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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]

By principal representation of toroidal Lie algebra sl 2 tor , we construct an integrable system: Bogoyavlensky–modified KdV (B–mKdV) hierarchy, which is (2 + 1) -dimensional generalization of modified KdV hierarchy. Firstly, bilinear equations of B–mKdV hierarchy are obtained by fermionic representation of sl 2 tor and boson–fermion correspondence, which are rewritten into Hirota bilinear forms. Also Fay-like identities of B–mKdV hierarchy are derived. Then from B–mKdV bilinear equations, we investigate Lax structure, which is another equivalent formulation of B–mKdV hierarchy. Conversely, we also derive B–mKdV bilinear equations from Lax structure. Other equivalent formulations of wave functions and dressing operator are needed when discussing bilinear equations and Lax structure. After that, Miura links between Bogoyavlensky–KdV hierarchy and B–mKdV hierarchy are discussed. Finally, we construct soliton solutions of B–mKdV hierarchy. [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]

In this paper, we construct a new integrable hierarchy by using charged free boson and Friedan–Martinec–Shenker (FMS) bosonization, called modified bosonic integrable hierarchy, which is an anologue of the classical (l − l ′) –th modified KP hierarchy. Firstly, the representation of g l ˆ ∞ is given by using charged free bosons. Then the modified bosonic integrable hierarchy is proposed. Next after discussing FMS bosonizations in the language of lattice vertex algebra, bilinear equations of modified bosonic integrable hierarchy are constructed by FMS bosonization, which are rewritten into Hirota bilinear equations by using Hirota derivatives. At last, we consider solutions of this modified bosonic integrable hierarchy. [ABSTRACT FROM AUTHOR]

The gauge transformation is a powerful method to solve integrable hierarchies. In the discrete KP hierarchy, there are two basic gauge transformations, T D (q) = Λ(q) ∘ Δ ∘ q −1 and T I (r) = Λ−1 (r −1) ∘ Δ−1 ∘ r. This paper is concerned with several integrable properties of the discrete KP hierarchy found by means of gauge transformations. The successive applications of T I to the constrained discrete KP hierarchy have been presented. Meanwhile, we derive two novel discrete equations as the orbits of gauge transformations T D and T I for the constrained KP hierarchy. Moreover, with the help of the spectral representations and the gauge transformations, Fay-similar equations of the tau functions for the constrained discrete KP have been investigated. In addition, we also discuss the relation between the gauge transformation and an additional symmetry for the discrete KP hierarchy. [ABSTRACT FROM AUTHOR]

In this paper, the modified KP hierarchy in the Kupershmidt–Kiso version is extended to the super case by Kac–van de Leur construction, that is, using highest weight representations of the even part in the tensor product of the infinite-dimensional Lie superalgebra gl∞|∞ with Grassmann algebra G. First, the super modified KP (SmKP) hierarchy is constructed in terms of superfermionic bilinear equations. Then, the superbosonic form of the SmKP hierarchy is given by super boson–fermion correspondence. With the help of super Hirota bilinear operators, the corresponding super Hirota bilinear equations of the SmKP hierarchy are obtained. Next, the Darboux transformations of this new SmKP hierarchy are expressed in the form of free superfermions and various solutions are derived. Finally, the super bilinear equations in the form of super wave functions are also constructed from the superbosonic ones, which is hoped to be helpful to obtain the corresponding Lax structures. [ABSTRACT FROM AUTHOR]

It was proved in 2010 that the principal Kac–Wakimoto hierarchy of type |$D$| is a reduction of the 2-component BKP hierarchy. On the other hand, it is known that the total descendant potential of a singularity of type |$D$| is a tau-function of the principal Kac–Wakimoto hierarchy. We find explicitly the point in the Grassmannian of the 2-component BKP hierarchy (in the sense of Shiota) that corresponds to the total descendant potential. We also prove that the space of tau-functions of Gaussian type is parametrized by the base of the miniversal unfolding of the simple singularity of type |$D$|⁠. [ABSTRACT FROM AUTHOR]

In a companion paper (arXiv:1910.03150) to this one, we proved that the Gromov–Witten theory of a Fano orbifold line of type D is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota Bilinear Equations determines a solution to a new integrable hierarchy of Lax equations. We suggest the name extended D-Toda hierarchy for this new system of Lax equations, because it should be viewed as the analogue of Carlet's extended bi-graded Toda hierarchy, which is known to govern the Gromov–Witten theory of Fano orbifold lines of type A. [ABSTRACT FROM AUTHOR]

