Variations of Enclosing Problem Using Axis Parallel Square(s): A General Approach

Let P be a set of n?points in two dimensional plane. For each point , we locate an axis- parallel unit square having one particular side passing through p and enclosing the maximum number of points from P. Considering all points , such n?squares can be reported in O(nlogn)?time. We show that this result can be used to (i) locate m>(2)?axis-parallel unit squares which are pairwise disjoint and they together enclose the maximum number of points from P (if exists) and (ii) find the smallest axis-parallel square enclosing at least k points of P , .

Zonal disintegration phenomenon in enclosing rock mass surrounding deep tunnels——Elasto-plastic analysis of stress field of enclosing rock mass

The zonal disintegration phenomenon （ZDP） is a typical phenomenon in deep block rock masses. In order to investigate the mechanism of ZDP, an improved non-linear Hock-Brown strength criterion and a bi-linear constitutive model of rock mass were used to analyze the elasto-plastic stress field of the enclosing rock mass around a deep round tunnel. The radius of the plastic region and stress of the enclosing rock mass were obtained by introducing dimensionless parameters of radial distance. The results show that tunneling in deep rock mass causes a maximum stress zone to appear in the vicinity of the boundary of the elastic and the plastic zone in the surrounding rock mass. Under the compression of a large tangential force and a small radial force, the rock mass in the maximum stress zone was in an approximate uniaxial loading state, which could lead to a split failure in the rock mass.

Theory and Experiments on Enclosing Control of Multi-Agent Systems

This paper proposes a control strategy called enclosing control.This strategy can be described as follows:the followers design their control inputs based on the state information of neighbor agents and move to specified positions.The convex hull formed by these followers contains the leaders.We use the single-integrator model to describe the dynamics of the agents and proposes a continuous-time control protocol and a sampled-data based protocol for multi-agent systems with stationary leaders with fixed network topology.Then the state differential equations are analyzed to obtain the parameter requirements for the system to achieve convergence.Moreover,the conditions achieving enclosing control are established for both protocols.A special enclosing control with no leader located on the convex hull boundary under the protocols is studied,which can effectively prevent enclosing control failures caused by errors in the system.Moreover,several simulations are proposed to validate theoretical results and compare the differences between the three control protocols.Finally,experimental results on the multi-robot platform are provided to verify the feasibility of the protocol in the physical system.

Minimal Enclosing of an MPT (v,λ) in a TS (v+1,μ)

Let MPT ( v,λ ) denote a maximum packing of triples of order v with index λ and TS ( u,λ ) denote a triple system of order u with index λ . In this paper, for v ≥6, we determine necessary and sufficient conditions for enclosing an MPT ( v,λ ) in a TS ( v+1,λ+m ) with one extra point and minimal increase in λ .

Minimal Enclosing of an MPT (v,λ) in a TS (u,λ+1)

Let MPT (v,λ) denote a maximum packing of triples of order v with index λ and TS (u,λ) denote a triple system of order u with index λ. In this paper, for v≥6, we determine necessary and sufficient condition for enclosing an MPT (v,λ) in a TS (v+m,λ+1) with index λ increased by 1 and minimal increase in extra points.

OBSERVATION ON THE THERAPEUTIC EFFECT OF ENCLOSING NEEDLING UNDER CT ORIENTATION FOR TREATMENT OF ISCHEMIC CEREBRAL STROKE AND ITS INFLUENCE ON PLASMA NO

In the present paper, 61 cases of ischemic cerebral apoplexy were randomly divided into enclosing needling group (n=31) and scalpacupuncture group (n=30). After 30 sessions of treatment, there was a significant difference between the two groups in the therapeutic effect (P<0.05), indicating enclosing needling being superior to scalpacupuncture. Both enclosing needling and scalpacupuncture could lower plasma NO content while the former was more apparent in lowering plasma NO level.

