Discrete & Continuous Dynamical Systems - S最新文献_第7页

Topological mild mixing of all orders along polynomials 沿多项式的所有阶的拓扑轻度混合

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-19 DOI: 10.3934/dcds.2021150

Yang Cao, S. Shao

{"title":"Topological mild mixing of all orders along polynomials","authors":"Yang Cao, S. Shao","doi":"10.3934/dcds.2021150","DOIUrl":"https://doi.org/10.3934/dcds.2021150","url":null,"abstract":"<p style='text-indent:20px;'>A minimal system <inline-formula><tex-math id=\"M1\">begin{document}$ (X,T) $end{document}</tex-math></inline-formula> is topologically mildly mixing if for all non-empty open subsets <inline-formula><tex-math id=\"M2\">begin{document}$ U,V $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M3\">begin{document}$ {nin {mathbb Z}: Ucap T^{-n}Vneq emptyset} $end{document}</tex-math></inline-formula> is an IP<inline-formula><tex-math id=\"M4\">begin{document}$ ^* $end{document}</tex-math></inline-formula>-set. In this paper we show that if a minimal system is topologically mildly mixing, then it is mild mixing of all orders along polynomials. That is, suppose that <inline-formula><tex-math id=\"M5\">begin{document}$ (X,T) $end{document}</tex-math></inline-formula> is a topologically mildly mixing minimal system, <inline-formula><tex-math id=\"M6\">begin{document}$ din {mathbb N} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M7\">begin{document}$ p_1(n),ldots, p_d(n) $end{document}</tex-math></inline-formula> are integral polynomials with no <inline-formula><tex-math id=\"M8\">begin{document}$ p_i $end{document}</tex-math></inline-formula> and no <inline-formula><tex-math id=\"M9\">begin{document}$ p_i-p_j $end{document}</tex-math></inline-formula> constant, <inline-formula><tex-math id=\"M10\">begin{document}$ 1le ineq jle d $end{document}</tex-math></inline-formula>. Then for all non-empty open subsets <inline-formula><tex-math id=\"M11\">begin{document}$ U , V_1, ldots, V_d $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M12\">begin{document}$ {nin {mathbb Z}: Ucap T^{-p_1(n) }V_1cap T^{-p_2(n)}V_2cap ldots cap T^{-p_d(n) }V_d neq emptyset } $end{document}</tex-math></inline-formula> is an IP<inline-formula><tex-math id=\"M13\">begin{document}$ ^* $end{document}</tex-math></inline-formula>-set. We also give the corresponding theorem for systems under abelian group actions.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90235734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Local well-posedness for the Zakharov system in dimension d ≤ 3 d维≤3的Zakharov系统的局部适定性

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-16 DOI: 10.3934/dcds.2021147

A. Sanwal

引用次数: 5

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction 带干摩擦的软式机车周期性扫掠过程的稳定性及渐近平均速度

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-04 DOI: 10.3934/dcds.2021135

G. Colombo, P. Gidoni, Emilio Vilches

引用次数: 8

Traveling wave solution for a diffusive simple epidemic model with a free boundary 具有自由边界的扩散简单流行病模型的行波解

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-01 DOI: 10.3934/dcdss.2020387

Yoichi Enatsu, E. Ishiwata, T. Ushijima

引用次数: 1

Convergence of a blow-up curve for a semilinear wave equation 半线性波动方程爆破曲线的收敛性

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-01 DOI: 10.3934/dcdss.2020388

