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Higher frequency of circulating regulatory T cells is associated with poor outcomes in patients with colorectal cancer. [PDF]
Discov OncolLu Y, Guo H, Guo T, Zhang L, Pan X.
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Discrete Anisotropic Curve Shortening Flow
SIAM Journal on Numerical Analysis, 1999A numerical scheme for the numerical solution of the nonlinear and degenerate problem of anisotropic curve shortening flow (which is a geometric evolution of a curve and is equivalent to the gradient flow of anisotropic interface energy) is developed. The analysis is based on the fact that the evolution problem can be transformed into a linear partial ...
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Linearised Euclidean Shortening Flow of Curve Geometry
International Journal of Computer Vision, 1999The geometry of a space curve is described in terms of a Euclidean invariant frame field, metric, connection, torsion and curvature. Here the torsion and curvature of the connection quantify the curve geometry. In order to retain a stable and reproducible description of that geometry, such that it is slightly affected by non-uniform protrusions of the ...
Salden, A.H. +2 more
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1987
This is an expository paper describing the recent progress in the study of the curve shortening equation $${X_{{t\,}}} = \,kN $$ (0.1) Here X is an immersed curve in ℝ2, k the geodesic curvature and N the unit normal vector. We review the work of Gage on isoperimetric inequalities, the work of Gage and Hamilton on the associated heat equation
C. L. Epstein, Michael Gage
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This is an expository paper describing the recent progress in the study of the curve shortening equation $${X_{{t\,}}} = \,kN $$ (0.1) Here X is an immersed curve in ℝ2, k the geodesic curvature and N the unit normal vector. We review the work of Gage on isoperimetric inequalities, the work of Gage and Hamilton on the associated heat equation
C. L. Epstein, Michael Gage
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Curve Shortening Flow in Arbitrary Dimensional Euclidian Space
Acta Mathematica Sinica, English Series, 2004Let \(\gamma: S^1\to R^\ell\) be an immersion and denote \(T=\partial\gamma/\partial s\), where \(s\) is the arc-length parameter. To seek solutions of the equation \(\frac{\partial\gamma}{\partial t}=\overline k\), \(\gamma(\cdot,0) =\gamma_0(\cdot)\), is referred to as the curve shortening problem, where \(\overline k\) is the first vector of the ...
Yang, Yunyan, Jiao, Xiaoxiang
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Weak solutions of the curve shortening flow
Calculus of Variations and Partial Differential Equations, 1997The author formulates a parametric notion of weak solution for the curve shortening flow in arbitrary codimensions, and he proves the existence of such a solution which is global in time for an arbitrary smooth closed initial curve in \(\mathbb{R}^n\).
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A revisit to the curve shortening flow
Discrete and Continuous Dynamical Systems - BzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Yarui +3 more
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