Search Results (77)

In this paper, the boundary value problem of wave diffraction on a semi-infinite circular pin is solved using the Wiener–Hopf method with compensation of eigenmodes. The solution to the problem is presented as an infinite series defined by a recurrence formula. The reliability and accuracy of the solution are verified numerically in terms of fulfillment of the law of energy conservation. Sufficiently reliable results are obtained at the first iteration. The method used for solving this problem can be applied to solving diffraction problems on axisymmetric volumetric structures. Full article

The conditional Feynman integral provides solutions to integral equations equivalent to heat and Schrödinger equations. The Cameron–Martin translation theorem illustrates how the Wiener measure changes under translation via Cameron–Martin space elements in abstract Wiener space. Translation theorems for analytic Feynman integrals have been established in many research articles. This study aims to present a translation theorem for the conditional function space integral of functionals on the generalized Wiener space $C_{a,b}[0,T]$ induced via a generalized Brownian motion process determined using continuous functions $a\left(t\right)$ and $b\left(t\right)$. As an application, we establish a translation theorem for the conditional generalized analytic Feynman integral of functionals on $C_{a,b}[0,T]$. We then provide explicit examples of functionals on $C_{a,b}[0,T]$ to which the conditional translation theorem on $C_{a,b}[0,T]$ can be applied. Our formulas and results are more complicated than the corresponding formulas and results in the previous research on the Wiener space $C_0[0,T]$ because the generalized Brownian motion process used in this study is neither stationary in time nor centered. In this study, the stochastic process used is subject to a drift function. Full article

Accurate assessments are vital for the effective conservation of desert steppe ecosystems, which are essential for maintaining biodiversity and ecological balance. Although geostatistical methods are commonly used for spatial modeling, they have limitations in terms of feature extraction and capturing non-linear relationships. This study therefore proposes a novel remote sensing framework that integrates geostatistical methods and machine learning to predict the Shannon–Wiener index in desert steppe. Five models, Kriging interpolation, Random Forest, Support Vector Machine, 3D Convolutional Neural Network and Graph Attention Network, were employed for parameter inversion. The Helmert variance component estimation method was introduced to integrate the model outputs by iteratively evaluating residuals and assigning relative weights, enabling both optimal prediction and model contribution quantification. The ensemble model yielded a high prediction accuracy with an R² of 0.7609. This integration strategy improves the accuracy of index prediction, and enhances the interpretability of the model regarding weight contributions in space. The proposed framework provides a reliable, scalable solution for biodiversity monitoring and supports scientific decision-making for grassland conservation and ecological restoration. Full article

In this paper, we introduce an integral transform with a kernel defined on the Wiener space. We first establish the existence of the integral transform and present several illustrative examples. As the main result, we derive an approximation theorem for the integral transform. Our approach demonstrates that the integral transform can be effectively computed even in cases where direct calculation is difficult or infeasible. Full article

In this paper, for a mixed elliptic-hyperbolic type equation with various degeneration orders and singular coefficients, theorems of uniqueness and existence of the solution to the problem with a missing Tricomi condition on boundary characteristic and with an analog of Frankl condition on different parts of the cut boundary along the degeneration segment in the mixed domain are proved. On the degeneration line segment, a general conjugation condition is set, and on the boundary of the elliptic domain and degeneration segment, the Bitsadze–Samarskii condition is posed. The considered problem, based on integral representations of the solution to the Dirichlet problem (in elliptic part of the domain) and a modified Cauchy problem (in hyperbolic part of the domain), is reduced to solving a non-standard singular Tricomi integral equation with a non-Fredholm integral operator (featuring an isolated first-order singularity in the kernel) in non-characteristic part of the equation. Non-standard approaches are applied here in constructing the solution algorithm. Through successive applications of the theory of singular integral equations and then the Wiener–Hopf equation theory, the non-standard singular Tricomi integral equation is reduced to a Fredholm integral equation of the second kind, the unique solvability of which follows from the uniqueness theorem for the problem. Full article

