In this paper, we introduce the notion of generalized rational Okamoto–Painlevé pair (S, Y ) by generalizing the notion of the spaces of initial conditions of Painlevé equations. After classifying those pairs, we will establish an algebro-geometric approach to derive the Painlevé differential equations from the deformation of Okamoto–Painlevé pairs by using the local cohomology groups. Moreover...

In this paper, we introduce the notion of generalized rational Okamoto–Painlevé pair (S, Y ) by generalizing the notion of the spaces of initial conditions of Painlevé equations. After classifying those pairs, we will establish an algebro-geometric approach to derive the Painlevé differential equations from the deformation of Okamoto–Painlevé pairs by using the local cohomology groups. Moreover...

a Department of Anesthesia and Analgesia, Chang Gung Memorial Hospital, Chang Gung University, College of Medicine, Chia-Yi, Taiwan b Division of Thoracic and Cardiovascular Surgery, Chang Gung Memorial Hospital, Chang Gung University, College of Medicine, Chia-Yi, Taiwan c Department of Radiology, Chang Gung Memorial Hospital, Chang Gung University, College of Medicine, Chia-Yi, Taiwan d Gradu...

Multiple regression is an extension to simple regression in several ways. First, instead of examining a linear relationship bewteen two measurements, Xi and Yi, multiple regression aims to explain relationships between p measurements of an object i, denoted as (Xi,1, ..., Xi,p) and Yi. Based on a sample of n points, with each point having measurements (Yi, Xi,1, ..., Xi,p), multiple regression ...

Let Y be a Banach space, 1 < p < ∞. We give a simple criterion for embedding lp ⊂ Y , namely it suffices that the positive cone l+p ⊂ Y . This result is applied to the study of highly smooth operators from lp into Y (p is not an even integer). The main result is that every such operator has a harmonic behaviour unless l p K ⊂ Y for some K ∈ N. In this note we establish a natural criterion for e...