Chimera states of phase oscillator populations with nonlocal higher-order couplings

The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.

Multi-Attribute Couplings-Based Euclidean and Nominal Distances for Unlabeled Nominal Data

Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between attributes has shown significant improvement in clustering and outlier detection,etc.However,typical existing work relies on learning pairwise value relations but weakens or overlooks the direct couplings between multiple attributes.This paper thus proposes two novel and flexible multi-attribute couplings-based distance(MCD)metrics,which learn the multi-attribute couplings and their strengths in nominal data based on information theories:self-information,entropy,and mutual information,for measuring both numerical and nominal distances.MCD enables the application of numerical and nominal clustering methods on nominal data and quantifies the influence of involving and filtering multi-attribute couplings on distance learning and clustering perfor-mance.Substantial experiments evidence the above conclusions on 15 data sets against seven state-of-the-art distance measures with various feature selection methods for both numerical and nominal clustering.

A Pd-metalated porous organic polymer as a highly efficient heterogeneous catalyst for C–C couplings

An efficient catalyst system based on a Pd-metalated porous organic polymer bearing phenanthroline ligands was designed and synthesized.This catalyst was applied to various C–C bond-forming reactions,including the Suzuki,Heck and Sonogashira couplings,and afforded the corresponding products while exhibiting excellent activities and selectivities.More importantly,this catalyst can be readily recycled.These features show that such catalysts have significant potential applications in the future.

Lie Algebras for Constructing Nonlinear Integrable Couplings

Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.

Matrix Lie Algebras and Integrable Couplings

Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.

Two new integrable couplings of the soliton hierarchies with self-consistent sources

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/（4） has been presented （Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613）. Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl（4）. In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.

Integrable Couplings of Classical-Boussinesq Hierarchy and Its Hamiltonian Structure

By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-form identity.

A New Integrable Couplings of Classical-Boussinesq Hierarchy with Self-Consistent Sources

A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with sl（4） is presented by Yu. Based on this method, we construct a new integrable couplings of the classical-Boussinesq hierarchy with self-consistent sources by using of loop algebra sl（4）. In this paper, we also point out that there exist some errors in Yu＇s paper and have corrected these errors and set up new formula. The method can be generalized other soliton hierarchy with self-consistent sources.

Dynamic analysis of spatial parallel manipulator with rigid and flexible couplings

The dynamics of spatial parallel manipulator with rigid and flexible links is explored. Firstly, a spatial beam element model for finite element analysis is established. Then, the differential equation of motion of beam element is derived based on finite element method. The kinematic constraints of parallel manipulator with rigid and flexible links are obtained by analyzing the motive parameters of moving platform and the relationships of movements of kinematic chains, and the overall kinetic equation of the parallel mechanism with rigid and flexible links is derived by assembling the differential equations of motion of components. On the basis of abovementioned analyses, the dynamic mechanical analysis of the spatial parallel manipulator with rigid and flexible links is conducted. After obtaining the method for force analysis and expressions for the calculation of dynamic stress of flexible components, the dynamic analysis and simulation of spatial parallel manipulator with rigid and flexible links is performed. The result shows that because of the elastic deformation of flexible components in the parallel mechanism with rigid and flexible links, the force on each component in the mechanism fluctuates sharply, and the change of normal stress at the root of drive components is also remarkable. This study provides references for further studies on the dynamic characteristics of parallel mechanisms with rigid and flexible links and for the optimization of the design of the mechanism.

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.

Residual Dipolar Couplings in Structure Determination of Natural Products

The determination of natural products stereochemistry remains a formidable task.Residual dipolar couplings(RDCs)induced by anisotropic media are a powerful tool for determination of the stereochemistry of organic molecule in solution.This review will provide a short introduction on RDCs-based methodology for the structural elucidation of natural products.Special attention is given to the current availability of alignment media in organic solvents.The applications of RDCs for structural analysis of some examples of natural products were discussed and summarized.Graphical Abstract This review provides a short introduction on RDCs-based methodology for the structural elucidation of natural products.Special attention is given to the current availability of alignment media in organic solvents.The applications of RDCs for structural analysis of some examples of natural products were discussed and summarized.

New Integrable Couplings of Generalized Kaup-Newell Hierarchy and Its Hamiltonian Structures

A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy.

A New Nonlinear Integrable Couplings of Yang Equations Hierarchy and Its Hamiltonian Structure

Based on a kind of non-semisimple Lie algebras, we establish a way to construct nonlinear continuous integrable couplings. Variational identities over the associated loop algebras are used to furnish Hamiltonian structures of the resulting continuous couplings.As an illustrative example of the scheme is given nonlinear continuous integrable couplings of the Yang hierarchy.

Multi-component KN Hierarchy and Associated two Integrable Couplings as Well as Their Hamiltonian Structure

Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.

A New Integrable Lattice Hierarchy and Its Two Discrete Integrable Couplings

A new and efficient way is presented for discrete integrable couplings with the help of two semi-direct sum Lie algebras. As its applications, two discrete integrable couplings associated with the lattice equation are worked out. The approach can be used to study other discrete integrable couplings of the discrete hierarchies of solition equations.

Nonlinear integrable couplings of a nonlinear Schrdinger-modified Korteweg de Vries hierarchy with self-consistent sources

By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries（NLS-mKdV） hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated.

Effects of Different Time-Dependent Couplings on Two-Atom Entanglement

The effects of different time-independent and time-dependent couplings on two-atom entanglement are studied. The results show that the effects depend on the initial state. For the initial state ｜eeO〉, it is found that different time-independent couplings make the case without entanglement exhibit entanglement, and time-dependent couplings turn the irregular entanglement regions into regular one. Under the case of decay, for the initial state ｜eg0〉, the different time-dependent couplings have disbenefit.

Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings

We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.

Effects of Tensor Couplings on Nucleonic Direct URCA Processes in Neutron Star Matter

The relativistic neutrino emissivity of the nucleonic direct URCA processes in neutron star matter is investigated within the relativistic Hartree-Fock approximation. We particularly study the influences of the tensor couplings of vector mesons ω and ρ on the nucleonic direct URCA processes. It is found that the inclusion of the tensor couplings of vector mesons w and p can slightly increase the maximum mass of neutron stars. In addition, the results indicate that the tensor couplings of vector mesons ω and ρ lead to obvious enhancement of the total neutrino emissivity for the nucleonic direct URCA processes, which must accelerate the cooling rate of the non- superfluid neutron star matter. However, when considering only the tensor coupling of vector meson ρ, the neutrino emissivity for the nucleonic direct URCA processes slightly declines at low densities and significantly increases at high densities. That is, the tensor coupling of vector meson ρ leads to the slow cooling rate of a low-mass neutron star and rapid cooling rate of a massive neutron star.