Extremal Presentations for Classical Lie Algebras [PDF]
The long-root elements in Lie algebras of Chevalley type have been well studied and can be characterized as extremal elements, that is, elements $x$ such that the image of $(\ad x)^2$ lies in the subspace spanned by $x$.
Cameron+16 more
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Extreme Lengths in Brownian and Bessel Excursions [PDF]
VI ( t) >~ V2(t) 0 ? . ??Vn(t) 3 . , (1.1) the ordered excursion lengths of R over (0, t), the last zero-free interval (A-(t), t) being considered as an (incomplete) excursion interval. Discussions on excursion intervals excluding (A-(t), t) are postponed to Section 5.
Hu, Yueyun, Shi, Zhan
openaire +3 more sources
The dual of non-extremal area: differential entropy in higher dimensions
The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-
Vijay Balasubramanian, Charles Rabideau
doaj +1 more source
The complexity of deciding whether a graph admits an orientation with fixed weak diameter [PDF]
An oriented graph $\overrightarrow{G}$ is said weak (resp. strong) if, for every pair $\{ u,v \}$ of vertices of $\overrightarrow{G}$, there are directed paths joining $u$ and $v$ in either direction (resp. both directions).
Julien Bensmail+2 more
doaj +1 more source
Extremal lengths on Denjoy domains [PDF]
We consider the problem of computing the extremal lengths of certain homotopy classes of curves in certain symmetric surfaces. Specifically, we concentrate on plane domains which are conformal to the Riemann sphere with a collection of slits in the real axis removed; such a conformal type is called a Denjoy domain.
openaire +2 more sources
EXTREMAL IOTA ENERGY OF A SUBCLASS OF TRICYCLIC DIGRAPHS AND SIDIGRAPHS [PDF]
The iota energy of an n-vertex digraph D is defined by Ec (š·) = ā ō1 |Im(š§ k)|, where z1, . . ., zn are eigenvalues of D and Im(zk) is the imaginary part of eigenvalue zk . The iota energy of an n-vertex sidigraph can be defined analogously.
Fareeha Jamal, Mehtab Khan
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Critical behavior in 2+1 dimensional black holes [PDF]
The critical behavior and phase transition in the 2+1 dimensional Ba\~nados, Teitelboim, and Zanelli (BTZ) black holes are discussed. By calculating the equilibrium thermodynamic fluctuations in the microcanonical ensemble, canonical ensemble, and grand ...
A. Curir+51 more
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Patellar Tendon Length is Associated with Lower Extremity Length but Not Gender [PDF]
The aim of this study was to evaluate the patellar tendon length (PTL) with focus on gender differences and possible correlations with the total leg length (TLL) and the long bones of the lower extremity.The sample involved 50 paired lower extremities from human adult cadavers.
Manuel Dreu+8 more
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Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction. [PDF]
Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands.
Zitong Zhang+4 more
doaj +1 more source
Some restrictions on the weight enumerators of near-extremal ternary self-dual codes and quaternary Hermitian self-dual codes [PDF]
We give restrictions on the weight enumerators of ternary near-extremal self-dual codes of length divisible by $12$ and quaternary near-extremal Hermitian self-dual codes of length divisible by $6$. We consider the weight enumerators for which there is a ternary near-extremal self-dual code of length $12m$ for $m =3,4,5,6$.
arxiv