Two New Approximations for Variable-Order Fractional Derivatives

We introduced a parameter σ(t) which was related to α(t); then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives α(t)∈(0,1) and 3-α(t)-order approximation for α(t)∈(1,2) are established. For the given parameter σ(t), the error estimations of formulas were proven, which were higher than some recently derived schemes. Finally, some numerical examples with exact solutions were studied to demonstrate the theoretical analysis and verify the efficiency of the proposed methods

A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation

A new high-order finite difference scheme to approximate the Caputo fractional derivative \frac{1}{2} \big ( \, _{0}^{C}D^{\alpha}_{t}f(t_{k})+ \, _{0}^{C}D^{\alpha}_{t}f(t_{k-1}) \big ), k=1, 2, \dots, N, with the convergence order $O(\Delta t^{4-\alpha}), \, \alpha\in(1,2)$ is obtained when $f^{\prime \prime \prime} (t_{0})=0$, where $\Delta t$ denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order $O(\Delta t^{4-\alpha} + h^2)$, where $h$ denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results

Design of school bell automatic control system based on single-chip microcomputer

This article introduces the basic components of the school's automatic control system, and makes a detailed introduction and comparison of the functions, application scenarios, and advantages of each part. The hardware design of the automatic control system is based on the STC89C52 single-chip control circuit as the core, supplemented by sensor circuits, clock circuits, bell circuits and human-computer interaction circuits to complete various functions. The human-computer interaction circuits include keyboard input circuits and liquid crystal display circuits. The software design of this system mainly includes sensor detection, button setting, and bell output part. The sensor detection part is composed of a temperature detection subprogram, the key setting part is composed of an independent key subprogram and a liquid crystal display subprogram, and the bell output part is composed of a voice recording and playback subprogram. The program and clock subroutine constitute

IOT network: models, structure, communications, problems

A brief analysis of the concepts and applications of IoT networks is carried out. Four models of building these networks as variants of component interaction are given: terminal, gateway, cloud, application. Variants of IoT network architectures are presented. Seven variants of interaction in Yota networks are considered. The analysis of problems in these networks and the direction of their solution are carried out

Optimal convergence rates for semidiscrete finite element approximations of linear space-fractional partial differential equations under minimal regularity assumptions

We consider the optimal convergence rates of the semidiscrete finite element approximations for solving linear space-fractional partial differential equations by using the regularity results for the fractional elliptic problems obtained recently by Jin et al. \cite{jinlazpasrun} and Ervin et al. \cite{ervheuroo}. The error estimates are proved by using two approaches. One approach is to apply the duality argument in Johnson \cite{joh} for the heat equation to consider the error estimates for the linear space-fractional partial differential equations. This argument allows us to obtain the optimal convergence rates under the minimal regularity assumptions for the solution. Another approach is to use the approximate solution operators of the corresponding fractional elliptic problems. This argument can be extended to consider more general linear space-fractional partial differential equations. Numerical examples are given to show that the numerical results are consistent with the theoretical results

Micromorphological leaf epidermal traits as potential taxonomic markers for infrageneric classification of Oxytropis (Fabaceae)

The characteristics of the leaf epidermis have proven to be useful criteria to support taxonomic studies within Fabaceae. However, there are few systematic studies on the taxonomic significance of leaf epidermis of Oxytropis DC. Here, we used light and scanning electron microscopy to investigate leaf epidermal characteristics of 18 species of genus Oxytropis from the Northeastern Margin of Qinghai-Tibet Plateau. Our examination showed two main types of leaf epidermal cells: polygonal and irregular, and four different patterns of anticlinal walls: straight-arched, sinuolate, undulate, and sinuate. All species studied possess anomocytic stomata. Two trichome shapes were identified: strip-like trichomes, that were present only in O. ciliata, and cylindrical trichomes, present in all other species. Epidermal cell shape and anticlinal wall pattern were constant within species and are useful for species delimitation within genus Oxytropis, when combined with other macroscopic traits. The shape of trichomes can be useful for distinguishing O. ciliata from the other investigated species. Stomatal type was the same within the genus and may be used to elaborate the phylogenetic relationships between genera in combination with data on stomata from other genera. Cluster analysis results were largely consistent with the classification of species and sections based on macro morphological data, indicating that foliar epidermis characteristics of Oxytropis can be used as markers for taxonomic identification at the infrageneric classification level. Lastly, our results support the delineation of the section Leucopodia as an independent section but do not support the merging of section Gobicola into section Baicalia

