Acta Mathematica Sinica-English Series最新文献

Let M = Sⁿ /Γ and h be a nontrivial element of finite order p in π₁(Μ), where the integers n, p ≥ 2, Γ is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that there are infinitely many non-contractible closed geodesics of class [h] on the compact space form with C^r-generic Finsler metrics, where 4 ≤ r ≤ ∞. The conclusion also holds for C^r-generic Riemannian metrics for 2 ≤ r ≤ ∞. The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

For a quasi-split Satake diagram, we define a modified q-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding ıquantum group. In other words, we provide a differential operator approach to ıquantum groups. Meanwhile, the oscillator representations of ıquantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

For a character χ of a finite group G, the number cod(χ)≔ ∣G: ker(χ)∣/χ(1) is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the ratio χ(1)²/cod(χ), when χ varies among the irreducible characters of G.

Let G be a semi-simple simply connected algebraic group over the field ℂ of complex numbers. Let T be a maximal torus of G, and let W be the Weyl group of G with respect to T. Let Z(w, i) be the Bott-Samelson-Demazure-Hansen variety corresponding to a tuple i associated to a reduced expression of an element w ∈ W. We prove that for the tuple i associated to any reduced expression of a minuscule Weyl group element w, the anti-canonical line bundle on Z(w, i) is globally generated. As consequence, we prove that Z(w, i) is weak Fano.

Assume that G is a simple algebraic group whose type is different from A₂. Let S = {α₁, …, α_n} be the set of simple roots. Let w be such that support of w is equal to S. We prove that Z(w, i) is Fano for the tuple i associated to any reduced expression of w if and only if w is a Coxeter element and ({w^{ - 1}}(sumnolimits_{t = 1}^n {{alpha _t}) in - S} ).

In this article, we consider a modified version of minimal L² integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As applications, we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces.

This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k. We find a class of comultiplications, such that if (sqrt{-1}in k), then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters q_ij = ±1. Also, it is proved that if (sqrt{-1}in k) then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter q = ±1. While if (sqrt{-1}notin k), then the exterior algebra with two variables admits no bi-Frobenius algebra structures. We prove that the quantum complete intersections admit a bialgebra structure if and only if it admits a Hopf algebra structure, if and only if it is commutative, the characteristic of k is a prime p, and every a_i a power of p. This also provides a large class of examples of bi-Frobenius algebras which are not bialgebras (and hence not Hopf algebras). In commutative case, other two comultiplications on complete intersection rings are given, such that they admit non-isomorphic bi-Frobenius algebra structures.

In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary. The strategy is to reestablish the Gehring-Hayman-type Theorem for these complex domains. Furthermore, the regularity of boundary extension map is given.

In this correspondence, we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements. Most of the results pertain to random elements which are M-dependent. We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces. One of the main contributions of the paper is to simplify and improve a recent result of Li, Presnell, and Rosalsky [Journal of Mathematical Inequalities, 16, 117–126 (2022)]. A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest. The sharpness of the results is illustrated by four examples.

In this paper, we study compressed data separation (CDS) problem, i.e., sparse data separation from a few linear random measurements. We propose the nonconvex ℓ_q-split analysis with ℓ_∞-constraint and 0 < q ≤ 1. We call the algorithm ℓ_q-split-analysis Dantzig selector (ℓ_q-split-analysis DS). We show that the two distinct subcomponents that are approximately sparse in terms of two different dictionaries could be stably approximated via the ℓ_q-split-analysis DS, provided that the measurement matrix satisfies either a classical D-RIP (Restricted Isometry Property with respect to Dictionaries and ℓ₂ norm) or a relatively new (D, q)-RIP (RIP with respect to Dictionaries and ℓ_q-quasi norm) condition and the two different dictionaries satisfy a mutual coherence condition between them. For the Gaussian random measurements, the measurement number needed for the (D, q)-RIP condition is far less than those needed for the D-RIP condition and the (D, 1)-RIP condition when q is small enough.

An extension of slant Hankel operator, namely, the k-th-order λ-slant Hankel operator on the Lebesgue space (L^{2}(mathbb{T}^{n})), where (mathbb{T}) is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially k-th-order λ-slant Hankel operators on (L^{2}(mathbb{T}^{n})).