A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

A Coupled AKNS-Kaup-Newell Soliton Hierarchy

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup-Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures.Comment: 15 pages, late

Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy

Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite dimensional integrable systems and the general involutive system engendered by binary nonlinearization is reduced to a specific involutive system generated by mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento

The effects of dog management on Echinococcus spp. prevalence in villages on the eastern Tibetan Plateau, China

Background The pastoral area of the eastern Tibetan plateau is a very important human echinococcosis endemic region. Domestic dogs are the main definitive host for the transmission of Echinococcus granulosus sensu lato (s.1.) and E. multilocularis to humans. To control the infection risks, a national-level canine echinococcosis prevention and control program has been implemented since 2015 in Shiqu County, Sichuan, China, The objective of this investigation was to evaluate its effect on Echinococcus spp. prevalence in dogs. Methods We surveyed 69 households with 84 owned dogs, for dog keeping information in the villages of Rizha and Eduoma. A total of 105 dog fecal samples, consisting of 75 from owned dogs and 30 unknown dog fecal samples were collected between 2015 and 2017 to determine Echinococcus spp. prevalence using copro-PCR. Eight variables based on household surveys were included into a logistic regression model for significantly relevant factors to canine echinococcosis prevalence in dogs. Results The overall Echinococcus spp. copro-DNA prevalence decreased significantly in dogs from 51.2% (2015) to 20.0% (2017) in Rizha, and insignificantly from 11.5% (2016) to 4.3% (2017) in Eduoma. Echinococcus multilocularis was the most prevalent species continually detected during the entire research period, while E. granulosus was rare and not detected in 2017. Echinococcus shiquicus prevalence was as high as E. multilocularis , although only detected in 2015 in Rizha. Unleashed dog feces were mainly collected in Rizha Village in 2015. Although 93.2% of owned dogs were leashed, and the monthly praziquantel dosing rate reached 97%, E. multilocularis infection could still be detected in 11.1% of owned dogs in 2017. Monthly deworming, leashing dogs 24h per day, and the avoidance of dogs feeding on livestock viscera are significant measures to prevent canine echinococcosis infection in owned dogs. Conclusion Carrying out a canine echinococcosis prevention and control program can significantly decrease the Echinococcus prevalence. The potential contact between leashed dogs and wild small mammals is still a risk to re-infect owned dogs. This study shows that the long term application of regular dog dosing in the vast remote echinococcosis endemic areas of west China is still challenging

Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001

A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks

Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally, conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002 and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140