The lower bound decay rate of global solution to the compressible viscous quantum magnetohydrodynamic model in three-dimensional whole space under the $H^5\times H^4\times H^4$ framework is investigated in this paper. We firstly show that the lower bound of decay rate for the density, velocity and magnetic field converging to the equilibrium state (1,0,0) in $L^2$-norm is $(1+t)^{-\frac{3}{4}}$ when the initial data satisfies some low frequency assumption. Moreover, we prove that the lower bound of decay rate of $k(k\in [1,3])$ order spatial derivative for the density, velocity and magnetic field converging to the equilibrium state (1,0,0) in $L^2$-norm is $(1+t)^{-\frac{3+2k}{4}}$. Then we show that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in $L^2$-norm is $(1+t)^{-\frac{5}{4}}$, but the lower bound of decay rate for the time derivative of magnetic field converging to zero in $L^2$-norm is $(1+t)^{-\frac{7}{4}}$.

In this paper, using the Lyapunov-like functions, the practical stability with respect to part of the variables of fractional-order nonlinear systems depending on a small parameter is studied.

We investigate mixed type boundary-transmission problems of the generalized thermo-electro-magneto elasticity (GTEME) theory for complex elastic anisotropic layered structures containing interfacial cracks. This type of problems are described mathematically by systems of partial differential equations with appropriate transmission and boundary conditions for six dimensional unknown physical field (three components of the displacement vector, electric potential function, magnetic potential function, and temperature distribution function). We apply the potential method and the theory of pseudodifferential equations and prove uniqueness and existence theorems of solutions to different type mixed boundary-transmission problems in appropriate Sobolev spaces. We analyze smoothness properties of solutions near the edges of interfacial cracks and near the curves where different type boundary conditions collide.

The widespread construction of photovoltaic (PV) power stations within northwest China poses an environmental threat because of severe wind erosion and land degradation attributed to unique wind control issues caused by the power stations. In this study, various engineering (E), plant (V), and biocrust (B) treatments were evaluated for their effectiveness in the reduction of wind erosion. The placement of solar panels with wide wind inlets and narrow wind outlets caused wind velocity reductions at the inlet that sharply increased at the outlet and formed distinct zones of deflation, direct shear abrasion (DSA), and deposition. The engineering treatments reduced the wind velocities and sand transport rates, in comparison to the control with E4 (DSA zone + a gravel/deposition zone + red clay) being the most effective with an 87% reduction in the total sand transport rate. Both plant treatments V1 (Sedum aizoon L.) and V2 (Pennisetum alopecuroides (L.) Spreng) increased the aerodynamic roughness, and decreased the sand transport rates and the sand erosion-deposition budget under or between the solar panels. Treatment B2 (moss crust) decreased the sand transport rate and sand erosion-deposition budget under the solar panels in comparison to the control. All the treatments had effects on reducing wind erosion, and we strongly recommend the use of moss crust, gravel mulch, and red clay mulch in the deflation zones, DSA zones, and deposition zones, respectively, to control the severe wind erosion at these PV power stations located in sandy areas.

We use adaptive dynamics models to study how changes in the abiotic environment affect patterns of evolutionary dynamics and diversity in evolving communities of organisms with complex phenotypes. The models are based on the logistic competition model and environmental changes are implemented as a temporal change of the carrying capacity as a function of phenotype. In general we observe that environmental changes cause a reduction in the number of species, in total population size, and in phenotypic diversity. The rate of environmental change is crucial for determining whether a community survives or undergoes extinction. Until some critical rate of environmental changes, species are able to follow evolutionarily the shifting phenotypic optimum of the carrying capacity, and many communities adapt to the changing conditions and converge to new stationary states. When environmental changes stop, such communities gradually restore their initial phenotypic diversity.

Satellite-based solar-induced chlorophyll fluorescence (SIF) has the potential for an early detection and accurate impact assessment of meteorological drought on vegetation photosynthesis. However, how the response of satellite SIF to meteorological drought varies under different climatic conditions and biome types remains poorly understood. In this study, we determined the drought time-scale at which the vegetation photosynthesis response was highest based on the standardized precipitation evapotranspiration index (SPEI) and satellite SIF, and examined how the sensitivity of SIF signals from different ecosystems to drought varied along an aridity gradient in northern China. The results showed that spatial variability of the annual maximum SIF was constrained by wetness conditions and biome types. Annual maximum SIF was positively correlated with SPEI in 57.9% of vegetated lands (P < 0.05). 34.8% of humid ecosystems were characterized by a significant SIF-SPEI correlation (P < 0.05). This percentage reached 44%, 71.4% and 86.2% for arid, sub-humid and semi-arid ecosystems, respectively. The variation of SIF-SPEI correlations was a Gaussian function of the aridity index (AI), with the highest SIF-SPEI correlation appearing in the AI bin of 0.4 (0.37-0.46). The drivers for this pattern were vegetation composition and water availability. The variation of SIF time-scales in response to SPEI was a linear function of the AI, but the slope varied among biomes. To summarize with increasing aridity drought-induced declines in vegetation photosynthesis will be quicker and more significant.

