Existence and uniqueness of solution for fractional differential equations with integral boundary conditions

This paper is devoted to the existence and uniqueness results of solutions for fractional differential equations with integral boundary conditions. $$\left\{ \begin{array}{l} ^C\hspace{-0.2em}D^\alpha x(t)+f(t,x(t),x'(t))=0,\quad t\in(0,1),\\ x(0)=\int^1_0 g_0(s,x(s))\mathrm{d}s ,\\ x(1)=\int^1_0 g_1(s,x(s))\mathrm{d}s ,\\ x^{(k)}(0)=0,\,\ k=2,3,\cdots, [\alpha]-1. \end{array} \right.$$ By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order $\alpha$

Biogeographic Patterns and Assembly Mechanisms of Bacterial Communities Differ Between Habitat Generalists and Specialists Across Elevational Gradients

A core issue in microbial ecology is the need to elucidate the ecological processes and underlying mechanisms involved in microbial community assembly. However, the extent to which these mechanisms differ in importance based on traits of taxa with different niche breadth is poorly understood. Here, we used high-throughput sequencing to examine the relative importance of environmental selection and stochastic processes in shaping soil bacterial sub-communities with different niche breadth (including habitat generalists, specialists and other taxa) across elevational gradients on the subalpine slope of Mount Wutai, Northern China. Our findings suggested that the composition of soil bacterial communities differed significantly different among elevational gradients. According to the niche breadth index, 10.9% of OTUs were defined as habitat generalists (B-value >8.7) and 10.0% of OTUs were defined as habitat specialists (B-value <1.5). Generalists and specialists differed distinctly in diversity and biogeographic patterns across elevational gradients. Environmental selection (deterministic processes) and spatial factors (stochastic processes) seemed to determine the assembly and biogeography of habitat generalists. However, for specialists, deterministic processes strongly influenced the distribution, while stochastic processes were not at play. Environmental drivers for generalists and specialists differed, as did their importance. Elevation, total nitrogen and pH were the main factors determining habitat generalists, and soil water content, nitrate nitrogen and pH had the strongest impacts on specialists. Moreover, variation partitioning analysis revealed that environmental selection had a much greater impact on both generalists (17.7% of pure variance was explained) and specialists (3.6%) than spatial factors. However, generalists had a much stronger response to spatial factors (2.3%) than specialists (0.3%). More importantly, null models of β-diversity suggested that specialists deviated significantly from non-neutral assembly mechanisms (relative null deviation= 0.64–0.74) relative to generalists (0.16–0.65) (P < 0.05). These results indicate that generalists and specialists are governed by different assembly mechanisms and present distinct biogeographical patterns. The large proportion of unexplained variation in specialists (93.3%) implies that very complex assembly mechanisms exist in the assembly of specialists across elevational gradients on the subalpine slope of Mount Wutai. It is essential to understand the microbial community assembly at a more refined level, and to expand the current understanding of microbial ecological mechanisms

Effects of AMF inoculation on the eco-physiological characteristics of Imperata cylindrica under differing soil nitrogen conditions

Arbuscular mycorrhizal fungi (AMF) play a key role in terrestrial ecosystems, while the ecological restoration application of AMF in mining areas has been progressively gaining attention. This study simulated a low nitrogen (N) environment in copper tailings mining soil to explore inoculative effects of four AMF species on the eco-physiological characteristics of Imperata cylindrica, and provided plant-microbial symbiote with excellent resistance to copper tailings. Results show that N, soil type, AMF species, and associated interactions significantly affected ammonium (NH4  +), nitrate nitrogen (NO3  −), and total nitrogen (TN) content and photosynthetic characteristics of I. cylindrica. Additionally, interactions between soil type and AMF species significantly affected the biomass, plant height, and tiller number of I. cylindrica. Rhizophagus irregularis and Glomus claroideun significantly increased TN and NH4  + content in the belowground components I. cylindrica in non-mineralized sand. Moreover, the inoculation of these two fungi species significantly increased belowground NH4  + content in mineralized sand. The net photosynthetic rate positively correlated to aboveground total carbon (TC) and TN content under the high N and non-mineralized sand treatment. Moreover, Glomus claroideun and Glomus etunicatum inoculation significantly increased both net photosynthetic and water utilization rates, while F. mosseae inoculation significantly increased the transpiration rate under the low N treatment. Additionally, aboveground total sulfur (TS) content positively correlated to the intercellular carbon dioxide (CO2) concentration, stomatal conductance, and the transpiration rate under the low N sand treatment. Furthermore, G. claroideun, G. etunicatum, and F. mosseae inoculation significantly increased aboveground NH4  + and belowground TC content of I. cylindrica, while G. etunicatum significantly increased belowground NH4  + content. Average membership function values of all physiological and ecological I. cylindrica indexes infected with AMF species were higher compared to the control group, while corresponding values of I. cylindrica inoculated with G. claroideun were highest overall. Finally, comprehensive evaluation coefficients were highest under both the low N and high N mineralized sand treatments. This study provides information on microbial resources and plant-microbe symbionts in a copper tailings area, while aiming to improve current nutrient-poor soil conditions and ecological restoration efficiency in copper tailings areas