Weather influenced nestling growth of an insectivorous but not a granivorous grassland passerine in Argentina

Nestling growth of birds can be affected by weather fluctuations.In general,it is expected that higher temper-atures favor growth by improving food availability and nestling metabolism,while rain hinders it by reducing foraging efficiency.However,most of these patterns have been described in insectivorous cavity-nesting birds in temperate forests.We tested these predictions in two neotropical grassland ground-nesting birds with contrasting nestling diets and therefore potentially different responses to weather.We measured nestlings of the Hellmayr’s Pipit(Anthus hellmayri,an insectivorous passerine)and the Grassland Yellow-Finch(Sicalis luteola,which feeds its nestlings exclusively with seeds)during three breeding seasons(2017-2020)in central-eastern Argentina.We took measurements of tarsus and body mass,modeled growth curves using nonlinear mixed-effects models,and evaluated the effects of minimum daily temperature and precipitation during the growth period and the 30 days prior to hatching.For pipits(60 nestlings from 21 nests),minimum temperatures during the growth period were positively associated with tarsus and body mass asymptotes.Also,there was a positive association between precipitation during the pre-hatching period and tarsus asymptote.Conversely,none of the weather variables analyzed had significant effects on nestling growth of finches(131 nestlings from 35 nests).Dietary contrast between species may explain the different results.Arthropod activity and abundance can be affected by weather variations within the span of a breeding season,whereas seeds may depend on conditions from previous years,making the effects harder to detect.Fledglings with reduced asymptotic size can have reduced chances of sur-vival.Hence,pipit populations could be impacted if they experience cold and dry conditions during their breeding season,which is of major relevance in the current context of climate change.

Responses of soil stoichiometry and soil enzyme activities in the different distance around opencast coal mine of the Hulun Buir Grassland of China

The objectives of this study were to explore the changes in soil stoichiometry and enzyme activities at different distances from an opencast coal mine in the Hulun Buir Grassland of China. Four transects were established on north and east sides of the opencast coal mining area, and samples were collected at 50 m, 550 m, and 1550 m from the pit on each transect. Control samples were collected from a grassland station 8 km from the opencast coal mining area that was not disturbed by mining. Four replicate soil samples were collected at each point on the four transects. Soil physicochemical properties and enzyme activities were determined, and correlations between soil properties and stoichiometric ratios and enzyme activities were explored using redundancy analysis. The increase in distance from mining did not significantly affect soil properties, although soil urease activity was significantly lower than that of the control area. Soil properties 1550 m from the mine pit were similar to those at the grassland control. In addition, soil total nitrogen had the greatest effect on soil stoichiometry, and soil total potassium had the greatest effect on soil enzyme activities. Coal dust from opencast mining might be the main factor affecting soil stoichiometry and enzyme activities. The results of this study provide direction for the next step in studying the influence of mining areas on soil properties and processes.

Effects of Enclosure on Grassland Ecological and Economic Benefits in Northern China

