Search Results (23)

This article presents several key findings for fractional-order delay differential equations. First, we establish the existence and uniqueness of solutions using two distinct approaches, the Chebyshev norm and the Bielecki norm, thereby providing a comprehensive understanding of the solution space. Notably, the uniqueness of the solution is rigorously demonstrated using the Lipschitz condition, ensuring a single solution under specific constraints. Additionally, we examine a specific form of constant delay and apply Burton’s method to further confirm the uniqueness of the solution. Furthermore, we conduct an in-depth investigation into the Hyers–Ulam stability of the problem, providing valuable insights into the behavior of solutions under perturbations. Notably, our results eliminate the need for contraction constant conditions that are commonly imposed in the existing literature. Finally, numerical simulations are performed to illustrate and validate the theoretical results obtained in this study. Fractional-order delay differential equations play a crucial role in real-life applications in systems where memory and delayed effects are essential. In biology and epidemiology, they model disease spread with incubation delays and immune memory. In control systems and robotics, they help design stable controllers by accounting for time-lagged responses and past behavior. Full article

Glioblastoma is the most aggressive and treatment-resistant form of primary brain tumors, characterized by rapid invasion and a poor prognosis. Its complex behavior continues to challenge both clinical interventions and research efforts. Mathematical modeling provides a valuable approach to unraveling a tumor’s spatiotemporal dynamics and supporting the development of more effective therapies. In this study, we built on the existing literature by refining and adapting mathematical models to better capture glioblastoma infiltration, using a partial differential equation (PDE) framework to simulate how cancer cell density evolves across both time and space. In particular, the role of cell diffusion and growth in tumor progression and their limitations due to cell crowding and competition were investigated. Experimental data of glioblastoma taken from the literature were exploited for the identification of the model parameters. The improved data reproduction when the limitations of cell diffusion and growth were taken into account proves the relevant impact of the considered mechanisms on the spread of the tumor population, which underscores the potential of the proposed framework. Full article

It is very important to enhance the risk resistance of the agricultural sector to realize the modernization transformation of the agricultural industry and strengthen the competitiveness of national agriculture. Based on the relevant spatial data of 30 provincial administrative regions in China from 2013 to 2022, this study constructs a multi-dimensional index framework to comprehensively evaluate the resilience of China’s agricultural economy by comprehensively considering the three key aspects of adaptability, management strategy, and innovation drive. This study adopts several quantitative analysis tools including the Theil index, global and local analysis of the Moran I index, and kernel density estimation (KDE), and further combines with the spatial Durbin model (SDM) to conduct an in-depth spatiotemporal analysis of the resilience of China’s agricultural economy. This study not only reveals the evolution trend of agricultural economic resilience in different times and spaces but also analyzes the differences in resilience among regions and its spread in space. Through these refined analytical tools, we aim to reveal how agricultural economic resilience changes over time, the differences in resilience levels among regions, and the geospatial interactions and diffusion. This study reveals a series of key findings: (1) The resilience of China’s agricultural economy shows a trend of steady improvement. (2) Differences within the three regions are the main factors generating differences in the development of resilience in China’s agricultural economy. (3) The resilience of the agricultural economy in different regions shows obvious spatial correlations. (4) Further analysis shows that the efficiency of agricultural production and the urbanization process have a positive direct impact on the resilience of the agricultural economy, and this impact has a significant positive spatial diffusion effect. Meanwhile, although the level of agricultural mechanization is not significant in its direct impact, it has a positive spatial impact on the enhancement of agricultural economic resilience in other regions. In addition, the restructuring of agricultural cropping has both direct negative impacts and positive spatial spillover effects on the resilience of the agricultural economy. Based on these findings, this paper suggests that agricultural policies should consider regional development differences, implement differentiated agricultural support policies, fully account for the spatial spillover effects of agricultural ecological efficiency, and strengthen the exchange and cooperation of resources between regions. This study deepens the understanding of the spatial and temporal characteristics of the resilience of China’s agricultural economy, reveals its inherent dynamic processes and spatial interactions, and provides valuable references for policymakers and practitioners to better cope with the various challenges encountered in agricultural production, and to jointly promote the sound development of China’s agricultural economy. Full article

We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussian distribution as the initial condition. Measuring the spread of the Gaussian distribution by $u{(0,t)}^{-2}$, our results show that the solution reaches a steady state governed by the parameters present in the logistic function in Fisher’s equation. The initial transient is an anomalous diffusion process, but a power law cannot describe the whole transient. In this sense, the main novelty of this work is to show that a q-exponential function gives a better description of the transient dynamics. In addition to this result, we extend the Fisher equation via non-integer operators. As a fractional definition, we employ the Caputo fractional derivative and use a discretized system for the numerical approach according to finite difference schemes. We consider the numerical solutions in three scenarios: fractional differential operators acting in time, space, and in both variables. Our results show that the time to reach the steady solution strongly depends on the fractional order of the differential operator, with more influence by the time operator. Our main finding shows that a generalized q-exponential, present in the Tsallis formalism, describes the transient dynamics. The adjustment parameters of the q-exponential depend on the fractional order, connecting the generalized thermostatistics with the anomalous relaxation promoted by the fractional operators in time and space. Full article

