scholarly journals Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds

2020 ◽  
Author(s):  
Mikołaj Frączyk
Keyword(s):  
Hyperbolic Surfaces ◽  
Strong Limit

Asymptotic Estimates of the First Eigenvalue of the p-Laplacian

2003 ◽  
Vol 3 (2) ◽  
Author(s):  
Bruno Colbois ◽  
Ana-Maria Matei
Keyword(s):  
Direct Application ◽  
Parameter Family ◽  
Precise Estimate ◽  
First Eigenvalue ◽  
Asymptotic Estimates ◽  
Hyperbolic Surfaces ◽  
The First Eigenvalue

AbstractWe consider a 1-parameter family of hyperbolic surfaces M(t) of genus ν which degenerate as t → 0 and we obtain a precise estimate of λAs a direct application, we obtain that the quotientTo prove our results we use in an essential way the geometry of hyperbolic surfaces which is very well known. We show that an eigenfunction for λ

scholarly journals Isometry groups of infinite-genus hyperbolic surfaces

2021 ◽  
Author(s):  
Tarik Aougab ◽  
Priyam Patel ◽  
Nicholas G. Vlamis
Keyword(s):  
Hyperbolic Surfaces ◽  
Isometry Groups

scholarly journals Proper contractions and invariant subspaces

2001 ◽  
Vol 28 (4) ◽  
pp. 223-230 ◽  
Author(s):  
C. S. Kubrusly ◽  
N. Levan
Keyword(s):  
Invariant Subspace ◽  
Invariant Subspaces ◽  
Strong Limit ◽  
Strict Contraction ◽  
Proper Contraction

LetTbe a contraction andAthe strong limit of{T∗nTn}n≥1. We prove the following theorem: if a hyponormal contractionTdoes not have a nontrivial invariant subspace, thenTis either a proper contraction of class𝒞00or a nonstrict proper contraction of class𝒞10for whichAis a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator[T*,T]is a strict contraction.

scholarly journals Pathways for intramolecular relaxation in S 1 benzene

1990 ◽  
Vol 332 (1625) ◽  
pp. 189-201 ◽  
Keyword(s):  
Energy Coupling ◽  
Weak Limit ◽  
Excess Energy ◽  
Matrix Elements ◽  
Strong Limit ◽  
Decay Channels ◽  
Two Photon ◽  
Decay Behaviour ◽  
Quantum Numbers ◽  
Fast Electronic

Sub-Doppler spectra of various one- and two-photon vibronic bands of benzene are discussed and analysed to determine the pathways of intramolecular relaxation for Sx benzene. New results are presented for the 14J1q16| band of C 6 H 6 and the 14^1^ band of 13 C 6 H 6 . The decay behaviour depends strongly on the excess energy and the rotational quantum numbers rather than on the vibrational character and symmetry of the excited state. At low vibrational excess energy the pathway for intramolecular relaxation is a coupling in the strong limit between pairs of states in Sx leading to shifts of lines, whereas at intermediate excess energy coupling in the weak limit to background states in Sx is present. These background states are strongly broadened due to a fast electronic non-radiative process. The intramolecular relaxation is found to be initiated by the coupling to the broadened S 1 background states and energy can flow via these states to the T 1 or S 0 state. The rotationally selective disappearance of lines is believed to be due to an intricate interplay of the rotational dependence of the coupling matrix elements and accidental resonances, which lead to interference of possible decay channels.

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