Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions on regional gradient exact and approximate controllability are first given and proved in detail. Secondly, we propose an approach on how to calculate the minimum number of $\omega-$strategic actuators. Moreover, the existence, uniqueness and the concrete form of the optimal controller for the system under consideration are presented by employing the Hilbert Uniqueness Method (HUM) among all the admissible ones. Finally, we illustrate our results by an interesting example.Comment: 16 page

An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave

Background: The structure of age groups and social contacts of the total population influenced infection scales and hospital-bed requirements, especially influenced severe infections and deaths during the global prevalence of COVID-19. Before the end of the year 2022, Chinese government implemented the national vaccination and had built the herd immunity cross the country, and announced Twenty Measures (November 11) and Ten New Measures (December 7) for further modifications of dynamic zero-COVID polity on the Chinese mainland. With the nation-wide vaccination and modified measures background, Fuzhou COVID-19 large wave (November 19, 2022–February 9, 2023) led by Omicron BA.5.2 variant was recorded and prevailed for three months in Fujian Province. Methods: A multi-age groups susceptible-exposed-infected-hospitalized-recovered (SEIHR) COVID-19 model with social contacts was proposed in this study. The main object was to evaluate the impacts of age groups and social contacts of the total population. The idea of Least Squares method was governed to perform the data fittings of four age groups against the surveillance data from Fujian Provincial Center for Disease Control and Prevention (Fujian CDC). The next generation matrix method was used to compute basic reproduction number for the total population and for the specific age group. The tendencies of effective reproduction number of four age groups were plotted by using the Epiestim R package and the SEIHR model for in-depth discussions. The sensitivity analysis by using sensitivity index and partial rank correlation coefficients values (PRCC values) were operated to reveal the differences of age groups against the main parameters. Results: The main epidemiological features such as basic reproduction number, effective reproduction number and sensitivity analysis were extensively discussed for multi-age groups SEIHR model in this study. Firstly, by using of the next generation matrix method, basic reproduction number R0 of the total population was estimated as 1.57 using parameter values of four age groups of Fuzhou COVID-19 large wave. Given age group k, the values of R0k (age group k to age group k), the values of R0k (an infected of age group k to the total population) and the values of R^0k (an infected of the total population to age group k) were also estimated, in which the explorations of the impacts of age groups revealed that the relationship R0k>R0k>R^0k was valid. Then, the fluctuating tendencies of effective reproduction number Rt were demonstrated by using two approaches (the surveillance data and the SEIHR model) for Fuzhou COVID-19 large wave, during which high-risk group (G4 group) mainly contributed the infection scale due to high susceptibility to infection and high risks to basic diseases. Further, the sensitivity analysis using two approaches (the sensitivity index and the PRCC values) revealed that susceptibility to infection of age groups played the vital roles, while the numerical simulation showed that infection scale varied with the changes of social contacts of age groups. The results of this study claimed that the high-risk group out of the total population was concerned by the local government with the highest susceptibility to infection against COVID-19. Conclusions: This study verified that the partition structure of age groups of the total population, the susceptibility to infection of age groups, the social contacts among age groups were the important contributors of infection scale. The less social contacts and adequate hospital beds for high-risk group were profitable to control the spread of COVID-19. To avoid the emergence of medical runs against new variant in the future, the policymakers from local government were suggested to decline social contacts when hospital beds were limited

Feedback stabilization control design for a class of nonlinear fractional order triangular systems

This paper investigates the design of feedback controls for a class of nonlinear homogeneous and inhomogeneous fractional order triangular systems with high power right-hand functions. By using the fractional Lyapunov method and the recursive method, we derive both state and output feedback controllers to stabilize the systems that we study. Finally, two numerical example are provided to illustrate the effectiveness of our results

Boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems

In this paper, the problem of boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems is studied. Firstly, the stability of the target system is analyzed. By using the backstepping method, the explicit kernel matrix function is obtained, and a new state feedback controller is designed to stabilize the original system. Then we consider two kinds of output measurements, that is, the non-collocated output and the collocated output. In the two cases, the corresponding observers and output feedback controllers are designed, respectively, to achieve the asymptotical stability of the studied system

Prediction of Sea Level Nonlinear Trends around Shandong Peninsula from Satellite Altimetry

Sea level change is a key indicator of climate change, and the prediction of sea level rise is one of most important scientific issues. In this paper, the gridded sea level anomaly (SLA) data from satellite altimetry are used to analyze the sea level variations around Shandong Peninsula from 1993 to 2016. Based on the Complete Ensemble Empirical Mode Decomposition (CEEMD) method and Radial Basis Function (RBF) network, the paper proposes an improved sea level multi-scale prediction approach, namely, CEEMD-RBF combined model. Firstly, the multi-scale frequency oscillatory modes (intrinsic mode functions (IMFs)) representing different oceanic processes are extracted by CEEMD from the highest frequency to the lowest frequency oscillating mode. Secondly, RBF network is used to establish prediction models for various IMF components to predict their future trends, and each IMF is used as an input factor of the RBF network separately. Finally, the prediction results of each IMF component with RBF network are reconstructed to obtain the final predictions of sea level anomalies. The results shows that CEEMD is particularly suitable for analyzing nonlinear and non-stationary time series and RBF network is applicable for regional sea level prediction at different scales

