Search Results (71)

The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order $0.5$ subject to a given initial condition. We establish the existence of a unique solution expressed via a Mittag-Leffler-type function. The delta-asymptotic behavior of the solution is examined, and its convergence properties are rigorously analyzed. Numerical experiments are conducted to illustrate the qualitative features of the solution. Furthermore, a neural network-based approximation is employed to validate and compare with the analytical results, confirming the accuracy, stability, and sensitivity of the proposed method. Full article

Despite the global imperative to enhance carbon sequestration in agricultural landscapes, saline–alkali soils present distinctive soil–microbe constraints that limit our understanding of optimal management strategies. This study addresses critical knowledge gaps regarding the mechanistic relationships between bacterial community structure and carbon stabilization processes in saline–alkali soil. A three-year field experiment was conducted in the Yellow River Delta, China, with two N levels (N1, 270 kg N ha⁻¹; N2, 210 kg N ha⁻¹) and three C treatments (S0, 0 kg C ha⁻¹; S1, 5000 kg C ha⁻¹; S2, 10,000 kg C ha⁻¹). SOC sequestration by straw incorporation increased by 16.34–22.86% and 8.18–11.91%, with no significant difference between the S1 and S2 treatments, because the specific C mineralization rate (SCMR) of the S2 treatment was 13.80–41.61% higher than the S1 treatment. The reduced nitrogen application (N2) enhanced SOC sequestration efficiency by 3.40–12.97% compared with conventional rates, particularly when combined with half straw incorporation. Furthermore, compared with the N1S1 treatment, the N2S1 treatment induced qualitative transformations in carbon chemistry, increasing aromatic carbon compounds (28.79%) while reducing carboxylic fractions (10.06%), resulting in enhanced structural stability of sequestered carbon. Bacterial community analysis revealed distinctive shifts in bacterial composition under different treatments. Half straw incorporation (S1) increased the abundance of oligotrophic strategists (Verrucomicrobiae and Acidimicrobiia) while decreasing copiotrophic bacteria (Bacteroidia), indicating a transition from r-strategy to k-strategy microbial communities that fundamentally altered carbon cycling. Half straw incorporation and reduced N application were beneficial to stabilize SOC composition, reduce mineralization rates, optimize bacterial survival strategy, and thus achieve SOC sequestration. Full article

River nodes play a crucial role in regulating water and sediment transport within river networks. The SiXianJiao (SXJ) node serves as a key exchange point between the West River (WR) and North River (NR) in the Pearl River Delta (PRD), South China. Understanding the differences in flood diversion dynamics between X-shaped and H-shaped configurations under varying geomorphic conditions is essential for flood management. This study employs the Delft3D-Flow model to investigate the flood diversion mechanisms of these composite river nodes. Results revealed distinct hydrodynamic behaviors: the X-shaped node facilitates greater water exchange due to a shared channel segment, whereas the H-shaped node experiences restricted exchange due to flow resistance in the connecting branch. Both configurations exhibit self-regulating flood diversion processes that significantly reduce flood risks. A critical flow fraction of approximately 75.9% [WR/(WR + NR)] is identified, at which water levels (WLs) at both ends of the SXJ node almost equalize. When the WR flow fraction exceeds this threshold, floodwaters are diverted toward the NR. Below it, the diversion direction reverses. Additionally, flood diversion synchronizes asynchronous flood waves, stabilizing the discharge fraction at Makou (Sanshui), which fluctuates around 75.8% (24.2%) for the X-shaped node and 76.6% (23.4%) for the H-shaped node. These findings enhance our understanding of flood diversion dynamics and provide valuable insights for optimizing flood mitigation strategies and hydraulic infrastructure planning in the PRD and comparable river systems worldwide. Full article

