A Simple Proof for a Result of Ollerenshaw on Steiner Trees

1994 ◽  
pp. 68-71 ◽  
Author(s):  
Xiufeng Du ◽  
Ding-Zhu Du ◽  
Biao Gao ◽  
Lixue Qü
Keyword(s):  
Simple Proof ◽  
Steiner Trees

Optimal Steiner trees under node and edge privacy conflicts

2021 ◽  
Author(s):  
Alessandro Hill ◽  
Roberto Baldacci ◽  
Stefan Voß
Keyword(s):  
Steiner Trees

scholarly journals Connected perimeter of planar sets

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
François Dayrens ◽  
Simon Masnou ◽  
Matteo Novaga ◽  
Marco Pozzetta
Keyword(s):  
Minimization Problem ◽  
Existence Of Solutions ◽  
Lower Semicontinuous ◽  
Representation Formula ◽  
Steiner Trees ◽  
Lower Semicontinuous Envelope ◽  
Simply Connected

AbstractWe introduce a notion of connected perimeter for planar sets defined as the lower semicontinuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is also studied. We prove a representation formula which links the connected perimeter, the classical perimeter, and the length of suitable Steiner trees. We also discuss the application of this notion to the existence of solutions to a nonlocal minimization problem with connectedness constraint.

A note on lower bounds for rectilinear Steiner trees

1992 ◽  
Vol 42 (3) ◽  
pp. 151-152
Author(s):  
J.S. Salowe
Keyword(s):  
Lower Bounds ◽  
Steiner Trees

scholarly journals Finding Steiner trees with degree 1 terminal nodes

2004 ◽  
Vol 1 (9) ◽  
pp. 258-262
Author(s):  
Hector Cancela ◽  
Franco Robledo ◽  
Gerardo Rubino
Keyword(s):  
Steiner Trees

scholarly journals A simple proof of Andrews’s 5 F 4 evaluation

2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  
Simple Proof

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

Packing Steiner trees: polyhedral investigations

1996 ◽  
Vol 72 (2) ◽  
pp. 101-123 ◽  
Author(s):  
M. Grötschel ◽  
A. Martin ◽  
R. Weismantel
Keyword(s):  
Steiner Trees

Directed Steiner trees with diffusion costs

2015 ◽  
Vol 32 (4) ◽  
pp. 1089-1106 ◽  
Author(s):  
Dimitri Watel ◽  
Marc-Antoine Weisser ◽  
Cédric Bentz ◽  
Dominique Barth
Keyword(s):  
Steiner Trees

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

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