Integrated network pharmacology and bioinformatics to identify therapeutic targets and molecular mechanisms of Huangkui Lianchang Decoction for ulcerative colitis treatment

Abstract Background Huangkui Lianchang Decoction (HLD) is a traditional Chinese herbal formula for treating ulcerative colitis (UC). However, its mechanism of action remains poorly understood. The Study aims to validate the therapeutic effect of HLD on UC and its mechanism by integrating network pharmacology, bioinformatics, and experimental validation. Methods UC targets were collected by databases and GSE19101. The active ingredients in HLD were detected by ultra-performance liquid chromatography-tandem mass spectrometry. PubChem collected targets of active ingredients. Protein–protein interaction (PPI) networks were established with UC-related targets. Gene Ontology and Kyoto Encyclopedia (KEGG) of Genes and Genomes enrichment were analyzed for the mechanism of HLD treatment of UC and validated by the signaling pathways of HLD. Effects of HLD on UC were verified using dextran sulfate sodium (DDS)-induced UC mice experiments. Results A total of 1883 UC-related targets were obtained from the GSE10191 dataset, 1589 from the database, and 1313 matching HLD-related targets, for a total of 94 key targets. Combined with PPI, GO, and KEGG network analyses, the signaling pathways were enriched to obtain IL-17, Toll-like receptor, NF-κB, and tumor necrosis factor signaling pathways. In animal experiments, HLD improved the inflammatory response of UC and reduced UC-induced pro-inflammatory factors such as Tumor Necrosis Factor Alpha (TNF-α), interleukin 1β (IL-1β), and interleukin 6 (IL-6). HLD suppressed proteins TLR4, MyD88, and NF-κB expression. Conclusions This study systematically dissected the molecular mechanism of HLD for the treatment of UC using a network pharmacology approach. Further animal verification experiments revealed that HLD inhibited inflammatory responses and improved intestinal barrier function through the TLR4/MyD88/NF-κB pathway

Discrepancies between self-reported medication in adherence and indirect measurement adherence among patients undergoing antiretroviral therapy: a systematic review

Abstract Background Given the critical importance of medication adherence in HIV/AIDS treatment, this study aims to compare medication adherence measured by self-report (SR) and indirect measurement among antiretroviral therapy (ART) patients, exploring the differences of adherence results measured by different tools. Methods We systematically searched PubMed, Embase, and the Cochrane Library to identify all relevant literature published up to November 22, 2023, without language restrictions, reporting adherence to ART measured by both SR and indirect measurement methods, while also analyzing individual and group adherence separately. Discrepancies between SR and indirect measurement results were assessed using the Mann–Whitney U test or Wilcoxon signed-rank test, with correlations evaluated using the Pearson correlation coefficient. Following one-to-one comparisons, meta-epidemiological one-step analysis was conducted, and network meta-analysis techniques were applied to compare results obtained through specific adherence assessment tools reported in the identified articles. Results The analysis encompassed 65 original studies involving 13,667 HIV/AIDS patients, leading to 112 one-to-one comparisons between SR and indirect measurement tools. Statistically significant differences were observed between SR and indirect measurement tools regarding both individual and group adherence (P < 0.05), with Pearson correlation coefficients of 0.843 for individual adherence and 0.684 for group adherence. During meta-epidemiological one-step analysis, SR-measured adherence was determined to be 3.94% (95% CI: -4.48–13.44%) higher for individual adherence and 16.14% (95% CI: 0.81–18.84%) higher for group adherence compared to indirectly measured results. Subgroup analysis indicated that factors such as the year of reporting and geographic region appeared to influence the discrepancies between SR and indirect measurements. Furthermore, network meta-analysis revealed that for both individual and group adherence, the results obtained from most SR and indirect measurement tools were higher than those from electronic monitoring devices, with some demonstrating statistical significance (P < 0.05). Conclusions The findings underscored the complexity of accurately measuring medication adherence among ART patients. Significant variability was observed across studies, with self-report methods showing a significant tendency towards overestimation. Year of reporting, geographic region, and adherence measurement tools appeared to influence the differences between SR and indirect measurements. Future research should focus on developing and validating integrated adherence measurements that can combine SR data with indirect measures to achieve a more comprehensive understanding of adherence behaviors. Graphical Abstrac