Acta Mathematica Sinica-English Series最新文献

In this paper, we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics. The existence and uniqueness of global solutions is proved in perturbation framework, for more general gases including ideal polytropic gas. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density, velocity, temperature, and radiation field.

Let ({cal F} = { {H_1}, ldots ,{H_k}} ,,(k ge 1)) be a family of graphs. The Turán number of the family ({cal F}) is the maximum number of edges in an n-vertex {H₁, …, H_k}-free graph, denoted by ex(n, ({cal F})) or ex(n, {H₁,H₂, … H_k}). The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. In this paper we determine the Turán number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Turán number of the family consisting of a cycle, a star and linear forests with k edges.

We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = ΓG of a simply-connected solvable Lie group G by a lattice Γ, admitting a symplectic structure.

In applications involving, e.g., panel data, images, genomics microarrays, etc., trace regression models are useful tools. To address the high-dimensional issue of these applications, it is common to assume some sparsity property. For the case of the parameter matrix being simultaneously low rank and elements-wise sparse, we estimate the parameter matrix through the least-squares approach with the composite penalty combining the nuclear norm and the l₁ norm. We extend the existing analysis of the low-rank trace regression with i.i.d. errors to exponential β-mixing errors. The explicit convergence rate and the asymptotic properties of the proposed estimator are established. Simulations, as well as a real data application, are also carried out for illustration.

We first study the Volterra operator V acting on spaces of Dirichlet series. We prove that V is bounded on the Hardy space ({cal H}_0^p) for any 0 < p ≤ ∞, and is compact on ({cal H}_0^p) for 1 <p ≤ ∞. Furthermore, we show that V is cyclic but not supercyclic on ({cal H}_0^p) for any 0 <p< ∞. Corresponding results are also given for V acting on Bergman spaces ({cal H}_{w,0}^p). We then study the Volterra type integration operators T_g. We prove that if T_g is bounded on the Hardy space ({{cal H}^p}), then it is bounded on the Bergman space ({cal H}_w^p).

In the setting of Fock–Sobolev spaces of positive orders over the complex plane, Choe and Yang showed that if the one of the symbols of two commuting Toeplitz operators with bounded symbols is non-trivially radial, then the other must also be radial. In this paper, we extend this result to the Fock–Sobolev space of negative order using the Fock-type space with a confluent hypergeometric function.

A great deal of economic problems are related to detecting the stability of time series data, where the main interest is in the unit root test. In this paper, we consider the unit root testing problem with errors being long-memory processes with the GARCH structure. A new test statistic is developed by using the random weighted bootstrap method. It turns out that the proposed statistic has a chi-squared distribution asymptotically regardless of the process being stationary or nonstationary, and with or without an intercept term. The simulation results show that the statistic has a desired finite sample performance in terms of both size and power. A real data application is also given relying on the inflation rate data of 17 countries.