Grasslands in northern China serve the country as both an ecological barrier and a livestock production base.There,installing enclosures has been becoming the major grassland restoration measure adopted by many local governments.However,the effects of restoration on both ecological and production benefits of grassland remain unclear for implemented grassland restoration policies.Therefore,a representative rangeland in northern China,the Maodeng pasture in Inner Mongolia Autonomous Region was selected as the study area,and remote sensing monitoring analyses were carried out to quantify the ecological benefits and economic benefits from 2015 to 2021.The results showed that:1) in terms of ecological benefits,the grassland area with a grassland coverage rate of more than 60% accounts for 32.3% of the regional area,and 86.4% of its grassland grew significantly better than the same period in2015,showing a significant improvement in grassland growth.Using the average amount of carbon per unit area as the ecological benefit evaluation index,it increased by 27.1% to 32.48Tg C/yr from 2015 to 2021.2) In terms of economic benefits,both theoretical grass production and livestock carrying capacity increased from 2015 to 2021.Compared to 2015,the theoretical grass production in 2021 increased by 24.8% to 71 900 t.The livestock carrying capacity reached 52 100 sheep units in 2021,nearly 11 000 sheep units more than that in 2015.During the study period,multiple economic indicators(on a per capita basis of permanent residents) for the pastoral area of Xilinhot City to which the Maodeng pasture belongs,have grown steadily.Per capita total income rose from 29 630 yuan(RMB) in2015 to 62 859 yuan(RMB) in 2021.Relying on grassland resources to develop the pastoral ecology also broadens the potential economic development space.Overall,the establishment of the reserve and the experiment of implanting an enclosure policy have had a significant and positive impact on Maodeng pasture’s development from both an ecological and economic perspective.With the support of scientific evidence,enclosure policy can be extended to more than 110 000 km~2 of grasslands in northern China with similar precipitation and temperature conditions,enhancing the productive and ecological potential of grasslands.The above research results will contribute to the scientific formulation of grassland pasture quality improvement plans in northern China.

Reasonable grazing may balance the conflict between grassland utilization and soil conservation in the semi-arid hilly areas, China

Soil erosion caused by unsustainable grazing is a major driver of grassland ecosystem degradation in many semi-arid hilly areas in China.Thus,grazing exclusion is considered as an effective method for solving this issue in such areas.However,some ecological and economic problems,such as slow grassland rejuvenation and limited economic conditions,have become obstacles for the sustainable utilization of grassland ecosystem.Accordingly,we hypothesized that the conflict between grassland use and soil conservation may be balanced by a reasonable grazing intensity.In this study,a two-year grazing fence experiment with five grazing intensity gradients was conducted in a typical grassland of the Loess Plateau in China to evaluate the responses of vegetation characteristics and soil and water losses to grazing intensity.The five grazing intensity gradients were 2.2,3.0,4.2,6.7,and 16.7 goats/hm2,which were represented by G1-G5,respectively,and no grazing was used as control.The results showed that a reasonable grazing intensity was conducive to the sustainable utilization of grassland resources.Vegetation biomass under G1-G4 grazing intensity significantly increased by 51.9%,42.1%,36.9%,and 36.7%,respectively,compared with control.In addition,vegetation coverage increased by 19.6%under G1 grazing intensity.Species diversity showed a single peak trend with increasing grazing intensity.The Shannon-Wiener diversity index under G1-G4 grazing intensities significantly increased by 22.8%,22.5%,13.3%,and 8.3%,respectively,compared with control.Furthermore,grazing increased the risk of soil erosion.Compared with control,runoff yields under G1-G5 grazing intensities increased by 1.4,2.6,2.8,4.3,and 3.9 times,respectively,and sediment yields under G1-G5 grazing intensities were 3.0,13.0,20.8,34.3,and 37.7 times greater,respectively,than those under control.This result was mainly attributed to a visible decrease in litter biomass after grazing,which decreased by 50.5%,72.6%,79.0%,80.0%,and 76.9%,respectively,under G1-G5 grazing intensities.By weighing the grassland productivity and soil conservation function,we found that both two aims were achieved at a low grazing intensity of less than 3.5 goats/hm2.Therefore,it is recommended that grassland should be moderately utilized with grazing intensity below 3.5 goats/hm2 in semi-arid hilly areas to achieve the dual goals of ecological and economic benefits.The results provide a scientific basis for grassland utilization and health management in semi-arid hilly areas from the perspective of determining reasonable grazing intensity to maintain both grassland production and soil conservation functions.

