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We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

This paper presents the analyses of toppling response of layered reverse-dip slopes under the influence of geometric factors of slope angle, strata thickness and dip. The toppling response of reverse-dip slopes under different geometric factors is obtained by using the discrete element code UDEC. Then, a prediction model for toppling deformation is developed by utilizing support vector machine and the toppling-prone combinations of these geometric factors are determined from a total of 120 samples of reverse-dip slopes. The study has shown that the geometric model is a quarter of a spheroid with a slope angle of 80°, a strata dip of 80°, and a strata thickness of 0.19 m as the center. The length of the long equatorial radius of the spheroid is 31° (strata dip axial), that of the short equatorial radius is 21° (slope angle axial), and the polar radius is 0.075 m (strata thickness axial). And the ratio of long equatorial radius, short equatorial radius, and polar radius is 2.48:1.68:1.00.

In the paper, in the form of series in the Papkovich–Fadle eigenfunctions, exact solutions of two inhomogeneous boundary value problems of elasticity theory for a half-strip with free long sides are constructed: (1) the half-strip end is free, (2) the half-strip end is rigidly clamped. To solve the inhomogeneous problem in a free strip, the Papkovich orthogonality relation is used. The exact solution for the half-strip is then added to it.

We derive the formulas that describe the exact solution of the boundary value problem in the theory of elasticity for a rectangle in which two opposite (horizontal) sides are free and stresses are specified (all cases of symmetry relative to the central axes) on the other two sides (rectangle ends). The formulas for a half-strip are also given. The solutions are represented as series in Papkovich–Fadle eigenfunctions whose coefficients are determined from simple formulas. The obtained formulas remain the same for other types of homogeneous boundary conditions, for example, when the horizontal sides of the rectangle are firmly clamped, have stiffening ribs that work in tension–compression and/or bending, etc. Obviously, in this case, the Papkovich–Fadle eigenfunctions will change, as well as the corresponding biorthogonal functions and normalizing factors. To solve a specific boundary value problem, it is enough to find the Lagrange coefficients, which are determined from simple formulas, as Fourier integrals of boundary functions specified at the ends of the rectangle, and then substitute them into the necessary formulas. Examples of solving two problems (even-symmetric deformation relative to the central coordinate axes) are given: (a) The normal stresses are known at the rectangle ends, and the tangential ones are zero; and (b) the longitudinal displacements conditioned by the action of some normal stresses are known at the rectangle ends (the tangential stresses are zero). These solutions are compared with the known solutions in trigonometric Fourier series. The basis of the exact solutions obtained is the theory of expansions in Papkovich–Fadle eigenfunctions based on the Borel transform in the class of quasi-entire functions of exponential type (developed by the authors in their previous studies).

Tailings dams, as essential mining structures, are being built globally for containing the chief waste stream of the mining industry. Catastrophic tailings dam breaches have occurred frequently over the past decade, causing severe impacts on the environment, economy, and human health. The foreknowledge of the tailings dam breach overland flow is crucial for the risk assessment and emergency response planning in order to prevent or minimize possible losses. Using unmanned aerial vehicles (UAV) photogrammetry and smoothed particle hydrodynamics (SPH) numerical method, this study proposed a multidisciplinary procedure for modelling a hypothetical tailings dam breach run out flow over the downstream complex terrain. A case study on a 97-m-height tailings dam in Shandong Province of China was carried out. The proposed procedure was proven applicable to determine the overland tailings flow. The submerged area and flow velocities suggested that the downstream G2 highway would hardly be threatened and more concerns should be paid on the factory plants and workers deployed between the dam toe and the highway. Additionally, the application of UAV photogrammetry in the mining industry as a supplementary surveying method can be further expanded, especially for the numerous small-scale mining sites. The proposed procedure is then recommended for the safety management of the tailings&rsquo, storage facilities globally.

