# American Institute of Mathematical Sciences

## Journals

JIMO
On the basis of capital structure theory and the option pricing model, the revenues and costs of debts are quantified. Combining with the financing characteristics of real estate enterprises, a mathematical model in consideration of the effect of interest-free debt was established in this paper to determine the optimal capital structure of real estate enterprises, and then a simulation analysis was conducted. The results indicated that the interest-bearing debt interest rate, the tax rate, the risk-free interest rate and the proportion of interest-bearing debt are all positively correlated with the optimal debt ratio of real estate enterprises, the annual average growth rate of housing price and the annual volatility of enterprise assets are negatively correlated with that, and as the debt maturity increases, the optimal debt ratio of real estate enterprises will decrease.
keywords: capital structure real estate enterprises interest-free debt Optimization interest-bearing debt simulation analysis.
DCDS
We give three families of parabolic rational maps and show that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetrically equivalent to the Julia set of one map in these families for suitable parameters. Combining a result obtained before, we give a complete classification of the Cantor circles Julia sets in the sense of quasisymmetric equivalence. Moreover, we study the regularity of the components of the Cantor circles Julia sets and establish a sufficient and necessary condition when a component of a Cantor circles Julia set is a quasicircle.
keywords: quasisymmetrically equivalent. Cantor circles Julia sets
DCDS-B

This paper is concerned with the spreading or vanishing of a epidemic disease which is characterized by a diffusion SIS model with nonlocal incidence rate and double free boundaries. We get the full information about the sufficient conditions that ensure the disease spreading or vanishing, which exhibits a detailed description of the communicable mechanism of the disease. Our results imply that the nonlocal interaction may enhance the spread of the disease.

keywords: SIS model reaction-diffusion free boundary spreading-vanishing dichotomy nonlocal incidence rate
DCDS-B
In this paper, we consider a Kermack-McKendrick epidemic model with nonlocal dispersal. We find that the existence and nonexistence of traveling wave solutions are determined by the reproduction number. To prove the existence of nontrivial traveling wave solutions, we construct an invariant cone in a bounded domain with initial functions being defined on, and apply Schauder's fixed point theorem as well as limiting argument. Here, the compactness of the support set of dispersal kernel is needed when passing to an unbounded domain in the proof. Moreover, the nonexistence of traveling wave solutions is obtained by Laplace transform if the speed is less than the critical velocity.
keywords: Kermack-McKendrick traveling waves nonlocal dispersal Schauder's fixed point theorem Laplace transform.
DCDS
This paper is concerned with the principal eigenvalues of some nonlocal operators. We first derive a result on the limit of certain sequences of principal eigenvalues associated with some nonlocal eigenvalue problems. Then, such a result is used to study the existence, uniqueness and asymptotic behavior of positive solutions to a nonlocal stationary problem with a parameter. Finally, the long-time behavior of the solutions of the corresponding nonlocal evolution equation and the asymptotic behavior of positive stationary solutions on parameter are discussed.
keywords: asymptotic behavior. principal eigenvalues existence and uniqueness positive solutions Nonlocal operator
DCDS-B
This paper is concerned with the traveling wave solutions of a diffusive SIR system with nonlocal delay. We obtain the existence and nonexistence of traveling wave solutions, which formulate the propagation of disease without outbreak threshold. Moreover, it is proved that at any fixed moment, the faster the disease spreads, the more the infected individuals, and the larger the recovery/remove ratio is, the less the infected individuals.
keywords: minimal wave speed predator-prey system. Outbreak threshold
CPAA

This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We introduce a basic reproduction number $R_0$ and establish threshold-type results on the global dynamic in terms of R0. More specifically, we show that if the basic reproduction number is less than one, then the disease will be extinct, and if the basic reproduction number is larger than one, then the disease will persist. Particularly, our results imply that the nonlocal dispersal of the infected individuals may suppress the spread of the disease even though in a high-risk domain.

keywords: Nonlocal dispersal epidemic model basic reproduction number disease-free equilibrium endemic equilibrium