Grasslands Response to Livestock Grazing Intensity in the Austral Pampas(Argentina):Testing the Intermediate Disturbance Hypothesis

Livestock grazing has a significant impact on natural grasslands,with approximately one-third of the world’s land area dedicated to this industry.Around 20%of global grasslands are highly degraded due to overgrazing,affecting their productivity and conservation capacity.Best practices are required to ensure sustainable livestock production that supports biodiversity.The Intermediate Disturbance Hypothesis(IDH)suggests that environments with moderate levels of disturbance exhibit a higher species diversity.Moderate grazing can reduce the dominance of certain species,thereby enhancing plant diversity.However,concerns arise regarding the increase of exotic and unpalatable species under moderate grazing levels,complicating grassland conservation efforts.The impact of livestock grazing on the functional structure of grasslands depends on factors such as grazing intensity,livestock species,and environmental conditions.Variations in grazing intensity may increase specific and functional diversity under moderate grazing,potentially masking the presence of invasive exotic species.In the Austral Pampas(Pampean phytogeographic province,Buenos Aires,Argentina),grasslands face various pressures from domestic livestock grazing that endanger their integrity if not properly managed.Therefore,our study aims to investigate potential differences in species richness and diversity,functional diversity,exotic plant abundance,and the number and distribution of plant functional groups across varying grazing intensities.The IDH is utilized as a tool to regulate livestock pressure for grassland conservation.Species and functional diversity indices were used to assess the impact of grazing on grassland diversity.Moderate grazing increased species and functional diversity,while intensively grazed or ungrazed areas showed reduced diversity.Livestock presence influenced the balance between native and exotic plants,with ungrazed areas having higher native plant abundance and grazed areas exhibiting higher exotic plant abundance.Grazing also influenced the composition of functional groups,with grazing-avoiding species being more prevalent in heavily grazed areas.Principal Component Analysis revealed a clear association between vegetation composition and livestock grazing intensity.These findings offer valuable insights into effectively managing grazing intensity for biodiversity conservation purposes.

Grassland-type ecosystem stability in China differs under the influence of drought and wet events

Ecological stability is a core issue in ecological research and holds significant implications forhumanity. The increased frequency and intensity of drought and wet climate events resulting from climatechange pose a major threat to global ecological stability. Variations in stability among different ecosystemshave been confirmed, but it remains unclear whether there are differences in stability within the sameterrestrial vegetation ecosystem under the influence of climate events in different directions and intensities.China's grassland ecosystem includes most grassland types and is a good choice for studying this issue.This study used the Standardized Precipitation Evapotranspiration Index-12 (SPEI-12) to identify thedirections and intensities of different types of climate events, and based on Normalized DifferenceVegetation Index (NDVI), calculated the resistance and resilience of different grassland types for 30consecutive years from 1990 to 2019 (resistance and resilience are important indicators to measurestability). Based on a traditional regression model, standardized methods were integrated to analyze theimpacts of the intensity and duration of drought and wet events on vegetation stability. The resultsshowed that meadow steppe exhibited the highest stability, while alpine steppe and desert steppe had thelowest overall stability. The stability of typical steppe, alpine meadow, temperate meadow was at anintermediate level. Regarding the impact of the duration and intensity of climate events on vegetationecosystem stability for the same grassland type, the resilience of desert steppe during drought was mainlyaffected by the duration. In contrast, the impact of intensity was not significant. However, alpine steppewas mainly affected by intensity in wet environments, and duration had no significant impact. Ourconclusions can provide decision support for the future grassland ecosystem governance.

Improving the Accuracy of Vegetation Index Retrieval for Biomass by Combining Ground-UAV Hyperspectral Data-A New Method for Inner Mongolia Typical Grasslands

