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By using vertex operator representation of polynomial Lie algebra b ∞ (n) , a theoretical interpretation of coupled BKP hierarchy is given, where corresponding Hirota bilinear equations are derived. Then based upon this, a wave function matrix is introduced, so that we can construct the corresponding dressing operator matrix and obtain the coupled BKP constraints and Sato equation, which allows us to define the Lax operator matrix and obtain the Lax equation. It is found that the coupled BKP hierarchy is a special case of matrix KP theory. Lastly, we present the Bäcklund–Darboux transformations for the coupled BKP equations from both fermionic and bosonic pictures. [ABSTRACT FROM AUTHOR]

The modified BKP (mBKP) hierarchy is an important integrable hierarchy related with BKP hierarchy. Darboux transformation is a powerful method to obtain various solutions of integrable systems. But for mBKP hierarchy, it is usually very difficult to construct the corresponding Darboux transformations, since it has a more complicated constraint on the Lax operator, compared with the BKP hierarchy. In this paper, we use the fermionic approach to obtain the explicit Darboux transformation operators of the mBKP hierarchy starting from the changes in tau functions. Also we investigate the relations among these new Darboux transformation operators. It is usually very difficult to convert the changes in tau functions to the ones in the Lax operator, while here we provide one successful example. [ABSTRACT FROM AUTHOR]

The modified Kadomtsev-Petviashvili hierarchy of B type (mBKP hierarchy) and its constrained cases are investigated from the aspect of the Lax formulation. Starting from the Lax equation of the mBKP hierarchy, we firstly derive the bilinear equations and show the existence of the tau functions. Then the additional symmetries are constructed, and the corresponding generator is showed to be the squared eigenfunction symmetry. After that, the actions of the additional symmetries on the tau functions are given. At last, the Lax formulation of the constrained mBKP hierarchy is investigated and the corresponding bilinear equations are also discussed. [ABSTRACT FROM AUTHOR]

A new generalization of the constrained modified KP hierarchy is presented in this paper, that is, (Lk)≤0=q∂−1r∂+cL−1$$ {\left({L}^k\right)}_{\le 0}=q{\partial}^{-1}r\partial +c{L}^{-1} $$. Then two equivalent formulations of this new generalization are given. One is the bilinear equations in terms of the wave functions and tau functions, where the corresponding Hirota bilinear forms are discussed. Another is expressed by the constraints on the tau functions. [ABSTRACT FROM AUTHOR]

Although advanced anode materials for the lithium‐ion battery have been investigated for decades, a reliable, high‐capacity, and durable material that can enable a fast charge remains elusive. Herein, we report that a metal phosphorous trichalcogenide of MnPS3 (manganese phosphorus trisulfide), endowed with a unique and layered van der Waals structure, is highly beneficial for the fast insertion/extraction of alkali metal ions and can facilitate changes in the buffer volume during cycles with robust structural stability. The few‐layered MnPS3 anodes displayed the desirable specific capacity and excellent rate chargeability owing to their good electronic and ionic conductivities. When assembled as a half‐cell lithium‐ion battery, a high reversible capacity of 380 mA h g−1 was maintained by the MnPS3 after 3000 cycles at a high current density of 4 A g−1, with a capacity retention of close to or above 100%. In full‐cell testing, a reversible capacity of 450 mA h g−1 after 200 cycles was maintained as well. The results of in‐situ TEM revealed that MnPS3 nanoflakes maintained a high structural integrity without exhibiting any pulverization after undergoing large volumetric expansion for the insertion of a large number of lithium ions. Their kinetics of lithium‐ion diffusion, stable structure, and high pseudocapacitance contributed to their comprehensive performance, for example, a high specific capacity, rapid charge–discharge, and long cyclability. MnPS3 is thus an efficient anode for the next generation of batteries with a fast charge/discharge capability. [ABSTRACT FROM AUTHOR]

