Search Results (316)

This paper proposes a Hybrid Recursive Trigonometric (HRT) technique for FPGA-based direct digital frequency synthesizers. The HRT technique integrates a recursive cosine generator with periodic reinitialization via a second-order Taylor polynomial to reduce cumulative errors without requiring ROMs or iterative CORDIC units. A resource-efficient combinational architecture is implemented and validated on the Lattice iCE40HX1K FPGA. The effectiveness of the proposed HRT technique is evaluated through simulation and FPGA-based experiments, with respect to spectral accuracy and resource efficiency, particularly for fixed-point cosine waveform synthesis in low-resource digital systems. Simulation results show that the system has a spurious-free dynamic range (SFDR) of −86.09 dBc and signal-to-noise ratio of 52.74 dB using 16-bit fixed-point arithmetic. Experimental measurements confirm the feasibility, achieving −58.86 dBc SFDR. Full article

Precipitation, as a key input in the water cycle, directly influences the formation and change process of runoff. Meanwhile, the return runoff intuitively reflects the available quantity of water resources in a river basin. An in-depth analysis of the evolution laws and response relationships between precipitation and return runoff over a long time scale serves as an important support for exploring the evolution of hydrometeorological conditions and provides an accurate basis for the scientific planning and management of water resources. Taking Lanzhou Station on the upper Yellow River as a typical case, this study proposes the VSSL (LSTM Fusion Method Optimized by SSA with VMD Decomposition) deep learning precipitation element series extension method and the SSVR (SVR Fusion Method Optimized by SSA) machine learning runoff element series extension method. These methods achieve a reasonable extension of the missing data and construct 100-year precipitation and return runoff series from 1921 to 2020. The research results showed that the performance of machine learning and deep learning methods in the precipitation and return runoff test sets is better than that of traditional statistical methods, and the fitting effect of return runoff is better than that of precipitation. The 100-year precipitation and return runoff series of Lanzhou Station from 1921 to 2020 show a non-significant upward trend at a rate of 0.26 mm/a and 0.42 × 10⁸ m³/a, respectively. There is no significant mutation point in precipitation, while the mutation point of return runoff occurred in 1991. The 100-year precipitation series of Lanzhou Station has four time-scale alternations of dry and wet periods, with main periods of 60 years, 20 years, 12 years, and 6 years, respectively. The 100-year return runoff series has three time-scale alternations of dry and wet periods, with main periods of 60 years, 34 years, and 26 years, respectively. During the period from 1940 to 2000, an approximately 50-year cycle, precipitation and runoff not only have strong common-change energy and significant interaction, but also have a fixed phase difference. Precipitation changes precede runoff, and runoff responds after a fixed time interval. Full article

Clarifying the coordination and impediments of social, economic, and spatial connection in rural areas is essential for advancing rural revitalization, urban-rural integration, and regional coordinated development. Utilizing the 24 counties and districts in western Hunan as case studies, we developed an evaluation index system for sustainable rural development across three dimensions: social, economic, and spatial. We employed the coupling model, coordination model, and obstacle factor model to investigate the comprehensive development level, coupling and coordination status, and obstacle factors of the villages in the study area at three temporal points: 2002, 2012, and 2022. The findings indicate the following: (1) The degree of rural development in western Hunan has escalated swiftly throughout the study period, transitioning from relative homogeneity to a heterogeneous developmental landscape, accompanied by issues such as inadequate development and regional polarization. (2) The overall rural social, economic, and spatial indices are low, and the degree of coupling has increased variably across different study periods; the average coordination degree has gradually improved over time, yet the level of coordination remains low, and spatial development is unbalanced. (3) The criterion-level impediments hindering the sustainable development of rural society, economy, and space are, in descending order, social factors, spatial factors, and economic factors. The urbanization rate, total fixed investment rate, and arable land change rate are the primary impediments in most counties and cities. The study’s findings will inform the planning of rural development in ethnic regions, promote sustainable social and spatial advancement in the countryside, and serve as a reference for rural revitalization efforts. Full article

Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, Boyd–Wong contraction, Pant contraction and relational contraction. We also establish the corresponding uniqueness theorem for the proposed contraction under some additional hypotheses. Several examples are furnished to illustrate the legitimacy of our newly proved results. In particular, we deduce a fixed-point theorem for almost Boyd–Wong contractions in the setting of abstract metric space. Our results generalize, enhance, expand, consolidate and develop a number of known results existing in the literature. The practical relevance of the theoretical findings is demonstrated by applying to study the existence and uniqueness of solution of a specific periodic boundary value problem. Full article

This paper investigates the dynamic behavior of a second-order nonlinear rational difference equation modeling a population system with nonlinear interactions between current and previous population states. We derive analytical conditions for the stability of fixed points, explore codim-1 bifurcations, and compute the associated topological normal forms. The analysis also establishes the existence of period-2 solutions and reveals the potential for chaotic dynamics within specific parameter ranges. To validate the theoretical findings, we conduct numerical simulations and bifurcation analysis using the MATLAB package MatContM (version 5p4). Chaotic behavior is further confirmed through the computation of the largest Lyapunov exponent. The results offer new insights into the complex dynamics of delayed population models with nonlinear feedback, extending classical models and suggesting potential applications in stochastic systems and epidemiological modeling. Full article

Background: This study aimed to evaluate the long-term stability of maxillary molar distalization in the treatment of Class II malocclusion. Methods: This study included 40 patients (31 males and 9 females) who received fixed orthodontic treatment after maxillary molar distalization. Orthodontic models and lateral cephalograms were evaluated at three time points: pre-treatment (T1), after orthodontic treatment (T2), and long-term follow-up (T3). The mean ages of the patients’ ages at T1, T2, and T3 were 13.02, 15.97, and 22.05 years, respectively. The statistical analysis included paired t-tests and Wilcoxon signed-rank tests. The statistical significance was set at p < 0.05. Results: The statistical analysis indicated no gender-related differences. A significant distalization of maxillary first molars was observed at T2 compared to T1 (p < 0.001). Despite a minor relapse, a statistically significant distalization was observed in T3-T1 (p < 0.001). The vertical skeletal angles, which increased during the treatment period, decreased at T3-T2. The molar relationship was almost maintained after long-term follow-up (p < 0.001). Conclusions: The maxillary molar distalization achieved in the Class II treatment was maintained in the long term. The vertical skeletal measurements decreased to their initial values in the long term. The Class I molar relationship did not change during the completion of the growth. This study hypothesized that the maxillary molar distalization achieved during fixed orthodontic treatment can be maintained in the long term without significant relapse. Full article

To address the engineering issues of difficult quality control, complex construction processes, and long construction periods in cast-in-place protective walls for manually excavated piles, a prefabricated protective wall structure is proposed. This study aims to investigate its mechanical properties and key influencing parameters through experiments. Six groups of prefabricated wall segment specimens with different wall thicknesses (50 mm, 65 mm) and concrete strengths (C50 concrete, reactive powder concrete RPC) were designed, and two-point bending tests were conducted to systematically analyze their failure characteristics, crack development patterns, and strain distribution laws. The test results show that the peak vertical bending displacements at mid-span of the specimens are 11–18 mm (1.83–2.71% of the radius). The 65-mm-thick specimens exhibit 3–10% higher flexural strength than the 50-mm-thick ones, and reactive powder concrete (RPC) specimens of the same thickness show an 8.3% increase in strength compared to C50 concrete specimens. When the load reaches 80% of the ultimate load, abrupt changes in concrete strain occur at the mid-span and loading points, while the strain at the fixed end is only 15–20% of the mid-span strain. The prefabricated protective wall demonstrates superior deformation resistance, with vertical displacements (3–5% of the radius) significantly lower than those of cast-in-place walls. This research clarifies the influence of wall thickness and concrete strength on the mechanical properties of prefabricated protective walls, providing key mechanical parameters to support their engineering applications. Full article

