On the 2-Center Problem Under Convex Polyhedral Distance Function

2016 ◽  
pp. 365-377
Author(s):  
Sergey Bereg
Keyword(s):  
Distance Function ◽  
Center Problem ◽  
Convex Polyhedral

Parallel Residues

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Distance Function ◽  
Length Function ◽  
Coxeter System ◽  
Vertex Set ◽  
Ordered Pairs

This chapter considers the notion of parallel residues in a building. It begins with the assumption that Δ‎ is a building of type Π‎, which is arbitrary except in a few places where it is explicitly assumed to be spherical. Δ‎ is not assumed to be thick. The chapter then elaborates on a hypothesis which states that S is the vertex set of Π‎, (W, S) is the corresponding Coxeter system, d is the W-distance function on the set of ordered pairs of chambers of Δ‎, and ℓ is the length function on (W, S). It also presents a notation in which the type of a residue R is denoted by Typ(R) and concludes with the condition that residues R and T of a building will be called parallel if R = projR(T) and T = projT(R).

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

ABOUT THE DISTANCE FUNCTION BETWEEN FUZZY SETS

2009 ◽  
Vol 12 (3) ◽  
pp. 151-154
Author(s):  
Sufyan A. Whaib ◽  
Keyword(s):  
Fuzzy Sets ◽  
Distance Function

scholarly journals A New Normal Form for Monodromic Nilpotent Singularities of Planar Vector Fields

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné
Keyword(s):  
Normal Form ◽  
Vector Fields ◽  
New Technique ◽  
Center Problem ◽  
New Normal ◽  
Planar Vector Fields ◽  
Planar Vector ◽  
A New Technique

AbstractIn this work, we present a new technique for solving the center problem for nilpotent singularities which consists of determining a new normal form conveniently adapted to study the center problem for this singularity. In fact, it is a pre-normal form with respect to classical Bogdanov–Takens normal formal and it allows to approach the center problem more efficiently. The new normal form is applied to several examples.

scholarly journals Directional Distance Function Technical Efficiency of Chili Production in Thailand

2021 ◽  
Vol 13 (2) ◽  
pp. 741
Author(s):  
Wirat Krasachat ◽  
Suthathip Yaisawarng
Keyword(s):  
Distance Function ◽  
Rainy Season ◽  
Sample Selection ◽  
Agricultural Practices ◽  
Directional Distance Function ◽  
Dry Season ◽  
Small Samples ◽  
Function Technique ◽  
Security Problem ◽  
Gap Technology

To overcome the challenging food safety and security problem, in 2003, the Thai government initiated ‘Good Agricultural Practices’ (GAP) technology. This paper used a sample of 107 small chili farms from the Chiyaphoom province for the 2012 crop year, and data envelopment analysis (DEA) meta-frontier directional distance function technique to answer two questions: (1) Are GAP-adopting farms, on average, more efficient than conventional farms? (2) Does access to GAP technology affect farmers’ decisions to adopt GAP technology? We also developed an ‘indirect’ approach to reduce the potential sample selection bias for small samples. For the dry-season subsample, GAP farms were more technically efficient when compared with non-GAP farms. These dry-season non-GAP farms may not adopt the GAP method because they have limited access to GAP technology. For the rainy-season subsample, on average, GAP farms were more efficient than non-GAP farms at the 5% level. Access to the GAP technology is not a possible reason for non-GAP rainy season farms to not adopt the GAP technology. To enable sustainable development, government agencies and nongovernmental organizations (NGOs) must develop and implement appropriate educational and training workshops to promote and assist GAP technology adoption for chili farms in Thailand.

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