The electrically evoked compound action potential (ECAP) is a crucial physiological signal used by clinicians to evaluate auditory nerve functionality. Clean ECAP recordings help to accurately estimate auditory neural activity patterns and ECAP magnitudes, particularly through the panoramic ECAP (PECAP) framework. However, noise—especially in low-signal-to-noise ratio (SNR) conditions—can lead to significant errors in parameter estimation. This study proposes a two-stage preprocessing denoising (TSPD) algorithm to address this issue and enhance ECAP signals. First, an ECAP matrix is constructed using the forward-masking technique, representing the signal as a two-dimensional image. This matrix undergoes spatial noise reduction via an improved spatial median (I-Median) filter. In the second stage, the denoised matrix is vectorized and further processed using a log-spectral amplitude (LSA) Wiener filter for spectral domain denoising. The enhanced vector is then reconstructed into the ECAP matrix for parameter estimation using PECAP. The above integrated spatial-spectral denoising framework is denoted as PECAP-TSPD in this work. Evaluations are conducted using a simulation-based ECAP model mixed with simulated and experimental noise, designed to emulate the spatial characteristics of real ECAPs. Three objective quality measures—namely, normalized root mean square error (RMSE), two-dimensional correlation coefficient (TDCC), and structural similarity index (SSIM)—are used. Simulated and experimental results show that the proposed PECAP-TSPD method has the lowest average RMSE of PECAP magnitudes (1.952%) and auditory neural patterns (1.407%), highest average TDCC (0.9988), and average SSIM (0.9931) compared to PECAP (6.446%, 5.703%, 0.9859, 0.8997), PECAP with convolutional neural network (CNN)-based denoising mask (PECAP-CNN) (9.700%, 7.111%, 0.9766, 0.8832), and PECAP with improved median filtering (PECAP-I-Median) (4.515%, 3.321%, 0.9949, 0.9470) under impulse noise conditions. Full article

Constructed wetlands (CWs) are widely implemented as nature-based solutions for delivering essential ecosystem services such as water purification, carbon sequestration, and habitat provision. However, biodiversity monitoring within CWs remains limited and unevenly integrated into performance evaluations. This scoping review analyzed 76 peer-reviewed studies to assess current methods for biodiversity monitoring, explore linkages to ecosystem functions, and examine the diversity indices most frequently applied. Results revealed a predominant focus on microbial communities, primarily assessed through high-throughput sequencing and general ecological indices such as the Shannon–Wiener Diversity Index and Chao1 Richness Estimator, with limited taxonomic depth or functional specificity. Plant and animal biodiversity were addressed less frequently and were rarely linked to treatment outcomes or ecosystem services beyond regulation. Vertical subsurface flow systems were the most studied configuration, particularly in lab-scale studies, while free water surface systems exhibited greater microbial phylum richness. These findings highlight a critical need for CW-specific biodiversity monitoring frameworks that integrate microbial, plant, and faunal assessments using functionally relevant phylogenetic indices such as Rao’s Quadratic Entropy and Faith’s Phylogenetic Diversity. Emphasis on standardization, trait-based analyses, and mechanistic approaches is essential for enhancing ecological interpretation and ensuring biodiversity is recognized as a central component of CW design, performance, and resilience. Full article

A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and the Hölder law of the local times for ABSs are derived under certain conditions, and some results of the intersection local times for two independent Brownian sheets are also given as special cases. Furthermore, the intersection local times for two independent Brownian sheets in a Hida distribution is proved through white noise analysis, and the Wiener chaos expansion of the intersection local times is expressed in terms of S-transform. Additionally, the large deviations for the intersection local time of two independent Brownian sheets are established. The multi-parameter Gaussian random fields have become a core tool for complex system analysis due to their flexible multidimensional modeling capabilities. With the improvement of computational efficiency and interdisciplinary integration, the ABS constructed in this article will unleash greater potential in fields such as metaverse simulation, financial mathematics, climate science, precision medicine, quantum physics, and string theory. Full article

The development of carbon sequestration projects in plantation forests has the potential to offer win–win outcomes for the environment and economy. The Climate, Community, and Biodiversity (CCB) Standards ensure that a particular forest project will deliver tangible climate, community, and biodiversity benefits. According to the CCB Standards, it is necessary to assess community diversity in plantation forests. Our study provides indicators of community diversity based on Forest Integrity Assessment (FIA) according to the CCB Standards for carbon sequestration projects in Tianshui City, Gansu Province, China, which is located in the western Qinba Mountains. Herein, we estimated plantation forest conditions based on a forest condition assessment. Linear regression models were used to explore the relationships between FIA scores and community diversity (such as species richness, Shannon–Wiener index, inverse Simpson’s index, and Pielou’s evenness index quantified by species abundance) in plantation forests managed under carbon sequestration projects. The high community diversity reaches the CCB Standards. FIA scores were closely associated with Pielou’s evenness index of plant communities in plantation forests managed under carbon sequestration projects (R² = 0.104; mean square error = 0.014; standard error = 0.104; p = 0.012). A complex topography had positive effects on species richness, while a rich standing condition had negative effects on the Shannon–Wiener index. Forest conditions have been used as indicators of community diversity in plantation forests managed under carbon sequestration projects. The occurrence of climber and animal species should be used as indicators for enhancing community diversity to meet the CCB Standards. Furthermore, plant species richness benefits from a complex topography. However, our study had the limitation that the FIA could not cover the full range of environmental conditions. Our study provides a practical reference for applying the CCB Standards to plantation forests managed under carbon sequestration projects. Full article