Monitoring vegetation change and their potential drivers are important to environmental management. Previous studies on vegetation change detection and driver discrimination were two independent fields. Specifically, change detection methods focus on nonlinear and linear change behaviors, i.e., abrupt change (AC) and gradual change (GC). But driver discrimination studies mainly used linear coupling models which rarely concerned the nonlinear behaviors of vegetation. The two diagnoses need be treated as sequential flow because they have inner causality mechanisms. Furthermore, ACs concealed in time series may induce over/under-estimate contributions from human. We chose the Yangtze River Basin of China (YRB) as a study area, first separated ACs from GCs using breaks for additive and seasonal trend method, then discriminated drivers of GCs using optimized Restrend method. Results showed that (1) 2.83% of YRB were ACs with hotspots in 1998 (30.2%), 2003 (10.4%), and 2002 (7.6%); 66.7% of YRB experienced GC with 94.8% of which were positive; and (2) climate induced more area but less dramatic GCs than human activities. Further analysis showed that temperature was the main climate driver to GCs, while human-induced GCs were related to local eco-policies. The widely occurring ACs in 1998 were related to the flooding catastrophe, while the dramatic ACs in sub-basin 12 in 2003 may result from urbanization. This paper provides clear insights on the vegetation changes and their drivers at a relatively long perspective (i.e., 34 years). Sequential combination of specifying different vegetation behaviors with driver analysis could improve driver characterizations, which is key to environmental assessment and management in YRB.

An assessment model for the satisfied degree of crop water requirements (CWR) on the grid scale, the CropWRA model, is developed to support precise management of agricultural water resources. On the grid scale, we urge that the CWR satisfied degree is not only rested with the abundance of water resources in a region, but also related to crop types, growing periods, water accessibility, etc. The CropWRA model also consists of corresponding indexes such as the CWR characteristics, crop planting combination and proportion, available water of agricultural production, water accessibility, etc. In this case study, the CWR satisfied degree of main food crops is evaluated with DEM data, hydrological data, meteorological and climate data, crop experiment and observation data, and statistical data in Hanjiang River Basin, China. In general, the results show that agricultural water resources can satisfy the CWR but the spatial differences are profoundly remarkable. The CropWRA index varies from -20% to 200%, and this difference is the comprehensive effects caused by the topography, river system, crop planting combination, land use, and water resources composition, etc. CropWRA model reveals the spatial differences in the relationships of CWR supply and demand and can provide the data support for precise water resource allocation.

We propose a method of solving mixed boundary value problems in the theory of elasticity in an infinite horizontal strip that has two points of change in the type of boundary conditions located on the upper and lower sides of the strip and lying at the ends of a vertical segment—the line of the joint between the left and right half-strips. The solutions to the right and the left of the joint line are represented as series in eigenfunctions that correspond to particular boundary conditions on the horizontal sides of the right and left half-strips. Solution continuity conditions or, on the contrary, discontinuities of the displacements or stresses can be specified at the joint between the half-strips. We illustrate the main idea of the method initially using a mixed boundary value problem for the harmonic equation as an example. Here, biorthogonal functions are constructed, their properties and the properties of the coefficients of expansions are investigated, and examples are given to illustrate the correctness of the obtained solutions. Subsequently we solve a mixed boundary value problem in which two trigonometric systems of functions with different eigenvalues are involved at the joint between the half-strips. We consider examples where (1) displacement and stress continuity conditions, (2) a discontinuity of the longitudinal displacements, and (3) a discontinuity of the transverse displacements are specified at the joint between the half-strips.

