Results 61 to 70 of about 2,701,761 (237)
Sparse graph signals – uncertainty principles and recovery
GAMM-Mitteilungen, Volume 48, Issue 2, June 2025.ABSTRACT We study signals that are sparse either on the vertices of a graph or in the graph spectral domain. Recent results on the algebraic properties of random integer matrices as well as on the boundedness of eigenvectors of random matrices imply two types of support size uncertainty principles for graph signals.
Tarek Emmrich +2 more
wiley +1 more source
The Picard group in equivariant homotopy theory via stable module categories
Journal of Topology, Volume 18, Issue 2, June 2025.Abstract We develop a mechanism of “isotropy separation for compact objects” that explicitly describes an invertible G$G$‐spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module category.
Achim Krause
wiley +1 more source
arXiv, 2017 There is no bad group of Morley rank 2n+1 with an abelian Borel subgroup of Morley rank n. In particular, there is no bad group of Morley rank 3 (O. Fr{\'e}con).
arxiv
Restart Perturbations for Reversible Markov Chains: Trichotomy and Pre‐Cutoff Equivalence
Random Structures &Algorithms, Volume 66, Issue 3, May 2025.ABSTRACT Given a reversible Markov chain Pn$$ {P}_n $$ on n$$ n $$ states, and another chain P˜n$$ {\tilde{P}}_n $$ obtained by perturbing each row of Pn$$ {P}_n $$ by at most αn$$ {\alpha}_n $$ in total variation, we study the total variation distance between the two stationary distributions, ‖πn−π˜n‖$$ \left\Vert {\pi}_n-{\tilde{\pi}}_n\right\Vert $$.
Daniel Vial, Vijay Subramanian
wiley +1 more source
A note on torsion-free abelian groups of finite rank [PDF]
Proceedings of the American Mathematical Society, 1973 Let G be a torsion-free abelian group of rank n and X= {xl, *. , x,j a maximal set of rationally independent elements in G. It is well known that any g e G can be uniquely written g= oc1xl?+ +x, for some cci, . , ?C72, E Q, the rational numbers. This enables us to define, for any such (G, X), a collection of subgroups of Q and "natural" isomorphisms ...
W. Wickless, C. Vinsonhaler
openaire +1 more source
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract In this paper, we extend the theory of minimal limit key polynomials of valuations on the polynomial ring K[x]$K[x]$. Minimal key polynomials are useful to describe, for instance, the defect of an extension of valued fields. We use the theory of cuts on ordered abelian groups to show that the previous results on bounded sets of key polynomials
Enric Nart, Josnei Novacoski
wiley +1 more source
On groups and counter automata [PDF]
, 2006 We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the ...
arxiv +1 more source
The rank of group of cyclotomic units in abelian fields
Journal of Number Theory, 1982 AbstractA formula about the rank of group of cyclotomic units in abelian fields is established. From that formula, a series of equivalent conditions for independence of the system of cyclotomic units in abelian fields is stated and proved. For the particular case of cyclotomic fields, further properties of the rank are researched.
openaire +2 more sources
An Algebraic Roadmap of Particle Theories
Annalen der Physik, Volume 537, Issue 4, April 2025.The SO(10) grand unified theory, the Georgi–Glashow SU(5) grand unified theory, the Pati–Salam model, the Left–Right Symmetric model, and the Standard model have been studied extensively since the 1970s. Recasting these models in a division algebraic language elucidates how they are each in fact connected.
Nichol Furey
wiley +1 more source
The ultrasimplicial property for simple dimension groups with unique state, the image of which has rank one [PDF]
arXiv, 2014 Let $G$ be an ordered group that is a direct sum of a rank-one torsion-free abelian group and a finite-rank torsion-free abelian group, with order structure arising from the natural order on the first summand. A necessary condition and a sufficient condition are given for $G$ to have an ordered-group inductive limit representation using injective maps.
arxiv