at and develops along α-Cu phase. Furthermore, the effect of alloy Sn content on the “inward growth” corrosion is also studied.

In this study, a novel brick-like NiCo2O4 material was synthesized via a facile hydrothermal method. The as-prepared NiCo2O4 material possessed high porosity with the BET specific surface area of 58.33 m2/g, and its pore size distribution was in a range of 5-15 nm with a dominant pore diameter of 10.7 nm. The electrochemical performance of the NiCo2O4 was further investigated as anode material for lithium-ion battery. The NiCo2O4 anode possessed a high lithium storage capacity up to 2353.0 mAh/g at the current density of 100 mA/g. Even at the high rate of 1 A/g, a reversible capacity of ∼600 mAh/g was still retained, and an average discharge capacity of ∼1145 mAh/g could be recovered when the current density was reduced back to 150 mA/g. Due to the simple and cost-effective process, the NiCo2O4 bricks anode material shows great potential for further large-scale applications on the area of lithium-ion battery.

Developing metal-based composite coatings with improved mechanical properties and good corrosion resistance has been an attractive research topic in recent years. Graphene (Gr), as a new type of two-dimensional (2D) carbon nanomaterial with excellent physical, chemical and mechanical properties, can be used as a reinforcement to improve hardness, tensile strength, wear and corrosion resistance of metal-based composites. There have been substantial efforts focused on the fabrication of metal-Gr composite coatings via various approaches. Electro-deposition is an effective electrochemical method with wide range of advantages, such as a fast deposition rate, simple set-up with large scale production and relatively low cost. This overview covers the previous research and development studies on metal-Gr composite coatings using electro-deposition method and the resulting properties. In addition, recent work in this area which provides a developed process with industrial production perspective, is discussed.

In this paper, a novel NiFe-LDH@ZnO composite was prepared by using a facile two-step process upon nickel foam (NF) substrate. The morphologies and chemical compositions of the samples were characterized by SEM, EDS, XRD and XPS. Photocatalytic degradation of Rhodamine B dye was tested with the samples NiFe-LDH@ZnO@NF, ZnO@NF and NiFe-LDH under the same conditions. The experimental results revealed that the NiFe-LDH@ZnO@NF composite exhibited excellent photocatalytic performance, i.e., 1.4 and 2.5 times higher than that of pure ZnO and NiFe-LDH, respectively. The reason was that the NiFe-LDH@ZnO@NF composite provided a possibility to effectively inhibit the recombination of the photogenerated electron-hole pairs, and therefore enhanced the photocatalytic efficiency. This composite is expected to have potential applications in wastewater treatment field.

As an emerging carbon material with advantages of thinnest, ultrahigh strength, superior thermal conductivity and electrical conductivity, graphene (Gr) is called the “black gold” and will have a profound applying potential in the field of materials science and engineering. Many researches concerning preparation of the Cu-Gr composite via various approaches have been reported. However, only few works are related to the electrochemical deposition method. As a simple, low cost, large scale production method, electrodeposition method has been widely used in industry for manufacturing foils involving copper-clad laminate (CCL), printed circuit board (PCB) and the negative current collector of lithium ion battery, where the copper foil not only serve as the carrier of the cathode active material but also play a role in collecting and conducting electrons. In the present article, we review the research progress on preparations and mechanical properties of the Cu-Gr composite foils by electrochemical method, and introduce our recent work in this area. The advancement of the process and the perspective industrial productions are also discussed.

In the past few years, our group worked on the area of transformation from the two-dimensional (2-D) nanocrystalline films to one-dimensional (1-D) nanomaterials by using thermal oxidation. In this paper, we overview the research work on the controllable growth processes, transformation phenomena, growth mechanisms and applications. In general, the preparation process includes the following steps: 1) prepare a pure metal nanocrystalline film via a pulse electro – deposition; 2) grow variant 1-D nanomaterials, such as carbon nanotubes (CNTs), carbon nanofibers (CNFs), and 1-D metal oxide nanoneedles involving ZnO, CuO and Fe3O4, etc. by using this film as catalyst. This process exhibits the following features: 1) the 1-D nanomaterials grow according to “base growth” model and no residual catalyst exists at the tip of the products; 2) the diameter of the 1-D nanomaterials can be controlled by controlling grain sizes of the 2-D films through adjusting pulse electro-deposition parameters; 3) it is more easily to get the 1-D nanomaterials with large area, uniform, vertical alignment and good shape on the substrates. We propose a “solid state based-up diffusion growth mechanism” for growth of the 1-D metal oxide nanoneedles, and “base growth model” for the 1-D carbon nanomaterials. The physical properties, such as Field emission and magnetics, of the 1-D metal oxide nanoneedles were studied, which showed desired values. In addition, we couple the ZnO nanoneedles with NiO, TiO2, graphene, Au nanoparticles, etc. for enhancing photocatalytic properties in the areas of environmental purification.

In this paper, a multilayer CNx/TiN composite film on high-speed steel substrate was prepared by using a multi-arc assisted DC reactive magnetron sputtering system. The cross-section observations of the fracture surface reveal that the films show a pure cleavage fracture due to its super-high hardness, and the interfacial strength between the film and substrate is associates with the film thickness, i.e., 2μm is a critical thickness for the present deposition. That is to say, there is no disbonding or cracking at the interface when the film thickness is less than 2μm, while the interfacial failure is generated if the film thickness is larger than 2μm. This direct SEM observation of the fracture surface provides a distinct image for evaluating the mechanical property and also analyzing the failure mechanism of the films.

In recent years, the graphene/metal nanoparticles (NPs) hybrids have sparked burgeoning interest in varied application fields due to its unique physicochemical properties. In this paper, we present an overview of preparation methods of the graphene/metal NPs hybrids, which includes some common routes as well as other particular strategies. In addition, we introduce a novel physical route to decorate metal NPs upon graphene sheets. Our expectation is that this review will provide references for the exploitation of emerging preparation technologies, and expand application fields for graphene/metal NPs hybrids in the future.

Since the discovery of glass-ceramics by Stookey in the 1950s, there has been increasing demand for glass-ceramics with high strength and toughness for medical, structural, and consumer electronics markets. This article reviews recent developments in composition, microstructure, and mechanical properties of glass-ceramics, with an emphasis on their mechanical performance. It reveals that glass-ceramics with strength and toughness comparable to structural ceramics, such as Al2O3, have been successfully developed. Meanwhile, efforts are being devoted to creating glass-ceramics with further improved damage resistance. With inspiration from natural materials such as jade, baddeleyite, bone, and nacre, glass-ceramics with unique microstructures and properties have been obtained. Further progress is needed in the design of novel compositions, microstructures, and phase assemblages to activate multiple toughening mechanisms in glass-ceramics for significant improvements in strength and toughness.

Supercapacitor is a newly-developed device for electrochemical energy storage with high power density, long life span, as well as rapid capture and storage of energy. Carbon-based materials, from carbon nanospheres, nanotubes and nanofibers to graphene, are the most commonly used electrode materials for supercapacitors. Our group has engaged in the research of carbon nanomaterials over the past decade. Herein we summarize some typical carbon nanomaterials and their synthetic routes based on our published works, which is expected to provide the theoretical and experimental basis for further applications on carbon-based energy storage devices.