Basic Coordination Research Articles

A Narrative Review: How Does ABC Running Affect Speed Improvement in Young Athletes?

The purpose of this study is to analyze the effect of ABC Running on increasing speed in young athletes. This type of research uses a narrative review method. Literature search through databases such as PubMed, Scopus, WOS, Semantic Scholar and Google Scholar. Keywords such as ABC running OR speed enhancement OR athletic performance OR athletic basic coordination OR youth or young athletes. The criteria for articles are open access, scientific journals, in English or Indonesian, and published from 2019 to 2024. From the literature search, 6 articles were found that met the criteria for analysis. The results of this study are that ABC running is effective in increasing running speed in young athletes. In addition, a combination of exercises such as Running Mechanics and Ladder Drills, as well as visualization exercises were found to help improve athletes' technical skills. In conclusion, ABC running exercises are very useful in building a strong physical foundation, preventing injuries, and improving technical understanding for young athletes. This shows the importance of integrating ABC running training into young athletes' training programs to support success at higher levels. Therefore, it is recommended to continue and develop research and practice of ABC running training with various training models. Then a deeper analysis of the methodology such as developing training models, adding control variables, details on training programs and a large number of samples.

GENERALIZED DEFINITION OF THE APPARENT POWER AND ENERGY-EFFICIENT STRATEGIES OF ACTIVE FILTRATION IN THE REDUCED COORDINATE BASIS OF A MULTIPHASE POWER SUPPLY SYSTEM

The paper substantiates the equivalence of determining the apparent power of a multiphase power supply system with different transmission line impedances using the Fryze-Buchholz-Deppenbrock method and on a reduced coordinate basis. Two energy-efficient control strategies for shunt active filtering in the reduced coordinate basis are proposed. The first strategy provides a unit value of the power factor, and the second strategy minimizes power losses in the transmission line while maintaining symmetry and the quasi-sinusoidal shape of the consumed currents. The advantages of using a reduced coordinate basis are a reduction in the number of sensors and key active filter regulators as well as the absence of the problem to organize the artificial grounding point for phase voltage measurements. A correction factor for the apparent power and power factor formulas was determined and verified in the presence of restrictions on the symmetrical and sinusoidal shape of the consumed currents. References 22, figures 5, tables 2.

Study on the Interaction Mechanism Between Urbanization and Ecological Resilience—The Case of Urban Agglomeration on the North Slope of Tianshan Mountain

Although it promotes national economic development, urbanization causes regional ecosystems to suffer from disturbances and impacts that cannot be completely avoided. Ecosystems urgently need to improve their resilience; however, existing studies lack an analysis of the interaction between urbanization and ecological resilience. In this study, the interaction between urbanization and ecological resilience is investigated, taking the urban agglomeration on the north slope of Tianshan Mountain (UANST) as a study area and using the entropy value method to construct an urbanization evaluation system. Based on land use change data, an ecological resilience evaluation model is constructed using the InVSET model, the landscape pattern index, and the unit area value equivalent factor method. The degree of coupling and coordination of the interaction coupling between urbanization and ecological resilience are measured for the years 1990–2020, and their internal action mechanisms are analyzed. The results show that (1) with the development of urbanization, ecological resilience shows a decreasing and then increasing double “U”-shaped change characteristic. (2) The coupling degree of urbanization and ecological resilience in the UANST increased from 0.6888 to 0.9485, and the coordination degree increased from 0.3367 to 0.4410. (3) There are three types of coupling coordination: basic coordination, basic dysfunction, and serious dysfunction. Basic coordination is mainly distributed in the central part of the urban agglomeration, and basic dysfunction and serious dysfunction are mainly concentrated on the east and west sides; the overall trend is to shift from dysfunction to coordination. (4) Economic urbanization plays a driving role, and population urbanization, spatial urbanization, and social urbanization have an inhibitory role in the degree of coupling coordination; base quality and structural stability have a driving role in the degree of coupling coordination, while ecological services have an inhibitory role; and the population density, the proportion of built-up area to the total land area of the city, and the value of ecosystem services have a stronger influence on the level of coupling coordination.