Background: The delta neutrophil index (DNI) represents the immature granulocyte fraction and is determined by subtracting the fraction of mature polymorphonuclear leucocytes from the sum of myeloperoxidase-reactive cells. The DNI has been proposed as a useful prognostic marker for sepsis. This study evaluated the clinical utility of DNI as a predictive marker in patients with pneumonia-induced sepsis in the intensive care unit (ICU). Methods: We conducted a retrospective study of pneumonia-induced sepsis in patients who were admitted to the Kangdong Sacred Heart Hospital’s medical ICUs from July 2022 to March 2024. The DNI was measured on three consecutive days after ICU admission. The primary outcome of this study was a 28-day mortality. Results: A total of 227 patients with pneumonia-induced sepsis were included in this study. A 28-day mortality occurred 20.3% of the time in our study. In a univariate analysis, age (p = 0.05), lymphocyte (p = 0.02), DNI 1 (p = 0.01), DNI 2 (p = 0.00), DNI 3 (p = 0.00), and lactic acid (p = 0.00) were significantly associated with 28-day mortality. In a multivariable analysis, lactate (adj. OR: 0.86, 95% CI: 0.78–0.95, p = 0.002), and DNI 3 (adj. OR: 0.94, 95% CI: 0.89–0.99, p = 0.048) were significantly associated with 28-day mortality. In our study, the most appropriate cut-off values were DNI 1 (7.15), DNI 2 (8.9), and DNI 3 (2.6). Patients with higher DNI 3 (≥2.6) showed higher 28-day mortality than patients with lower DNI 3 values of <2.6 (67.4% vs. 32.6%; p < 0.001). However, those aged ≥70 did not show statistically significantly different DNI 1 values between the survivor and non- survivor groups. Conclusions: The DNI at 72 h after ICU admission is a promising predictive prognostic marker of 28-day mortality in patients with pneumonia-induced sepsis in the ICU. However, the interpretation of the DNI in sepsis patients aged 70 and older on the first day of hospitalization should be approached with caution. Full article

Coastal saltmarsh wetlands are vital “blue carbon” ecosystems. Fractional vegetation cover (FVC) is a key indicator revealing the spatial distribution and growth status of vegetation. Remote sensing has proven a vital tool for FVC estimation at regional or landscape scales. Establishing a species-level FVC estimation model usually requires sufficient field measurements as training/validation samples. However, field-based sample collection in wetlands is challenging because of the harsh environment. In this study, we proposed a Fractional Vegetation Cover Wasserstein Generative Adversarial Network (FVC-WGAN) model for FVC sample expansion. We chose the Yellow River Delta as the study area and utilized the time series Sentinel-2 imagery and random forest regression model for species-level FVC estimation with the assistance of FVC-WGAN-generated samples. To assess the efficacy of FVC-WGAN, we designed 13 experimental schemes using different combinations of real and generated samples. Our results show that the FVC-WGAN-generated samples had similar feature values to the real samples. Supplementing 500 real samples with generated samples can achieve good accuracy with an average RMSE < 0.1. As the number of real samples increased, the accuracies of FVC estimation improved. When the number of the generated samples was balanced with the real samples, the accuracy improved in terms of both R², RMSE and the spatial consistency. Full article

Special functions have been widely used in fractional calculus, particularly for addressing the symmetric behavior of the function. This paper provides improved delta Mittag–Leffler and exponential functions to establish new types of fractional difference operators in the setting of Riemann–Liouville and Liouville–Caputo. We give some properties of these discrete functions and use them as the kernel of the new fractional operators. In detail, we propose the construction of the new fractional sums and differences. We also find the Laplace transform of them. Finally, the relationship between the Riemann–Liouville and Liouville–Caputo operators are examined to verify the feasibility and effectiveness of the new fractional operators. Full article

