scholarly journals Modelling white matter in gyral blades as a continuous vector field

NeuroImage ◽  
2020 ◽  
pp. 117693
Author(s):  
Michiel Cottaar ◽  
Matteo Bastiani ◽  
Nikhil Boddu ◽  
Matthew F. Glasser ◽  
Suzanne Haber ◽  
...  
Keyword(s):  
Vector Field ◽  
White Matter ◽  
Continuous Vector ◽  
Continuous Vector Field

scholarly journals Weak solutions of differential equations in Banach spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 407-418 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Vector Field ◽  
Banach Spaces ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Continuous Vector ◽  
Weakly Continuous ◽  
Continuous Vector Field ◽  
The Cauchy Problem

We consider the Cauchy problem x (t) = f (t,x (t)), x (0) = x0 in a nonreflexive Banach space X and for f: T × X → X a weakly continuous vector field. Using a compactness hypothesis involving a weak measure of noncompactness we prove an existence result that generalizes earlier theorems by Chow-Shur, Kato and Cramer-Lakshmikantham-Mitchell.

Remarks on a semilinear system in ℝn motivated by difference equations

2018 ◽  
Vol 68 (5) ◽  
pp. 1075-1082
Author(s):  
Diogo Caetano ◽  
Luís Sanchez
Keyword(s):  
Vector Field ◽  
Difference Equations ◽  
Nonlinear Term ◽  
Linear Part ◽  
Continuous Vector ◽  
One Dimensional ◽  
Continuous Vector Field

Abstract We study some conditions of solvability of a semilinear system in ℝn, where the linear part is represented by an n × n matrix with one-dimensional kernel and the nonlinear term is a sublinear, continuous vector field.

White matter fiber tract modeling based on reconstruction of fiber orientation vector field in DT-MRI

2005 ◽  
Vol 1281 ◽  
pp. 1289
Author(s):  
Y. Masutani ◽  
S. Aoki ◽  
O. Abe ◽  
K. Ino ◽  
K. Ohtomo
Keyword(s):  
Vector Field ◽  
White Matter ◽  
Fiber Orientation ◽  
Fiber Tract ◽  
Orientation Vector
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