Effects of Soil Properties and Altitude on Phylogenetic and Species Diversity of Forest Plant Communities in Southern Subtropical China

The altitudinal distribution pattern of biodiversity is a hot topic in ecological research. This study specifically aims to investigate how altitude influences the spatial distribution of species and phylogenetic and functional diversity within plant communities. By examining three range-gradient communities of Daqing Mountain-Community I (0–300 m), Community II (300–600 m), and Community III (600–900 m), we explore the interrelationship between species diversity, phylogenetic indices, and environmental drivers (altitude, soil physical properties, and chemical properties). We found (1) a correlation between species diversity and phylogenetic structure in Daqing Mountain. Species diversity decreased and then increased with increasing altitude; phylogenetic diversity decreased with increasing altitude, and the phylogenetic structure changed from dispersed to aggregated; (2) Altitude and soil physical and chemical properties are important drivers of species richness, phylogenetic diversity, and phylogenetic structure along the altitude gradient; (3) The structural equations showed that soil physical properties and altitude rise were the key factors contributing to the decrease in biodiversity in Daqing Mountain, with total soil porosity directly influencing soil physical properties and soil water content indirectly. This study not only reveals the pattern of plant diversity along the altitude of Daqing Mountain but also provides a basis for plant conservation planning, habitat maintenance, and management coordination.

A Physical Approach to Lagrangian Equations with Bundle Structure for Minkowski 3-Space

Minkowski 3-space is important because it is the spatial structure in which physical events occur. Therefore, in this study, we examined the time-dependent Lagrangian energy equations in Minkowski 3-space. To facilitate the examination of the necessary mechanical structure and solutions with respect to time, we employed the jet bundle structure. This approach has made the creation of the necessary geometric structures more comprehensible in terms of coordinate basis. To interpret the obtained Lagrangian energy equations and to understand the significance of the time parameter, an example is also provided in our study.

The left primary motor cortex and cerebellar vermis are critical hubs in bimanual sequential learning

We conducted an fMRI study to investigate the neural basis of bimanual coordination, which is fundamental to upper extremity control. Considering bimanual movement as a combination of bimanual chord formation and sequence control, we hypothesized that the areas with the learning effect of both chord formation and sequence learning are critical in bimanual coordination. We adopted the serial reaction time task (SRTT) to test this hypothesis. Thirty-five healthy right-handed volunteers practiced visually cued bimanual SRTT, including the “mirror” and more complex “parallel” modes of random movements or repeating fixed sequences to separately depict the neural substrates of bimanual posture control for chord formation and those of sequence. Random movements’ reaction time (RT) continuously declined, indicating learning of bimanual chord formation. The RT in the sequential condition declined more rapidly than in the random condition, confirming sequence learning. The parallel random conditions evoked a more prominent learning-related decrease of task-related activation in the left M1 and cerebellar vermis than the less difficult mirror random conditions. The left M1 showed learning-related enhancement of functional connectivity with the anterior cingulate cortex during the parallel random conditions compared with the mirror random conditions. Thus, the left M1, anterior cingulate cortex, and cerebellar vermis are related to learning bimanual chord formation. The left M1 and cerebellar vermis also showed sequence-specific learning-related activity increments more prominent in the parallel mode than in the mirror mode. Thus, the left M1 and cerebellar vermis are critical in the bimanual motor learning network.

Coupling Coordination Measurement and Obstacle Diagnosis of New Urbanization and Rural Revitalization in the Basin Area of Sichuan Province, China

