Dynamics of a Stochastic SIS Epidemic Model with Saturated Incidence

We introduce stochasticity into the SIS model with saturated incidence. The existence and uniqueness of the positive solution are proved by employing the Lyapunov analysis method. Then, we carry out a detailed analysis on both its almost sure exponential stability and its pth moment exponential stability, which indicates that the pth moment exponential stability implies the almost sure exponential stability. Additionally, the results show that the conditions for the disease to become extinct are much weaker than those in the corresponding deterministic model. The conditions for the persistence in the mean and the existence of a stationary distribution are also established. Finally, we derive the expressions for the mean and variance of the stationary distribution. Compared with the corresponding deterministic model, the threshold value for the disease to die out is affected by the half saturation constant. That is, increasing the saturation effect can reduce the disease transmission. Computer simulations are presented to illustrate our theoretical results

Shining A Light On Galactic Outflows: Photo-Ionized Outflows

We study the ionization structure of galactic outflows in 37 nearby, star forming galaxies with the Cosmic Origins Spectrograph on the Hubble Space Telescope. We use the O I, Si II, Si III, and Si IV ultraviolet absorption lines to characterize the different ionization states of outflowing gas. We measure the equivalent widths, line widths, and outflow velocities of the four transitions, and find shallow scaling relations between them and galactic stellar mass and star formation rate. Regardless of the ionization potential, lines of similar strength have similar velocities and line widths, indicating that the four transitions can be modeled as a co-moving phase. The Si equivalent width ratios (e.g. Si IV/Si II) have low dispersion, and little variation with stellar mass; while ratios with O I and Si vary by a factor of 2 for a given stellar mass. Photo-ionization models reproduce these equivalent width ratios, while shock models under predict the relative amount of high ionization gas. The photo-ionization models constrain the ionization parameter (U) between -2.25 < log(U) < -1.5, and require that the outflow metallicities are greater than 0.5 Z$_\odot$. We derive ionization fractions for the transitions, and show that the range of ionization parameters and stellar metallicities leads to a factor of 1.15-10 variation in the ionization fractions. Historically, mass outflow rates are calculated by converting a column density measurement from a single metal ion into a total Hydrogen column density using an ionization fraction, thus mass outflow rates are sensitive to the assumed ionization structure of the outflow.Comment: 30 pages, 17 tables, 14 figures. Accepted for publication in MNRA

Chloridobis(1,10-phenanthroline-κ2 N,N′)copper(I) dichloridocopper(II)

The asymmetric unit of the title compound, [CuCl(C12H8N2)2]·[CuCl2], contains two complex Cu(II) cations and two cuprate(I) anions. The Cu(II) atom is coordinated by two phenanthroline (phen) mol­ecules and one chloride anion in a distorted trigonal–bipyramidal geometry. The Cu(II) complex cations form layers through π–π stacking [interplanar distance = 3.481 (2) Å]. The dichloridocuprate(I) anions are located between the layers, forming a sandwich-like structure

A Spatially Explicit Evaluation of the Economic Performance of a Perennial Energy Crop on the Marginal Land of the Loess Plateau and China

Funding Information: This study was supported by the Chinese Scholarship Council (CSC) and partially supported by the National Key Project of Intergovernmental Cooperation in International Scientific and Technological Innovation (2018YFE0112400 to SC). Astley Hastings was funded by the ADVENT project funded by the UK Natural Environment Research Council (NE/M019691/1) and ADVANCES funded by the UK Natural Environment Research Council (NE/M019691/1), EPSRC-funded UKERC-4, and the BBSRC-funded PCB4GGR project (BB/V011553/1). Funding Information: The basic data on land use, climate, and soil properties were supported by the Loess Plateau Data Center, the National Earth System Science Data Sharing Infrastructure, and the National Science & Technology Infrastructure of China ( http://loess.geodata.cn (accessed on 1 January 2021). The marginal land data and land suitability data of the Loess Plateau are available in []. The spatially explicit yield data of switchgrass on the Loess plateau are available in [], and the data can download at https://figshare.com/articles/figure/Spatial_distribution_of_the_yield_biomass_of_switchgrass_on_the_marginal_land_of_the_Loess_plateau/21047224 (accessed on 6 May 2022). Acknowledgments Publisher Copyright: © 2023 by the authors.Peer reviewedPublisher PD

Bilateral boundary control of an input delayed 2-D reaction-diffusion equation

In this paper, a delay compensation design method based on PDE backstepping is developed for a two-dimensional reaction-diffusion partial differential equation (PDE) with bilateral input delays. The PDE is defined in a rectangular domain, and the bilateral control is imposed on a pair of opposite sides of the rectangle. To represent the delayed bilateral inputs, we introduce two 2-D transport PDEs that form a cascade system with the original PDE. A novel set of backstepping transformations is proposed for delay compensator design, including one Volterra integral transformation and two affine Volterra integral transformations. Unlike the kernel equation for 1-D PDE systems with delayed boundary input, the resulting kernel equations for the 2-D system have singular initial conditions governed by the Dirac Delta function. Consequently, the kernel solutions are written as a double trigonometric series with singularities. To address the challenge of stability analysis posed by the singularities, we prove a set of inequalities by using the Cauchy-Schwarz inequality, the 2-D Fourier series, and the Parseval's theorem. A numerical simulation illustrates the effectiveness of the proposed delay-compensation method.Comment: 11 pages, 3 figures(including 8 sub-figures