Equilibrium problems on Riemannian manifolds with applications

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on Hadamard manifolds.National Natural Science Foundation of ChinaNatural Science Foundation of Guizhou Province (China)Dirección General de Enseñanza SuperiorJunta de AndalucíaNational Science Council of Taiwa

Exploration and practice of talent training mode in Sino-foreign cooperative schools -- taking Software engineering as an example

With the deepening of globalization, Sino-foreign cooperation in running schools plays an important role in China’s higher education. Sino-foreign cooperation in running schools refers to the degree education program set up by Chinese higher education institutions and foreign higher education institutions. This mode of cooperation can not only provide Chinese students with broader learning opportunities and international educational resources, but also promote educational exchanges and cooperation between China and foreign countries. As an important subject in the field of information technology, software engineering has broad employment prospects and development potential, so it has been widely used and promoted in Chinese-foreign cooperative education. This paper will take the software engineering major as an example to explore and practice the talent training model of Sino-foreign cooperation in running schools, aiming to provide reference for other majors and Chinese-foreign cooperation in running schools

Physical essence of propagable fractional-strength optical vortices in free space

Fractional-order vector vortex beams are recently demonstrated to be new carriers of fractional-strength optical vortices. However, why can those new vortex beams formed by the combination of both unstable states propagate stably in free space? Here, we solve this scientific problem by revealing the physical essence of propagable fractional-strength optical vortices in free space.Three new understandings regarding those peculiar vortex beams are therefore proposed, namely Abbe diffraction limit, phase evolution of vortex beam, and phase binary time vector property.For the first one, owing to Abbe diffraction limit, the inherent polarization modes are intertwined together, thereby maintaining the entire peculiar vortex beams in free space. For the second one, we demonstrate the phase evolution of vortex beam, which is the physical reason of polarization rotation of fractional-order VVBs. For the third one, the phase is not merely a scalar attribute of light beam, but manifests a binary time vector property. This work provides entirely different physical viewpoints on the phase of vortex beam and Abbe diffraction limit, which may deepen our knowledge on the behavior of light beam in classical optics

A Resilience Approach to Symbiosis Networks of Ecoindustrial Parks Based on Cascading Failure Model

Evaluation and improvement of resilience in ecoindustrial parks have been the pressing issues to be addressed in the study of safety. In this paper, eco-industrial systems are extracted as symbiosis networks by using social network analysis first. We then construct a novel cascading failure model and propose an evaluation method of node importance according to the features of symbiosis networks of eco-industrial parks. Based on the cascading model, an effective new method, that is, the critical threshold, is put forward to quantitatively assess the resilience of symbiosis networks of eco-industrial parks. Some theoretical analysis is furthermore provided to the critical threshold. Finally, we take Jinjie eco-industrial system in Shanxi Province of China as a case to investigate its resilience. The key potential nodes are identified by using our model. We also find the respective relation among the resilience of symbiosis networks and the parameters in our cascading model. Theoretical analysis results and numerical simulations both show the optimal value of the tunable load parameter with which the strongest resilience level against cascading failures can be attained in symbiosis networks of eco-industrial parks

Bias control in the analysis of case-control studies with incidence density sampling.

BACKGROUND: Previous simulation studies of the case-control study design using incidence density sampling, which required individual matching for time, showed biased estimates of association from conditional logistic regression (CLR) analysis; however, the reason for this is unknown. Separately, in the analysis of case-control studies using the exclusive sampling design, it has been shown that unconditional logistic regression (ULR) with adjustment for an individually matched binary factor can give unbiased estimates. The validity of this analytic approach in incidence density sampling needs evaluation. METHODS: In extensive simulations using incidence density sampling, we evaluated various analytic methods: CLR with and without a bias-reduction method, ULR with adjustment for time in quintiles (and residual time within quintiles) and ULR with adjustment for matched sets and bias reduction. We re-analysed a case-control study of Haemophilus influenzae type B vaccine using these methods. RESULTS: We found that the bias in the CLR analysis from previous studies was due to sparse data bias. It can be controlled by the bias-reduction method for CLR or by increasing the number of cases and/or controls. ULR with adjustment for time in quintiles usually gave results highly comparable to CLR, despite breaking the matches. Further adjustment for residual time trends was needed in the case of time-varying effects. ULR with adjustment for matched sets tended to perform poorly despite bias reduction. CONCLUSIONS: Studies using incidence density sampling may be analysed by either ULR with adjustment for time or CLR, possibly with bias reduction