scholarly journals An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs

2019 ◽  
Vol 10 (1) ◽  
pp. 115-145
Author(s):  
H. Daniel Lenz ◽  
Peter Stollmann ◽  
Gunter Stolz
Keyword(s):  
Lower Bounds ◽  
Uncertainty Principle ◽  
Dirichlet Laplacian

scholarly journals Bounds on large extra dimensions from the Generalized Uncertainty Principle

2017 ◽  
Vol 32 (15) ◽  
pp. 1750082
Author(s):  
Marco Cavaglià ◽  
Benjamin Harms ◽  
Shaoqi Hou
Keyword(s):  
Black Hole ◽  
Lower Bounds ◽  
Uncertainty Principle ◽  
Extra Dimensions ◽  
Large Extra Dimensions ◽  
Production Cross ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Minimum Length ◽  
Minimum Length Scale

The Generalized Uncertainty Principle (GUP) implies the existence of a physical minimum length scale [Formula: see text]. In this scenario, black holes must have a radius larger than [Formula: see text]. They are hotter and evaporate faster than in standard Hawking thermodynamics. We study the effects of the GUP on black hole production and decay at the LHC in models with large extra dimensions. Lower bounds on the fundamental Planck scale and the minimum black hole mass at formation are determined from black hole production cross-section limits by the CMS Collaboration. The existence of a minimum length generally decreases the lower bounds on the fundamental Planck scale obtained in the absence of a minimum length.

scholarly journals Energy-Time Uncertainty Principle and Lower Bounds on Sojourn Time

2016 ◽  
Vol 17 (9) ◽  
pp. 2513-2527 ◽  
Author(s):  
Joachim Asch ◽  
Olivier Bourget ◽  
Victor Cortés ◽  
Claudio Fernandez
Keyword(s):  
Lower Bounds ◽  
Uncertainty Principle ◽  
Sojourn Time ◽  
Time Uncertainty

scholarly journals Convex duality for principal frequencies

2021 ◽  
Vol 4 (4) ◽  
pp. 1-28
Author(s):  
Lorenzo Brasco ◽  
Keyword(s):  
Lower Bounds ◽  
Variational Formulation ◽  
Torsional Rigidity ◽  
First Eigenvalue ◽  
Convex Minimization Problem ◽  
Dirichlet Laplacian ◽  
The First Eigenvalue ◽  
Divergence Type ◽  
Poincaré Constant ◽  
Type Constraint

<abstract><p>We consider the sharp Sobolev-Poincaré constant for the embedding of $ W^{1, 2}_0(\Omega) $ into $ L^q(\Omega) $. We show that such a constant exhibits an unexpected dual variational formulation, in the range $ 1 &lt; q &lt; 2 $. Namely, this can be written as a convex minimization problem, under a divergence–type constraint. This is particularly useful in order to prove lower bounds. The result generalizes what happens for the torsional rigidity (corresponding to $ q = 1 $) and extends up to the case of the first eigenvalue of the Dirichlet-Laplacian (i.e., to $ q = 2 $).</p></abstract>

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base
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