Acta Mathematica Sinica-English Series最新文献

We prove that there exists an open and dense subset ({cal U}) in the space of C² expanding self-maps of the circle ({mathbb T}) such that the Lyapunov minimizing measures of any (T in {cal U}) are uniquely supported on a periodic orbit. This answers a conjecture of Jenkinson-Morris in the C² topology.

In this paper, we prove the Wulff–Gage isoperimetric inequality for origin-symmetric convex bodies and the uniqueness of the log-Minkowski problem in ℝ². Then we give a new proof of the log-Minkowski inequality of curvature entropy for origin-symmetric convex bodies with C² boundaries.

The case–cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In this paper, we study the high-dimensional accelerated failure time (AFT) model under the case–cohort design. Based on ℓ₀-regularization and a newly defined weight function, we propose a weighted least squares procedure for variable selection and parameter estimation. Computationally, we develop a support detection and root finding (SDAR) algorithm, where the support is first determined based on the primal and dual information, then the estimator is obtained by solving the weighted least squares problem restricted to the estimated support. We show the proposed algorithm is essentially one Newton-type algorithm, thus it is more efficient and stable compared with other regularized methods. Theoretically, we establish a sharp error bound for the solution sequences generated from the proposed method. Furthermore, we propose an adaptive version of the proposed SDAR algorithm, which determines the support size of the estimated coefficient in a data-driven manner. Extensive simulation studies demonstrate the superior performance of the proposed procedures, especially for the computational efficiency. As an illustration, we apply the proposed method to a malignant breast tumor gene expression data.

The present paper is devoted to studying local derivations on the N = 2 super-BMS₃ algebra based on such researches for the super Virasoro algebra and the Lie algebra W(2, 2). We prove that every local derivation on the N = 2 super-BMS₃ algebra is a derivation. It contributes to determine all local derivations on the general truncated super Virasoro algebras.

In this paper, we describe the wall-crossing of the two-parameter K-moduli space of pairs (ℙ², aQ + bL), where Q is a plane quintic curve and L is a line.

In this paper, we provide a sufficient condition, in the case of 0 < p < 1, for the existence of solutions to the general L_p Minkowski problem for polytopes.

In this article, we continue to study Kähler metrics on line bundles over projective spaces to find complete Kähler metrics with positive holomorphic sectional curvatures with two very special properties. These two special kinds of examples were not able to be found in our earlier paper of the first author and Ms. Duan. And therefore, we give a further step toward a famous Yau conjecture with the method in the co-homogeneity one geometry.

In this article, we show that the universal covering of any complete normal Kähler space of constant holomorphic sectional curvature on the regular locus is exactly biholomorphic to one of the complex projective space, the complex Euclidean space or the complex Euclidean ball. Moreover, we also prove that in a normal Stein space any bounded domain with complete Bergman metric of constant holomorphic sectional curvature on the regular locus is necessarily biholomorphic to the complex Euclidean ball, by which we generalize the classical Lu Qi-Keng uniformization theorem to the singular setting.

In this paper, we investigate the existence of normalized solutions for a quasilinear elliptic problem as follows

where −Δ_p is the p-Laplace operator, 1 < p < N, N ≥ 3, ρ > 0 and λ > 0. f is a continuous function and satisfies some suitable conditions. Based on a Nehari–Pohozaev manifold, we show the existence of positive normalized solutions by using the minimization method.

In this paper, we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system: u″(t) − L(t)u(t) + ⊽V(t,u) = 0, where L(t) and V(t,u) are not periodic in t. First, we introduce the definition of index and establish the corresponding index theory. Then, by using the index theory and critical point theory, we prove our main results under the asymptotic quadratic conditions of the potential function.