Let i ≥ 2, ∆ ≥ 0, 1 ≤ a ≤ b − ∆, n > (a+b)(ib+2m−2) a + n and δ(G) ≥ b 2 a + n + 2m, and let g, f be two integer-valued functions defined on V (G) such that a ≤ g(x) ≤ f (x) − ∆ ≤ b − ∆ for each x ∈ V (G). In this article, it is determined that G is a fractional (g, f, n , m)-critical deleted graph if max{d 1 , d 2 , • • • , d i } ≥ b(n+n) a+b for any independent subset {x 1 , x 2 ,. .. , x i } ⊆ V (G). The result is tight on independent set degree condition.
The focal point of this study is to assess the efficacy of a state-ofthe-art optimization technique namely, particle swarm optimization (PSO) for enhancing the performance of the artificial neural network (ANN) in modeling the seismic landslides at Ludian districts, China. Twelve geological and hydrological landslide-conditioning factors namely, elevation, lithology, slope degree, slope aspect, stream power index, peak ground acceleration, topographic wetness index, distance to river, distance to road, distance to fault, normalized difference vegetation index and plan curvature were considered within a geographic information system (GIS). After achieving the optimal structure of the multilayer perceptron neural network, the PSO algorithm was applied to improve its efficiency. The landslide susceptibility maps were generated in a GIS environment and area under the curve (AUC) criterion was used to assess the integrity of employed predictive models. The results showed that after applying the PSO algorithm, AUC experiences a significant increase from 0.765 to 0.825 in the validation phase. Moreover, respective AUCs of 0.812 and 0.828 obtained for the training phase of ANN and PSO-ANN reveal the efficiency of the proposed algorithm in improving the ANN accuracy. ARTICLE HISTORY
In this paper, we determine the Geometric-arithmetic indexand Zagreb indicesof fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs.
As urban construction has been leaping forward recently, large-scale land subsidence has been caused in Kunming due to the special hydrogeological conditions of the city; the subsidence scope has stretched out, and the subsidence rate has been rising year by year. As a consequence, Kunming’s sustainable development has seriously hindered. The PS-InSAR (Persistent Scatterer Interferometric Synthetic Aperture Radar) and the SBAS-InSAR (Small Baseline Subsets Interferometric Synthetic Aperture Radar) technologies were adopted to process the descending Sentinel-1A data stacks from July 2018 to November 2020 to monitor the land subsidence of Kunming, so as to ensure the sustainable development of the city. Moreover, the causes were analyzed. As revealed by the results, (1) the overall subsidence trend of Kunming was large in the south (Dian lakeside), whereas it was relatively small in the north. The significant subsidence areas showed major distributions in Xishan, Guandu and Jining district. The maximal average subsidence rates of PS-InSAR and SBAS-InSAR were −78 mm/a and −88 mm/a, respectively. (2) The ground Subsidence field of Kunming was analyzed, and the correlation coefficient R2 of the two methods was reported as 0.997. In comparison with the leveling data of the identical period, the root mean square error (RMSE) is 6.5 mm/a and 8.5 mm/a, respectively. (3) Based on the urban subway construction data, geological structure, groundwater extraction data and precipitation, the causes of subsidence were examined. As revealed by the results, under considerable urban subways construction, special geological structures and excessive groundwater extraction, the consolidation and compression of the ground surface could cause the regional large-area subsidence. Accordingly, the monthly average precipitation in Kunming in the identical period was collected for time series analysis, thereby indicating that the land subsidence showed obvious seasonal variations with the precipitation. The results of this study can provide data support and facilitate the decision-making for land subsidence assessment, forecasting and construction planning in Kunming.
In complex mountainous areas where earthquakes are frequent, landslide hazards pose a significant threat to human life and property due to their high degree of concealment, complex development mechanism, and abrupt nature. In view of the problems of the existing landslide hazard susceptibility evaluation model, such as poor effectiveness and inaccuracy of landslide hazard data and the need for experts to participate in the calculation of a large number of evaluation factor weight classification statistics. In this paper, a combined SBAS-InSAR (Small Baseline Subsets-Interferometric Synthetic Aperture Radar) and PSO-RF (Particle Swarm Optimization-Random Forest) algorithm was proposed to evaluate the susceptibility of landslide hazards in complex mountainous regions characterized by frequent earthquakes, deep river valleys, and large terrain height differences. First, the SBAS-InSAR technique was used to invert the surface deformation rates of the study area and identified potential landslide hazards. Second, the study area was divided into 412,585 grid cells, and the 16 selected environmental factors were analyzed comprehensively to identify the most effective evaluation factors. Last, 2722 landslide (1361 grid cells) and non-landslide (1361 grid cells) grid cells in the study area were randomly divided into a training dataset (70%) and a test dataset (30%). By analyzing real landslide and non-landslide data, the performances of the PSO-RF algorithm and three other machine learning algorithms, BP (back propagation), SVM (support vector machines), and RF (random forest) algorithms were compared. The results showed that 329 potential landslide hazards were updated using the surface deformation rates and existing landslide cataloguing data. Furthermore, the area under the curve (AUC) value and the accuracy (ACC) of the PSO-RF algorithm were 0.9567 and 0.8874, which were higher than those of the BP (0.8823 and 0.8274), SVM (0.8910 and 0.8311), and RF (0.9293 and 0.8531), respectively. In conclusion, the method put forth in this paper can be effectively updated landslide data sources and implemented a susceptibility prediction assessment of landslide disasters in intricate mountainous areas. The findings can serve as a strong reference for the prevention of landslide hazards and decision-making mitigation by government departments.
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