The integrated study on the evolution of the regional social-ecological system (RSES) is one of many complex and classical research topics. An innovative approach of conjugate analysis is introduced to describe the RSES evolution in this paper. We select land use intensity (L), bilateral dynamic change of land use types (S), landscape pattern index (P), ecological security index (Q), and the RSES composite index (T) to describe the RSES. We analyze and express the conjugacy of the RSES evolution: for the spatial correlations, they are revealed by variance analysis, spatial autocorrelation, and regionalized variable analysis; and for the temporal correlations, they are described by the analysis of spatiotemporal correlation. We use a case study of the Hanjiang River basin in Hubei province (China) to test the conjugate evolution of the RSES. We find that the RSES evolution in this region is driven by dual-source forces, both resource driven and economic power driven. These driving forces result in the spiral rise of the RSES evolution, where L, S, Q, P, and T have high self-autocorrelations, and there are remarkable and highly positive correlations and inheritance between the RSES and their subsystems. These results can corroborate the hypothesis about conjugate evolvement of the RSES. The spatial patterns of the RSES evolution are controlled by physical factors, especially geomorphology, where as its direction is guided by human activities, and its progress is pushed forward by human-environment interactions. The analysis of the RSES conjugate evolution can provide a new perspective for the RSES management, that is, the RSES management decisions should consider conjugate effects, because these effects can directly influence regional sustainable development.

Fifteen individual perfluoroalkyl substances (PFASs) were analyzed in 22 sediment samples collected from Anqing urban lakes (Anhui province, China) by ultra-performance liquid chromatography–tandem mass spectrometry (UPLC–MS/MS). Total PFAS concentration was between 0.61 and 26 ng g− 1 dry weight. Perfluorooctane sulfonate (PFOS) was the dominant PFAS contaminant, with a concentration range of

Traditional assessments of water resources use water availability as an evaluating metric. Water availability is a statistical average and cannot reflect the spatial differences of water resources in a region or basin. This assessment usually engenders a paradox, that is, water resources are abundant in a region but it is difficult to obtain water for the people on some spatial points in this region. In this study we define a new term, water accessibility, to eliminate this paradox and develop a model of water accessibility (the SHRD model) to meet the need of spatial details in water resources assessment at the grid scale. In the case study the water accessibility of the Hanjiang River Basin is mapped and assessed by the SHRD model. The comprehensive index of water accessibility is 0 to 4.5 and tends to increase from northwest to southeast in the study area. The results of the SHRD model can show the spatial pattern of water accessibility in a region, and can server a more finely-tuned water resources management approach. This model and method push the macroscopic (regional) water resources assessment forward from the microcosmic (raster cell) analysis.

The changes of lakes directly affect the sustainable development of regional ecological environment and social economy. Affected by the environmental changes and human activities, most of the inland lakes globally have suffered from the area shrinkage and wetland degradation. The protection and restoration of lakes have become a hot public issue. In this study, a lake spatial database of Hubei Province (China) is built to analyze the temporal-spatial dynamic change of lakes in Hubei Province from 1974 to 2014, with the analysis models of lake dynamic change rate (LDCR), lake landscape shape index (LLSI), and lake centroid shift rate (LCSR). The results are as follows: (1) Lakes in Hubei Province showed a shrinking and fragmenting trend from 1975 to 2014. The total area of lakes decreased by 23.08%, and the number of lake increased by 68.03%. (2) The value of LLSI firstly increased and then decreased after 1995, meaning that the lake disturbance degree of human activities decreased firstly and then increased. (3) The lake centroids of Hubei Province were in the Jianghan Plain and shifted to the northwest by 33.67 km from 1975 to 2014, due to the lake shrinkage was more serious in the southeastern than in the northwest. The situation of inland lakes’ shrinkage and degeneration is still very severe. The national and local governments should strengthen the lake management and protection, curb the lake shrinkage and degradation, and promote the healthy and sustainable development of lakes.

Using the boundary value problem on the bending of a thin elastic semi-infinite plate in which the long sides are free, while a self-balanced bending moment and a generalized shearing force are specified at its end as an example, we consider the main steps in constructing exact solutions to the boundary value problems of bending of thin elastic rectangular plates. The solutions are constructed in the form of series in Papkovich–Fadle eigenfunctions. The unknown expansion coefficients are determined in the same way as in classical periodic solutions in trigonometric series and have the same structure, i.e., are expressed via the Fourier integrals of the boundary functions specified at the half-strip end. The systems of functions biorthogonal to the Papkovich–Fadle eigenfunctions constructed here are used in this case. The exact solutions possess properties that are not inherent in any of the known solutions in the theory of plate bending. Some of them are discussed in the paper. The final formulas describing the exact solution of the boundary value problem are simple and can be easily used in engineering practice. The results that we have obtained previously when solving the boundary values problems of the plane theory of elasticity in a rectangular region form the basis for our work.

