Optimization of multiple covering of a bounded set with circles

2010 ◽  
Vol 50 (4) ◽  
pp. 721-732 ◽  
Author(s):  
Sh. I. Galiev ◽  
M. A. Karpova
Keyword(s):  
Multiple Covering ◽  
Bounded Set

scholarly journals Optimization of a k-covering of a bounded set with circles of two given radii

2021 ◽  
Vol 11 (1) ◽  
pp. 232-240
Author(s):  
Alexander V. Khorkov ◽  
Shamil I. Galiev
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Numerical Results ◽  
Programming Models ◽  
Bounded Set ◽  
The Given

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

The Bounded Set

1989 ◽  
pp. 215-243
Author(s):  
Charles Lins
Keyword(s):  
Bounded Set

scholarly journals Some related fixed point theorems for multivalued mappings on two metric spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 392-400
Author(s):  
Ö. Biçer ◽  
M. Olgun ◽  
T. Alyildiz ◽  
I. Altun
Keyword(s):  
Fixed Point ◽  
Classical Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Compact Set ◽  
Complete Metric Spaces ◽  
Bounded Set ◽  
Contraction Type ◽  
Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

scholarly journals Approximation of a semigroup model of anomalous diffusion in a bounded set

2013 ◽  
Vol 2 (1) ◽  
pp. 173-192 ◽  
Author(s):  
Stephen Thompson ◽  
◽  
Thomas I. Seidman ◽  
Keyword(s):  
Anomalous Diffusion ◽  
Bounded Set

Global Attractor of the Liquid Helium-4 System in Hk Space

2013 ◽  
Vol 444-445 ◽  
pp. 731-737
Author(s):  
Zhi Bo Hou ◽  
Li Mei Li
Keyword(s):  
Existence Theorem ◽  
Liquid Helium ◽  
Global Attractor ◽  
Iteration Procedure ◽  
Helium 4 ◽  
Bounded Set ◽  
Regularity Estimates

In this paper, by using an iteration procedure, regularity estimates of the linear semi-groups and a generalized existence theorem of global attractor, we prove that the liquid helium-4 system possesses a global attractor in space for all , which attracts any bounded set of in the-norm.

scholarly journals Uniqueness for diffusions degenerating at the boundary of a smooth bounded set

2004 ◽  
Vol 32 (4) ◽  
pp. 3167-3190 ◽  
Author(s):  
Dante DeBlassie
Keyword(s):  
Bounded Set

scholarly journals Subdifferential Properties of Minimal Time Functions Associated with Set-Valued Mappings with Closed Convex Graphs in Hausdorff Topological Vector Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Optimization Problems ◽  
Time Function ◽  
Vector Spaces ◽  
Directional Derivatives ◽  
Minimal Time Function ◽  
Topological Vector Spaces ◽  
Minimal Time ◽  
Set Valued Mapping ◽  
Bounded Set ◽  
Normed Vector

For a set-valued mappingMdefined between two Hausdorff topological vector spacesEandFand with closed convex graph and for a given point(x,y)∈E×F, we study the minimal time function associated with the images ofMand a bounded setΩ⊂Fdefined by𝒯M,Ω(x,y):=inf{t≥0:M(x)∩(y+tΩ)≠∅}. We prove and extend various properties on directional derivatives and subdifferentials of𝒯M,Ωat those points of(x,y)∈E×F(both cases: points in the graphgph Mand points outside the graph). These results are used to prove, in terms of the minimal time function, various new characterizations of the convex tangent cone and the convex normal cone to the graph ofMat points insidegph Mand to the graph of the enlargement set-valued mapping at points outsidegph M. Our results extend many existing results, from Banach spaces and normed vector spaces to Hausdorff topological vector spaces (Bounkhel, 2012; Bounkhel and Thibault, 2002; Burke et al., 1992; He and Ng, 2006; and Jiang and He 2009). An application of the minimal time function𝒯M,Ωto the calmness property of perturbed optimization problems in Hausdorff topological vector spaces is given in the last section of the paper.

scholarly journals Multiple covering of a closed set on a plane with non-Euclidean metrics

2018 ◽  
Vol 51 (32) ◽  
pp. 850-854 ◽  
Author(s):  
Lempert Anna ◽  
Le Quang Mung
Keyword(s):  
Closed Set ◽  
Multiple Covering ◽  
Euclidean Metrics

scholarly journals Nonlocal Variational Principles with Variable Growth

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yongqiang Fu ◽  
Miaomiao Yang
Keyword(s):  
Sobolev Spaces ◽  
Lower Semicontinuity ◽  
Variable Exponent ◽  
Variational Principles ◽  
Young Measures ◽  
Bounded Set ◽  
Weak Lower Semicontinuity ◽  
Variable Exponent Sobolev Spaces ◽  
Regular Open

This paper is concerned with the functionalJdefined byJ(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, whereΩ⊂ℝNis a regular open bounded set andWis a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation ofJ.

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