The coupling coordination of new urbanization (NU) and rural revitalization (RR) is the key research that focuses on promoting integrated development between urban and rural areas. The entropy weight method, coupling coordination model, and obstacle model were used to explore the development level, coupling coordination degree, and obstacle factors of NU and RR in the basin area of Sichuan Province from 2013 to 2021 in this study. The results show the following: The levels of NU and RR in the basin area of Sichuan Province show an uptrend. Central cities exhibit higher levels of RR and NU. Under the influence of a central city, regional central cities have obvious growth in RR and NU. There are fluctuations in the RR and NU indicators in node cities. The coupling coordination degree of NU and RR in the basin area of Sichuan Province continues to rise, and the coordination levels are mainly basic coordination and moderate coordination. The coupling coordination degree is higher in central and regional central cities, while the coupling coordination degree of node cities is relatively lower. The levels of agricultural modernization, public infrastructure and medical resources, and rural governance are the main factors influencing the coupling coordination of NU and RR in the basin area of Sichuan Province. Affected by terrain, economy, and other factors, the level of urban–rural integration in the basin area of Sichuan Province is obviously different. With the continuous improvement of policies, the coupling coordination level of NU and RR is gradually developing towards a positive trend.

Multi-Scale Evaluation and Simulation of Livelihood Efficiency in Post-Poverty Mountainous Areas

Promoting the coordination of livelihoods at the county and farmers’ scales is essential for achieving balanced regional development and rural revitalization in post-poverty mountainous areas. Existing studies predominantly focus on farmers’ or regional livelihood capital and livelihood efficiency at a single scale, lacking research on cross-scale coordination between farmers’ and county livelihoods. Consequently, these studies fail to reveal the interactions and synergistic enhancement pathways between the two scales. This study, using the Qinba mountains in southern Shaanxi as a case, employs system dynamics to construct a coupled system dynamics model of farmers’ livelihood efficiency and county livelihood efficiency. From the perspective of livelihood capital, five regulatory modes, comprising a total of 17 scenarios, were designed and simulated. The results indicate the following data: (1) The coupling coordination degree between farmers’ livelihood efficiency and county livelihood efficiency in the Qinba mountains is 0.623, indicating a moderate level of coordination overall. However, the coupling coordination relationship requires further optimization and adjustment. Specifically, Foping exhibits a severe imbalance, while the coupling coordination degree of Shiquan, Zhashui, Baihe, Pingli, and Lan’gao is in a state of basic coordination. Additionally, 19 other counties, including Lueyang, Ningqiang, Yang, and others, exhibit moderate coordination. (2) Enhancing social or financial capital through various means typically promotes the coordinated development of farmers’ and county livelihood efficiency. On average, social capital and financial capital regulation models can increase the coupling coordination degree by 0.08 and 0.17, respectively. Additionally, strategies such as increasing fixed asset investment and regulating other capital types, including reducing arable land, also effectively improve the coupling coordination degree of farmers’ and county livelihood efficiency. This study provides a decision-making basis for improving the coordination of farmers’ and county livelihoods in post-poverty mountainous areas, thereby promoting economic development and intensive resource utilization. It assists in formulating more precise policy measures and offers a reference for sustainable development and rural revitalization in similar regions.

Neural Transformation from Retinotopic to Background-Centric Coordinates in the Macaque Precuneus.

Visual information is initially represented in retinotopic coordinates and later in craniotopic coordinates. Psychophysical evidence suggests that visual information is further represented in more general coordinates related to the external world; however, the neural basis of nonegocentric coordinates remains elusive. This study investigates the automatic transformation from egocentric to nonegocentric coordinates in the macaque precuneus (two males, one female), identified by a functional imaging study as a key area for nonegocentric representation. We found that 6.2% of neurons in the precuneus have receptive fields (RFs) anchored to the background rather than to the retina or the head, while 16% had traditional retinotopic RFs. Notably, these two types were not exclusive: many background-centric neurons initially encode a stimulus' position in retinotopic coordinates (up to ∼90 ms from the stimulus onset) but later shift to background coordinates, peaking at ∼150 ms. Regarding retinotopic information, the stimulus dominated the initial period, whereas the background dominated the later period. In the absence of a background, there is a dramatic surge in retinotopic information about the stimulus during the later phase, clearly delineating two distinct periods of retinotopic encoding: one focusing on the figure to be attended and another on the background. These findings suggest that the initial retinotopic information of the stimulus is combined with the background retinotopic information in a subsequent stage, yielding a more stable representation of the stimulus relative to the background through time-division multiplexing.