The study improves the understanding of the basal part of the Eocene Seeb Formation of Oman, informally known as “Unit 1”, in terms of microfacies, lithostratigraphy and shale migration within the context of regional tectonics. We logged four sections bed-by-bed over a distance of 8.3 km, collected samples and analyzed thin-sections as well as XRD samples. For the first time, the microfacies and stratigraphic correlation of the lowermost part of the limestone-dominated Seeb Formation were studied in detail. In the analyzed area, Unit 1 is ~20 to 40 m thick, with the thickness increasing to the SE. In the upper part of Unit 1 is a laterally continuous shale horizon. The limestones of Unit 1 contain mostly packstones and grainstones. The dominant standard microfacies types are SMF 18-FOR and SMF 16. The former is dominated by benthic foraminifera, and the latter by peloids. Both SMFs indicate restricted lagoonal conditions. Foraminifera are common in Unit 1 and indicate a middle Eocene age. Considering the abundance of encountered foraminiferal bioclasts, it appears probable that the lagoon barrier was mainly composed of foraminiferal tests. Gutter casts, slumps and debrites indicate an active, partly unstable syndepositional slope, which was likely initially created by uplift of the Saih Hatat Dome and Jabal Nakhl Subdome. Differential regional uplift due to a more pronounced overall doming in the NW (Jabal Nakhl Subdome) than in the SE (Saih Hatat Dome) explains more accommodation space and greater thickness towards the SE. For the first time, we report visco-plastic shale migration/intrusion within the Seeb Formation, related to a shale horizon of Unit 1. This shale locally migrated as indicated by (1) local thickness variations, (2) detached limestone boulders floating in the shale, (3) limestone beds that have been cut-off by the shale and (4) dragged by the shale (5) an upward shale intrusion/injection which then spread parallelly to bedding similar to a salt tongue and (6) tilting overlying limestones. We suggest that shale migration is related to post-“mid”-Eocene E-W convergence between Arabia and India and to faulting or to the second, late Paleogene/early Neogene, faulting interval of the Frontal Range Fault. The shale horizon in the upper part of Unit 1 is a marker bed, which can be correlated across the study area. Full article

We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet. Full article

Around the world, the COVID-19 pandemic has created significant obstacles for education, driving people to discover workarounds to maintain education. Because of the excellent benefit of cheap-cost information distribution brought about by the advent of the Internet, some offline instructional activity started to go online in an effort to stop the spread of the disease. How to guarantee the quality of teaching and promote the steady progress of education has become more and more important. Currently, one of the ways to guarantee the quality of online learning is to use independent online learning behavior data to build learning performance predictors, which can provide real-time monitoring and feedback during the learning process. This method, however, ignores the internal correlation between e-learning behaviors. In contrast, the e-learning behavior classification model (EBC model) can reflect the internal correlation between learning behaviors. Therefore, this study proposes an online learning performance prediction model, SA-FEM, based on adaptive feature fusion and feature selection. The proposed method utilizes the relationship among features and fuses features according to the category that achieved better performance. Through the analysis of experimental results, the feature space mined by the fine-grained differential evolution algorithm and the adaptive fusion of features combined with the differential evolution algorithm can better support online learning performance prediction, and it is also verified that the adaptive feature fusion strategy based on the EBC model proposed in this paper outperforms the benchmark method. Full article

Ubiquitous computing has enabled the proliferation of low-cost solutions for capturing information about the user’s environment or biometric parameters. In this sense, the do-it-yourself (DIY) approach to build new low-cost systems or verify the correspondence of low-cost systems compared to professional devices allows the spread of application possibilities. Following this trend, the authors aim to present a complete DIY and replicable procedure to evaluate the performance of a low-cost video luminance meter consisting of a Raspberry Pi and a camera module. The method initially consists of designing and developing a LED panel and a light cube that serves as reference illuminance sources. The luminance distribution along the two reference light sources is determined using a Konica Minolta luminance meter. With this approach, it is possible to identify an area for each light source with an almost equal luminance value. By applying a frame that covers part of the panel and shows only the area with nearly homogeneous luminance values and applying the two systems in a dark space in front of the low-cost video luminance meter mounted on a professional reference camera photometer LMK mobile air, it is possible to check the discrepancy in luminance values between the low-cost and professional systems when pointing different homogeneous light sources. In doing so, we primarily consider the peripheral shading effect, better known as the vignetting effect. We then differentiate the correction factor S of the Radiance Pcomb function to better match the luminance values of the low-cost system to the professional device. We also introduce an algorithm to differentiate the S factor depending on the light source. In general, the DIY calibration process described in the paper is time-consuming. However, the subsequent applications in various real-life scenarios allow us to verify the satisfactory performance of the low-cost system in terms of luminance mapping and glare evaluation compared to a professional device. Full article