There are two ways to choose the generating functions of the gauge transformations T D (Φ) = (Φ − 1) x − 1 ∂ Φ − 1 and T I (Ψ) = Ψ − 1 ∂ − 1 Ψ x , when dicussing the gauge transformations for the constrained modified KP hierarchy. The first is to select the (adjoint) eigenfunctions, while the second is the (adjoint) wave functions. In this paper, we will mainly discuss the gauge transformations obtained by the second method. The corresponding successive applications are considered. Also, we investigate the results of the gauge transformation derived through the union of these two methods. [ABSTRACT FROM AUTHOR]

Recent research on supercapacitors (SCs) has been attractive due to the potential application in a variety of fields related to energy storage. Electrode materials play a very important role for the performance of SCs and various metal nanoparticles are involved in the SC electrodes. In this paper, the roles of metal nanoparticles for SCs are reviewed and discussed. They can serve as a dopant to modify the surface of electrode materials, or be embedded in a composite to effectively reduce the resistance and lead to an enhanced specific capacitance. Some metal nanoparticles can be also employed as electrode materials directly, but easily being oxidized. Metallic nanoparticles can even act as current collectors, especially for these noble metals with excellent stability and high conductivity. Nanoporous metals prepared by dealloying and electrochemical method can be used as both pseudocapacitive materials and current collector of SCs. Some important experimental data on this issue are summarized. A brief discussion on the future directions, challenges and opportunities in this topic is also provided. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the constrained multicomponent modified KP hierarchy and its Virasoro type additional symmetries. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the modified KP hierarchy in the Kupershmidt–Kiso version is investigated starting from the tau functions. There are two tau functions for the modified KP hierarchy. We firstly give some properties about the tau functions, including Hirota bilinear identities and Fay identities. And it is showed that these two functions can be viewed as two different tau functions of the KP hierarchy. Then after constructing the spectral representations of the eigenfunction and the adjoint eigenfunctions, the expressions of all the squared eigenfunction potentials in the modified KP hierarchy are obtained. Next, the study of the squared eigenfunction symmetries and the additional symmetries is considered, whose actions on the two tau functions are derived. At last, the Virasoro additional symmetries in the constrained cases are given, also with the actions on the tau functions. [ABSTRACT FROM AUTHOR]

Abstract We report a simple and general strategy to optimize the composite of reduced graphene oxide (rGO) and polyaniline (PANI) via introducing a small quantity of divalent metal ions M (M = Ni2+, Co2+, Cu2+, Mn2+) as mediators. This simple approach can not only inhibit the aggregation of both the graphene sheets and the PANI nanoparticles, yielding a uniform PANI−rGO morphology with increased specific surface area, but also strengthen the utilization of the good conductivity of rGO, leading to reduced charge transfer resistance. The metal ions modified binary PANI−rGO aerogels (P−GA− M s) exhibit all fairly high specific charges or capacities of 271 (Ni2+), 211(Co2+), 200 (Cu2+) and 181 mA h· g−1(Mn2+), at 1 A g−1 in a three-electrode system, with an average retention of 93% over 10000 cycles of charge-discharge at 3 A g−1. Additionally, as a proof of generality, a ternary system of MoS 2 −PANI−GA with additive Ni2+ showing better electrochemical performance than that without Ni2+ is demonstrated as well. This study provides a rational way on improving the specific charges or capacities of GA-based composites by adopting metal ions as mediators. Graphical abstract The morphology and the interface of the hybrid composite of PANI−rGO can be optimized by introducing of a tiny amount of divalent metal ions M (M = Ni2+, Co2+, Cu2+, Mn2+) as mediators, resulting in the significantly improved supercapacitive performance. Image 1 Highlights • Electrochemical performance of PANI−rGO aerogels can be significantly improved by introducing of divalent metal ions. • The effect of metal ions is mainly to promote the uniform-morphology and homogeneous-composition of PANI-rGO. • The metal ions mediator can strengthen the utilization of the good conductivity of rGO. • The generality to improve the performance of GA-based composites by adopting the facile strategy is verified. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the squared eigenfunction symmetries under the Miura and reverse-Miura transformations, between the discrete KP and modified discrete KP hierarchies, in unconstrained and constrained cases. What is more, the squared eigenfunction symmetries for the constrained discrete KP and constrained modified discrete KP hierarchies are constructed by imposing the additional conditions on the generating eigenfunctions of the corresponding symmetries. [ABSTRACT FROM AUTHOR]

