Fixed points and asymptotic stability of nonlinear fractional difference equations

In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results

Asymptotic Stability Results for Nonlinear Fractional Difference Equations

We present some results for the asymptotic stability of solutions for nonlinear fractional difference equations involvingRiemann-Liouville-likedifference operator. The results are obtained by using Krasnoselskii's fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results

New Scheme of Finite Difference Heterogeneous Multiscale Method to Solve Saturated Flow in Porous Media

A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media. In the discretization framework of FDHMM, we follow some ideas from the multiscale finite element method and construct basic microscopic elliptic models. Tests on a variety of numerical experiments show that, in the case that only about a half of the information of the whole microstructure is used, the constructed scheme gives better accuracy at a much lower computational time than FDHMM for the problem of aquifer response to sudden change in reservoir level and gives comparable accuracy at a much lower computational time than FDHMM for the weak drawdown problem

Effect of Different Arbuscular Mycorrhizal Fungi on Growth and Physiology of Maize at Ambient and Low Temperature Regimes

The effect of four different arbuscular mycorrhizal fungi (AMF) on the growth and lipid peroxidation, soluble sugar, proline contents, and antioxidant enzymes activities of Zea mays L. was studied in pot culture subjected to two temperature regimes. Maize plants were grown in pots filled with a mixture of sandy and black soil for 5 weeks, and then half of the plants were exposed to low temperature for 1 week while the rest of the plants were grown under ambient temperature and severed as control. Different AMF resulted in different root colonization and low temperature significantly decreased AM colonization. Low temperature remarkably decreased plant height and total dry weight but increased root dry weight and root-shoot ratio. The AM plants had higher proline content compared with the non-AM plants. The maize plants inoculated with Glomus etunicatum and G. intraradices had higher malondialdehyde and soluble sugar contents under low temperature condition. The activities of catalase (CAT) and peroxidase of AM inoculated maize were higher than those of non-AM ones. Low temperature noticeably decreased the activities of CAT. The results suggest that low temperature adversely affects maize physiology and AM symbiosis can improve maize seedlings tolerance to low temperature stress

Could AGN Outbursts Transform Cool Core Clusters?

The origin of the bimodality in cluster core entropy is still unknown. At the same time, recent work has shown that thermal conduction in clusters is likely a time-variable phenomenon. We consider if time-variable conduction and AGN outbursts could be responsible for the cool-core (CC), non cool-core (NCC) dichotomy. We show that strong AGN heating can bring a CC cluster to a NCC state, which can be stably maintained by conductive heating from the cluster outskirts. On the other hand, if conduction is shut off by the heat-flux driven buoyancy instability, then the cluster will cool to the CC state again, where it is stabilized by low-level AGN heating. Thus, the cluster cycles between CC and NCC states. In contrast with massive clusters, we predict the CC/NCC bimodality should vanish in groups, due to the lesser role of conductive heating there. We find tentative support from the distribution of central entropy in groups, though firm conclusions require a larger sample carefully controlled for selection effects.Comment: Slightly revised version, accepted for publication in MNRAS. 9 pages, 3 figure

Asthma prevalence based on the Baidu index and China's Health Statistical Yearbook from 2011 to 2020 in China

BackgroundDue to environmental pollution, changes in lifestyle, and advancements in diagnostic technology, the prevalence of asthma has been increasing over the years. Although China has made early efforts in asthma epidemiology and prevention, there is still a lack of unified and comprehensive epidemiological research within the country. The objective of the study is to determine the nationwide prevalence distribution of asthma using the Baidu Index and China's Health Statistical Yearbook.MethodsBased on China's Health Statistical Yearbook, we analyzed the gender and age distribution of asthma in China from 2011 to 2020, as well as the length of hospitalization and associated costs. By utilizing the Baidu Index and setting the covering all 31 provinces and autonomous regions in China, we obtained the Baidu Index for the keyword 'asthma'. Heatmaps and growth ratios described the prevalence and growth of asthma in mainland China.ResultsThe average expenditure for discharged asthma (standard deviation) patients was ¥5,870 (808). The average length of stay (standard deviation) was 7.9 (0.38) days. During the period of 2011 to 2020, hospitalization expenses for asthma increased while the length of hospital stay decreased. The proportion of discharged patients who were children under the age of 5 were 25.3% (2011), 19.4% (2012), 16% (2013), 17.9% (2014), 13.9% (2015), 11.3% (2016), 10.2% (2017), 9.4% (2018), 8.1% (2019), and 7.2% (2020), respectively. The prevalence of asthma among boys was higher than girls before the age of 14. In contrast, the proportion of women with asthma was larger than men after the age of 14. During the period from 2011 to 2020, the median [The first quartile (Q1)-the third quartile (Q3)] daily asthma Baidu index in Guangdong, Beijing, Jiangsu, Sichuan, and Zhejiang were 419 (279–476), 328 (258–376), 315 (227–365), 272 (166–313), and 312 (233–362) respectively. Coastal regions showed higher levels of attention toward asthma, indicating a higher incidence rate. Since 2014, there has been a rapid increase in the level of attention toward asthma, with the provinces of Qinghai, Sichuan, and Guangdong experiencing the fastest growth.ConclusionThere are regional variations in the prevalence of asthma among different provinces in China, and the overall prevalence of asthma is increasing