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviours. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.

The enhanced thermal properties being the prominent objective behind the usage of nanofluids. Hence it is necessary to study the base/nanofluid physical properties at various conditions. This article projects the experimental results of thermal conductivity and viscosity of two different nanofluids. The ratio was considered as 60:40 and 40:40 by volume in water and ethylene glycol respectively. The preparation of nanofluids was started by scattering SiO2 nano-particles in EG and “water” (W) blended in “60:40” (60EGW) and “40:60” (40EGW) ratio by volume. The ratio was considered as 60:40 and 40:40 by volume in water and ethylene glycol respectively. The regression analysis was conducted with available data and correlations were formulated for thermal properties. The nanofluids were used in evaluating “viscosity” and “thermal conductivity” experimentally. From the results, the SiO2 particles have achieved enhancement of 34% and 32% in thermal conductivity with the two base-fluids. Similarly, enhancement of 102% and 62% were reported in viscosity. Hence, it can be observed that SiO2 nanofluids in 40EGW nanofluid are a better heat transfer fluid when compared to SiO2 in 60EGW nanofluid.

In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the “φ-η-θ model’‘ of grain boundary motion, proposed by Kobayashi [16]. The system is a coupled system of: an Allen–Cahn type equation as in (1.1) with a given temperature source; and a phase-field model of grain boundary motion, known as “Kobayashi–Warren–Carter type model”. The focus of the study is on a special kind of solution, called energy-dissipative solution, which is to reproduce the energy-dissipation of the governing energy in time. Under suitable assumptions, two Main Theorems, concerned with: the existence of energy-dissipative solution; and the large-time behavior; will be demonstrated as the results of this paper.

The aim of this paper is to study the existence and multiplicity of nonnegative solutions for the following critical Kirchhoff equation involving the fractional p-Laplace operator ( − Δ)ps. More precisely, we consider $$ M\left(^{2N}}}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_{p}^{s} u=\lambda f(x)|u|^{q-2}u+K(x)|u|^{p_{s}^{*}-2}u,\quad &{\rm in}\ \Omega,\\ u=0, \quad\quad &{\rm in}\ ^{N}\setminus \Omega, \\ $$ where Ω ⊂ ℝN is an open bounded domain with Lipschitz boundary ∂Ω, M(t)=a + btm − 1 with m > 1, a > 0, b > 0, dimension N > sp, $ p_{s}^{*}={N-ps}$ is the fractional critical Sobolev exponent, and the parameters λ > 0, 0 < s < 1 < q < p < ∞. Applying Nehari manifold, fibering maps and Krasnoselskii genus theory, we investigate the existence and multiplicity of nonnegative solutions.

Bertoin, Roynette et Yor \cite{bertion} described new connections between the class $\Bd$ of L\’evy-Laplace exponents $\Psi$ (also called the class (sub)critical branching mechanism) and the class of Bernstein functions ($\BF$) which are internal, i.e. those Bernstein functions $\phi$ s.t. $\Psi \circ \phi$ remains a Bernstein function for every $\Psi$. We complete their work and illustrate how the class f internal function is rich from the stochastic point of view. It is well known that every $\phi \in \BF$ corresponds univocally to: (i) a subordinator ${(X_t)}_{t\geq 0}$ (or equivalently to transition semigroups ${\big(\pr(X_t\in dx)\big)}_{t\geq 0}$; (ii) a L\’evy measure $\mu$ (which controls the jumps of the subordinator). It is also known that, on $\oi$, the measure $\pr(X_t \in dx)/t$ converges vaguely to $\dd \delta_0(dx)+ \mu(dx)$ as $t\to 0$, where $\dd$ is the drift term, but rare are the situations where we can compare the transition semigroups with the L\’evy measure. Our extensive investigations on the composition of L\’evy-Laplace exponents $\Psi$ with Bernstein functions show, for instance, this remarkable facts: $\phi$ is internal is equivalent to: (a) $\phi^2 \in \BF$ or to (b) $t\mu(dx) - \pr(X_t\in dx)$ is a positive measure on $\oi$. We also provide conditions on $\mu$ insuring that $\phi$ is internal. We also show L\’evy-Laplace exponents are closely connected to the class of Thorin Bernstein function and provide conditions on $\mu$ insuring that $\phi$ is internal.