We construct soliton solutions of the complex time fractional Schrodinger model (tFSM), as well as the space–time fractional differential model (stFDM), leading wave spread through electrical transmission lines model (ETLM) in low pass with the help of modified simple equation scheme. The approach provides us with generalized rational exponential function solutions with some free parameters. A few well-known solitary wave resolutions are derived, starting from the generalized rational solutions selecting specific values of the free constants. The precise solutions acquired via the technique signify that the scheme is comparatively easier to execute and attractive in view of the results. No auxiliary equation is needed to solve any nonlinear fractional models by the scheme. Additionally, we observed that the numerical results are very encouraging for researchers conducting further research on stFDMs in mathematics and physics. Full article

Discarded plastic is subjected to weather effects from different ecosystems and becomes microplastic particles. Due to their small size, they have spread across the planet. Their presence in living organisms can have several harmful consequences, such as altering the interaction between prey and predator. Huang et al. successfully modeled this system presenting numerical results of ecological relevance. Here, we have rewritten their equations and solved a set of them analytically, confirming that microplastic particles accumulate faster in predators than in prey and calculating the time values from which it happens. Using these analytical solutions, we have retrieved the Lotka–Volterra predator–prey model with time-varying intraspecific coefficients, allowing us to interpret ecological quantities referring to microplastics dispersion. After validating our equations, we solved analytically particular situations of ecological interest, characterized by extreme effects on predatory performance, and proposed a second-order differential equation as a possible next step to address this model. Our results open space for further refinement in the study of predator–prey models under the effects of microplastic particles, either exploring the second-order equation that we propose or modify the Huang et al. model to reduce the number of parameters, embedding in the time-varying intraspecies coefficients all the adverse effects caused by microplastic particles. Full article

Burkholderia (B.) mallei is a host-adapted equine pathogen that causes glanders, a re-emerging zoonotic disease, which is endemic in Pakistan and other developing countries and seriously impacts the global equine movement. Due to globalization, the geographical restriction of diseases vanishes and the lack of awareness of and experience with eradicated diseases in industrialized countries also promotes the re-introduction of infections in these regions. Owing to the high equine population, the Pakistani province Punjab is a potential hotspot where several glanders outbreaks have been seen over last two decades. For determining the genomic diversity of B. mallei in this and other equine-populated prefectures, the genomes of 19 B. mallei strains isolated between 1999 and 2020 in different locations were sequenced and their genotypes were determined. Particularly, for genetically highly homogenous pathogens like B. mallei genotyping techniques require a high discriminatory power for enabling differentiation on the strain level. Thus, core-genome single nucleotide polymorphism (cgSNP) analysis was applied for distinguishing the highly similar strains. Furthermore, a whole-genome sequence-based core genome multi locus sequence typing (cgMLST) scheme, specific to B. mallei, was developed and additionally applied to the data. It was found that B. mallei genotypes in Pakistan persisted over time and space and genotype clusters preferred connection with a time point rather than the place of isolation, probably due to frequent equine movement, which promotes the spread of glanders. The cgMLST approach proved to work in accord with SNP typing and may help to investigate future glanders outbreaks. Full article

The aim of this study was to evaluate gingival fibroblasts and human osteoblasts’ response to textured Nd:YAG laser microgrooves, with different dimensions, on zirconia implant surfaces. A total of 60 zirconia disks (8 mm in diameter and 2 mm in thickness) were produced and divided between four study groups (N = 15): three laser-textured (widths between 125.07 ± 5.29 μm and 45.36 ± 2.37 μm and depth values from 50.54 ± 2.48 μm to 23.01 ± 3.79 μm) and a control group without laser treatment. Human osteoblasts and gingival fibroblasts were cultured on these surfaces for 14 days. FEG-SEM (Field Emission Gun–Scanning Electron Microscope) images showed cellular adhesion at 24 h, with comparable morphology in all samples for both cell types. A similar cell spreading within the grooves and in the space between them was observed. Cell viability increased over time in all study groups; however, no differences were found between them. Additionally, proliferation, ALP (Alkaline phosphatase) activity, collagen type I, osteopontin and interleukin levels were not significantly different between any of the study groups for any of the cell types. Analysis of variance to compare parameters effect did not reveal statistically significant differences when comparing all groups in the different tests performed. The results obtained revealed similar cell behavior based on cell viability and differentiation on different microtopographic laser grooves, compared to a microtopography only established by sandblasting and acid-etching protocol, the reference surface treatment on zirconia dental implants. Full article

