The Steiner problem for convex boundaries, II: the regular case

1993 ◽  
pp. 93-131
Author(s):  
A. O. Ivanov and A. A. Tuzhilin
Keyword(s):  
Steiner Problem ◽  
Regular Case

scholarly journals On different notions of calibrations for minimal partitions and minimal networks in ℝ2

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Marcello Carioni ◽  
Alessandra Pluda
Keyword(s):  
Minimal Surfaces ◽  
Steiner Problem ◽  
Minimal Networks

Abstract Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of the Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner problem and for planar minimal partitions that are already present in the literature. The paper is then complemented with remarks on the convexification of the problem, on nonexistence of calibrations and on calibrations in families.

scholarly journals A Modica–Mortola approximation for the Steiner Problem

2014 ◽  
Vol 352 (5) ◽  
pp. 451-454 ◽  
Author(s):  
Antoine Lemenant ◽  
Filippo Santambrogio
Keyword(s):  
Steiner Problem

The multitype continuous-time Markov branching process in a periodic environment

1980 ◽  
Vol 12 (1) ◽  
pp. 81-93 ◽  
Author(s):  
B. Klein ◽  
P. D. M. MacDonald
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Cell Kinetics ◽  
Initial Conditions ◽  
Random Variable ◽  
Diurnal Rhythms ◽  
Biological Applications ◽  
Regular Case ◽  
Markov Branching Process ◽  
Periodic Environment

The multitype continuous-time Markov branching process has many biological applications where the environmental factors vary in a periodic manner. Circadian or diurnal rhythms in cell kinetics are an important example. It is shown that in the supercritical positively regular case the proportions of individuals of various types converge in probability to a non-random periodic vector, independent of the initial conditions, while the absolute numbers of individuals of various types converge in probability to that vector multiplied by a random variable whose distribution depends on the initial conditions. It is noted that the proofs are straightforward extensions of the well-known results for a constant environment.

scholarly journals Solution of the Bernstein Problem in the Non-regular Case

2000 ◽  
Vol 223 (1) ◽  
pp. 109-132 ◽  
Author(s):  
J.Carlos Gutiérrez Fernández
Keyword(s):  
Regular Case ◽  
Bernstein Problem

scholarly journals On the finite W-algebra for the Lie superalgebra Q(N) in the non-regular case

2017 ◽  
Vol 58 (11) ◽  
pp. 111701 ◽  
Author(s):  
Elena Poletaeva ◽  
Vera Serganova
Keyword(s):  
Lie Superalgebra ◽  
Regular Case

scholarly journals A node-based ILP formulation for the node-weighted dominating Steiner problem

Networks ◽  
2016 ◽  
Vol 69 (1) ◽  
pp. 33-51 ◽  
Author(s):  
Andreas Bley ◽  
Ivana Ljubić ◽  
Olaf Maurer
Keyword(s):  
Steiner Problem
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