Coincidence Degree

2021 ◽  
pp. 289-332
Author(s):  
James K. Peterson
Keyword(s):  
Author(s):  
Zhihui Huang ◽  
Huimin Zhao ◽  
Jin Zhan ◽  
Huakang Li

AbstractSiamPRN algorithm performs well in visual tracking, but it is easy to drift under occlusion and fast motion scenes because it uses $$\ell _1$$ ℓ 1 -smooth loss function to measure the regression location of bounding box. In this paper, we propose a multivariate intersection over union (MIOU) loss in SiamRPN tracking framework. Firstly, MIOU loss includes three geometric factors in regression: the overlap area ratio, the center distance ratio, and the aspect ratio, which can better reflect the coincidence degree of target box and prediction box. Secondly, we improve the definition of aspect ratio loss to avoid gradient explosion, improve the optimization performance of prediction box. Finally, based on SiamPRN tracker, we compared the tracking performance of $$\ell _1$$ ℓ 1 -smooth loss, IOU loss, GIOU loss, DIOU loss, and MIOU loss. Experimental results show that the MIOU loss has better target location regression than other loss functions on the OTB2015 and VOT2016 benchmark, especially for the challenges of occlusion, illumination change and fast motion.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Assia Guezane-Lakoud ◽  
Adem Kılıçman

Abstract The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional derivatives. The proofs of the existence of solutions are mainly based on Mawhin’s coincidence degree theory. We provide an example to illustrate the main result.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.


Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.


2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.


2005 ◽  
Vol 2005 (3) ◽  
pp. 281-297 ◽  
Author(s):  
Hong Xiang ◽  
Ke-Ming Yan ◽  
Bai-Yan Wang

By using coincidence degree theory as well as a priori estimates and Lyapunov functional, we study the existence and global stability of periodic solution for discrete delayed high-order Hopfield-type neural networks. We obtain some easily verifiable sufficient conditions to ensure that there exists a unique periodic solution, and all theirs solutions converge to such a periodic solution.


2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Yuanke Li

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.


Sign in / Sign up

Export Citation Format

Share Document