Grassland biomass is an important parameter of grassland ecosystems.The complexity of the grassland canopy vegetation spectrum makes the long-term assessment of grassland growth a challenge.Few studies have explored the original spectral information of typical grasslands in Inner Mongolia and examined the influence of spectral information on aboveground biomass(AGB)estimation.In order to improve the accuracy of vegetation index inversion of grassland AGB,this study combined ground and Unmanned Aerial Vehicle(UAV)remote sensing technology and screened sensitive bands through ground hyperspectral data transformation and correlation analysis.The narrow band vegetation indices were calculated,and ground and airborne hyperspectral inversion models were established.Finally,the accuracy of the model was verified.The results showed that:(1)The vegetation indices constructed based on the ASD FieldSpec 4 and the UAV were significantly correlated with the dry and fresh weight of AGB.(2)The comparison between measured R^(2) with the prediction R^(2) indicated that the accuracy of the model was the best when using the Soil-Adjusted Vegetation Index(SAVI)as the independent variable in the analysis of AGB(fresh weight/dry weight)and four narrow-band vegetation indices.The SAVI vegetation index showed better applicability for biomass monitoring in typical grassland areas of Inner Mongolia.(3)The obtained ground and airborne hyperspectral data with the optimal vegetation index suggested that the dry weight of AGB has the best fitting effect with airborne hyperspectral data,where y=17.962e^(4.672x),the fitting R^(2) was 0.542,the prediction R^(2)was 0.424,and RMSE and REE were 57.03 and 0.65,respectively.Therefore,established vegetation indices by screening sensitive bands through hyperspectral feature analysis can significantly improve the inversion accuracy of typical grassland biomass in Inner Mongolia.Compared with ground monitoring,airborne hyperspectral monitoring better reflects the inversion of actual surface biomass.It provides a reliable modeling framework for grassland AGB monitoring and scientific and technological support for grazing management.

Future Development Direction of the Restoration of Mountains,Rivers,Forests,Farmlands,Lakes,and Grasslands and the Faced Problems

In this paper,the definition,connotation,and internal relationship of mountains,rivers,forests,farmlands,lakes,and grasslands in China are elaborated,and the current situation of ecological restoration projects for mountains,rivers,forests,farmlands,lakes,and grasslands was introduced.Moreover,the problems that have arisen in the specific implementation process of pilot projects were analyzed,such as unclear target positioning,inaccurate analysis of ecological problems,insufficient engineering design systematicness,weak operability of evaluation standards,and weak coordination in engineering management.The development direction and major needs for the protection and restoration of mountains,rivers,forests,farmlands,lakes,and grasslands in the future have been proposed from four aspects:theoretical research,engineering design,effect evaluation,and monitoring and supervision.

Correlation Analysis between the Evapotranspiration Quantity and Climatic Factors of Artificial Grassland in Three River Sources Areas

Based on observation data from the mini-type automatic weather station,the evapotranspiration quantity of reference crops from artificial grassland in three river sources areas was estimated by the method of FAO Penman-Monteith.The actual evapotranspiration quantity of grassland was calculated according to the synthetic crop coefficients referenced by FAQ-56,and the change of the actual evapotranspiration quantity of artificial grassland in three river sources areas as well as the relationship between the evapotranspiration quantity and climatic factors were studied.The results suggested that the seasonal change of actual evapotranspiration quantity in grassland was expressed in a single peak curve with the peak in the middle August,and daily transpiration quantity in summer was significantly larger than that in winter.The evapotranspiration was significantly correlated with air temperature,solar radiation and relative humidity,but not significantly correlated with wind speed.Effects of climatic factors on the evapotranspiration quantity of artificial grassland were ordered as follow:air temperature(T)>solar radiation(Ra)>relative humidity(RH)>wind speed(u2).

Advances in Grassland Ecosystem Research in Northern Tibetan Plateau

With the aggravation of global change, the response and adaptation of the unique ecosystem in Qinghai-Tibet Plateau to global change have been increasingly concerned by scientific community day by day, which makes the sensitivity and fragility of this ecosystem in response to global change widely recognized by scholars. On the basis of introducing the present research process on the degenerate mechanisim, measures of and approaches to recovery, carbon cycle and primary productivity toward global change, we put forward several propositions on studying the alpine grassland ecosystem in Northern Tibetan Plateau.