Supplementation with Fermented Feedstuff Enhances Orexin Expression and Secretion Associated with Increased Feed Intake and Weight Gain in Weaned Pigs

The health status of weaned pigs is crucial for their subsequent growth performance. Supplementation with fermented feedstuff is able to improve the feed intake and growth of weaned pigs; however, the exact mechanism behind this is not clear. Hence, in the present study a total of 320 Duroc × Landrace × Yorkshire weaned pigs were selected and allocated to the following two groups: unfermented diet group (UFD) and fermented diet group (FD). The experimental period lasted 21 days. At the end of the experiment, feces, blood, and gastrointestinal tissue samples (including the stomach, jejunum, and ileum) were collected and used for further analysis. The results of growth performance suggested that the FD group had significantly increased (p p p p p < 0.05) serum orexin level and prepro-orexin (PPOX) expression in the gastric fundus, jejunum, and ileum mucosa and increased IGF-1 and IGFR expression in the jejunum. Collectively, these results indicated that supplementation with fermented feedstuff in the diet effectively enhanced the feed intake and growth of weaned pigs and that this may have been caused by the increased orexin, IGF-1, and IGFR serum levels

Urbanization Influences CO2 Emissions in the Pearl River Delta: A Perspective of the &ldquo;Space of Flows&rdquo;

As the largest carbon emitter in the world, China is facing increasing challenge to reduce CO2 emissions. Given this issue, exploring the influencing factors is of great significance for scientific low-carbon emission policymaking. Although previous literature has explored the effects of urbanization on CO2 emissions, the impact of the space of flow on urban carbon emissions have been less explored. Due to the increasing connection between cities, its impact on urban carbon emissions cannot be ignored. Thus, this paper takes the space of flows into account as an aspect of urbanization to supplement the existing literature and empirically examines the multiple effects of urbanization on CO2 emissions in the Pearl River Delta (PRD) urban agglomeration. By using a STIRPAT model, statistical data, and web crawler data, we examined impacts of different types of urbanization on CO2 emissions. Our empirical results show that: (1) Within the PRD urban agglomeration, urban linkage intensity is strongly connected to urban socioeconomic growth, establishing a geographical structure with Guangzhou and Shenzhen as the double core. (2) Our results show that urbanization exerts two opposite effects on CO2 emissions: positively connects carbon emissions with population urbanization, integrated urban linkage flow, and energy intensity, whereas economic urbanization and social urbanization are shown to be negatively correlated. However, spatial urbanization has no significant positive effect on urban CO2 emissions. (3) It is worth noting that urban linkage flows are the second most important factor affecting urban carbon emissions after economic urbanization. Our study could formulate effective planning suggestions for future CO2 emission reduction paths and development modes in the PRD

Pre treatment of melatonin rescues cotton seedlings from cadmium toxicity by regulating key physio-biochemical and molecular pathways

Melatonin, a plant/animal origin hormone, regulates plant response to abiotic stresses by protecting them from oxidative damage. This study identified physiochemical and molecular mechanism of melatonin-induced cadmium (Cd) stress tolerance and detoxification in cotton seedlings. Cotton seedlings, with or without melatonin (15 µM) pretreatment, were subjected to Cd (100 µM) stress in a hydroponic medium for eight days. We found that higher cellular Cd accumulation in leaf tissues significantly inhibited the growth and physiology of cotton seedlings. In contrast, melatonin-treated seedlings maintained leaf photosynthetic capacity, producing relatively higher fresh (17.4%) and dry (19.3%) weights than non-melatonin-treated plants under Cd-contaminated environments. The improved growth and leaf functioning were strongly linked with the melatonin-induced repression of Cd transporter genes (LOC107894197, LOC107955631, LOC107899273) in roots. Thus, melatonin induced downregulation of the Cd transporter genes further inhibited Cd ion transport towards leaf tissues. This suggests that the differentially expressed transporter genes (DEG) are key drivers of the melatonin-mediated regulation of Cd transportation and sequestration in cotton. Melatonin also protected cotton seedlings from Cd-induced oxidative injury by reducing tissues malondialdehyde (MDA) and hydrogen peroxide (H2O2) levels and increasing the activities of superoxide dismutase (SOD), peroxidase (POD), catalase (CAT), and ascorbate peroxidase (APX) enzymes. Transcriptomic analysis revealed that melatonin activated mitogen-activated protein kinase (MAPK) signaling pathways to simulate stomatal adjustment and photosynthesis in Cd-stressed leaves. Further, melatonin protects intercellular organs, particularly ribosomes, from Cd-induced oxidative damage by promoting ribosomal biosynthesis and improving translational efficiency. The findings elucidated the molecular basis of melatonin-mediated Cd stress tolerance in plants and provided a key for the effective strategy of Cd accumulation in cotton.This work was financially supported by National Natural Science Foundation of China (32161143012), Hainan Provincial Natural Science Foundation Joint Project of China (2021JJLH0032) and Hainan Yazhou Bay Seed Laboratory Program Postdoctoral Project (Grant B22Y10205)