In a previous work (Ozawa et al. Calc. Var. Partial Diff. Equ. 59(4), 39 2020), the authors introduced Lin-Lu-Yau type Ricci curvature for directed graphs referring to formulation of Chung Laplacian. The aim this note is provide von Renesse-Sturm characterization our lower bound via gradient estimate heat semigroup, and transportation inequality along flow. As an application, we will conclude c...

conclusion using standard imaging parameters, each mri sequence reaches its maximum si in a specific contrast concentration, which is highest in se and least in ir in a comparison between se, fse and ir sequences. results this study shows that maximum si will appear at different ranges in different sequences. the maximum si can be seen at concentrations of 5.95, 4.96 and 3.98mmol/l for se, fse ...