The housing type of apartments, spread widely across South Korea, has penetrated deep into its domestic housing culture, thanks to their advantages in terms of convenience, resulting from the mass production of industrial capitalism, which prioritizes functionality and efficiency. However, capitalist social structures have been undergoing transformation in the 21st century. Under a new paradigm emphasizing creativity over functionality and efficiency, the characteristics of everyday life are also changing. We started with the question of apartment spaces, which featured there are only basic minimum functions with simple combinations of similar rooms, without being able to capture the current changed lifestyle. Therefore, this study focuses on newly emerging lifestyles resulting from this transition of social structures and the characteristics of residential spaces at present, centering on the “function of housing”. Based on these considerations, we aimed to establish the essential function of housing that is prioritized by this era. To this end, we first looked at the changes in the functions of housing before and after modern times. We found that the functions of housing that were complex in traditional society have been differentiated and that houses have changed into a more private space along with the post-modern advent of urban public areas. However, the recent shift in social structure has led to the emergence of new lifestyles, which has also called for new functions of housing. Therefore, in this study, through the analysis of recent lifestyle magazines and architectural magazines, we compared the general public’s and architectural experts’ perspectives on the changed functions of housing and the characteristics of the required residential space. Accordingly, this research analyzed articles containing interviews with residents in lifestyle magazines and articles of architects and critics in architectural magazines. In addition to our previous literatures on changes in “characteristics of residents” and “relationship between individual and family”, this study will ignite discussions on contemporary urban housing from diverse and multi-layered levels as an attempt to achieve sustainable housing where residents’ everyday lives and their residential spaces match. Full article

Abandoned semi-natural grasslands are characterized by lower plant diversity as a consequence of tall grasses spreading. Mowing is a widely used restoration practice, but its effects to maintain the restored diversity over time is poorly investigated in sub-Mediterranean grasslands. Since 2010 in the central Apennines, we fenced a grassland, invaded by Brachypodium rupestre, which was mowed twice a year. Before the experiment started, we recorded species cover in 30 random sampling units (0.5 m × 0.5 m). The sampling was repeated every two years for a total of ten years. We used linear mixed-effect models to investigate the trajectory of functional diversity and community weighted mean for traits related to space occupation, resource exploitation, temporal niche exploitation, and Grime’s CSR strategies. The reduction of the weaker competitor exclusion exerted by B. rupestre affected the functional plant community. In the short term (4–6 years), this fostered space occupation strategies, decreasing convergence of clonal strategies and horizontal space occupation types. In the longer term (8–10 years), mowing filtered ruderal strategies, i.e., species with faster resource acquisition (lower leaf dry matter content, LDMC). LDMC and CSR strategies, initially convergent due to the dominance of B. rupestre, lowered convergence over time due to higher differentiation of strategies. Full article

The introduction of 5G with excessively high speeds and ever-advancing cellular device capabilities has increased the demand for high data rate wireless multimedia communication. Data compression, transmission robustness and error resilience are introduced to meet the increased demands of high data rates of today. An innovative approach is to come up with a unique setup of source bit codes (SBCs) that ensure the convergence and joint source-channel coding (JSCC) correspondingly results in lower bit error ratio (BER). The soft-bit assisted source and channel codes are optimized jointly for optimum convergence. Source bit codes assisted by iterative detection are used with a rate-1 precoder for performance evaluation of the above mentioned scheme of transmitting sata-partitioned (DP) H.264/AVC frames from source through a narrowband correlated Rayleigh fading channel. A novel approach of using sphere packing (SP) modulation aided differential space time spreading (DSTS) in combination with SBC is designed for the video transmission to cope with channel fading. Furthermore, the effects of SBC with different hamming distances $d_{(H,min)}$ but similar coding rates is explored on objective video quality such as peak signal to noise ratio (PSNR) and also the overall bit error ratio (BER). EXtrinsic Information Transfer Charts (EXIT) are used for analysis of the convergence behavior of SBC and its iterative scheme. Specifically, the experiments exhibit that the proposed scheme of error protection of SBC $d_{(H,min)}$ = 6 outperforms the SBCs having same code rate, but with $d_{(H,min)}$ = 3 by 3 dB with PSNR degradation of 1 dB. Furthermore, simulation results show that a gain of 27 dB $E_b/N_0$ is achieved with SBC having code rate 1/3 compared to the benchmark Rate-1 SBC codes. Full article