The Impact of Variational Primary Collaterals on Cerebral Autoregulation

The influence of the anterior and posterior communicating artery (ACoA and PCoA) on dynamic cerebral autoregulation (dCA) is largely unknown. In this study, we aimed to test whether substantial differences in collateral anatomy were associated with differences in dCA in two common types of stenosis according to digital subtraction angiography (DSA): either isolated basal artery and/or bilateral vertebral arteries severe stenosis/occlusion (group 1; group 1A: with bilateral PCoAs; and group 1B: without bilateral PCoAs), or isolated unilateral internal carotid artery severe stenosis/occlusion (group 2; group 2A: without ACoA and with PCoA; group 2B: with ACoA and without PCoAs; and group 2C: without both ACoA and PCoA). The dCA was calculated by transfer function analysis (a mathematical model), and was evaluated in middle cerebral artery (MCA) and/or posterior cerebral artery (PCA). Of a total of 231 non-acute phase ischemic stroke patients who received both dCA assessment and DSA in our lab between 2014 and 2017, 51 patients met inclusion criteria based on the presence or absence of ACoA or PCoA, including 21 patients in the group 1, and 30 patients in the group 2. There were no significant differences in gender, age, and mean blood pressure between group 1A and group 1B, and among group 2A, group 2B, and group 2C. In group 1, the PCA phase difference values (autoregulatory parameter) were significantly higher in the subgroup with patent PCoAs, compared to those without. In group 2, the MCA phase difference values were higher in the subgroup with patent ACoA, compared to those without. This pilot study found that the cross-flow of the ACoA/PCoA to the affected area compensates for compromised dCA in the affected area, which suggests an important role of the ACoA/PCoA in stabilizing cerebral blood flow

Experimental study on LBL beams

Six specimens were made and tested to study the mechanical properties of LBL beams. The mean ultimate loading value is 68.39 MPa with a standard deviation of 6.37 MPa, giving a characteristic strength (expected to be exceeded by 95% of specimens) of 57.91 MPa, and the mean ultimate deflection is 53.3 mm with a standard deviation of 5.5 mm, giving the characteristic elastic modulus of 44.3 mm. The mean ultimate bending moment is 20.18 kN.m with a standard deviation of 1.88 kN.m, giving the characteristic elastic modulus of 17.08 kN.m. The mean elastic modulus is 9688 MPa with a standard deviation of 1765 MPa, giving the characteristic elastic modulus of 6785 MPa, and the mean modulus of rupture is 93.3 MPa with a standard deviation of 8.6 MPa, giving the characteristic elastic modulus of 79.2 MPa. The strain across the cross-section for all LBL beams is basically linear throughout the loading process, following standard beam theory

Non-Negative Matrix Factorization Based on Smoothing and Sparse Constraints for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is a technique for estimating a set of pure source signals (end members) and their proportions (abundances) from each pixel of the hyperspectral image. Non-negative matrix factorization (NMF) can decompose the observation matrix into the product of two non-negative matrices simultaneously and can be used in HU. Unfortunately, a limitation of many traditional NMF-based methods, i.e., the non-convexity of the objective function, may lead to a sub-optimal solution. Thus, we put forward a new unmixing method based on NMF under smoothing and sparse constraints to obtain a better solution. First, considering the sparseness of the abundance matrix, a weight sparse regularization is introduced into the NMF model to ensure the sparseness of the abundance matrix. Second, according to the similarity prior of the same feature in the adjacent pixels, a Total Variation regularization is further added to the NMF model to improve the smoothness of the abundance map. Finally, the signatures of each end member are modified smoothly in spectral space. Moreover, it is noticed that discontinuities may emerge due to the removal of noisy bands. Therefore, the spectral data are piecewise smooth in spectral space. Then, in this paper, a piecewise smoothness constraint is further applied to each column of the end-member matrix. Experiments are conducted to evaluate the effectiveness of the proposed method based on two different datasets, including a synthetic dataset and the real-life Cuprite dataset, respectively. Experimental results show that the proposed method outperforms several state-of-the-art HU methods. In the Cuprite hyperspectral dataset, the proposed method’s Spectral Angle Distance is 0.1694, compared to the TV-RSNMF method’s 0.1703, L1/2NMF method’s 0.1925, and VCA-FCLS method’s 0.1872