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Based on the notions of conciseness and semiconciseness, we show that these properties are not equivalent by proving that a word originally presented by Ol’shanskii is semiconcise but not concise. We further establish that every (1/m)-concise word is semiconcise by proving that when the group-word w takes finitely many values in G, the iterated commutator subgroup ([w(G), G, {mathop {dots }limits ^{(m)}}, G]) is finite for some (m in mathbb {N}) if and only if ([w(G), G]) is finite.

In this paper, a strengthened Bonnesen inequality for closed convex plane curves will be given by strengthening its right-hand side into a nonnegative function S(r). For constant width curves, S(r) can be further written in a clearer form which can give us a strengthened Bonnesen-type inequality and an enhanced Gage inequality.

If G is p-solvable, we prove that there exists a McKay bijection that respects the decomposition numbers (d_{chi varphi }), whenever (varphi ) is linear.

In this paper, we strengthen a result of Seager regarding the number of orbits of a solvable primitive linear group.

Classically, Gohberg-type lemmas provide lower bounds for the distance of suitable pseudodifferential operators acting in a Hilbert space to the ideal of compact operators, in terms of “the behavior of the symbol at infinity”. In this article, the pseudodifferential operators are associated to a compact Abelian group (textsf{X}) and an important role is played by its Pontryagin dual ({widehat{textsf{X}}}) . Hörmander-type classes of symbols are not always available; they will be replaced by crossed product (C^*)-algebras involving a vanishing oscillation condition, which anyway is more general even in the particular cases allowing a full pseudodifferential calculus. In addition, the distance to a large class of operator ideals is controlled; the compact operators only form a particular case. This involves invariant closed subsets of certain compactifications of the dual group or, equivalently, invariant ideals of (ell ^infty ({widehat{textsf{X}}})) .

In this work, we investigate and characterize linear functionals (L: mathcal {V}subsetneq mathbb {R}[x_1,dots ,x_n]rightarrow mathbb {R}) with finite-dimensional (mathcal {V}) and absolutely continuous representing measures (mu ), i.e., (textrm{d}mu (x) = g(x),textrm{d}x) for some density g. We focus on the regularity of the density g.

In this paper, we explicitly compute two kinds of algebraic Belyi functions on Bring’s curve. One is related to a congruence subgroup of (textrm{SL}_2({mathbb {Z}})) and the other is related to a congruence subgroup of the triangle group (Delta (2,4,5)subset textrm{SL}_2({mathbb {R}}).) To carry out the computation, we use elliptic cusp forms of weight 2 for the former case and the automorphism group of Bring’s curve for the latter case. We also discuss a suitable base field (a number field) for describing isomorphisms between Hulek–Craig’s curve, Bring’s curve, and another algebraic model obtained as a modular curve.

In this paper, we obtain the (L^p) boundedness of the Berezin transform on fat Hartogs triangles for a restricted range of p, which is proved to be sharp.

In this short paper, we establish the local Noetherian property for the linear categories of Brauer, partition algebras, and other related categories of diagram algebras with no restrictions on their various parameters.

The statement in the title was proved in [1] by introducing dominant sets of seeds, which are analogs of torsion classes in representation theory. In this note, we observe a short proof by the existence of consistent cluster scattering diagrams.