Planetary system trajectory is inherently related to sun movement. Considering that planetary system movement affects solar activity and even global climate change, studies on its changing law and characteristic are of significance and values. In this study, the kinematic index of planet heliocentric longitude is created based on the orbital elements of planets in the solar system. Both the planet juncture index and heliocentric longitude are used to investigate the periodic planetary system movement around the barycentre of the solar system. The planet juncture index is the norm of the total quality-vector-weights for planetary system. It represents the distance between the barycentre of the planetary system and the sun. When all planets nearly align, the planet juncture index peaks; otherwise, it falls. The planet heliocentric longitude is the angle between the line from the projection of the barycentre of the planetary system onto the datum to that of the sun and the datum axis. The planet heliocentric longitude ranges from 0 to 2 π . The planet juncture index and heliocentric longitude are two important kinematic indexes for researching the changing law and characteristic of planetary system movement. The former represents the distance between the barycentre of the planetary system and the sun and the degree of convergence and separation of the planetary system. The latter represents the exact location of the barycentre of the planetary system relative to that of the solar system. This study explores the changing rule and characteristic of planetary system movement through the two kinematic indexes. Results of this study bear significance and value on theories of studies on solar movement, solar activity and global climate change. The power spectrum analysis method is a spectral analysis indicating digital time-series in different frequencies of energy distribution, which reflects the distribution of power spectrum in different frequencies of stochastic signal. The implied periodic trends in the frequency domain are revealed with the power spectrum analysis method by analysing the character of signal and processing every coordinate time-series with Fourier transform. Both the planet heliocentric longitude and juncture index are studied through numerical simulation. The base data of the variations of planet juncture index and heliocentric longitude for nearly 2000 years are derived. The comparison between the base data of the two kinematic indexes show that both exhibit periodic trends and varying characteristics similar to those of the planetary system movement. The power spectra of results reveal that both the planet juncture index and heliocentric longitude are complicated, with remarkable periodicity parameters of 35.958, 19.873, 13.768 and 12.807 a for the former and 162.602, 29.446, 11.865, 8.457, 7.421 and 5.936 a for the latter. The most remarkable periodicity parameters are 19.873 and 11.865 a. To a certain extent, these periodic trends provide basis for analysing solar activity and global climate change. Planet juncture index indicates the moving pattern of the barycentre of the planetary system around that of the solar system and thus specify the moving pattern of the sun around the barycentre of the solar system. Planet heliocentric longitude indicates the accurate position of the barycentre of the planetary system relative to that of the sun and thus indicates the accurate position of the barycentre of the solar system relative to that of the sun. Both provide an effective means to investigate the relationship between sun movement and solar activity.

The origin, spatial pattern, and evolution of urban system have been hot research issues in the field of urban system. In this study, the theory of “urban tree (UT)” was proposed to address these issues. The spatial pattern of urban system can be expressed by the phrase UT and the growth of the UT reflects the origin, spatial pattern, and evolution of urban system. Analysis of the UT growth can reveal the evolutionary mechanisms of the urban system. We present an UT resistance model to determine spatial extension in the evolutionary processes of urban system. The Thiessen polygon method and spatial re-mapping were used to construct the UT. Data collected in 1995, 2000, 2005 and 2010 from cities in the Huai River Basin were used to construct the UT model to analyze the origin, spatial pattern, and evolution of urban system in this region. Xuzhou City was the UT “tree root” and the UT growth the followed four paths. Growth of cities on the nodes of these paths promoted the evolution of urban system. The UT theory expresses the spatial pattern and evolution of urban system in an intuitive way and helps to explain the origin and evolution mechanisms of urban system. Empirical research supported the UT theory. Because of the operational and visual expression, this theory has broad application prospects in the urban system research.