Biochar amendment alters root morphology of maize plant: Its implications in enhancing nutrient uptake and shoot growth under reduced irrigation regimes

IntroductionBiochar amendment provides multiple benefits in enhancing crop productivity and soil nutrient availability. However, whether biochar addition affects root morphology and alters plant nutrient uptake and shoot growth under different irrigation regimes remain largely unknown.MethodsA split-root pot experiment with maize (Zea mays L.) was conducted on clay loam soil mixed with 2% (w/w) of wheat-straw (WSP) and softwood (SWP) biochar. The plants were subjected to full (FI), deficit (DI), and alternate partial root-zone drying (PRD) irrigation from the fourth leaf to the grain-filling stage.Results and discussionThe results showed that, compared to plants grown in unamended soils, plants grown in the biochar-amended soils possessed greater total root length, area, diameter, volume, tips, forks, crossings, and root length density, which were further amplified by PRD. Despite a negative effect on soil available phosphorus (P) pool, WSP addition improved soil available nitrogen (N), potassium (K), and calcium (Ca) pool and cation exchange capacity under reduced irrigation. Even though biochar negatively affected nutrient concentrations in shoots as exemplified by lowered N, P, K (except leaf), and Ca concentration, it dramatically enhanced plant total N, P, K, Ca uptake, and biomass. Principal component analysis (PCA) revealed that the modified root morphology and increased soil available nutrient pools, and consequently, the higher plant total nutrient uptake might have facilitated the enhanced shoot growth and yield of maize plants in biochar-added soils. Biochar amendment further lowered specific leaf area but increased leaf N concentration per area-to-root N concentration per length ratio. All these effects were evident upon WSP amendment. Moreover, PRD outperformed DI in increasing root area-to-leaf area ratio. Overall, these findings suggest that WSP combined with PRD could be a promising strategy to improve the growth and nutrient uptake of maize plants

A comparative analysis of morphology, microstructure, and volatile metabolomics of leaves at varied developmental stages in Ainaxiang (Blumea balsamifera (Linn.) DC.)

IntroductionAinaxiang (Blumea balsamifera (Linn.) DC.) is cultivated for the extraction of (-)-borneol and other pharmaceutical raw materials due to its abundant volatile oil. However, there is limited knowledge regarding the structural basis and composition of volatile oil accumulation in fresh B. balsamifera leaves.MethodsTo address this problem, we compare the fresh leaves’ morphology, microstructure, and volatile metabonomic at different development stages, orderly defined from the recently unfolded young stage (S1) to the senescent stage (S4).Results and discussionDistinct differences were observed in the macro-appearance and microstructure at each stage, particularly in the B. balsamifera glandular trichomes (BbGTs) distribution. This specialized structure may be responsible for the accumulation of volatile matter. 213 metabolites were identified through metabolomic analysis, which exhibited spatiotemporal accumulation patterns among different stages. Notably, (-)-borneol was enriched at S1, while 10 key odor metabolites associated with the characteristic balsamic, borneol, fresh, and camphor aromas of B. balsamifera were enriched in S1 and S2. Ultra-microstructural examination revealed the involvement of chloroplasts, mitochondria, endoplasmic reticulum, and vacuoles in the synthesizing, transporting, and storing essential oils. These findings confirm that BbGTs serve as the secretory structures in B. balsamifera, with the population and morphology of BbGTs potentially serving as biomarkers for (-)-borneol accumulation. Overall, young B. balsamifera leaves with dense BbGTs represent a rich (-)-borneol source, while mesophyll cells contribute to volatile oil accumulation. These findings reveal the essential oil accumulation characteristics in B. balsamifera, providing a foundation for further understanding