Институт уполномоченных по правам человека в России: концептуальные основы и эволюция

The article examines the development of the institution of human rights commissioners in Russia. The author comes to the conclusion that Russian practice demonstrates the evolutionary development of the institution of human rights commissioners. This institution is a reflection of the federal structure of the state. The Human Rights Commissioner in the Russian Federation and the Human Rights Commissioners in the constituent entities of the Russian Federation are competently independent constitutional figures. Their interaction is carried out on the basis of coordination through various forms, which largely developed on the basis of practical activities and were subsequently enshrined in federal legislation. There is a clear tendency to expand the powers of Russian human rights defenders in all areas of their activities, and the «legal tools» of the commissioners are being strengthened. All this allows us to conclude that the institution of human rights commissioners has high authority and is in demand both at the state level and in the environment of civil relations.

Assessing the impact of various irrigation technologies on agricultural production: A water-energy‑carbon nexus perspective

Effective coordination of water, energy, and carbon is vital for the sustainable development of irrigated agriculture. However, limited research has been conducted on the impact of irrigation technology on the coupling and coordination relationship of these elements, especially on the North China Plain (NCP) where irrigation is applied extensively. This study establishes a water-energy‑carbon (WEC) nexus framework based on footprint theory and energy analysis. Water utilization, energy consumption, and carbon emissions in a wheat production system under conventional irrigation (CI), sprinkler irrigation (SI), and drip irrigation (DI) technology on the NCP from 2000 to 2019 were quantified. Subsequently, the coupling coordination degree (CCD) model is used to analyze the interactions and correlations of the WEC nexus. Results indicated that SI and CI effectively reduced water consumption and mitigated water degradation, but this came at the expense of increased energy consumption and carbon emissions. The irrigation process represented the predominant share of energy consumption, representing 40.54 % and 37.64 % of the production-based energy consumption under SI and DI, respectively. The primary contributors to the production-based carbon footprint under CI, SI, and DI were N fertilizer (23.67 %), pipeline production (59.10 %), and irrigation electricity (21.85 %), respectively. The CCD range of WEC systems under the three irrigation technologies varied from 0.35 to 0.50 on the NCP during the investigation period. There were some slight differences in the average annual CCD between each irrigation technology, with DI (0.43) > SI (0.40) > CI (0.39). SI and DI was in basic coordination, while CI was in imbalanced type. Meanwhile, the spatial heterogeneity of CCD was fully reflected over time. Promoting water-saving irrigation technologies, developing clean energy, controlling the expansion of irrigation areas, and strengthening the connections among various subsystems are crucial measure to achieve regional WEC nexus coupling coordination.

Observation of Enhanced Long-Range Elliptic Anisotropies Inside High-Multiplicity Jets in pp Collisions at sqrt[s]=13 TeV.

A search for collective effects inside jets produced in proton-proton collisions is performed via correlation measurements of charged particles using the CMS detector at the CERN LHC. The analysis uses data collected at a center-of-mass energy of sqrt[s]=13 TeV, corresponding to an integrated luminosity of 138 fb^{-1}. Jets are reconstructed with the anti-k_{T} algorithm with a distance parameter of 0.8 and are required to have transverse momentum greater than 550GeV and pseudorapidity |η^{jet}|<1.6. Two-particle correlations among the charged particles within the jets are studied as functions of the particles' azimuthal angle and pseudorapidity separations (Δϕ^{*} and Δη^{*}) in a jet coordinate basis, where particles' η^{*}, ϕ^{*} are defined relative to the direction of the jet. The correlation functions are studied in classes of in-jet charged-particle multiplicity up to N_{ch}^{j}≈100. Fourier harmonics are extracted from long-range azimuthal correlation functions to characterize azimuthal anisotropy for |Δη^{*}|>2. For low-N_{ch}^{j} jets, the long-range elliptic anisotropic harmonic, v_{2}^{*}, is observed to decrease with N_{ch}^{j}. This trend is well described by MonteCarlo event generators. However, a rising trend for v_{2}^{*} emerges at N_{ch}^{j}≳80, hinting at a possible onset of collective behavior, which is not reproduced by the models tested. This observation yields new insights into the dynamics of jet evolution in the vacuum.

