Groups with weak minimality and maximality conditions for subgroups which are not normal

1989 ◽  
Vol 41 (12) ◽  
pp. 1474-1477 ◽  
Author(s):  
L. A. Kurdachenko ◽  
V. �. Goretskii
Keyword(s):  
Weak Minimality

scholarly journals Variational Inequalities Characterizing Weak Minimality in Set Optimization

2014 ◽  
Vol 166 (3) ◽  
pp. 804-824 ◽  
Author(s):  
Giovanni P. Crespi ◽  
Matteo Rocca ◽  
Carola Schrage
Keyword(s):  
Variational Inequalities ◽  
Set Optimization ◽  
Weak Minimality

scholarly journals Weak Minimal Area in Entanglement Entropy

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Shesansu Sekhar Pal ◽  
Shubhalaxmi Rath
Keyword(s):  
Black Hole ◽  
Upper Bound ◽  
Entanglement Entropy ◽  
Necessary Condition ◽  
Minimality Condition ◽  
Higher Derivative ◽  
Entropy Functional ◽  
Derivative Term ◽  
Weak Minimality ◽  
Minimal Area

We revisit the minimal area condition of Ryu-Takayanagi in the holographic calculation of the entanglement entropy, in particular, the Legendre test and the Jacobi test. The necessary condition for the weak minimality is checked via Legendre test and its sufficient nature via Jacobi test. We show for AdS black hole with a strip type entangling region that it is this minimality condition that makes the hypersurface unable to cross the horizon, which is in agreement with that studied earlier by Engelhardt et al. and Hubeny using a different approach. Moreover, demanding the weak minimality condition on the entanglement entropy functional with the higher derivative term puts a constraint on the Gauss-Bonnet coupling; that is, there should be an upper bound on the value of the coupling,λa<(d-3)/4(d-1).

A monotonicity theorem for dp-minimal densely ordered groups

2010 ◽  
Vol 75 (1) ◽  
pp. 221-238 ◽  
Author(s):  
John Goodrick
Keyword(s):  
General Notion ◽  
Ordered Group ◽  
Common Generalization ◽  
Unary Function ◽  
Monotonic Functions ◽  
Minimal Theory ◽  
Ordered Groups ◽  
Weak Minimality

AbstractDp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inp-minimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitely many continuous locally monotonic functions (Theorem 3.2).

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