Acta Mathematicae Applicatae Sinica, English Series最新文献

In this paper, we study the following quasi-linear elliptic equation

where Ω ⊂ ℝ^N is a bounded domain, λ > 0 is a parameter. The function ψ(∣t∣)t is the subcritical term, and ϕ(∣t∣)t is the critical Orlicz-Sobolev growth term with respect to φ. Under appropriate conditions on φ, ψ and ϕ, we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation, for λ ∈ (0, λ₀), where λ₀ > 0 is a fixed constant.

This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator. Such systems have the form (dot x = - y + xf(x,,y),,,dot y = x + yf(x,,y)), where f(x, y) = a₁x + a₂xy + a₃xy² + a₄xy³ + a₅xy⁴ = xσ(y), and any zero of 1 + a₁y + a₂y² + a₃y³ + a₄y⁴ + a₅y⁵, (y = bar y) is an invariant straight line. At last, all global phase portraits are drawn on the Poincaré disk.

A scheme for generating nonisospectral integrable hierarchies is introduced. Based on the method, we deduce a nonisospectral hierarchy of soliton equations by considering a linear spectral problem. It follows that the corresponding expanded isospectral and nonisospectral integrable hierarchies are deduced based on a 6 dimensional complex linear space (widetilde{mathbb{C}}^{6}). By reducing these integrable hierarchies, we obtain the expanded isospectral and nonisospectral derivative nonlinear Schrödinger equation. By using the trace identity, the bi-Hamiltonian structure of these two hierarchies are also obtained. Moreover, some symmetries and conserved quantities of the resulting hierarchy are discussed.

In this paper, we study the optimal timing to convert the risk of business for an insurance company in order to improve its solvency. The cash flow of company evolves according to a jump-diffusion process. Business conversion option offers the company an opportunity to transfer the jump risk business out. In exchange for this option, the company needs to pay both fixed and proportional transaction costs. The proportional cost can also be seen as the profit loading of the jump risk business. We formulated this problem as an optimal stopping problem. By solving this stopping problem, we find that the optimal timing of business conversion mainly depends on the profit loading of the jump risk business. A larger profit loading would make the conversion option valueless. The fixed cost, however, only delays the optimal timing of business conversion. In the end, numerical results are provided to illustrate the impacts of transaction costs and environmental parameters to the optimal strategies.

Let a and b be positive integers such that a ≤ b and a ≡ b (mod 2). We say that G has all (a, b)-parity factors if G has an h-factor for every function h: V(G) → {a, a + 2, ⋯, b − 2, b} with b∣V(G)∣ even and h(v) ≡ b (mod 2) for all v ∈ V(G). In this paper, we prove that every graph G with n ≥ 2(b + 1)(a + b) vertices has all (a, b)-parity factors if δ(G) ≥ (b² − b)/a, and for any two nonadjacent vertices (u,,v, in ,V,(G),,max {{d_G}(u),,{d_G}(v)} , ge {{bn} over {a + b}}). Moreover, we show that this result is best possible in some sense.

For a 2-station and 3-class reentrant line under first-buffer first-served (FBFS) service discipline in light traffic, we firstly construct the strong approximations for performance measures including the queue length, workload, busy time and idle time processes. Based on the obtained strong approximations, we use a strong approximation method to find all the law of the iterated logarithms (LILs) for the above four performance measures, which are expressed as some functions of system parameters: means and variances of interarrival and service times, and characterize the fluctuations around their fluid approximations.

In this article, we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. Our results of strong limit theorems are more general than some related results previously obtained by Thrum (1987), Li et al. (1995) and Wu (2010) in classical probability space.

Tensor data have been widely used in many fields, e.g., modern biomedical imaging, chemometrics, and economics, but often suffer from some common issues as in high dimensional statistics. How to find their low-dimensional latent structure has been of great interest for statisticians. To this end, we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation (SAVE) to estimate the corresponding dimension reduction subspaces. The first one, entitled tensor sliced average variance estimation (TSAVE), works well when the response is discrete or takes finite values, but is not (sqrt n) consistent for continuous response; the second one, named bias-correction tensor sliced average variance estimation (CTSAVE), is a de-biased version of the TSAVE method. The asymptotic properties of both methods are derived under mild conditions. Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.