Search

Исследуется дискретная иерархия КП с ограничениями двух типов, а именно с условием на тау-функцию и условием на калибровочное преобразование. Для этой иерархии показана эквивалентность условия $(L^k)_{

NiCo2O4 is a promising electrode material for supercapacitors and it has been widely investigated. However, its low conductivity restricts the reaction kinetics. Combining it with carbon materials can efficiently overcome the issue. But, very limited research about the homogenous coatings of NiCo2O4 nanocrystals on carbon nanotubes (CNTs) is reported. In this work, thin nanosheets and small nanoparticles of NiCo2O4 densely coated on CNTs are synthesized by tuning the annealing time with a hybrid of metal hydroxide@CNTs as a precursor. In the precursor, core−shell structures are formed by conformally coating 2D metal hydroxides on CNTs. After annealing it at 300 °C for different time, NiCo2O4 nanosheets or nanoparticles are then obtained and the core−shell structure is remained. Due to the reduced crystal size of NiCo2O4 and the high conductivity of CNTs, the composites have large specific capacitances, excellent rate performances, and good stability. The composite of NiCo2O4 nanoparticles on CNTs has a higher specific capacitance, about 1786 F g−1 at 0.5 A g−1, than the hybrid of NiCo2O4 nanosheets on CNTs due to their different morphologies. Using the composite as positive electrode and activated carbon as negative electrode, a hybrid capacitor cell can work in a voltage of 1.6 V, delivering an energy density of 32.5 Wh kg−1 at 800 W kg−1, showing a large potential for supercapacitors.

Cobalt monoxide is a low–valence compound with a face–centered cubic structure and has been deemed as a promising electrode material for energy storage, such as batteries and supercapacitors (SC). In this work, the recent progress of CoO and its composites for SC application is briefly reviewed. The preparation methods for CoO are summarized at first. With the development of nanotechnologies, various CoO nanostructures are thus synthesized for SC, but most architectures grown on conductive substrates show higher specific capacitance than the corresponding power materials. If integrated with some typical guest materials, such as transition metal oxides, hydroxides, sulfides, and carbon materials (including carbon nanotubes, graphene and porous carbon) as well as conductive polymers, the CoO composites usually deliver promoted electrochemical performances. Thus, much attention is focused on the composites of CoO. An outlook for future work is finally put forward.

Non-noble metal catalysts now play a key role in promoting efficiently and economically catalytic reduction of CO

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 TiO

Developing advanced electrochemical double-layer supercapacitors (EDLCs) with high energy density and capacitance can be realized by exploring the electrodes possessing large specific surface area ...

Constructing composite electrodes is considered to be a feasible way to realize high-specific-capacity Li-ion batteries. The core-double-shell-structured Si@C@TiO2 would be an ideal design for such batteries, considering that carbon (C) can buffer the volume change and TiO2 can constrain the structural deformation of Si. Although the electrochemical performance of the shells themselves is relatively clear, the complexity of the multishell heterointerface always results in an ambiguous understanding about the influence of the heterointerface on the electrochemical properties of the core material. In this work, a multilayer film model that can simplify and simultaneously expand the area of the heterointerface is used to study the heterointerfacial behavior. First, a multilayer film TiO2/C with different numbers of TiO2/C heterointerfaces is studied. It shows that the electrochemical performance is enhanced apparently by increasing the number of TiO2/C heterointerfaces. On the one hand, the TiO2/C heterointerface exhibits a strong lithium-ion storage capacity. On the other hand, the TiO2/C heterointerface appears to effectively promote the local Li-ion concentration gradient and thus boost the Li-ion transport kinetics. Then, TiO2/C is combined with Si to construct a composite anode Si/C/TiO2. An obvious advantage of TiO2/C over single TiO2 and C is observed. The utilization rate of Si is greatly improved in the first cycle and reaches up to 98% in Si/C/TiO2. The results suggest that the electrochemical performance of Si can be greatly manipulated by the heterointerface between the multishells.

Li2MnO3, as one traditional member of lithium-rich layered cathodes, gives batteries with large specific capacity. However, it suffers from unexpected severe capacity fading and discharge voltage d...

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 H

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.

Titanium dioxide (TiO2) is proposed as a promising anode material for lithium-ion batteries (LIBs) due to its highly stable structure and slight side reaction at the electrode/electrolyte interface...

We report the existence of ferromagnetism in the thiospinel compound CuCo2S4 with Tc ∼ 125 K. The magneto-electronic transport of the CuCo2S4 demonstrates a metallic conductivity and positive magnetoresistance at high temperature. At low temperature, in the ferromagnetic state, there is evidence of spin-transport coupling with magnetic domains giving a region of negative magnetoresistance near the coercive field. The electronic band structure of CuCo2S4 was calculated using density-functional theory (DFT), which shows a ferromagnetic metallic state, in agreement with experiment. With nickel doping, both the spinel CuCo1.5Ni0.5S4 and CuCoNiS4 display paramagnetism down to the lowest measured temperature (3 K). This indicates that, as in other itinerant magnetic sulfides, the exchange interactions are highly sensitive to electron/hole doping. The tunable magnetism in the spinel CuCo2S4, together with its high conductivity, suggests that this thiospinel material could be a candidate for spintronic applications.