Discriminating the significant human-induced vegetation changes over the past 15 years could help local governments review the effects of eco-programs and develop sustainable land use policies in arid/semi-arid ecosystems. We used the residual trends method (RESTREND) to estimate the human-induced and climate-induced vegetation changes. Two typical regions in the Horqin Sandy Land of China were selected as study areas. We first detected vegetation dynamics between 2000–2014 using Sen’s slope estimation and the Mann–Kendall test detection method (SMK) based on the Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index (NDVI) time series, then used RESTREND to profile human modifications in areas of significant vegetation change. RESTREND was optimized using statistical and trajectory analysis to automatically identify flexible spatially homogeneous neighborhoods, which were essential for determining the reference areas. The results indicated the following. (1) Obvious vegetation increases happened in both regions, but Naiman (64.1%) increased more than Ar Horqin (16.8%). (2) Climate and human drivers both contributed to significant changes. The two factors contributed equally to vegetation change in Ar Horqin, while human drivers contributed more in Naiman. (3) Human factors had a stronger influence on ecosystems, and were more responsible for vegetation decreases in both regions. Further evidences showed that the primary human drivers varied in regions. Grassland eco-management was the key driver in Ar Horqin, while farming was the key factor for vegetation change in Naiman.

In this paper, a comprehensive analysis of spatiotemporal characteristics of reverse-dip slope toppling is conducted by taking the Xiaodongcao slope as an example. First, a spatial partitioning analysis of toppling deformation is performed based on the field reconnaissance and interpretation of engineering geological data. Then, the variations of toppling deformation in time domain are analyzed for different areas of the slope with monitored data of surface displacement. Finally, the isochrones of toppling displacement evolution are constructed by using inverse distance weighted interpolation of surface monitoring data at discrete locations. The results presented in the study have shown that: (1) the displacement at the rear of the slope is dominated by vertical deformation, whereas the horizontal deformation is predominant at the slope front which also controls the overall deformation of the bank slope; (2) the overall evolution of slope deformation is dominated by the strip area at the center of the slope. In particular, the overall deformation of the slope lags behind the central region, and the displacement in this strip area could trigger an overall displacement of the bank slope. It is thus inferred that the stripe area serves as the locked segment for the toppling deformation of the slope.

Laterally loaded piles may entail large deformation under some circumstances such as ship impact, earthquake and long-term horizontal thrust of arch bridges, etc. The arch bridges are especially sensitive to horizontal displacement of foundation. Lateral load test was performed on a full-scale pile in virgin soil and pile with post-grouted soil around pile. Further numerical simulation analysis was carried out by PLAXIS3D based on field test result. The analytical and measured results are found to be in fairly satisfactory agreement. According to test results of single pile, lateral response of piles largely depends on profile of limiting force in shallow soil. Horizontal bearing capacity of bored piles is improved via grouting technique. For pile with post-grouted soil around, horizontal displacement of pile top is significantly reduced. The maximum bending moments of pile with grouting decrease dramatically. The grouted upper soil expands range of effective soil around pile, and more horizontal thrust was shared.

Discriminating human-induced vegetation change is essential for sustainable managements of arid and semi-arid ecosystems. Residual Trends method (RESTREND), an effective quantitative method, has been widely used to discriminate human-induced vegetation changes in specific arid and semi-arid ecosystems. However, how to define homogeneous spatial neighborhood to determine reference pixel for estimating potential climate-solely-induced vegetation growth is still a challenge. This paper firstly detected vegetation dynamics in ArHorqin Banner of China from 2000 to 2014 by Mann-Kendall method, and then used RESTREND to profile human-induced changes. We optimized strategy in RESTREND by using statistical analysis and trajectory analysis to automatically define flexible homogeneous neighborhood. Results indicated that 18.6% of study area had significantly changes. Both climate change and human activities contributed to the changes. The influence of human activities on vegetation dynamics is more than climate change, and it was the main driver for vegetation decrease in study area.