This study presents the first scientific evaluation of food web integrity in the Black Sea under the Marine Strategy Framework Directive (MSFD) Descriptor 4 (Food Webs), utilizing zooplankton indicators to assess the environmental status during the warm season (May to October) from 2018 to 2023. The research aims to analyze trophic interactions, biodiversity patterns, and ecological stability by examining three key indicators: the Shannon–Wiener diversity index, Copepoda biomass, and Mnemiopsis leidyi biomass. The findings reveal that the Shannon–Wiener diversity index failed to achieve Good Environmental Status (GES) in any of the four Marine Reporting Units (MRUs), suggesting insufficient community diversity and potential ecological imbalances. Copepoda biomass met GES criteria only in marine and offshore waters, indicating spatial variability in copepod population stability across the Black Sea. Meanwhile, M. leidyi biomass remained within GES thresholds in all MRUs, suggesting that its population levels do not currently threaten the food web, despite its known invasive impact. This study provides critical baseline data on food web structure and dynamics in the Black Sea, offering a scientifically grounded framework for future ecological monitoring and management strategies. The results emphasize the need for targeted conservation efforts and adaptive management approaches to enhance the ecological health of the Black Sea in alignment with MSFD objectives. Full article

The global degradation and loss of natural wetlands are increasingly threatening wetland-dependent taxa, particularly waterbirds, which are highly vulnerable to environmental changes. In response to these threats, an increasing number of waterbirds are relocating to surrounding satellite wetlands in search of compensatory habitats. However, how waterbirds utilize these satellite wetlands and respond to varying environmental variables remain poorly understood. In the winter of 2022–2023 and summer of 2023, we conducted surveys on waterbird assemblages in 49 satellite wetlands of different types (reservoirs, aquaculture ponds, paddy fields and natural ponds) surrounding Shengjin Lake, a Ramsar site, and analyzed the relationship between community metrics and environmental factors. Large numbers of waterbirds were recorded during both summer and winter, including several threatened and nationally protected species. Species richness and number of individuals varied significantly across wetland types, with aquaculture ponds supporting the highest number of species and individuals. These two metrics showed positive correlations with wetland areas and landscape connectivity in both seasons. Species richness was also positively correlated with habitat diversity in summer. The number of individuals was positively correlated with habitat diversity and negatively with distance to human settlements, but the pattern was in contrast to that in winter. The Shannon–Wiener diversity index displayed a similar pattern among wetland types in winter but did not in summer. We detected no effects of environmental factors on the diversity index. Species composition differed markedly between wetland types in both seasons, especially between reservoirs and aquaculture ponds. To safeguard waterbird communities in the middle and lower reaches of the Yangtze River, we recommend integrating surrounding satellite wetlands into the regional wetland network and reducing human disturbances, particularly during the winter months. Full article

Macrophytes taxa composition determines microinvertebrates utilized as environmental indicators in freshwater ecosystems. This study was conducted in Shengjin Lake. In this lake, local communities have been practicing using sine fishing nets for fishing and this has a disrupting effect on macrophyte vegetation, even though it was the major for the disappearance of submerged vegetation before it was banned. As a result of this sine fishing net ban by the local authorities, the vegetation that had disappeared began to recover. Thus, this study investigated the role of architecturally differentiated macrophytes restoration effect on zooplankton communities’ diversity, abundance, and species composition; open water was used as a control. For this, the data were collected from different habitats via site 1 (open water) site 2, (free-floating), site 3 (emergent and submerged), site 4 (submerged), and site 5 (emergent) macrophytes. In the present study, the results demonstrated that the relative mean density of Rotifer was measured high which ranged from (219 ± 141–678 ± 401 ind L⁻¹), mainly dominated by Keratella cochlearis and Lecane cornuta species. Following Rotifera, Cladocera population density was reported high and ranged within (36 ± 6.2–262.5 ± 49.4 ind L⁻¹). The Cladocera group was dominated by Daphnia spp., Moina micura, Ceriodaphnia reticulata, and Chydorus latus species. Compared to Rotifer and Cladocera, Copepod community were recoded least with relative mean density ranged within (11.52 ± 2.22–85.5 ± 27 ind L⁻¹) and dominated by Microcyclops javanus, Thermodiaptomus galebi, and Sinocalanus doerrii species. From environmental variables and the zooplankton density relationship analyzed, the redundancy analysis (RDA) results indicated that Water Temperature, Chlorophyll a, Dissolved Oxygen, Total Phosphorus, and Ammonium Nitrogen were found the most influential variables on zooplankton communities. Stepwise regression correlation showed that Copepod and Cladocera were found more dependent on environmental factors. For instance, Nitrate Nitrogen was negatively correlated with Cladocera, Copepod, and total zooplankton biomass but positively with Cladocera diversity. Water Temperature showed a positive relationship with Rotifer diversity; however, both Chlorophyll a and Electrical Conductivity were correlated positively with Cladocera biomass. Species diversity by the Shannon–Wiener index (H) illustrated a dynamic trend among the monitored sites which ranged between (0.65–4.25). From the three groups of zooplankton communities in contrast to Cladocera and Copepod, Rotifer species obtained more diversity across the studied sites. The Cladocera diversity (H′) index indicated a similar tendency in all sites. However, more Copepod diversity (H′) was observed in site 4. In conclusion, this study results can provide valuable insights into the health and dynamics of the aquatic ecosystem to understand factors deriving ecological imbalance and develop an integrated approach for effective strategies for management and conservation. Full article