Takiko Sasaki

{"title":"Convergence of a blow-up curve for a semilinear wave equation","authors":"Takiko Sasaki","doi":"10.3934/dcdss.2020388","DOIUrl":"https://doi.org/10.3934/dcdss.2020388","url":null,"abstract":"We consider a blow-up phenomenon for begin{document}$ { partial_t^2 u_ varepsilon} $end{document} begin{document}$ {- varepsilon^2 partial_x^2u_ varepsilon } $end{document} begin{document}$ { = F(partial_t u_ varepsilon)}. $end{document} The derivative of the solution begin{document}$ partial_t u_ varepsilon $end{document} blows-up on a curve begin{document}$ t = T_ varepsilon(x) $end{document} if we impose some conditions on the initial values and the nonlinear term begin{document}$ F $end{document} . We call begin{document}$ T_ varepsilon $end{document} blow-up curve for begin{document}$ { partial_t^2 u_ varepsilon} $end{document} begin{document}$ {- varepsilon^2 partial_x^2u_ varepsilon } $end{document} begin{document}$ { = F(partial_t u_ varepsilon)}. $end{document} In the same way, we consider the blow-up curve begin{document}$ t = tilde{T}(x) $end{document} for begin{document}$ {partial_t^2 u} $end{document} begin{document}$ = $end{document} begin{document}$ {F(partial_t u)}. $end{document} The purpose of this paper is to show that, for each begin{document}$ x $end{document} , begin{document}$ T_ varepsilon(x) $end{document} converges to begin{document}$ tilde{T}(x) $end{document} as begin{document}$ varepsilonrightarrow 0. $end{document}","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"47 4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83189448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Segmentation of color images using mean curvature flow and parametric curves 利用平均曲率流和参数曲线分割彩色图像

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-01 DOI: 10.3934/dcdss.2020389

P. Paus, S. Yazaki

引用次数: 1

Numerical and mathematical analysis of blow-up problems for a stochastic differential equation 随机微分方程爆破问题的数值与数学分析

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-01 DOI: 10.3934/dcdss.2020391

T. Ishiwata, Young Chol Yang

引用次数: 1

Signed-distance function based non-rigid registration of image series with varying image intensity 基于符号距离函数的变图像强度序列非刚性配准

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-01 DOI: 10.3934/DCDSS.2020386

Kateřina Škardová, T. Oberhuber, J. Tintěra, R. Chabiniok

{"title":"Signed-distance function based non-rigid registration of image series with varying image intensity","authors":"Kateřina Škardová, T. Oberhuber, J. Tintěra, R. Chabiniok","doi":"10.3934/DCDSS.2020386","DOIUrl":"https://doi.org/10.3934/DCDSS.2020386","url":null,"abstract":"In this paper we propose a method for locally adjusted optical flow-based registration of multimodal images, which uses the segmentation of the object of interest and its representation by the signed-distance function (OF dist method). We deal with non-rigid registration of the image series acquired by the Modiffied Look-Locker Inversion Recovery (MOLLI) magnetic resonance imaging sequence, which is used for a pixel-wise estimation of T 1 relaxation time. The spatial registration of the images within the series is necessary to compensate the patient's imperfect breath-holding. The evolution of intensities and a large variation of image contrast within the MOLLI image series, together with the myocardium of left ventricle (the object of interest) typically not being the most distinct object in the scene, makes the registration challenging. The paper describes all components of the proposed OF dist method and their implementation. The method is then compared to the performance of a standard mutual information maximization-based registration method, applied either to the original image (MIM) or to the signed-distance function (MIM dist). Several experiments with synthetic and real MOLLI images are carried out. On synthetic image with a single object, MIM performed the best, while OF dist and MIM dist provided better results on synthetic images with more than one object and on real images. When applied to signed-distance function of two objects of interest, MIM dist provided a larger registration error (but more homogeneously distributed) compared to OF dist. For the real MOLLI image series with left ventricle pre-segmented using a level-set method, the proposed OF dist registration performed the best, as is demonstrated visually and by measuring the increase of mutual information in the object of interest and its neighborhood.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76847295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow 结晶eikonal曲率流演化螺旋的ODE和水平集方法的数值分析

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-01 DOI: 10.3934/dcdss.2020390

T. Ishiwata, T. Ohtsuka

引用次数: 3

A proof by foliation that lawson's cones are $ A_{Phi} $-minimizing 用叶理法证明劳森锥是$ A_{ φ} $-最小化的

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-02-16 DOI: 10.3934/DCDS.2021077

Connor Mooney, Yang Yang

引用次数: 6