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Landslides are a common hazard in the highly urbanized hilly areas in Chittagong Metropolitan Area (CMA), Bangladesh. The main cause of the landslides is torrential rain in short period of time. This area experiences several landslides each year, resulting in casualties, property damage, and economic loss. Therefore, the primary objective of this research is to produce the Landslide Susceptibility Maps for CMA so that appropriate landslide disaster risk reduction strategies can be developed. In this research, three different Geographic Information System-based Multi-Criteria Decision Analysis methods—the Artificial Hierarchy Process (AHP), Weighted Linear Combination (WLC), and Ordered Weighted Average (OWA)—were applied to scientifically assess the landslide susceptible areas in CMA. Nine different thematic layers or landslide causative factors were considered. Then, seven different landslide susceptible scenarios were generated based on the three weighted overlay techniques. Later, the performances of the methods were validated using the area under the relative operating characteristic curves. The accuracies of the landslide susceptibility maps produced by the AHP, WLC_1, WLC_2, WLC_3, OWA_1, OWA_2, and OWA_3 methods were found as 89.80, 83.90, 91.10, 88.50, 90.40, 95.10, and 87.10 %, respectively. The verification results showed satisfactory agreement between the susceptibility maps produced and the existing data on the 20 historical landslide locations.

Improper disposal of solid waste obstructs drainage systems and pollutes surface water. Additionally, the dumping of unsorted garbage generates emissions and leachate, which harm local ecosystems and contribute to climate change. With Rewari City’s growing population, effective municipal solid waste management, including landfill site selection, is crucial. This study employs Geographic Information System (GIS), Analytical Hierarchical Process (AHP), and Weighted Linear Combination (WLC) methodologies to determine appropriate sites for landfills. The FAO, ALOS PALSAR DEM, Sentinel 2B images, Google Earth Pro, and interviews were employed to gather data. The results of the Analytic Hierarchy Process (AHP) indicate that 35.4% of the parameters under consideration are associated with Land Use Land Cover (LULC), whereas roads rank as the second most significant criterion, accounting for 24.0%. The WLC technique determined that 4.65 square kilometers were inappropriate for dump sites, while 0.11 square kilometers were extremely favorable. These findings can assist decision-makers in determining the order of importance for variables when selecting a landfill location.

Landfill has been taken to the bottom of the hierarchy of options for waste disposal but has been the most used method for urban solid waste disposal. However, landfill has become more difficult to implement because of its increasing cost, community opposition, and more restrictive regulations regarding the siting and operation of landfills. Land is a finite and scarce resource that needs to be used wisely. Appropriate allocation of landfills involves the selection of areas that are suitable for waste disposal. The present work describes a type of multi-criteria evaluation (MCE) method called weighted linear combination (WLC) in a GIS environment to evaluate the suitability of the study region for landfill. The WLC procedure is characterized by full tradeoff among all factors, average risk and offers much flexibility than the Boolean approaches in the decision making process. The relative importance weights of factors are estimated using the analytical hierarchy process (AHP). In the final aggregated suitability image, zones smaller than 20 hectares are eliminated from the allocation process. Afterwards, the land suitability of a zone is determined by calculating the average of the suitability of the cells belonging to that zone, a process called zonal land suitability. The application of the presented method to the Gorgan city (Iran) indicated that there are 18 zones for landfill with their zonal land suitability varying from 155.426117 to 64.149024. The zones were ranked in descending order by the value of their zonal land suitability. The results showed the use of GIS as a decision support system (DSS) available to policy makers and decision makers in municipal solid waste (MSW) management issues.

Let P and Q be two orthogonal projections in Hilbert space 𝓗. For α, β ∈ ℂ\\{0}, the lower bound and the upper bound of the pseudospectra of αP + βQ are obtained. The bounds are represented by the product PQ which are independent of the choice of scalars α, β. For α, β ∈ ℂ\\{0}, α + β ≠ ξ, ξ ∈ C, the bounds of the pseudospectra of αP + βQ − ξPQ are also obtained in the same way. Finally, two examples are constructed to show the effectiveness of the results.

The name of an author in the article by Saurette et al. (2022) [J. Synchrotron Rad. 29, 1198-1208] is corrected.The name of an author in the article by Saurette et al. (2022) [J. Synchrotron Rad. 29, 1198-1208] is corrected.