In this article, the successive application of three gauge transformation operators for the modified semidiscrete Kadomtsev–Petviashvili(mdKP) hierarchy has been provided. The commutativity of the Bianchi diagram of these gauge transformation operators is investigated. [ABSTRACT FROM AUTHOR]

The Miura links between the KP and modified KP hierarchies are extended to the SUSY KP (SKP) and SUSY modified KP hierarchies (SmKP) of Manin Radul and Jacobian types. The corresponding Darboux transformations in the SUSY case are constructed by using Miura links. In this sense, one can better understand why one step Darboux transformation of the SKP hierarchy can not keep the odd flows. In addition, the Darboux transformations in the SmKP case can be obtained naturally by the Miura links. Then the squared eigenfunction symmetry of the SmKP hierarchy is obtained by using Miura link from the SKP hierarchy. At last, starting from the results in the SKP hierarchy, the constrained SmKP hierarchy of Manin Radul type can also be constructed by Miura link, that is, by adding appropriate squared eigenfunction symmetry in odd flow parts. The Darboux transformations of the constrained SKP and SmKP hierarchies are also discussed by using the Miura links. [ABSTRACT FROM AUTHOR]

Bilinear equation is an important property for integrable nonlinear evolution equation. Many famous research objects in mathematical physics, such as Gromov–Witten invariants, can be described in terms of bilinear equations to show their connections with the integrable systems. Here in this paper, we mainly discuss the bilinear equations of the transformed tau functions under the successive applications of the Darboux transformations for the KP hierarchy, the modified KP hierarchy (Kupershmidt–Kiso version) and the BKP hierarchy, by the method of the Boson–Fermion correspondence. The Darboux transformations are considered in the Fermionic picture, by multiplying the different Fermionic fields on the tau functions. Here the Fermionic fields are corresponding to the (adjoint) eigenfunctions, whose changes under the Darboux transformations are showed to be the ones of the squared eigenfunction potentials in the Bosonic picture, used in the spectral representations of the (adjoint) eigenfunctions. Then the successive applications of the Darboux transformations are given in the Fermionic picture. Based upon this, some new bilinear equations in the Darboux chain are derived, besides the ones of (l − l ′) -th modified KP hierarchy. The corresponding examples of these new bilinear equations are given. • Darboux transformations for KP, mKP and BKP hierarchies are formulated in the Fermionic picture. • Successive applications of the Darboux transformations in the Fermionic picture are given. • New bilinear equations in the Darboux chains are obtained. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we systematically study the “ghost” symmetry in the CKP hierarchy through its actions on the Lax operator, dressing operator, eigenfunctions and the tau function. In this process, the spectral representation of the eigenfunction is developed and the squared eigenfunction potential is investigated. [Copyright &y& Elsevier]

Abstract: In this paper, we investigated four applications of the gauge transformation for the BKP hierarchy. Firstly, it is found that the orbit of the gauge transformation for the constrained BKP hierarchy defines a special -dimensional Toda lattice equation structure. Then the tau function of the BKP hierarchy generated by the gauge transformation is shown to be the Pfaffian. And the higher Fay-like identities for the BKP hierarchy is also obtained through the gauge transformation. At last, the compatibility between the additional symmetry and the gauge transformation of the BKP hierarchy is proven. [Copyright &y& Elsevier]

In this paper, the gauge transformation of the constrained semi-discrete KP(cdKP) hierarchy is constructed explicitly by the suitable choice of the generating functions. Under the m-step successive gauge transformation Tm, we give the transformed (adjoint) eigenfunctions and the τ-function of the transformed Lax operator of the cdKP hierarchy. [ABSTRACT FROM AUTHOR]

Abstract: We report a one-step synthesis of a nanocomposite of goethite (α-FeOOH) nanorods and reduced graphene oxide (RGO) using a solution method in which ferrous cations serve as a reducing agent of graphite oxide (GO) to graphene and a precursor to grow goethite nanorods. As-prepared goethite nanorods have an average length of 200nm and a diameter of 30nm and are densely attached on both sides of the RGO sheets. The electrochemical properties of the nanocomposite were characterized by cyclic voltammetry (CV) and chronopotentiometry (CP) charge–discharge tests. The results showed that goethite/RGO composites have a high electrochemical capacitance of 165.5Fg−1 with an excellent recycling capability making the material promising for electrochemical capacitors. [Copyright &y& Elsevier]

