This article focuses on studying mild solutions of an original frac- tional partial differential equation disturbed by multiplicative white noise. We employ techniques of semi group theory, Hausdorff measure, and Darbo xed point theorem.

In this paper, we consider an electromagnetic obstacle scattering problem in a piecewise homogeneous medium. We assume that the incident field is the electromagnetic plane wave and the obstacle consists of metallic and nonmetallic parts. We firstly establish uniqueness and existence for the solution to the electromagnetic obstacle scattering problem. Then we prove that the electric far field pattern satisfies the reciprocity relation and the set of electric far field patterns is complete in a Hilbert space. These results have an important bearing on the solution of the inverse electromagnetic scattering problem i.e. determination of the shape of the obstacle from the knowledge of the electric far field patterns.

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 $(1+t)^{-\frac{7}{4}}$.

A new four-component nonlinear Schrödinger equation is first proposed in this work and studied by Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a $5\times5$ matrix spectral problem for the four-component nonlinear Schrödinger equation. Then based on the Lax pair, we analyze the spectral problem and the analytical properties of the Jost functions, from which the Riemann-Hilbert problem of the equation is successfully established. Moreover, we obtain the $N$-soliton solutions of the equation by solving the Riemann-Hilbert problem without reflection. Finally, we derive two special cases of the solutions to the equation for $N=1$ and $N=2$, and the local structure and dynamic behavior of the one-and two-soliton solutions are analyzed graphically.

A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg’s uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional fractional Fourier transform domains. The conditions that reach the equality relation of the uncertainty inequalities are deduced. Example and simulation are performed to illustrate that the newly derived uncertainty principles are truly sharper than the existing ones in the literature. The new proposals’ applications in time-frequency analysis and optical system analysis are also given.

We are concerned with the following polyharmonic equation: \begin{equation*} \Delta_p^L u+V(x)|u|^{p-2}u = K(x)f(x,u) and u>0 in \Bbb R^N, \end{equation*} where $1< p<\infty$, $N>Lp$, $L=1,2,\cdots$ and the potential functions $V, K:\Bbb R^{N}\to(0,\infty)$ are continuous. We study the existence and multiplicity of nontrivial positive weak solutions for the problem above via mountain pass theorem and fountain theorem.

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.

This paper proposes a seven-compartment Markov decision process model for control of epidemic infections. Decision variables include vaccination, treatment, and quarantine. Cost function includes cost of treatment, cost of quarantine, and cost of vaccination. Transition probabilities have been represented by Bayesian network. Scalability of the proposed model has been discussed. Extensions of the proposed approach has also been included as well as comparison with the existing models. Superiority of the proposed approach has been elaborated through a case study.

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.

Droplet impact on a hydrophobic surface is considered and the influence of the droplet volume on the impact characteristics is analyzed. Pressure variation and the characteristics of the droplet in the spreading and retraction cycles are numerically predicted incorporating the conditions adopted in the experiments. The dynamics of the impacting droplet on the hydrophobic surface is simulated and the impacting droplet motion is recorded using the high speed recording system. It is found that the numerical predictions of the impacting droplet shape and height ratios during the spreading and the contraction cycles are in good agreement with those of the experimental data. Increasing droplet volume increases: i) the peak pressure in the droplet fluid upon the impact and ii) the transition period of the droplet on the hydrophobic surface. Increasing droplet volume enhances peak velocity of the droplet spreading on the surface.

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.