The decomposition of a square matrix into a sum of Pauli strings is a classical pre-processing step required to realize many quantum algorithms. Such a decomposition requires significant computational resources for large matrices. We present an exact and explicit formula for the Pauli string coefficients which inspires an efficient algorithm to compute them. More specifically, we show that up to a permutation of the matrix elements, the decomposition coefficients are related to the original matrix by a multiplication of a generalised Hadamard matrix. This allows one to use the Fast Walsh-Hadamard transform and calculate all Pauli decomposition coefficients in O ( N 2 log ⁡ N ) time and using O ( 1 ) additional memory, for an N × N matrix. A numerical implementation of our equation outperforms currently available solutions.

Flood susceptibility mapping and assessment is an important element of flood prevention and mitigation strategies because it identifies the most vulnerable areas based on physical characteristics that determine the propensity for flooding. This study aims to define the flood susceptibility zones for the territory of Slovakia using a multi-criteria approach, particularly the analytical hierarchy process (AHP) technique, and geographic information systems (GIS). Seven flood conditioning factors were chosen: hydrography—distance from rivers, river network density; hydrology—flow accumulation; morphometry—elevation, slope; and permeability—curve numbers, lithology. All factors were defined as raster datasets with the resolution of 50 x 50 m. The AHP technique was used to calculate the factor weights. The relative importance of the selected factors prioritized slope degree as the most important factor followed by river network density, distance from rivers, flow accumulation, elevation, curve number, and lithology. It was found that 33.1% of the territory of Slovakia is characterized by very high to high flood susceptibility. The flood susceptibility map was validated against 1513 flood historical points showing very good agreement between the computed susceptibility zones and historical flood events of which 70.9% were coincident with high and very high susceptibility levels, thus confirming the effectiveness of the methodology adopted.

The convex linear combination of the controllability pairs of linear continuous-time linear systems is defined and its properties are discussed. The main result is obtained using pure algebraic methods. In the illustrative examples different cases of linear convex combinations are analyzed.

Landslides have a profound impact on landscape geology, resulting in extensive devastation and loss of human lives. Mapping landslide susceptibility is crucial for effective land use planning in mountainous country like Ethiopia. This study was conducted in the upper Didessa sub-basin, southwestern parts of Ethiopia using Geographic Information System (GIS) and multi criteria evaluation (MCE) technique. This study employed a blend of primary data, encompassing field surveys and interviews with experts, as well as secondary data derived from diverse source, such as remote sensing data, digital soil maps, and geological maps. A total of eleven critical factors were employed to assess the triggers of landslides. These factors include slope, aspect, drainage density, topographic wetness index (TWI), stream power index (SPI), topographic ruggedness index (TRI), hypsometric integral, lithology, land use land cover (LULC), soil texture, and distance from roads. The analytical hierarchy process (AHP) method was used to determine the significance of each indicator through pairwise comparison matrix. The study area was categorized into different zones based on the susceptibility to landslides, namely very high, high, moderate, low, and very low. Results revealed that cultivated land had the highest likelihood of experiencing landslides, with a total of nine incidents out of 25, followed by built-up areas with seven landslides. Conversely, dense forests, sparse forests, and grazing land experienced a lower likelihood of landslides. Out of the 11 factors contributing to landslides, 24% of the surveyed region was deemed to have a moderate susceptibility, with 12% and 6% falling into the categories of high and very high susceptibility to landslides, respectively. The findings of this research provide important information for policymakers to develop efficient measures for preventing and reducing the risks of landslides.

The aim of this research is to investigate multi-criteria decision making [spatial multi-criteria evaluation (SMCE)], bivariate statistical methods [frequency ratio (FR), index of entropy (IOE), weighted linear combination (WLC)] and machine learning [support vector machine (SVM)] models for estimating landslide susceptibility at the Wuning area, China. A total of 445 landslides were randomly classified into 70% (311 landslides) and 30% (134 landslides) to train and validate landslide models, respectively. Fourteen landslide conditioning factors including slope angle, slope aspect, altitude, topographic wetness index, stream power index, sediment transport index, soil, lithology, NDVI, land use, rainfall, distance to road, distance to river and distance to fault were then studied for landslide susceptibility assessment. Performances of five studied models were evaluated using area under the ROC curve (AUROC) for training (success rate curve) and validation (prediction rate curve) datasets, statistical-based measures and tests. Results indicated that the area under the success rate curve for the FR, IOE, WLC, SVM and SMCE models was 88.32%, 82.58%, 78.91%, 85.47% and 89.96%, respectively, demonstrating that SMCE could provide the higher accuracy. The prediction capability findings revealed that the SMCE model (AUC = 86.81%) was also the highest approach among the five studied models, followed by the FR (AUC = 84.53%), the SVM (AUC = 81.24%), the IOE (AUC = 79.67%) and WLC (73.92%) methods. The landslide susceptibility maps derived from the above five models are reasonably accurate and could be used to perform elementary land use planning for hazard extenuation.