In this paper, we construct the additional symmetries for the Toda lattice hierarchies of B type and C type (the BTL and CTL hierarchies), and show their algebraic structures are w∞B×w∞B and w∞C×w∞C , respectively. And also we discuss the generating functions of the additional symmetries. [ABSTRACT FROM AUTHOR]

Fano orbifold lines are classified by the Dynkin diagrams of type A , D , and E. It is known that the corresponding total descendant potential is a tau-function of an appropriate Kac–Wakimoto hierarchy. It is also known that in the A-case the Kac–Wakimoto hierarchies admit an extension and that the total descendant potential is a tau-function of an extended Kac–Wakimoto hierarchy. The goal of this paper is to prove that in the D-case the total descendent potential is also a tau-function of an extended Kac–Wakimoto hierarchy. [ABSTRACT FROM AUTHOR]

Abstract: Aligned ZnO nanorod arrays were fabricated by chemical solution deposition based on Si substrate which was spin coated with ZnO colloid as nucleation seeds. Their microstructures were characterized by X-ray diffraction, scanning electron microscopy, and high-resolution transmission electron microscopy. The results indicated that ZnO nanorods nucleated and grew vertically on Si substrates along the [001] direction with single-crystalline structure. The diameter of ZnO nanorods was greatly affected by the grain size of ZnO seeds. Room-temperature photoluminescence of nanorods has a strong emission band at about 384nm. [Copyright &y& Elsevier]

Abstract: A typical naturally occurring mineral, marine manganese nodule, could be developed as a catalyst for the catalytic chemical vapor deposition synthesis of helical carbon nanotubes by changing the experimental conditions. In the product, a novel one-dimensional carbon nanostructure with triple helices was first observed. The possible origin is briefly discussed. It points out a facile method to obtain helical carbon nanostructures. [Copyright &y& Elsevier]

Abstract: The preparation of multi-walled carbon nanotubes (MWCNTs) by chemical vapor deposition (CVD) method using nanocrystalline CaCO3 as metal catalyst support was investigated, where acetylene was used as carbon source, and Co, Fe and Ni, as well as their bimetallic compounds as the active component of the catalyst. The smaller size of the CaCO3 support led to a much higher yield of CNTs than previously reported. It was noteworthy that the best performance was Fe-Co nanoparticles, which gave a high yield of CNTs, as judged by experimental results. Growth temperature affected catalytic activity and the disintegration of the support. The raw product was purified to a high level, with little damage on the CNT structure, as confirmed by thermal gravimetric (TG), micro-Raman and transmission electron microscopy (TEM) analyses. [Copyright &y& Elsevier]

Abstract: Nickel nanoparticles were prepared and uniformly supported on multi-walled carbon nanotubes (MWCNTs) by reduction route with CNTs as a reducing agent at 600°C. As-prepared nickel nanoparticles were single crystalline with a face-center-cubic phase and a size distribution ranging from 10 to 50nm, and they were characterized by transmission electron microscopy (TEM), high-resolution TEM and X-ray diffraction (XRD). These nickel nanoparticles would be coated with graphene layers, when they were exposed to acetylene at 600°C. The coercivity values of nickel nanoparticles were superior to that of bulk nickel at room temperature. [Copyright &y& Elsevier]

Long bundles up to several millimeters of aligned carbon nanofibers (CNFs) have been prepared by pyrolysis of a mixture of acetylene and ferrocene in a vertically installed quartz reactor by floating catalyst method. After a long period of reaction, the product of thick blocks closely adhered on the reactor wall was obtained. Field emission scanning electron microscopy (FESEM) verified that blocks were composed of aligned CNF bundles with a high purity that was attested by the means of X-ray diffraction (XRD) and thermal gravimetric (TG) analysis. The morphology and structure features of the CNFs were checked by transmission electron microscopy (TEM) and Raman spectroscopy, respectively. It was originally reported that aligned CNF bundles were synthesized by vertically floating catalyst method. [Copyright &y& Elsevier]

