Acta Mathematicae Applicatae Sinica, English Series最新文献

In this paper, we are concerned with the the Schrödinger-Newton system with L²-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate.

The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.

This paper considers a multi-state repairable system that is composed of two classes of components, one of which has a priority for repair. First, we investigate the well-posedenss of the system by applying the operator semigroup theory. Then, using Greiner’s idea and the spectral properties of the corresponding operator, we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.

Given a graph G, the adjacency matrix and degree diagonal matrix of G are denoted by A(G) and D(G), respectively. In 2017, Nikiforov^[24] proposed the A_α-matrix: A_α(G) = αD(G) + (1 − α)A(G), where α ∈ [0, 1]. The largest eigenvalue of this novel matrix is called the A_α-index of G. In this paper, we characterize the graphs with minimum A_α-index among n-vertex graphs with independence number i for α ∈ [0, 1), where (i = 1,,,leftlfloor {{n over 2}} rightrfloor,leftlceil {{n over 2}} rightrceil,,leftlfloor {{n over 2}} rightrfloor + 1,n - 3,n - 2,n - 1), whereas for i = 2 we consider the same problem for (alpha in [0,{3 over 4}]). Furthermore, we determine the unique graph (resp. tree) on n vertices with given independence number having the maximum A_α-index with α ∈ [0, 1), whereas for the n-vertex bipartite graphs with given independence number, we characterize the unique graph having the maximum A_α-index with (alpha in [{1 over 2},1)).

This paper introduces two local conditional dependence matrices based on Spearman’s ρ and Kendall’s τ given the condition that the underlying random variables belong to the intervals determined by their quantiles. The robustness is studied by means of the influence functions of conditional Spearman’s ρ and Kendall’s τ. Using the two matrices, we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency, null and alternative asymptotic distributions. Simulation studies illustrate a superior power performance of the proposed Kendall-based test. Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.

We prove that the weak Morrey space WM ^p_q is contained in the Morrey space (M_{{q_1}}^p) for 1 ≤ q₁ < q ≤ p < ∞. As applications, we show that if the commutator [b, T] is bounded from L^p to L^p,∞ for some p ∈ (1, ∞), then b ∈ BMO, where T is a Calderón-Zygmund operator. Also, for 1 < p ≤ q < ∞, b ∈ BMO if and only if [6, T] is bounded from M ^p_q to WM ^p_q . For b belonging to Lipschitz class, we obtain similar results.

In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce the frequency of credit rating changes. Mathematically, this model is a system of partial differential equations with overlapping area. The existence, uniqueness, regularity and asymptotic behavior of the solution are obtained. Furthermore, a numerical scheme and its stability, convergence and accuracy are discussed in detail. Calibration and analysis of the parameters are also suggested.

In this paper, we investigate the global solution and the structures of interaction between two dimensional non-selfsimilar shock wave and rarefaction wave of general two-dimensional scalar conservation law in which flux functions f(u) and g(u) do not need to be convex, and the initial value contains three constant states which are respectively separated by two general initial discontinuities. When initial value contains three constant states, the cases of selfsimilar shock wave and rarefaction wave had been studied before, but no results of the cases of neither non-selfsimilar shock wave or non-selfsimilar rarefaction wave. Under the assumption that Condition H which is generalization of one dimensional convex condition, and some weak conditions of initial discontinuity, according to all the kinds of combination of elementary waves respectively staring from two initial discontinuities, we get four cases of wave interactions as S + S, S + R, R + S and R + R. By studying these interactions between non-selfsimilar elementary waves, we obtain and prove all structures of non-selfsimilar global solutions for all cases.

We study the following quasilinear Schrödinger equation

where the nonlinearity g(u) is asymptotically cubic at infinity, the potential V(x) may vanish at infinity. Under appropriate assumptions on K(x), we establish the existence of a nontrivial solution by using the mountain pass theorem.

In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time. The proof for large deviation principle is based on the weak convergence approach. For small time asymptotics we use the exponential equivalence to prove the result.

Optical vortices arise as phase dislocations of light fields and they are of importance in modern optical physics. In this study, we employ the calculus of variations method to develop an existence theory for the steady state vortex solutions of a nonlinear Schrödinger type equation to model light waves that propagate in a medium with a new focusing-defocusing nonlinearity. First, we demonstrate the existence of positive radially symmetric solutions by constrained minimization, where we give some interesting explicit estimates related to vortex winding numbers and the wave propagation constant. Second, we establish the existence of saddle-point solutions through a mountain-pass argument.