Deep learning in standard least-squares theory of linear models: Perspective, development and vision

Inspired by the attractive features of least-squares theory in many practical applications, this contribution introduces least-squares-based deep learning (LSBDL). Least-squares theory connects explanatory variables to predicted variables, called observations, through a linear(ized) model in which the unknown parameters of this relation are estimated using the principle of least-squares. Conversely, deep learning (DL) methods establish nonlinear relationships for applications where predicted variables are unknown (nonlinear) functions of explanatory variables. This contribution presents the DL formulation based on least-squares theory in linear models. As a data-driven method, a network is trained to construct an appropriate design matrix of which its entries are estimated using two descent optimization methods: steepest descent and Gauss–Newton. In conjunction with interpretable and explainable artificial intelligence, LSBDL leverages the well-established least-squares theory for DL applications through the following three-fold objectives: (i) Quality control measures such as covariance matrix of predicted outcome can directly be determined. (ii) Available least-squares reliability theory and hypothesis testing can be established to identify mis-specification and outlying observations. (iii) Observations’ covariance matrix can be exploited to train a network with inconsistent, heterogeneous and statistically correlated data. Three examples are presented to demonstrate the theory. The first example uses LSBDL to train coordinate basis functions for a surface fitting problem. The second example applies LSBDL to time series forecasting. The third example showcases a real-world application of LSBDL to downscale groundwater storage anomaly data. LSBDL offers opportunities in many fields of geoscience, aviation, time series analysis, data assimilation and data fusion of multiple sensors.

Aspect ratio-dependent volume resistivity in unidirectional composites: Insights from electrical conduction behavior

The electrical properties of carbon fibers serve as the foundation for the multifunctional applications of carbon fiber-reinforced composite structures. In scenarios that exploit the electrical characteristics of materials, accurate estimation of electrical resistivity stands as a critical factor. This study endeavors to elucidate the electrical conduction behaviors in unidirectional composites with different fiber orientation angles (0°, 15°, 30°, 45°, 60°, 75°, and 90°) and aspect ratios, thereby deriving the volume resistivity within an arbitrary Cartesian coordinate system. Employing thermal infrared imaging technology and finite element analysis, we identified distinctive electrical conduction behaviors associated with aspect ratios in carbon fiber composite plates. Notably, a critical aspect ratio exists wherein the diagonal yarn is the only conductive path between two electrodes. Below this critical threshold, no direct conductive path exists, and current flows through the shortest distance between parallel yarns. Conversely, beyond the critical aspect ratio value, multiple yarns form conductive paths between the two electrodes. Based on the electrical conduction behavior of unidirectional composites under different angles and aspect ratios, the volume resistivity with finite boundaries was derived and examined under an arbitrary Cartesian coordinate basis.

Association of oral frailty and gait characteristics in patients with cerebral small vessel disease

BackgroundThe objectives of this study were twofold: (1) to compare gait characteristics between cerebral small vessel disease (CSVD) patients with low-risk oral frailty (OF) and high-risk OF, particularly during dual-task walking (DTW); (2) to investigate the association of OF, the gait characteristics of DTW, and falls among older adults patients with CSVD.MethodsA total of 126 hospitalized patients diagnosed with CSVD were recruited and classified into a low-risk group (n = 90) and a high-risk group (n = 36) based on OF status in our study. Comprehensive data pertaining to basic parameters (cadence, as well as stride time, velocity and length), variability, asymmetry, and coordination were gathered during both single-task walking (STW) and DTW. Additionally, the number of falls was calculated. Subsequently, t-test or chi-squared test was used for comparison between the two groups. Furthermore, linear regression analysis was employed to elucidate the association of the OF index-8 score and gait parameters during cognitive DTW. Also, logistic regression models were utilized to assess the independent association of OF risk and falls.ResultsDuring cognitive DTW, the high-risk group demonstrated inferior performance in terms of basic parameters (p < 0.01), coefficient of variation (CV) of velocity and stride length (p < 0.05), as well as phase coordination index (PCI) when compared with the low-risk group (p < 0.05). Notably, differences in basic gait parameters were observed in cognitive DTW and STW conditions between the two groups (p < 0.01). However, only the high-risk group evinced significant variations in CV and PCI during cognitive DTW, as opposed to those during STW (p < 0.05). Furthermore, our findings also revealed the association of OF, the gait characteristics of cognitive DTW, (p < 0.01) and falls (p < 0.05).ConclusionCSVD patients with a high risk of OF need to pay more attention to their gait variability or coordination. Also, they are recommended to undergo training involving dual-task activities while walking in daily life, thereby reducing the deterioration and mitigating the risk of falls. Besides, this study has confirmed an association of OF and DTW gait as well as falls in patients with CSVD.