Fluorescent in situ hybridization (FISH) has been extensively used in the past decades for the detection and localization of nucleic acid sequences or of the microorganisms themselves within samples. However, a mechanistic approach of the whole FISH process is still missing, and the main limiting steps for the hybridization to occur remain unclear. In here, FISH is approached as a particular case of a diffusion-reaction kinetics, where molecular probes move from the hybridization solution to the target RNA site within the cells. Based on literature models, the characteristic times taken by different molecular probes to diffuse across multiple cellular barriers, and the reaction time associated with the formation of the duplex molecular probe-RNA were estimated. Structural and size differences at the membrane level of bacterial and animal cells were considered. For bacterial cells, the limiting step for diffusion is likely to be the peptidoglycan layer (characteristic time of 2700-4524 s), whereas for animal cells the limiting step should be the diffusion of the probe through the bulk (1.8-5.0 s) followed by the diffusion through the lipid membrane (1 s). The information provided here may serve as a basis to optimize FISH protocols.

The influences of the initial states of HCl on the stereodynamics properties of the Ca+HCl reaction are investigated by utilizing the method based on the quasi-classical trajectory (QCT) theory and the analytical potential energy surface (APES). The orientation and alignment behaviors for the rotational angular momentum of the product, along with the generalized differential cross-section (PDDCS) dependent polarization, are employed to explore the stereodynamics properties. The initial rotational states of the HCl molecule impose a remarkable affection on the vector correlation distributions, regardless of the orientation, alignment, or PDDCS. The obvious forward or backward scattering, as well as the weak sideway scattering phenomena, are found for the different initial rotational states of the HCl molecule. The initial higher rotational-excited state of j=3 results in more obvious stereodynamics effects.

The biogeographical distribution of diversity among populations of threatened mammalian species is generally investigated through population genetics. However, intraspecific phenotypic diversity is rarely assessed beyond taxonomy-focused linear measurements or qualitative descriptions. Here, we use a technique widely used in the evolutionary sciences – geometric morphometrics – to characterize shape diversity in the skull of an endangered marsupial, the northern quoll, across its 5,000 km distribution range along the northern Australian coast. Skull shape is a proxy of feeding, behaviour, and phenotypic differentiation, allowing us to ask if populations can be distinguished and if patterns of variation indicate adaptability to changing environmental conditions. We analysed skull shape in 101 individuals across the four mainland populations and several islands. We assessed the contribution of population, size, sex, rainfall, temperature, and latitude/longitude to skull shape variation through Principal Components, Procrustes ANOVA, and variation partitioning analyses. Regardless of land area inhabited, northern quoll populations harbour similar amounts of broadly overlapping skull shape variation. Size predicted skull shape best, coinciding with braincase size variation and differences in the cheekbone shape. Size-adjusted population differences explained less variation with far smaller effect sizes, relating to changes in insertion areas of masticatory muscles, as well as the upper muzzle and incisor region. Climatic and geographic variables contributed little or nothing. Strikingly, the vast majority of shape variation - 76% - remained unexplained. Our results suggest a uniform within-species scope for shape variation, possibly due to phenotypic plasticity or allometric constraints. The lack of local adaptation indicates that cross-breeding between populations will not reduce local morphological skull (and probably general musculoskeletal) adaptation because none exists. However, the potential for heritable morphological variation (e.g. specialization to local diets) seems exceedingly limited. We conclude that 3D geometric morphometrics can provide a comprehensive, statistically rigorous phenomic contribution to genetics-based conservation studies.

Letter to the Editor, BJOG Exchange

Since December 2019, a new coronavirus (COVID-19) infection has rapidly become prevalent in central China [1]. On the basis of knowledge obtained from a previous coronavirus outbreak [2], pregnant women are believed to be susceptible to this virus. Once a maternal infection of 2019-nCoV is suspected or confirmed, childbirth becomes complicated and challenging. Efficient obstetric treatment is required, and is key to optimizing the prognosis for both mother and child. Care should be taken in determination of the timing of delivery, assessment of the indications for caesarean section, preparation of the delivery room to prevent infection, choice of the type of anesthesia, and newborn management.

The comment by Gamisch (2020) draws the attention of users of the R-package RPANDA (Morlon et al. 2016) on situations when properly interpreting the results of linear diversification dependencies requires caution. Here we provide clarifications to help users interpreting their results when using any type of functional diversification dependencies with time or the environment.

Detailed information on the H/D isotope effects for adsorption on the surface and absorption in the bulk is important for understanding the nuclear quantum effect. To achieve this purpose, we developed a new theoretical approach, namely, the combined plane wave and localized basis set (CPLB) method. By using the multi-component quantum chemical method, which takes into account the quantum effect of proton or deuteron, with localized part in CPLB method, direct analysis of H/D isotope effect about adsorption and absorption is achieved. In this study, we performed a theoretical investigation of the H/D isotope effects for adsorption on a Pd(111) surface and absorption in bulk Pd. We clearly showed H/D isotope effect on geometry during adsorption and absorption. Our developed CPLB approach is a powerful tool for analyzing the quantum nature of H/D in surface, bulk, and inhomogeneous systems.