Impacts of climate change and fruit tree expansion on key hydrological components at different spatial scales

Assessing how fruit tree expansion and climate variability affect hydrological components (e.g., water yield, surface runoff, underground runoff, soil water, evapotranspiration, and infiltration) at different spatial scales is crucial for the management and protection of watersheds, ecosystems, and engineering design. The Jiujushui watershed (259.32 km2), which experienced drastic forest changes over the past decades, was selected to explore the response mechanisms of hydrological components to fruit tree expansion and climate variability at different spatial scales (whole basin and subbasin scale). Specifically, we set up two change scenarios (average temperature increase of 0.5°C and fruit tree area expansion of 18.97%) in the SWAT model by analyzing historical data (1961∼2011). Results showed that climate change reduced water yield, surface runoff, and underground runoff by 6.75, 0.37, and 5.91 mm, respectively. By contrast, the expansion of fruit trees increased surface runoff and water yield by 2.81 and 4.10 mm, respectively, but decreased underground runoff by 1 mm. Interestingly, the sub-basins showed different intensities and directions of response under climate change and fruit tree expansion scenarios. However, the downstream response was overall more robust than the upstream response. These results suggest that there may be significant differences in the hydrological effects of climate change and fruit tree expansion at different spatial scales, thus any land disturbance measures should be carefully considered

Stability analysis of a k-out-of-N:G reparable system

A k-out-of-N:G reparable system with an arbitrarily distributed repair time is studied in this paper. We translate the system into an Abstract Cauchy Problem (ACP). Analysing the spectrum of the system operator helps us to prove the well-posedness and the asymptotic stability of the system

Computational Scheme for the First-Order Linear Integro-Differential Equations Based on the Shifted Legendre Spectral Collocation Method

First-order linear Integro-Differential Equations (IDEs) has a major importance in modeling of some phenomena in sciences and engineering. The numerical solution for the first-order linear IDEs is usually obtained by the finite-differences methods. However, the convergence rate of the finite-differences method is limited by the order of the differences in L1 space. Therefore, how to design a computational scheme for the first-order linear IDEs with computational efficiency becomes an urgent problem to be solved. To this end, a polynomial approximation scheme based on the shifted Legendre spectral collocation method is proposed in this paper. First, we transform the first-order linear IDEs into an Cauchy problem for consideration. Second, by decomposing the system operator, we rewrite the Cauchy problem into a more general form for approximating. Then, by using the shifted Legendre spectral collocation method, we construct a computational scheme and write it into an abstract version. The convergence of the scheme is proven in the sense of L1-norm by employing Trotter-Kato theorem. At the end of this paper, we summarize the usage of the scheme into an algorithm and present some numerical examples to show the applications of the algorithm

Dynamic Analysis of Software Systems with Aperiodic Impulse Rejuvenation

This paper aims to obtain the dynamical solution and instantaneous availability of software systems with aperiodic impulse rejuvenation. Firstly, we formulate the generic system with a group of coupled impulsive differential equations and transform it into an abstract Cauchy problem. Then we adopt a difference scheme and establish the convergence of this scheme by applying the Trotter–Kato theorem to obtain the system’s dynamical solution. Moreover, the instantaneous availability as an important evaluation index for software systems is derived, and its range is also estimated. At last, numerical examples are shown to illustrate the validity of theoretical results

Stability on coupling SIR epidemic model with vaccination

We develop a mathematical model for the disease which can be transmitted via vector and through blood transfusion in host population. The host population is structured by the chronological age. We assume that the instantaneous death and infection rates depend on the age. Applying semigroup theory and so forth, we investigate the existence of equilibria. We also discuss local stability of steady states

Asymptotic stability of a repairable system with imperfect switching mechanism

This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and 0 is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue 0

Stability results on age-structured SIS epidemic model with coupling impulsive effect

We develop an age-structured epidemic model for malaria with impulsive effect, and consider the effect of blood transfusion and infected-vector transmission. Transmission rates depend on age. We derive the condition in which eradication solution is locally asymptotically stable. The condition shows that large enough pulse reducing proportion and relatively small interpulse time lead to the eradication of the diseases