Silicon phosphide (SiP) has attracted a great deal of attention in the field of energy storage because of its unique properties of stable semiconducting two-dimensional structure and promising theo...

The composites of NiCo2O4 with unique structures are extensively explored as promising electrodes. In this work, core-shell structured nanowires anchored on nickel foam are synthesized by the hydrothermal synthesis of NiCo2O4 as core and subsequent electrodeposition of α-Co(OH)2 as shell. The core-shell composites exhibit enhanced electrochemical performances ascribing to the synergistic reactions from both materials, showing higher specific capacitance than any single component. By changing the deposition time, the mass loading of α-Co(OH)2 can be easily controlled. The electrochemical performances of the hybrid electrodes are diverse with the mass loading of Co(OH)2. The optimized hybrid electrode with 3 mins electrodeposition exhibits the highest specific capacitance (1298 F g−1 at 1 A g−1) among all electrodes. The redox reaction is a main contributor to the total specific capacitance through electrochemical kinetics analysis. An asymmetric supercapacitor assembled by the optimized material as positive electrode and activated carbon as negative electrode can achieve a relatively high energy density of 39.7 Wh kg−1 at a power density of 387.5 W kg−1 (at 0.5 A g−1) in a voltage of 1.55 V.

The composites of Fe2O3 nanoparticles and carbon nanotubes (CNTs) can be applied in many fields including energy storage. The synthesis of Fe2O3/CNTs composite is usually carried out under high temperatures with complicated processes. To solve these problems, we report a novel one-step chemical bath deposition method to synthesize it at a very low temperature in this work. With DMF as a complex agent, ferrous cations can be well combined with the external surface of CNTs to form small Fe2O3 nanoparticles just at 70 °C for 2-h reaction. XRD, SEM, and TEM analyses confirm that as-prepared Fe2O3 nanoparticles are ultra-small, well crystallized, and highly dispersed onto the surface of CNTs. When being used as an electrode material for supercapacitor, the composite has a specific capacitance of 942 F g−1 at 2 A g−1 and 645 F g−1 at 15 A g−1, exhibiting a higher specific capacitance than previously reported Fe2O3/CNTs composites due to its smaller size.

Currently, ternary CuCo2S4 sulfides are intensively investigated as electrode materials for electrochemical capacitors due to their low cost, high conductivity, and synergistic effect. The research of CuCo2S4 materials for energy storage has gradually grown from 2016. The supercapacitive performances of CuCo2S4 electrodes for electrochemical capacitors are briefly reviewed in this work. The structure, morphology, and particle size of CuCo2S4 are related to the synthesis conditions and electrochemical performances. The thin films of CuCo2S4 nanostructures deposited on conductive substrates and their composites both show better properties than single CuCo2S4. CuCo2S4 and its composites reveal large potential for asymmetric capacitors, delivering high energy densities. However, there is still much new space remaining for future research. The possible development directions, challenges, and opportunities for CuCo2S4 materials are also discussed.

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 $D$.

Developing safe, efficient and environment-friendly energy storage systems continues to inspire researchers to synthesize new electrode materials. Doping or substituting host material by some guest elements has been regarded as an effective way to improve the performance of supercapacitors. In this work, single-phase CuCo2−xNixS4 materials were synthesized by a facile two-step hydrothermal method, where Co in CuCo2S4 was substituted by Ni. Cobalt could be easily substituted with Ni in a rational range to keep its constant phase. But, a high content of Ni resulted in a multi-phase composite. Among a series of CuCo2−xNixS4 materials with different Ni/Co mole ratios, CuCo1.25Ni0.75S4 material presented a significantly high specific capacitance (647 F g−1 or 272 C g−1 at 1 A g−1) and the best cycling stability (∼98% specific capacitance retention after 10,000 charge-discharge cycles), which was mainly due to the modified composition, specific single phase, higher electroconductivity, more electroactive sites and the synergistic effect between Ni and Co. Moreover, the assembled asymmetric capacitor using CuCo1.25Ni0.75S4 as a positive electrode and activated carbon as a negative electrode delivered a high energy density of 31.8 Wh kg−1 at the power density of 412.5 W kg−1. These results demonstrated that ternary metal sulfides of CuCo2−xNixS4 are promising electrode materials for high-performance supercapacitors.