Alzheimer’s disease (AD) is the most widespread neurodegenerative disorder. Recently, it was found that mucus extract from Cornu aspersum has beneficial effects on memory and cognitive processes in a rat scopolamine model of AD. The present study elucidated the mechanisms of action of standardized mucus snail extract (SE) enriched with a fraction above 20 kDa on Alzheimer-type dementia in rats. Using proteomic analysis on two-dimensional polyacrylamide gel electrophoresis (2D–PAGE) on rat cortex extracts, we compared protein expression in both groups: the first group was treated intraperitoneally with scopolamine (Sco, 2 mg/kg, 11 days) and the second (Sco + SE) group was treated intraperitoneally with Sco (Sco, 2 mg/kg) and protected by SE (0.5 mL/100 g bw) applied daily orally for 11 days. Brain cortex was separated and the expressions of various proteins related to memory and cognitive functions were identified. We found that the expression of Ubiquitin carboxyl-terminal hydrolase isozyme L1, Calbindin, Vacuolar ATP synthase catalytic subunit A, Tropomyosin beta chain, 14-3-3 zeta/delta, Kinesin-1 heavy chain, and Stathmin-4 significantly differs in SE-protected rats as compared to dement animals treated only by Sco, and these brain proteins might be potential therapeutic targets for Alzheimer’s-type dementia treatment. Full article

(1) Background: Considering the increasing workload of pathologists, computer-assisted methods have the potential to come to their aid. Considering the prognostic role of myocardial fibrosis, its precise quantification is essential. Currently, the evaluation is performed semi-quantitatively by the pathologist, a method exposed to the issues of subjectivity. The present research proposes validating a semi-automatic algorithm that aims to quantify myocardial fibrosis on microscopic images. (2) Methods: Forty digital images were selected from the slide collection of The Iowa Virtual Slidebox, from which the collagen volume fraction (CVF) was calculated using two semi-automatic methods: CIELAB-MATLAB^® and CIELAB-Python. These involve the use of color difference analysis, using Delta E, in a rectangular region for CIELAB-Python and a region with a random geometric shape, determined by the user’s cursor movement, for CIELAB-MATLAB^®. The comparison was made between the stereological evaluation and ImageJ. (3) Results: A total of 36 images were included in the study (n = 36), demonstrating a high, statistically significant correlation between stereology and ImageJ on the one hand, and the proposed methods on the other (p < 0.001). The mean CVF determined by the two methods shows a mean bias of 1.5% compared with stereology and 0.9% compared with ImageJ. Conclusions: The combined algorithm has a superior performance compared to the proposed methods, considered individually. Despite the relatively small mean bias, the limits of agreement are quite wide, reflecting the variability of the images included in the study. Full article

The present paper is dedicated to the examination of maximum and minimum results based on Green’s functions via delta fractional differences for a class of fractional boundary problems. For such a purpose, we built the corresponding Green’s functions based on the falling factorial functions. In addition, using the constructed Green’s function, the positivity of the function and its corresponding delta function are presented. We also verified the occurrence of two distinct functions with the same Green’s function. The maximality and minimality of the Green’s function show a good qualitative agreement. Finally, we considered some special examples to explain the obtained results. Full article

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor monomial falling function and presents some properties of this function in a delta fractional model with Green’s function kernel. In the deterministic case, Green’s function will be non-negative, and this shows that the function has an upper bound for its maximum point. More precisely, in this paper, based on the properties of the Taylor monomial falling function, we investigate Lyapunov-type inequalities for a delta fractional boundary value problem of Riemann–Liouville type. Full article

Combining rice cultivation and aquaculture into an integrated cropping system is a management approach that enhances the sustainability of rice fields. However, how soil characteristics influence soil microbial community characteristics following implementation of such an integrated system, particularly in the waterlogged paddies of the Pearl River Delta, is poorly understood. An integrated cropping system (rice–fish–duck integrated cropping system, RFD) and a rice–pepper rotation system (RPS) were compared using a conventional rice cropping system (CRS) as a reference. We used phospholipid-derived fatty acid (PLFA) analysis to assess soil microbial community structure and function and measured soil nutrient content and organic carbon fractions. Our results indicated that the soil nutrient content, organic carbon fractions, and C-hydrolyzing activities differed among the cropping systems. The RFD resulted in higher microbial PLFA concentrations and a lower ratio of Gram-positive to Gram-negative bacteria than CRS. Additionally, the integrated system reduced microbial nutrient stress by increasing soil pH. Further analysis revealed that active soil organic carbon significantly affected the soil microbial community. Thus, the RFD integrated cropping systems that alter the combined actions of pH and active organic carbon fractions can be used to improve soil microbial communities. Full article