Multi-walled carbon nanotubes (MWCNTs) have been successfully synthesized with titanate-modified palygorskite as catalyst and acetylene as carbon source by chemical vapor deposition (CVD) at high temperature. Transmission electron microscopy (TEM) studies showed that there were a lot of carbon nanotubes partially filled with elongated foreign material in their inner cavities. X-ray energy dispersive spectrum (EDS) analyses and selected area electron diffraction (SAED) investigations on the encapsulated material revealed that it was single crystalline iron carbide (Fe3C) derived from ferric precursors in the mineral. The yield of carbon nanotubes was influenced by preparation temperature based on thermal gravimetric analyses (TGA). The relative quantity of Fe3C nanowires was influenced by the temperature and the local structure of nanotubes upon TEM observations. A growth mechanism is also proposed in the paper. [Copyright &y& Elsevier]

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]

In this paper, we work out the reciprocal transformations generated by the adjoint eigenfunctions, and write down the corresponding changes of the Lax operators, eigenfunctions and adjoint eigenfunctions under this kind of new reciprocal transformations at first. Then we discuss the successive actions of the reciprocal transformations generated by the eigenfunctions and the adjoint eigenfunctions. Also we investigate the commutativity of different types of the reciprocal transformations. The above results are very useful to construct the new type solutions. [ABSTRACT FROM AUTHOR]

In this paper, free bosons are used to study some integrable properties of Kadomtsev-Petviashvili (KP) hierarchy of C type (CKP hierarchy), from the aspects of tau functions. First, the modified CKP hierarchy is constructed by using free bosons, and the corresponding Lax structure is given. Then, the constrained CKP hierarchy is found to be related to the modified CKP hierarchy, and the corresponding solutions are derived by using free bosons. Next, by using the relations between the Darboux transformations and the squared eigenfunction symmetries, we express the Darboux transformations of the CKP hierarchy in terms of free bosons, by which one can better understand the essential properties of the CKP Darboux transformations. In particular, the additional symmetries of the CKP hierarchy can be viewed as the infinitesimal generator of the CKP Darboux transformations. Based on these results, we finally obtain the actions of the CKP additional symmetries on the CKP tau functions constructed by free bosons. [ABSTRACT FROM AUTHOR]

In this paper, the BKP hierarchy is viewed as the Kupershmidt reduction of the modified KP hierarchy. Then based upon this fact, the gauge transformation of the BKP hierarchy are obtained again from the corresponding results of the modified KP hierarchy. Also the constrained BKP hierarchy is constructed from the constrained modified KP hierarchy, and the corresponding gauge transformations are investigated. Particularly, it is found that there is a new kind of gauge transformations generated by the wave functions in the constrained BKP hierarchy. [ABSTRACT FROM AUTHOR]

Additional symmetry is an important kind of symmetries depending explicitly on the time and space variables, which can be expressed through Sato–Bäcklund transformations. In this paper, we construct Sato–Bäcklund transformations of the modified KP hierarchy and its constrained cases. Then the string equations of the p -reduced modified KP hierarchy are established by requiring the system independent on some additional symmetry flows, which are expressed by the Lax operator L and the Orlov–Shulman's operator M. At last, we obtain the negative Virasoro constraint on the two tau functions of the 2-reduced modified KP hierarchy satisfying the string equations. [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]

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]

The generalized additional symmetries of the two-Toda lattice hierarchy are investigated in this paper. The algebraic structure of this generalized additional symmetry is showed as w∞xw∞. And the actions of the generalized additional symmetries on τ-function are also discussed, by restricting the two-Toda lattice hierarchy to the semi-infinite case. [ABSTRACT FROM AUTHOR]

The squared eigenfunction symmetry for the Toda lattice hierarchy is explicitly constructed in the form of the Kronecker product of the vector eigenfunction and the vector adjoint eigenfunction, which can be viewed as the generating function for the additional symmetries when the eigenfunction and the adjoint eigenfunction are the wave function and the adjoint wave function, respectively. Then after the Fay-like identities and some important relations about the wave functions are investigated, the action of the squared eigenfunction related to the additional symmetry on the tau function is derived, which is equivalent to the Adler-Shiota-van Moerbeke formulas. [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]

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]

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]