Transition metal compounds containing nickel and copper have been investigated as electrode materials for energy storage. (Ni,Cu)(OH)2CO3 and α-Ni(OH)2 with different Ni/Cu ratios are synthesized by a simple hydrothermal method. All the samples show the similar dandelion-like morphology. It is demonstrated that the mole ratio of Ni to Cu is a key factor to influence the phase and electrochemical performances of the products. Carbonate anions will be intercalated into nickel copper layered double hydroxides with a hydrotalcite structure when the sample is nickel-rich, which will lead to much better electrochemical properties compared with the copper-rich samples with crystalline (Ni,Cu)(OH)2CO3 structure. Among all the materials, sample (Ni0.89Cu0.11)2(OH)2CO3 can deliver the highest specific capacitance of 1017.3 F g−1 at 1 A g−1 and retain 68.5% of the original value after 4000 cycles at 5 A g−1. Meanwhile, an asymmetric capacitor which is assembled by using the optimized material as a positive electrode and activated carbon as a negative electrode exhibits a high energy density of 38.56 Wh kg−1 at a power density of 850.01 W kg−1 and a high power density of 8407.4 W kg−1 at an energy density of 21.7 Wh kg−1. Based on the above results, nickel copper carbonate hydroxides are of potential application for energy storage.

A series of mixed metal sulfides of NixCu1−xCo2S4 were synthesized by a facile two-step hydrothermal method and they were investigated as electrode materials for supercapacitor. A substitutional solid solution can be easily formed due to the same atom occupation and similar crystal radius of Ni and Cu in the metal sulfides. The electrochemical performances of the mixed metal sulfides are strongly influenced by the chemical compositions, though they have the same crystal structure. Among all the as-prepared materials, Ni0.67Cu0.33Co2S4 shows the best electrochemical performances with the highest specific capacitance of 1340.48 F g−1 at 1 A g−1, outstanding rate capability and excellent cycling stability. The improved performances can be attributed to the high crystallinity, modified microstructure, increased electrochemical sites and improved electroconductivity caused by lattice distortion as well as the synergistic effect in the Cu-substituted NiCo2S4. Furthermore, the assembled two-electrode hybrid device Ni0.67Cu0.33Co2S4//activated carbon can deliver a high energy density of 40 Wh kg−1 at the power density of 412.5 W kg−1, showing a great potential for energy storage.

The highest weight representation of the infinite Lie algebras is used to construct various soliton equations by the famous Kyoto school. In this chapter, we firstly review the construction of the BKP hierarchy corresponding to o(∞) by using the neutral free Fermions. As an important reduction of the BKP hierarchy, the constrained BKP hierarchy is further investigated in the aspect of the bilinear equations. It is shown that the bilinear equations in the form of tau functions can fully determine the constrained BKP hierarchy. Then the bilinear equations of the constrained BKP hierarchy are given in the Fermionic picture, and further interpretations of these bilinear equations are obtained. Particularly, there is the structure of the modified BKP hierarchy in the constrained BKP hierarchy, which is presented in the forms of the bilinear equations. Last, we investigate the dressing structure and the Lax structure of the modified BKP hierarchy. Note that the soliton equations obtained by the highest weight representation are usually given in the forms of the bilinear equations; therefore, the work here may be one try in further study of the integrable properties for these soliton equations.

In a companion paper 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 $A$, 73 pages

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., Comment: 47 pages

In this paper, two kinds of gauge transformations for the constrained q-deformed modified KP hierarchy and their relations with additional symmetries are discussed. The corresponding gauge transformations are required to keep both the Lax equation and the Lax operator, which can be obtained by choosing the special generating functions. Then the successive gauge transformations for the constrained q-modified KP hierarchy are investigated. Finally, we find that additional symmetry flows commute with the gauge transformation for the q-mKP hierarchy.

In this paper, ZnCo2O4 nanowire arrays with a uniform carbon coating were introduced when polyvinyl alcohol (PVA) served as the carbon source. The coating process was completed by a facile bath method in PVA aqueous solution and subsequent pyrolyzation. The PVA-derived carbon-coated ZnCo2O4 nanowire array composites can be used directly as the binder-free and self-supported anode materials for lithium-ion batteries. In the carbon-coated ZnCo2O4 composites, the carbon layer carbonized from PVA can accelerate the electron transfer and accommodate the volume swing during the cycling process. The lithium storage properties of the carbon-coated ZnCo2O4 composites are investigated. It is believed that the novel carbon-coating method is universal and can be applied to other nanoarray 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

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 [Formula: see text]. 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.

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.

Prussian blue analogues (PBA) recently have received great interest for promising applications in low-cost sodium-ion batteries (SIBs). However, controlled synthesis of high-performance PBA is still challenging. In this work, a facile precipitation route was used to synthesize Na-rich PBAs with superior electrochemical performance. It was found that two shapes of the products, namely, small irregular particles and large cuboid particles, coexist by adding sodium citrate in the sodium hexacyanoferrate side during the synthesis. The product shows large capacity (144 mAh g–1 under a 0.1 C rate), good rate performance (115.6 mAh g–1 under a 1 C rate, 86.6 mAh g–1 under a 10 C rate), and long-term cycling stability (73.4% retention after 780 cycles under a 0.5 C rate, 72.7% retention after 2100 cycles under a 1 C rate). This work offers a promising route to prepare PBA-based cathode materials for high-performance SIBs.