The configuration of energy storage systems in offshore wind farms can effectively suppress fluctuations in wind power and enhance the stability of the power grid. However, the economic balance between the cost of energy storage systems and the fluctuations in wind power remains an urgent challenge to be addressed, especially against the backdrop of widespread spot trading in the electricity market. How to achieve effective wind power stabilization at the lowest cost has become a key issue. This paper proposes three different energy storage configuration strategies and adopts the non-dominated sorting genetic algorithm (NSGA-II) to conduct multi-objective optimization of the system. NSGA-II performed stably in dual-objective scenarios and effectively balanced the relationship between the investment cost of the energy storage system and power fluctuations through the explicit elite strategy. Furthermore, this study analyzed the correlation between the rated power and rated capacity of the energy storage system and the battery life, and corrected the battery life of the Pareto frontier solution obtained by NSGA-II. The research results show that when only considering the investment cost of the energy storage, the optimal configuration was a rated power of 4 MW and a rated capacity of 28 MWh, which could better balance the investment economy and power fluctuation. When further considering the participation of energy storage systems in the electricity spot market, the economic efficiency of the energy storage systems could be significantly improved through the fixed-period electricity price arbitrage method. At this point, the optimal configuration was a rated power of 8 MW and a rated capacity of 37 MWh. The corresponding project investment cost was CNY 242.77 million, and the annual fluctuation rate of the wind power output decreased to 17.84%. Full article

This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form approach and bifurcation theory to explore codimension-one and two bifurcation behaviors for this model. The primary conclusions are substantiated by a combination of rigorous theoretical analysis and meticulous computational simulations. Additionally, utilizing fractal basin boundaries, periodicity variations, and Lyapunov exponent distributions within two-parameter spaces, we observe a mode-locking structure akin to Arnold tongues. These periods are arranged in a Farey tree sequence and embedded within quasi-periodic/chaotic regions. These findings enhance comprehension of bifurcation cascade emergence and structural patterns in diverse biological systems with discrete dynamics. Full article

A continuous point of a trajectory for an ordinary differential equation can be viewed as a special impulsive point; i.e., the pulsed proportional change rate and the instantaneous increment for the prey and predator populations can be taken as 0. By considering the variation multiple pulse intervention effects (i.e., several indefinite continuous points are regarded as impulsive points), an impulsive predator–prey model for characterizing chemical and biological control processes at different fixed times is first proposed. Our modeling approach can describe all possible realistic situations, and all of the traditional models are some special cases of our model. Due to the complexity of our modeling approach, it is essential to examine the dynamical properties of the periodic solutions using new methods. For example, we investigate the permanence of the system by constructing two uniform lower impulsive comparison systems, indicating the mathematical (or biological) essence of the permanence of our system; furthermore, the existence and global attractiveness of the pest-present periodic solution is analyzed by constructing an impulsive comparison system for a norm $V\left(t\right)$, which has not been addressed to date. Based on the implicit function theorem, the bifurcation of the pest-present periodic solution of the system is investigated under certain conditions, which is more rigorous than the corresponding traditional proving method. In addition, by employing the variational method, the eigenvalues of the Jacobian matrix at the fixed point corresponding to the pest-free periodic solution are determined, resulting in a sufficient condition for its local stability, and the threshold condition for the global attractiveness of the pest-free periodic solution is provided in terms of an indicator $R_a$. Finally, the sensitivity of indicator $R_a$ and bifurcations with respect to several key parameters are determined through numerical simulations, and then the switch-like transitions among two coexisting attractors show that varying dosages of insecticide applications and the numbers of natural enemies released are crucial. Full article

This work is mainly focused on square-mean S-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean S-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze some qualitative properties of this type of processes. These properties, combined with the inequality technique, evolution operator theory, fixed-point theory, and stochastic analysis approach, allow us to establish conditions for the existence and uniqueness of square-mean S-asymptotically Bloch type periodicity of bounded mild solutions for a class of stochastic evolution equations with infinite delay and piecewise constant argument. In the end, examples are given to illustrate the feasibility of our results. Full article

