Results 121 to 130 of about 5,027 (259)
Chains of Dense Gδ Sets in Perfect Polish Spaces
International Journal of TopologyWe prove that in every nonempty perfect Polish space, every dense Gδ subset contains strictly decreasing and strictly increasing chains of dense Gδ subsets of length c, the cardinality of the continuum. As a corollary, this holds in Rn for each n≥1. This
Sidney A. Morris
doaj +1 more source
Finite-infinite range inequalities in the complex plane
International Journal of Mathematics and Mathematical Sciences, 1991 Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property.
H. N. Mhaskar
doaj +1 more source
, 2023 This article the properties of sets F and G , which are Borel sets, in topological spaces were studied and the following results were obtained: a) Preimage of the set F (resp. G ) under the continuous mapping is also the set F (resp. G ); b) The image of the set G under the continuous mapping is not the set G ; c) The image of the set G ...
openaire +2 more sources
Plant, Cell &Environment, Volume 49, Issue 7, Page 4166-4177, July 2026.Abstract Abscisic acid (ABA) is a key phytohormone in plant responses to water deficit. Although there is extensive evidence that roots can synthesise ABA, recent findings suggest that local synthesis in response to dehydration contributes little to the root ABA pool compared to shoot‐sourced ABA.
Jaime Puértolas +4 more
wiley +1 more source
An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank
, 2004 International audienceOmega-powers of finitary languages are omega languages in the form V^omega, where V is a finitary language over a finite alphabet X. Since the set of infinite words over X can be equipped with the usual Cantor topology, the question
Finkel, Olivier
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Roots of polynomial sequences in root‐sparse regions
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Given a family (qk)k$(q_k)_k$ of polynomials, we call an open set U$U$root‐sparse if the number of zeros of qk$q_k$ is locally uniformly bounded on U$U$. We study the interplay between the individual zeros of the polynomials qk$q_k$ and those of the m$m$th derivatives qk(m)$q_k^{(m)}$ in a root‐sparse open set U$U$, as k→∞$k\rightarrow \infty$.
Christian Henriksen +2 more
wiley +1 more source
Reflectionless Schrodinger operators and Marchenko parametrization
Математичні СтудіїLet $T_q=-d^2/dx^2 +q$ be a Schr\"odinger operator in the space $L_2(\mathbb{R})$. A potential $q$ is called reflectionless if the operator $T_q$ is reflectionless.
Ya. Mykytyuk, N. Sushchyk
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Sections and projections of the outer and inner regularizations of a convex body
Mathematika, Volume 72, Issue 3, July 2026.Abstract We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santaló point is at the origin, with those of its inner and outer regularizations. We also provide functional extensions of these inequalities to the setting of log‐concave functions. Our approach relies on the recent
Natalia Tziotziou
wiley +1 more source
On the Lang–Trotter conjecture for Siegel modular forms
Mathematika, Volume 72, Issue 3, July 2026.Abstract Let f$f$ be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with f$f$, generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues ap$a_p$ of f$f$, and obtain upper
Arvind Kumar, Moni Kumari, Ariel Weiss
wiley +1 more source
A Normal Form of Borel Sets of Finite Rank
, 2008 For each Borel set of reals A, of finite rank, we obtain a ``normal form'' of A, by finding a canonical Borel set Ω, such that A and Ω continuously reduce to each other.
Duparc, J.
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