Conductive polymer polypyrrole (PPy)-coated lithium-rich manganese-based Li1.2Mn0.54Ni0.13Co0.13O2 (LMNCO) nanotube cathode materials were synthesized by electrospinning and subsequently subjected to low-temperature vapor-phase polymerization. X-ray diffraction (XRD), scanning electron microscopy (SEM) and high-resolution transmission electron microscopy (HRTEM) results confirm that the successful coating of the PPy layer (~2 nm) on the surface of LMNCO nanotubes did not destroy their morphologies or structures. Electrochemical tests indicate that the electrochemical performance of PPy-coated LMNCO nanotubes has been significantly enhanced. At a rate of 1 C, the discharge capacity of the PPy-coated LMNCO cell is 200.1 mAh g−1, and the capacity retention is 99% after 120 cycles. This excellent stability is attributed to the inhibition of side reactions and the protective function of the tubular structure due to the PPy coating layer. Additionally, the rate capability is also improved at a high current density due to the higher electronic and ionic conductivity. [ABSTRACT FROM AUTHOR]

Non‐noble metal catalysts now play a key role in promoting efficiently and economically catalytic reduction of CO2 into clean energy, which is an important strategy to ameliorate global warming and resource shortage issues. Here, a non‐noble bimetallic catalyst of CoFe/Fe3O4 nanoparticles is successfully designed with a core–shell structure that is well dispersed on the defect‐rich carbon substrate for the hydrogenation of CO2 under mild conditions. The catalysts exhibit a high CO2 conversion activity with the rate of 30% and CO selectivity of 99%, and extremely robust stability without performance decay over 90 h in the reverse water gas shift reaction process. Notably, it is found that the reversible exsolution/dissolution of cobalt in the Fe3O4 shell will lead to a dynamic and reversible deactivation/regeneration of the catalysts, accompanying by shell thickness breathing during the repeated cycles, via atomic structure study of the catalysts at different reaction stages. Combined with density functional theory calculations, the catalytic activity reversible regeneration mechanism is proposed. This work reveals the structure–property relationship for rational structure design of the advanced non‐noble metallic catalyst materials with much improved performance. [ABSTRACT FROM AUTHOR]

MnS has been explored as an anode material for lithium-ion batteries due to its high theoretical capacity, but low electronic conductivity and severe volume change induce low reversible capacity and poor cycling performance. In this work, the nanocapsule consisting of MnS nanopolyhedrons confined in independent, closed and conductive hollow polyhedral nanospheres is prepared by embedding MnCO3 nanopolyhedrons into ZIF-67, followed by coating of RF resin and gaseous sulfurization/carbonization. Benefiting from the unique nanocapsule structure, especially inner CoS/C shell and outer pure C shell, the MnS@CoS/C@C composite as anode material presents excellent cycling performance (674 mAh g−1 at 1 A g−1 after 300 cycles; 481 mAh g−1 at 5 A g−1 after 300 cycles) and superior rate capability (1133.3 and 650.6 mAh g−1 at 0.1 and 4 A g−1), compared to the control materials (MnS and MnS@CoS/C) and other MnS composites. Kinetics measurements further reveal a high proportion of the capacitive effect and low reaction impedance of MnS@CoS/C@C. SEM and TEM observation on the cycled electrode confirms superior structural stability of MnS@CoS/C@C during long-term cycles. Excellent lithium storage performance and the convenient synthesis strategy demonstrates that the MnS@CoS/C@C nanocapsule is a promising high-performance anode material. [ABSTRACT FROM AUTHOR]

Antimony-based electrodes have earned a place among anodes for sodium-ion batteries (SIBs) on account of their high specific capacity and appropriate reaction potential. However, significant volume changes during charge/discharge cycles directly lead to poor cycling ability, prohibiting their further practical application. Doping is recognized as a valid approach to tuning the electrochemical properties of electrodes for better electrochemical performances. In this work, Se-doped Sb solid solution (Sb1-xSex) nanoparticles are reported as a variety of anode materials for SIBs via a straightforward solvothermal method. The nanoparticles are uniformly distributed with a small size of about 20 nm. The diffusion properties of Na+ are studied by the galvanostatic intermittent titration technique (GITT), and the coefficient is acquired by calculation to be 1.8 × 10–12 cm2 s–1. The electrochemical measurement results show that the nanoparticle electrode yields reversible capacities of 514, 500, 464, and 313 mAh g–1 at 0.5, 1, 2, and 5 A g–1, respectively. An initial charging specific capacity of 556.3 mAh g–1 could be stable for 100 cycles at 100 mA g–1, retaining up to 96.8% of battery capacity. It is believed that a solution is provided based on our findings to polish the electrochemical characteristics applied in SIBs by means of doping. [ABSTRACT FROM AUTHOR]