Assessment of rural sustainable development and analysis and prediction of obstacles and coupled coordinated development: A case study of Zaozhuang City

In China, the Innovation Demonstration Zone for the National Sustainable Development Agenda is a key initiative for executing the United Nations (UN) 2030 Agenda for Sustainable Development. The Zone also plays critical roles in addressing the developmental bottlenecks that China faces and sharing Chinese insights into global sustainable development efforts. On July 15, 2022, the State Council endorsed the Zone’s establishment in Zaozhuang City, Shandong Province, where it focuses on innovation-led sustainable development in rural areas. Research into the levels, impediments, interdependencies, and evolutionary trends of rural sustainable development is crucial. Therefore, this research aimed to assist in comprehensively assessing developmental challenges and facilitating the harmonious advancement of social, economic, and environmental aspects in rural areas. In pursuit of the three fundamental dimensions of the UN’s Sustainable Development Goals (SDGs), namely development’s drivers, quality, and equity, this study was grounded in China’s national Rural Revitalization Strategy and the demands of sustainable development strategies. It also aligns with the UN 2030 Agenda for Sustainable Development and the associated SDG indicators. Focusing on four key areas, namely production elements, natural elements, social elements, and rural governance, this study developed an evaluation index system for assessing the level of rural sustainable development. It employed a range of analytical models, including the game theory-based combination empowerment method, barrier degree model, coupling degree model, coupling coordination degree model, and gray prediction GM(1,1) model, to analyze the status and evolving trends of rural sustainable development in Zaozhuang City from 2015 to 2022. The key findings were as follows: ① Relative to the baseline year 2015, the sustainable development level in Zaozhuang’s rural areas has shifted toward an improved state overall. ② The primary barrier to achieving rural sustainable development in Zaozhuang is the city’s rural governance system. ③ While the components of rural sustainable development in Zaozhuang are in the early stages of both basic and moderate coordination, an overall enhancement has occurred in their integrative coordination. ④ Between 2023 and 2025, the level of integrative coordination in Zaozhuang is expected to rise steadily. However, reaching a state of advanced coordination will require additional time for development.

A novel phase measuring deflectometry based on polar coordinate

Phase measuring deflectometry (PMD) is a method measure the surface of a mirror. However, when measuring convex mirrors, Cartesian coordinate fringes experience extreme compression. To address this issue, this paper proposes a novel PMD based on polar coordinate. This new method defines two linearly independent phase modulation directions, using the orthogonal basis of polar coordinate. It establishes polar coordinate fringes with rotational symmetry and radial pre-modulation, effectively reducing the impact of extreme compression at the edges. To correct the phase errors in polar coordinate fringes, a phase error compensation algorithm based on greyscale gradient is introduced. The algorithm calculates the influence factor of the eight connected domains around the error points to be compensated, utilising the phase grey gradient. The wavefront gradient data obtained through polar coordinate fringes are radial and tangential. Hence, a surface reconstruction method is proposed based on the Zernike partial derivative polynomial based on polar coordinate. In this method, the tangential partial derivatives and radial partial derivatives of the first 36 terms of Zernike in polar coordinate to construct Gram matrix equations. As a result, linearly independent Zernike recovery coefficients are obtained from coupled aliasing gradient data. Compared to the Cartesian coordinate system, the proposed method significantly reduces the fitting coefficient errors. Experimental measurements of convex mirrors with radii of curvature of 200 mm and 100 mm were conducted. The results demonstrate that compared to traditional PMD, this technique not only effectively suppresses extreme compression and increases the measurement area but also improves measurement accuracy by six times.