Temporal-spatial Changes in Inner Mongolian Grassland Degradation during Past Three Decades

[Objective] This study aimed to analyze the temporal-spatial variation of Inner Mongolian grassland degradation during past three decades. [Method] The dis- tribution characteristics of grassland were described by land use types supervised classification with TM/ETM. Then, temporal-spatial changes of grassland coverage were quantified by the mean of maximum vegetation coverage in last 30 years. Lastly, the grassland degradation reasons were explored through statistic analysis between the grassland coverage and precipitation, temperature and grazing intensity. [Result] The grassland degradation index of Inner Mongolia was increased from 1.38 to 1.68, and the smallest was 1.28 in 2005s. Grassland degradation and improve- ment were concurrent after 1980s, but grassland degradation was the major change trend for Inner Mongolia grassland. The area of grassland degradation was enlarged from 18.08×10^4 km2 in 1980s to 22.47×10^4 km2 in 2010s on the whole and distribu- tion range was shifted from central-eastern to west in Inner Mongolia that mainly distributed on Hulun Buir and Xilin Gol grassland in 1980s and Ordos and Alax grassland in 2010s. The grassland area of degradation had a rising trend form 1980s to 1995s, then reduced to 10.8x104 km2 in 2005s, and decreased in 2010s, which mainly speared in the west of Xilin Gol grassland. [Conclusion] Inner Mongo-lian grassland degradation were become more seriously in last 30 years because that temperature, precipitation and graze intensities change, which not performance on decreasing coverage but grassland areas.

Effects of Grassland Eco-Protection Compensation and Reward System

Grassland ecological protection compensation and reward policy is the largest-scale investment concerning themost extensive areas since foundation of the PRC. It will be the long-term implementationpolicy for grassland ecological protection. In this study,based on macro-perspective, the policy effects ofgrasslandproductivity, ecological protection, animal husbandryoutput, pastoralists＇ income were ana- lyzed. The resultsshow that, afterimplementation of the policy, naturalgrass production and grasslandtheoretical stocking rateincreased. The averagenatural grasslandlivestockoverloading ratedecreased significantly, comprehensivenationalgrasslandvegetation coverageis increasing. Besides, adult cattleandbeef yield arefluctuated. Sheep head, adult sheep, sheep production, milk productionincreasedin varying degrees. The per capita netincomeof farmers and pastoralists, livestock income, the proportion oflivestockincomewere higher than those beforeimplementation of the policy.

Target-enclosing affine formation control of two-layer networked spacecraft with collision avoidance

This paper addresses a target-enclosing problem for multiple spacecraft systems by proposing a two-layer affine formation control strategy. Compared with the existing methods,the adopted two-layer network structure in this paper is generally directed, which is suitable for practical space missions. Firstly, distributed finite-time sliding-mode estimators and formation controllers in both layers are designed separately to improve the flexibility of the formation control system. By introducing the properties of affine transformation into formation control protocol design,the controllers can be used to track different time-varying target formation patterns. Besides, multilayer time-varying encirclements can be achieved with particular shapes to surround the moving target. In the sequel, by integrating adaptive neural networks and specialized artificial potential functions into backstepping controllers, the problems of uncertain Euler-Lagrange models, collision avoidance as well as formation reconfiguration are solved simultaneously. The stability of the proposed controllers is verified by the Lyapunov direct method. Finally, two simulation examples of triangle formation and more complex hexagon formation are presented to illustrate the feasibility of the theoretical results.

Study on Evaluation of Grassland Eco-system Coordination Based on Environment-Economy Coordination Degree Model

Based on the current studies,a reasonable evaluation index system was established by the development coordination of analysis systems.Furthermore,taking grassland resources in Nagchu Tibet as an example and according to the coordination degree evaluation model of the environmental economy system,a coordination degree evaluation index system of environmental economy was set up,and the coordination conditions of 11 counties in Nagchu district were analyzed by coordination function.