Multilayer graphene (MLG) prepared via ultrasonic exfoliation has many advantages such as its low-cost and defect-free nature, high electronic conductivity, and large specific surface area, which make it an apt conductive substrate for TiO2 composites. To synthesize graphene/TiO2 hybrids, traditional methods that greatly depend on the chemical bond of oxygen-containing functional groups on graphene with titanium cations are not applicable due to the absence of these functional groups on MLG. In this work, a facile chemical method is developed to directly deposit TiO2 on the MLG surface without the introduction of chemically active groups. With this method, four types of TiO2 materials, that is pure anatase TiO2 nanoparticles, a mixture of anatase TiO2 nanoparticles and rutile TiO2 nanoflowers, pure rutile TiO2 nanoflowers, and pure rutile TiO2 nanorods, are homogeneously anchored on the MLG surface by controlling the amount of HCl in the reactant. Interestingly, the rutile TiO2 nanorods in the TiO2/MLG composite are assembled by many TiO2 nanowires with an ultra-small diameter and ultra-long length, which provides a better synergetic effect for high performances as LIB anodes than other composites. A specific capacity of 631.4 mAh g−1 after 100 cycles at a current density of 100 mA g−1 is delivered, indicating it to be a valuable LIB anode material with low cost and high electrochemical performances. [ABSTRACT FROM AUTHOR]

Supercapacitors have played an important role in electrochemical energy storage. Recently, researchers have found many effective methods to improve electrode materials with more robust performances through the increasing volume of scientific publications in this field. Though nickel cobaltite (NiCo2O4), as a promising electrode material, has substantially demonstrated potential properties for supercapacitors, its composites usually show much better performances than the pristine NiCo2O4. The combination of carbon-based materials and NiCo2O4 has been implemented recently due to the dual mechanisms for energy storage and the unique advantages of carbon materials. In this paper, we review the recent research on the hybrids of NiCo2O4 and carbon nanomaterials for supercapacitors. Typically, we focused on the reports related to the composites containing graphene (or reduced graphene oxide), carbon nanotubes, and amorphous carbon, as well as the major synthesis routes and electrochemical performances. Finally, the prospect for the future work is also discussed. [ABSTRACT FROM AUTHOR]

Metal–organic framework (MOF)-derived pure ZnO and Cu-doped ZnO nanocages were fabricated by calcining a zeolitic imidazole framework (ZIF-8) and Cu-doped ZIF-8. The morphology and crystal structure of the samples were characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM), and high-resolution transmission electron microscopy (HRTEM). It was found that Cu doping did not change the crystal structures and morphologies of MOF-derived ZnO nanocages. The H2S-sensing properties of the sensors based on ZnO and Cu-doped ZnO nanocages were investigated. The results indicated that the H2S-sensing properties of MOF-derived ZnO nanocages were effectively improved by Cu doping, and the optimal doping content was 3 at%. Moreover, 3 at% Cu-doped ZnO nanocages showed the highest response of 4733 for 5 ppm H2S at 200 °C, and the detection limit could be as low as 20 ppb. The gas-sensing mechanism was also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the constrained Kadomtsev–Petviashvili (KP) and modified KP (mKP) hierarchies. Squared eigenfunction (SE) symmetry is an important symmetry defined by eigenfunctions and adjoint eigenfunctions, which can be viewed as the generator of the additional symmetries. Due to special constraints on the Lax operators, it is found that there are three different cases for the generating eigenfunctions and adjoint eigenfunctions of the SE symmetries. Then we discuss the changes of the SE symmetries under the Miura links between the KP and mKP hierarchies. Next, the exponential of the SE symmetries is shown to be the binary Darboux transformations. At last based upon the results above, new additional symmetries for the constrained KP and mKP hierarchies are constructed, different from the additional Virasoro symmetries defined by Aratyn. [ABSTRACT FROM AUTHOR]