A new high-order spectral problem of the mKdV and its associated integrable decomposition

A new approach to formulizing a new high-order matrix spectral problem from a normal 2 × 2 matrix modified Korteweg-de Vries （mKdV） spectral problem is presented. It is found that the isospectral evolution equation hierarchy of this new higher-order matrix spectral problem turns out to be the well-known mKdV equation hierarchy. By using the binary nonlinearization method, a new integrable decomposition of the mKdV equation is obtained in the sense of Liouville. The proof of the integrability shows that r-matrix structure is very interesting,

A New m × m Matrix Kaup-Newell Spectral Problem and Its Associated Integrable Decomposition

A new m × m matrix Kaup-Newell spectral problem is constructed from a normal 2 × 2 matrix Kaup-Newell spectral problem, a new integrable decomposition of the Kaup-Newell equation is presented. Through this process, we find the structure of the r-matrix is interesting.

Scheduling optimization of task allocation in integrated manufacturing system based on task decomposition

How to deal with the collaboration between task decomposition and task scheduling is the key problem of the integrated manufacturing system for complex products. With the development of manufacturing technology, we can probe a new way to solve this problem. Firstly, a new method for task granularity quantitative analysis is put forward, which can precisely evaluate the task granularity of complex product cooperation workflow in the integrated manufacturing system, on the above basis; this method is used to guide the coarse-grained task decomposition and recombine the subtasks with low cohesion coefficient. Then, a multi-objective optimieation model and an algorithm are set up for the scheduling optimization of task scheduling. Finally, the application feasibility of the model and algorithm is ultimately validated through an application case study.

A new hybrid method with data‑characteristic‑driven analysis for artificial intelligence and robotics index return forecasting

Forecasting returns for the Artificial Intelligence and Robotics Index is of great significance for financial market stability,and the development of the artificial intelligence industry.To provide investors with a more reliable reference in terms of artificial intelligence index investment,this paper selects the NASDAQ CTA Artificial Intelligence and Robotics(AIRO)Index as the research target,and proposes innovative hybrid methods to forecast returns by considering its multiple structural characteristics.Specifically,this paper uses the ensemble empirical mode decomposition(EEMD)method and the modified iterative cumulative sum of squares(ICSS)algorithm to decompose the index returns and identify the structural breakpoints.Furthermore,it combines the least-square support vector machine approach with the particle swarm optimization method(PSO-LSSVM)and the generalized autoregressive conditional heteroskedasticity(GARCH)type models to construct innovative hybrid forecasting methods.On the one hand,the empirical results indicate that the AIRO index returns have complex structural characteristics,and present time-varying and nonlinear characteristics with high complexity and mutability;on the other hand,the newly proposed hybrid forecasting method(i.e.,the EEMD-PSO-LSSVM-ICSS-GARCH models)which considers these complex structural characteristics,can yield the optimal forecasting performance for the AIRO index returns.