Predictive maintenance, recognized as an effective health management strategy for extending the lifetime of devices, has emerged as a hot research topic in recent years. A general method is to execute two separate steps: data-driven remaining useful life (RUL) prediction and a maintenance strategy. However, among the numerous studies that conducted maintenance and replacement activities based on the results of RUL prediction, little attention has been paid to the impact of preventive maintenance on sensor-based monitoring data, which further affects the RUL for repairable degrading devices. In this paper, an adaptive RUL prediction method is proposed for repairable degrading devices in order to improve the accuracy of prediction results and achieve adaptability to future degradation processes. Firstly, a phased degradation model based on an adaptive Wiener process is established, taking into account the impact of imperfect maintenance. Meanwhile, integrating the impact of maintenance activities on the degradation rate and state, the probability distribution of RUL can be derived based on the concept of first hitting time (FHT). Secondly, a method is proposed for model parameter identification and updating that incorporates the individual variation among devices, integrating maximum likelihood estimation and Bayesian inference. Finally, the effectiveness of the RUL prediction method is ultimately validated through numerical simulation and its application to repairable gyroscope degradation data. Full article

Urban areas serve as critical habitats for numerous plant species. Existing studies suggest that, due to human-mediated introductions, urban environments often harbor a greater variety of plant species compared to suburban areas, potentially becoming focal points for biodiversity. Consequently, investigating the driving forces and complex mechanisms by which urban environmental factors influence plant species distribution is essential for establishing the theoretical foundation for urban biodiversity conservation and future urban planning and management. Solar radiation, among these factors, is a critical determinant of plant growth, development, and reproduction. However, there is a notable lack of research on how this factor affects the distribution of urban plant species and influences species’ richness and composition within plant communities. We present for the first time an analysis of how solar radiation drives the spatial distribution of plant species within the built-up areas of Nanchang City, China. Based on three years of monitoring and survey data from experimental sites, this study employs three evaluation models—Species Richness Index (R), Simpson’s Diversity Index (D), and Shannon–Wiener Index (H)—to analyze and validate the survey results. Additionally, MATLAB and ArcGIS Pro software are utilized for the numerical simulation and visualization of spatial data. Our study shows that areas with low solar radiation exhibit higher plant species richness, while plots with high plant diversity are primarily concentrated in regions with strong solar radiation. Moreover, the Diversity Index D proves to be more sensitive than the Shannon–Wiener Index (H) in evaluating the spatial distribution of plant species, making it a more suitable metric for studying urban plant diversity in our study area. Among the 18 plant species analyzed, Mulberry and Dandelion are predominantly dispersed by birds and wind, showing no significant correlation with solar radiation. This finding indicates that the spatial distribution of urban plant species is influenced by multiple interacting factors beyond solar radiation, highlighting the critical need for long-term observation, monitoring, and analysis. This study also suggests that shaded urban areas may serve as hubs of high species richness, while regions with relatively strong solar radiation can sustain greater plant diversity. These findings underscore the practical significance of this research, offering essential insights to guide urban planning and management strategies. Additionally, this study offers valuable insights for the future predictions of plant species distribution and potential areas of high plant diversity in various urban settings by integrating computational models, building data, Digital Elevation Models (DEMs), and land cover data. Full article

The Fokas method (also known as the unified transform method) is used to investigate acoustic scattering by thin, infinite grating by extending the methodology to apply to spatially periodic domains. Infinite grating is used to model a perforated screen, a material of interest in aeroacoustics and noise reduction. Once the method is established, its numerical results are verified against the Wiener–Hopf (WH) technique, which has solved the problem only for a special case. A key benefit of the novel approach is that the scatterer, modelled as an infinitely repeating unit cell consisting of a thin, rigid plate, can take any length. This is in contrast to the WH method, where the plate length is restricted to half the width of the unit cell (for this method, no such restriction exists). The numerical method is an over-sampled collocation method of the integral equation resulting from applying the Fokas method: the global relation. The only increase in complexity in adapting the Fokas method to more complicated cell geometries is a higher number of terms in the global relation. The proportion of energy transmitted and reflected by the grating structure is assessed for varying incident wave angles, frequencies, and plate lengths. Full article