Results 21 to 30 of about 39,739 (245)

From homogeneous metric spaces to Lie groups

Comptes Rendus. Mathématique
We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively.After a review of a number of classical results, we use the Gleason–Iwasawa–Montgomery–Yamabe–Zippin structure theory to ...
Cowling, Michael G., Kivioja, Ville, Le Donne, Enrico, Nicolussi Golo, Sebastiano, Ottazzi, Alessandro   +4 more
doaj   +1 more source

Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups

, 2010
In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics.
Alekseevskiĭ, Besse, Birkes, Eberlein, Eberlein, Jablonski, Jablonski, Jensen, Kempf, Kirwan, Lauret, Marian, Michael Jablonski, Mostow, Mostow, Whitney   +15 more
core   +1 more source

Exponential Radicals of Solvable Lie Groups

Journal of Algebra, 2002
For any connected Lie group \(G\), we consider the metric induced by some left-invariant Riemannian structure on \(G\). An element \(g\) of \(G\) is said to be strictly exponentially distorted in \(G\) if the length of \(g^n\) in \(G\) grows as \(\log(|n|+ 1)\).
openaire   +1 more source

Superrigid subgroups of solvable Lie groups

, 1996
Let $\Gamma$ be a discrete subgroup of a simply connected, solvable Lie group~$G$, such that $\Ad_G\Gamma$ has the same Zariski closure as $\Ad G$. If $\alpha \colon \Gamma \to \GL_n(\real)$ is any finite-dimensional representation of~$\Gamma $,we show ...
Communicated Roe Goodman, Dave Witte
core   +4 more sources

Pre‐analytical optimization of cell‐free DNA and extracellular vesicle‐derived DNA for mutation detection in liquid biopsies

Molecular Oncology, EarlyView.
Pre‐analytical handling critically determines liquid biopsy performance. This study defines practical best‐practice conditions for cell‐free DNA (cfDNA) and extracellular vesicle–derived DNA (evDNA), showing how processing time, storage conditions, tube type, and plasma input volume affect DNA integrity and mutation detection.
Jonas Dohmen, Lucrezia De Santis, Bret M. Stephens, Vincent Bernard, Jörg C. Kalff, Lara Braun, Phillipp Leyendecker, Johannes Röttgen, Daniel Weissinger, Anirban Maitra, Paola A. Guerrero, Alexander Semaan   +11 more
wiley   +1 more source

Boundedness control sets for linear systems on Lie groups

Open Mathematics, 2018
Let Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior
Ayala Víctor, Todco María Torreblanca
doaj   +1 more source

Solvegeometry gravitational waves

, 2004
In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric).
Alekseevskii D V, Benedetti R, Berenstein D, Besse A L, Bi?ák J, Bianchi L, Blau M, Coley A A Hervik S, Coley A A Hervik S Pelavas N, Defrise L, Ellis G F R, Feinstein A, Goldman W H, Gutperle M, Helgason S, Hervik S, Hervik S, Kaigorodov V R, Kundt W, Milnor J, Ozsváth I, Podolský J, Pravda V, Salazar H, Sigbjørn Hervik, Siklos S T C, Stephani H, Thurston W P, Thurston W P, Wolter T H, Wolter T H   +30 more
core   +3 more sources

Cell‐cycle‐specific lesion evolution rather than inhibition of double‐strand‐break repair underpins cisplatin radiosensitization

Molecular Oncology, EarlyView.
We analyze cisplatin–DNA adducts (CDAs) and double‐strand breaks (DSBs) in a cell‐cycle‐dependent manner. We find that CDAs form similarly across all cell cycle phases. DSBs arise only in S‐phase. CDAs might not directly impair DSB repair, but S‐phase DSB lesions evolve in the presence of CDAs and disrupt repair in G2, also causing radiosensitization ...
Ye Qiu, Xixi Lin, Emil Mladenov, Veronika Mladenova, Jürgen Thomale, Ali Sak, Yao Wang, Yunxuan Deng, Eleni Gkika, Martin Stuschke, George Iliakis   +10 more
wiley   +1 more source

Killing Vector Fields of Invariant Metrics on Five-Dimensional Solvable Lie Groups

Mathematics
In this paper we study the existence of Killing vector fields for right-invariant metrics on five-dimensional Lie groups. We begin by providing some explanation of the classification lists of the low-dimensional Lie algebras.
Gerard Thompson
doaj   +1 more source

The A-theoretic Farrell–Jones conjecture for virtually solvable groups

, 2017
We prove the A -theoretic Farrell–Jones conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S -arithmetic groups and lattices in almost connected Lie ...
Kasprowski, D., Ullmann, M., Wegner, C., Winges, C.   +3 more
core   +1 more source