Конечно-элементное моделирование нелинейных задач упругости в абсолютных узловых координатах на неструктурированных шестигранных сетках

We consider a finite element approach to solving the problem of elasticity theory in terms of absolute nodal coordinate formulation (ANCF), in which large body displacements are described in a global reference frame without using any local coordinate system. The main feature of the method is the absence of gyroscopic effects and, as a result, constancy of the mass matrix and the vector of the generalized force of gravity. In contrast to the traditional ANCF approach, the sets of nodal degrees of freedom of the finite element are formed only on the basis of absolute coordinates of nodes, which allows us to solve the problem using, in particular, unstructured hexahedral meshes. To construct the stiffness matrix, we apply a second-order automatic differentiation algorithm, which ensures its symmetrical form (Hessian matrix) and is analytically accurate in calculating the derivative. This approach also makes it possible to carry out calculations for models of hyperelastic materials without the corresponding Piola-Kirchhoff tensor. It has been shown that within the framework of discretization of the equation of motion, along with the well-known Newmark numerical integration scheme, it is possible to use the HTT-α scheme, which is unconditionally stable, second-order accurate and dissipative for high frequencies. We present several examples of solving static and dynamic elasticity problems for compressible and incompressible models of hyperelastic materials, in which the functions of internal energy density of the body are specified in terms of the deformation gradient.

Coupling Coordination Relationship and Spatiotemporal Heterogeneity between Functional Diversification and Settlement Evolution in Traditional Mountain Areas (2000–2020): A Case Study of Fengjie County, China

Since the socio-economic reform in 1978, rural China has undergone drastic spatial restructuring, and the trend of multifunctional development and dynamic evolution of settlements in the countryside have become increasingly obvious. Functions and settlements are the important parts of rural areas. Rural multifunction is a new perspective to explore the diversified development paths of the countryside, and rural settlements provide basic support for rural multifunction. Clarifying the complex coupling coordination relationship between rural functional diversification (RFD) and rural settlement evolution (RSE), and identifying the spatial heterogeneity of their interactions is the key to promoting the rural revitalization strategy. This study analyzes the spatiotemporal changes in rural functions and rural settlements at the township level, alongside assessing various forms and the extent of coupled development. Therein, we consider the advantages of different coupling types of townships and propose four development paths for rural settlements to improve the adaptability of rural functions and settlements. The results show that: (1) The functions and settlements in the study area are characterized by significant spatial and temporal dynamics, indicating that the traditional mountainous countryside is in a process of rapid development and change. (2) The coupling coordination degree of RFD and RSE increases yearly, generally transitioning from the moderate imbalance to the basic coordination stage, and the coordinated townships have obvious spatial agglomeration. (3) Based on the elasticity coefficient model, this paper summarizes four coupling models of RFD and RSE to guide the optimization of rural settlement development paths. This research provides scientific guidance for developing countries in the spatial planning of rural territories and the optimization of rural settlements.

Coupling Study of Green Finance and High-Quality Economic Development

Based on panel data from 16 prefecture-level cities in Shandong Province from 2012 to 2021, a comprehensive evaluation system for the development of green finance and high-quality economic development in Shandong Province was constructed. The entropy weight method was used to calculate the comprehensive index of both. The research shows that, temporally, from 2012 to 2021, the coupling degree between green finance development and high-quality economic development in the prefecture-level cities of Shandong Province was mostly at a high or relatively high level, with the coordination degree increasing year by year. However, the overall level remained low, with most cities in a state of mild or near imbalance. Spatially, only coastal cities such as Qingdao, Dongying, Weihai, and Rizhao achieved basic coordination, with the coordination degree of coastal cities being higher than that of inland cities. Among them, coastal cities mainly exhibited high-high or high-low types, while inland areas mostly showed low-low types, failing to form a good linkage effect.