In this work, we present a novel four-species periodic diffusive predator–prey model, which incorporates delay and feedback control mechanisms, marking substantial progress in ecological modeling. This model offers a more realistic and detailed portrayal of the intricate dynamics of predator–prey interactions. Our primary objective is to establish the existence of a periodic solution for this new model, which depends only on time variables and is independent of spatial variables (we refer to it as a spatially homogeneous periodic solution). By employing the comparison theorem and the fixed point theorem tailored for delay differential equations, we derive a set of sufficient conditions that guarantee the emergence of such a solution. This analytical framework lays a solid mathematical foundation for understanding the periodic behaviors exhibited by predator–prey systems with delayed and feedback-regulated interactions. Moreover, we explore the global asymptotic stability of the aforementioned periodic solution. We organically combine Lyapunov stability theory, upper and lower solution techniques for partial differential equations with delay, and the squeezing theorem for limits to formulate additional sufficient conditions that ensure the stability of the periodic solution. This stability analysis is vital for forecasting the long-term outcomes of predator–prey interactions and evaluating the model’s resilience against disturbances. To validate our theoretical findings, we undertake a series of numerical simulations. These simulations not only corroborate our analytical results but also further elucidate the dynamic behaviors of the four-species predator–prey model. Our research enhances our understanding of the complex interactions within ecological systems and carries significant implications for the conservation and management of biological populations. Full article

Background/Objectives: Primary chest wall tumors or malignancies of adjacent organs with chest wall infiltration present a significant challenge for surgical resection and reconstruction. Larger defects involving the sternum, resections in the area of the thoracic apertures, or those near the spine are difficult to reconstruct. The reconstruction has to ensure stability, to prevent paradoxical movements and lung herniation, while also achieving a satisfactory cosmetic result. The “spider web” technique restores chest wall stability by creating a web-like framework made of non-resorbable threads fixed to adjacent bony structures. Additionally, a synthetic mesh is placed over the web construct, and both layers are covered with muscles (local muscles or different types of flaps). In this prospective study, clinical data from patients who underwent surgery using the “spider web” technique were analyzed with respect to chest wall stability, procedure-specific complications, pulmonary function, and patient satisfaction. Methods: A total of 16 patients receiving 18 chest wall resections and reconstructions using the “spider web” technique were followed for at least one year. Chest wall stability and lung function (FEV1 and DLCO) were assessed. Quality of life, cosmetic satisfaction, potential functional impairment, and analgesic consumption were measured using a modified EORTC QLQ-C30 questionnaire. Results: The follow-up period ranged from 12 to 32 months. In all cases, optimal chest wall stability was maintained without impairment of respiratory mechanics. Procedure-specific complications occurred in five cases (27.8%), including seroma (one case), hematoma (two cases), necrosis at the TRAM flap donor site (one case), and mesh infection (one case), all of which were resolved without further complications. Postoperative FEV1 and DLCO were not significantly reduced compared with preoperative values. The global health status score for quality of life was 60 ± 27 points. Nine patients reported being able to ascend at least one floor of stairs without shortness of breath and half of the patients were able to participate in sports activities. One patient required prolonged analgesic medication due to chronic pain. In all cases, patients were satisfied with the cosmetic result. Both 30-day and 90-day mortality were 0%. No local recurrence at the chest wall reconstruction site occurred. Conclusions: The “spider web” technique is a highly suitable method for chest wall reconstruction, allowing covering all types of chest wall defects, regardless of size and location. This cost-effective technique not only provides optimal stability but also good functional results. Full article

Reducing pesticide use is of great significance for ensuring the quality and safety of agricultural products, as well as alleviating agricultural non-point source pollution. Exploring the mechanisms by which environmental regulation drives pesticide reduction under different scenarios can help improve policy effectiveness and promote the sustainable development of agriculture. Utilizing panel data from 30 Chinese provinces spanning the period of 2010 to 2023, this study empirically analyzed the impact of environmental regulation on pesticide use through a fixed-effect model and further explored the moderating role of agricultural economic scale in this process. Moreover, a heterogeneity analysis was conducted based on regional and environmental regulation dimensions, respectively. The findings reveal that, overall, there exists an inverted U-shaped relationship between environmental regulation and pesticide use, where it initially increases and then decreases. Agricultural economic scale, serving as a moderating variable, amplifies the promotional effect of environmental regulation on pesticide reduction and accelerates the attainment of the inflection point of the inverted U-shaped curve. Regional heterogeneity analyses reveal an inverted U-shaped relationship between environmental regulation and pesticide use in the eastern and central regions, while this relationship is not significant in the western region. Notably, market-based environmental regulation exhibits a more pronounced impact compared to command-and-control environmental regulation. Full article

The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived equations that allow calculations of asymptotically periodic and bifurcation points contain coefficients defined as slowly converging infinite sums. In this paper, I derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic and bifurcation points in fractional difference maps. Full article