Background and purpose: Being exposed to acute stress may cause people to behave more habitual, which purportedly is associated stress-induced increased dopamine release. In contrast, experimental rises in systemic dopamine levels have been shown to increase goal-directed behaviour and, thus, decrease habitual control. Whether experimentally increased dopamine functioning can modulate stress-induced reductions in goal-directed behaviour and its neural substrates, is currently unknown. Experimental approach: To assess whether increased dopamine functioning reduces stress effects on goal-directed behaviour, 100 participants were recruited who were randomly assigned to one of four conditions in a 2x2 between participants design. Participants underwent a stress induction protocol (Maastricht Acute Stress Test; MAST) or a control procedure and received methylphenidate (40 mg, oral) or placebo. In a well-established instrumental learning paradigm, participants were trained to learn stimulus-response-outcome associations, after which rewards were selectively devalued and participants’ goal-directed behaviour was assessed at peak cortisol/methylphenidate concentrations in a magnetic resonance imaging scanner to assess brain activation. Key results: The MAST effectively increased physiological measures of stress (salivary cortisol, blood pressure) and subjective stress. Methylphenidate also increased cortisol levels over time. While stress selectively reduced goal-directed behaviour, this effect was not modulated by methylphenidate. However, methylphenidate modulated stress effects on activation in paracingulate, orbitofrontal cortex, and anterior cingulate associated with expected value representation in goal-directed behaviour. Conclusion and implications: Our neuroimaging data suggest increased dopamine levels reverse stress-induced changes in brain activation associated with goal-directed behaviour. These effects may be relevant for preventing stress-induced relapse in addictive behaviour.

If phenotypic plasticity is adaptive, then prior exposure to a stressor should reduce effects arising from subsequent stressor exposure. Here, we test the hypothesis that corals exhibit adaptive plasticity to a stressor (vermetid gastropods) mediated by their extended phenotype (coral-associated bacteria). We used a reciprocal transplant experiment to evaluate corals that varied in their prior exposure to vermetid gastropods, a known biotic stressor. We measured a suite of traits associated with coral performance, many of which showed a plastic response to vermetid exposure: decreased calcification, increased microbial diversity, and shifted microbial composition. Most traits (e.g., tissue thickness) also showed a signature of previous exposure environment that persisted after exposure reversal. These phenotypic differences are likely genetic, as reefs with and without vermetids largely comprised of two mitotypes. We suggest cryptic coral variation contributes to different community trajectories, with thin-tissue types more prone to disturbance and subsequent colonization by other species.

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 purpose of the present paper is to formulate some new supplements to perturbation theory of linear operators [15] by considering a non-analytic perturbation involving more than one perturbation parameter. An application to a Gribov operator in Bargmann space illustrates the mathematical problem involved in this paper.

In this work, we consider the inverse spectral problem for the impulsive Dirac systems on $(0,\pi)$ with the jump condition at the point $\frac{\pi}{2}$. We conclude that the matrix potential $Q(x)$ on the whole interval can be uniquely determined by a set of eigenvalues for two cases: (i) the matrix potential $Q(x)$ is given on $\Big(0,\frac{(1+\alpha)\pi}{4}\Big)$; (ii) the matrix potential $Q(x)$ is given on $\Big(\frac{(1+\alpha)\pi}{4},\pi\Big)$, where $0<\alpha<1$.

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.

In this study, the generalized modified variable-coefficient KdV equation with external-force term (gvcmKdV) arising in fluid mechanics, plasma physics and ocean dynamics is studied for integrability by using consistent Riccati expansion (CRE) solvability and reduced to nonlinear integrable ordinary differential equation by Clarkson and Kruskal (CK) similarity reduction method. By using the solutions of Riccati equations given before in literature many novel solitary and periodic wave solutions obtained for the gvcmKdV.

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.

Yeast cell flocculation is a common cellular adhesion process which increases the efficiency of yeast cell harvest and recovery in the beer industry and biofuel production. The flocculation involves the binding of exopolysaccharides to the flocculation protein of neighboring cell. It is of great interest to examine the roles of key amino acid residues in modulating polysaccharide binding which regulates the flocculation. In this work, proper mutation sites were identified via alanine scanning mutagenesis incorporated with molecular dynamics simulations of protein-mannobiose complexes based on the crystal structure of flocculation protein Flo1p. Two mutants Q117N and Q117R have been selected out of nine examined mutants, with stronger binding free energies for the mannobiose binding, comparing to the wild type protein. The two mutants also show enhanced binding in the protein-mannotriose complexes which consist of three mannose residues, fulfilling the capacity of the binding site, and can be used to evaluate the binding strength of oligomannose. Hydrogen bonding, conformational stability and shape change were analyzed to help understand the protein-mannotriose interactions. This study also shows a way to alternate oligosaccharide binding to proteins functioning in other biological processes.