The electronic information manufacturing industry is characterized by a very significant intra-product specialization and can display the characteristics of a regional division of labor. Looking at the existing literature, most studies have mainly examined the position of different countries in the spatial division of labor from the perspective of global value chains, with fewer empirical analyses at the city level or regional scale. Furthermore, deepening the regional division of labor in value chains is an effective way to promote regional industrial synergy and high-quality economic development. Based on the number of listed enterprises and the total number of parent–subsidiary investment connections in the electronic information manufacturing industry, this study reveals the characteristics of the deeper regional division of labor among cities by analyzing the Value Chain Division Index (VCDI). Subsequently, we used the fractional response regression model to analyze influencing factors. We found that, firstly, the core cities are dominated by the production of high-value parts, while the peripheral cities are mainly dominated by the production of middle- and low-value parts. Specifically, northern Anhui, northern Jiangsu, and southwestern Zhejiang are obviously in a disadvantaged position regarding the regional division of labor in the value chain. In the production of middle- and high-value parts, there are close investment connections between the core cities, and only a few peripheral cities maintain a certain degree of connection with the core cities. Therefore, there is a need to further strengthen industrial investment connections between the core and peripheral cities. Secondly, the regional division of labor in the value chain in the Yangtze River Delta region shows the following characteristic: a “one super, many strong” pattern. That is to say, the VCDI value of Shanghai is the highest, and the VCDI value of Suzhou, Ningbo, and Wuxi is also relatively high, while the VCDI value of peripheral cities is relatively low. Furthermore, we found that there is a relatively obvious regional division of labor among cities, but the core cities have strong homogeneity in the high-value areas. Therefore, it is necessary to further strengthen the dislocation of competition between core cities. Thirdly, the model results show that rising land prices and construction in the development zones at the provincial and national levels both have significant contributing effects on the enhancement of the regional division of labor in the value chain, while the innovation inputs, innovation outputs, and their interaction terms show a negative effect. There is a need to further enhance the efficiency of innovation transformation and improve the quality of innovation transformation in order to promote upgrading in the value chain. Full article

As the most economically developed region in China, the Yangtze River Delta (YRD) region contributed to ~17% of the total anthropogenic CO₂ emissions from China. However, the studies of atmospheric CO₂ and CH₄ in this area are relatively sparse and unsystematic. Here, we analyze the changing characters of those gases in different development periods of China, based on the 11-year atmospheric CO₂ and CH₄ records (from 2010 to 2020) at one of the four Chinese sites participating in the World Meteorological Organization/Global Atmospheric Watch (WMO/GAW) program (Lin’an regional background station), located in the center of YRD region, China. The annual average atmospheric CO₂ and CH₄ mole fractions at LAN have been increasing continuously, with growth rates of 2.57 ± 0.14 ppm yr⁻¹ and 10.3 ± 1.3 ppb yr⁻¹, respectively. Due to the complex influence of regional sources and sinks, the characteristics of atmospheric CO₂ and CH₄ varied in different periods: (i) The diurnal and seasonal variations of both CO₂ and CH₄ in different periods were overall similar, but the amplitudes were different. (ii) The elevated mole fractions in all wind sectors tended to be uniform. (iii) The potential source regions of both gases expanded over time. (iv) The growth rate in recent years (2016–2020) changed significantly less than that in the earlier period (2010–2015). Our results indicated that the CO₂ and CH₄ mole fractions were mainly correlated to the regional economic development, despite the influence of special events such as the G20 Summit and COVID-19 lockdown. Full article

White noise is fundamentally linked to many processes; it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise. Full article

A review of the literature demonstrates that the Fox–Wright function is not only a mathematical puzzle, but its role is naturally to represent basic physical phenomena. Motivated by this fact, we studied a new representation of this function in terms of complex delta functions. This representation was useful to compute its Laplace transform with respect to the third parameter γ for which it also generalizes the one and two-parameter Mittag-Leffler functions. New identities involving the Fox–Wright function were discussed and used to simplify the results. Different fractional transforms were evaluated and the solution of a fractional kinetic equation was obtained by using its new representation. Several new properties of this function were discussed as a distribution. Full article