Acta Mathematica Scientia最新文献

Let {Z_n}_n≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on ℝ^d. Denote by R_n:= sup{u > 0: Z_n({x ∈ ℝ^d: ∣x∣ < u}) = 0} the radius of the largest empty ball centered at the origin of Z_n. In this work, we prove that after suitable renormalization, R_n converges in law to some non-degenerate distribution as n → ∈. Furthermore, our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk. This completes the results of Révész [13] for the critical binary branching Wiener process.

In this paper, we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field. By estimating the probability value of a time-stationary random field in a small range, we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region. It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1. In addition, we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

In this paper, we consider pseudoharmonic heat flow with small initial horizontal energy and give the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds into closed Riemannian manifolds.

In this paper, X is a locally compact Hausdorff space and ({cal A}) is a Banach algebra. First, we study some basic features of C₀(X, ({cal A})) related to BSE concept, which are gotten from ({cal A}). In particular, we prove that if C₀(X, ({cal A})) has the BSE property then ({cal A}) has so. We also establish the converse of this result, whenever X is discrete and ({cal A}) has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that C₀ (X, ({cal A})) has the BSE-norm property if and only if ({cal A}) has so.

In this paper, we consider a model of compressible isentropic two-fluid magneto-hydrodynamics without resistivity in a strip domain in three dimensional space. By exploiting the two-tier energy method developed in [Anal PDE, 2013, 6: 1429–1533], we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. Compared to the work of Tan and Wang [SIAM J Math Anal, 2018, 50: 1432–1470], we need to overcome the difficulties caused by particles.

This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in (widetilde{L}_{q}). We estimate the relative widths of (widetilde{W}^{r}H^{omega}_{p}) and its generalized class K_pH^ω (P_r), where K_pH^ω (P_r) is defined by a self-conjugate differential operator P_r (D) induced by

Also, the modulus of continuity of the r-th derivative, or r-th self-conjugate differential, does not exceed a given modulus of continuity ω. Then we obtain the asymptotic results, especially for the case p = ∞, 1 ≤ q ≤ ∞.

Let μ be a positive Borel measure on the interval [0, 1). The Hankel matrix (cal{H}_{mu}=(mu_{n,k})_{n,kgeq 0}) with entries μ_n,k = μ_n+k, where μ_n = ⨜_[0,1) tⁿdμ(t), induces, formally, the operator

where (f(z)=sumlimits_{n=0}^infty a_nz^n) is an analytic function in ⅅ. We characterize the measures μ for which (cal{DH}_mu) is bounded (resp., compact) operator from the logarithmic Bloch space (mathscr{B}_{L^{alpha}}) into the Bergman space (cal{A}^p), where 0 ≤ α < ∞, 0 < p < ∞. We also characterize the measures μ for which (cal{DH}_mu) is bounded (resp., compact) operator from the logarithmic Bloch space (mathscr{B}_{L^{alpha}}) into the classical Bloch space (mathscr{B}).

In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive, by a subordination principle for the solution, that the solution is positive when the initial value is non-negative. As an application, we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

This paper is the sequel to our study of heat kernel on Ricci shrinkers [29]. In this paper, we improve many estimates in [29] and extend the recent progress of Bamler [2]. In particular, we drop the compactness and curvature boundedness assumptions and show that the theory of (mathbb{F})-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.

We study equations in divergence form with piecewise C^α coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise C^1,α estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.