In this paper, we investigate some topics involving the modified D-type Kadomtsev-Petviashvili (DKP) hierarchy. Note that the modified DKP (mDKP) hierarchy is just the modified B-type Kadomtsev-Petviashvili (BKP) hierarchy in the bosonic forms. Based on this fact, we first proved the conjecture in You [Physica D 50, 429–462 (1991)], that is, the product of the two tau functions of the mDKP hierarchy is some tau function of the KP hierarchy. Then, we investigate the Darboux transformations of the DKP and mDKP hierarchy. Finally, the solutions of the constrained BKP hierarchy are given in the context of the fermionic representation of infinite Lie algebra d∞. [ABSTRACT FROM AUTHOR]

Abstract: Undoped and Al-doped ZnO nanofibers were synthesized via a simple electrospinning method, and then characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman scattering and photoluminescence (PL) spectroscopy. The ethanol sensing properties of the sensor based on the nanofibers were also investigated. The results show that the sensor fabricated from Al-doped ZnO nanofibers exhibits better gas sensing performance than that fabricated from the undoped ZnO nanofibers, and the gas sensing mechanism is discussed. [Copyright &y& Elsevier]

Abstract: Novel multi-branched carbon nanotubes (BCNTs) have been synthesized using alkali-element modified Cu/MgO catalyst. It was found that alkali-element doping to the catalyst played a key role in the synthesis of CNTs, signifying a novel approach to modify Cu catalyst. Based on the transmission electron microscopy observations, a simple model is developed to describe the growth of BCNTs. [Copyright &y& Elsevier]

Short multi-wall carbon nanotubes (MWNTs) with open tips were obtained by mechanical ball milling. The microstructure characteristics of MWNTs before and after ball milling were checked by transmission electron microscopy (TEM). The effect of ball milling on the hydrogen adsorption behavior of the MWNTs was studied. The hydrogen adsorption experiments were carried out at room temperature under a pressure of 8–9 MPa. The hydrogen adsorption capacity of carbon nanotubes milled for 10 h was 0.66 wt%, which was about six times that of MWNTs without milling. For the carbon nanotubes milled with MgO for 1 h, a hydrogen adsorption capacity of 0.69 wt% was obtained. The enhancement of hydrogen adsorption might result from the increase of defects and surface area of the MWNTs caused by ball milling. [Copyright &y& Elsevier]

SnO2/ZnO@ZIF‐8 core‐shell nanofibers were synthesized by electrospinning and hydrothermal etching ZnO component of SnO2/ZnO nanofibers. It is found that the ZIF‐8 coated SnO2/ZnO nanostructures are obtained, and the ZIF‐8 coating can obviously increase the specific surface area of nanofibers. H2S sensing properties of the sensors based on composite nanofibers were investigated. The results show that SnO2/ZnO@ZIF‐8 core‐shell nanostructures can not only improve the response to H2S, but also effectively reduce the interference of ambient humidity on semiconductor gas sensors. The response of the optimal sample to 5 ppm H2S can reach 202.3, which is about 19 times higher than that of pure SnO2 nanofibers. Compared with the response at the ambient humidity of 55 %RH, the response at the ambient humidity of 90 %RH can still maintain 84.7 %. Good selectivity and stability are also observed in our investigations. [ABSTRACT FROM AUTHOR]

• A unique Sb2S3-graphene composite with amorphous nature was fabricated via sonochemical method. • The amorphous samples significantly surpass the crystalline counterpart in electrochemical performance. • Ultrasound sonochemical synthesis shows great potential for the energy storage materials. Different from traditional methods, ultrasound sonochemical synthesis can create very special reaction conditions by virtue of the effects of acoustic cavitation. The localized spots in the medium liquids can reach the temperature of ~5000 K, and the pressure of ~1000 bar with the treatment of ultrasonic irradiation. The extreme conditions make it possible to fabricate a series of nanostructured materials with peculiar properties. Herein, we successfully prepared a unique amorphous composite of Sb 2 S 3 -graphene via sonochemical method at room temperature. Thanks to the opening frame of ion diffusion channels and higher reversibility in thermodynamics, the amorphous composite displayed superior electrochemical properties in comparison with the crystalline counterpart for sodium-ion batteries. Specifically, the amorphous Sb 2 S 3 -graphene composite delivered a first discharge capacity of 1867.1 mAh g−1 and a high reversible capacity of over 880 mAh g−1 after 50 cycles. The nanostructured materials synthesized by ultrasound sonochemical method with unique properties have well prospect in the field of energy storage. [ABSTRACT FROM AUTHOR]