Land Use/Cover Change (LUCC) has gradually became an important direction in the research of global changes. LUCC is a complex system, and entropy is a measure of the degree of disorder of a system. According to land use information entropy, this paper analyzes changes in land use from the perspective of the system. Research on the entropy of LUCC structures has a certain “guiding role” for the optimization and adjustment of regional land use structure. Based on the five periods of LUCC data from the year of 1990 to 2010, this paper focuses on analyzing three types of LUCC entropies among counties in China—namely, Shannon, Renyi, and Tsallis entropies. The findings suggest that: (1) Shannon entropy can reflect the volatility of the LUCC, that Renyi and Tsallis entropies also have this function when their parameter has a positive value, and that Renyi and Tsallis entropies can reflect the extreme case of the LUCC when their parameter has a negative value., (2) The entropy of China’s LUCC is uneven in time and space distributions, and that there is a large trend during 1990–2010, the central region generally has high entropy in space.

A highly sensitive acetylcholinesterase (AChE) electrochemical biosensor for the quantitative determination of organophosphate pesticides (OPs) in vegetables and fruits based on palladium-copper nanowires (Pd-Cu NWs) was reported. AChE immobilized on the modified electrode could catalyze hydrolysis of acetylthiocholine chloride (ATCl), generating an irreversible oxidation peak. When exposed to the OPs, the activity of the AChE was inhibited and the current significantly decreased. The detection mechanism is based on the inhibition of AChE. The Pd-Cu NWs not only provide a large active surface area (0.268 ± 0.01) cm 2 for the immobilization of AChE, which was approximately 3.8 times higher than the bare glass carbon electrode, but also exhibit excellent electro-catalytic activity and remarkable electron mobility. The biosensor modified with Pd-Cu NWs displayed a good affinity to ATCl and catalyzed hydrolysis of ATCl, with a low Michaelis–Menten constant ( K M ) of 50.56 μM. Under optimized conditions, the AChE-Cs/Pd-Cu NWs/GCE biosensor detected malathion with wide linear ranges of 5–1000 ppt and 500–3000 ppb, and the low detection limit was 1.5 ppt (4.5 pM). In addition, the OPs biosensor has been applied to the analysis of malathion in commercial vegetable and fruit samples, with excellent recoveries in the range of 98.5%–113.5%. This work provides a simple, sensitive and effective platform for biosensors and exhibits future potential in practical application for the OPs assay.

This paper introduces the statistical methods and application for the quantitative analysis of a site-specific landslide risk on the north slope of Lishan Mountain which is regarded being in an active state that could become a disastrous loess landslide. Based on the theory of probability statistics (Monte Carlo statistical methods) and the slope failure mechanical model, the overall failure probability and the local failure probabilities of the Lishan landslide were calculated. The results of the failure probability and stability analysis showed that the northern slope of Lishan Mountain is highly prone to lose stability during seasonal intense rainfall, whereas it is stable but still exhibits failure probability under arid conditions. The analysis of the safety margin and local failure probability evidenced that the upper part of the slope is less stable than the lower part. Under the intense rainfall condition, the local failure probability and hazard of local unstable failure of the slope will increase. According to the calculation results, it is deduced that the landslide on the north of Lishan Mountain will be a gradual process evolving from the local slope failure to an overall unstable failure.

Water resources are one of the important factors that influence regional crop production and the food security of humans. Most traditional models of crop water demand analysis are built on the basis of a certain crop or macroscopic analysis, which neglect regional crop allocation and the difference of water demand in different crop growing periods. In this paper, a new assessing model, the satisfied degree of crop water requirement, is developed to assess the impacts of water resources on production of six main food crops in China. The six main food crops are spring wheat, winter wheat, corn, early season rice, middle-season rice and late rice. The results show that: (1) there are serious risks of water shortage in China, even in south China with its abundant precipitation; (2) the satisfied degree of crop water demand represents great temporal-spatial changes. On spatial distribution the risks are high in major bases of food production due to influences of cropping system and crop-combinations. Northwest China is a special interesting case. In seasonal fluctuation water shortage is severe in March and September. These risks seriously restrict food production in China. The results also show that the strategic measures of water resources management must be chosen carefully to deal with food security and regional sustainable development in China.