Acta Mathematica Sinica-English Series最新文献

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})).

The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously, but these existing methods may fail to be consistent for the setting with highly correlated covariates. In this paper, the semi-standard partial covariance (SPAC) method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates, and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions. Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.

In this paper, we study the concept of split monotone variational inclusion problem with multiple output sets. We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces. Our proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued operators. Moreover, some parameters are relaxed to accommodate a larger range of values for the step sizes. Under some mild conditions on the control parameters and without prior knowledge of the operator norms, we obtain strong convergence result for the proposed method. Finally, we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed method. Several of the existing results in the literature could be viewed as special cases of our result in this paper.

In this paper, we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids. We prove the existence and uniqueness of global classical solution, weak solution and strong solution under the assumption of spherically symmetry condition for initial data ρ₀ without vacuum state.