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Cutting edge preparation has become more important for tool performance. The micro-shape, radius and surface topography of the cutting edge play a significant role in the machining process. The cutting edge of solid carbide end mills has some micro-defects after grinding. For eliminating aforementioned problem, this study investigates drag finishing (DF) preparation for solid carbide end mills to reconstruct cutting edge micro-geometry. This paper is to present the design of DF experimental setup and analyze the characterization of various abrasive media (K3/600, K3/400, HSC 1/300 and HSO 1/100) on the evolution of the surface/roughness along the cutting edge. In parallel, the mechanism of material removal and the kinematics trajectory of the drag finishing are presented. In fact, the form factor (also called as “K-factor”) of the cutting edge micro-geometry is quantified. Comparing with four lapping media, the higher material removal rate (MRR) and the lower surface roughness are obtained by HSO 1/100 abrasive process. The results show that the cutting edge K-factor, MRR and surface topography are influenced by the abrasive particles size, composition and process time.

For a nonnegative integer k , a graph G is said to be k -factor-critical if G - Q admits a perfect matching for any Q ⊆ V ( G ) with | Q | = k . In this article, we prove spectral radius conditions for the existence of k -factor-critical graphs. Our result generalizes one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.

Soil erodibility (K-Factor) is one of the fundamental parameters to estimate its rainfall erosion through mathematical models such as RUSLE. Carrying out an erodibility analysis at different pedological depths allows identifying what would be its susceptibility to erosion processes. Soil unit parcel data obtained by long-term field measurements are required, ensuring that the analyzed sections remain uncovered throughout observation period, investing large amounts of time and money. However, the lack of a good and extensive field database is the main limitation to apply this methodology. The objective of this work was to analyze the spatial distribution of soil erodibility in different pedological profiles, through the implementation of satellite data of soil characteristics. The methodology consisted in delimiting and analyzing the environmental characteristics of the Ecuadorian basins, obtaining the clay, silt, sand SOC contents of the analyzed depths, determining the K-Factor values and comparing them with environmental layers. Basins delimitation and environmental characteristics were extracted from regional literature; soil layer contents were obtained from SoilGrids; K-Factor calculation was made from soil characteristics using Software R and QGIS; results comparison against the elevation and land cover parameters were carried out using QGIS. The results allowed to identify very small variations between pedological profiles; determine that clay and silt are the most incident elements of K-Factor; identify that Crop and Grass are coverages that concentrate on the highest values of K-Factor as well as the highest areas. This allows the administrators of the territory to generate measures to reduce soil loss.

With the current advancements in GIS and remote sensing methods, especially the use of high-precision LiDAR data, there is a significant disparity in the accuracy of morphological and soil data in erosion assessment. In current practice, a soil geospatial database is used to determine erodibility (K factor), often causing step changes in value within a field. However, soil properties influencing the K factor typically vary smoothly with terrain morphology and the soil catena pattern. Terrain morphology should therefore be taken into account, and it will lead to a more precise spatial distribution of K-factor values, significantly refining soil loss calculations and erosion control planning. For this purpose, the Czech Soil-Morphological Geospatial Database containing 1,417 soil samples was created. All soil samples were analyzed in the laboratory, and their K values were linked to morphometric characteristics (MMCH) based on geographical coordinates. The correlation dependences of the MMCH and spatial changes of K values, as deviations from the average values for the drainage areas within the closed erosion units, were calculated. The results of the methodology validation show a statistically high significant dependence between the K values obtained from field measurements and the values generated by the K-terrain model, created to automate the calculation. The tool can be used for down-scaling of K factor maps of large areas according to digital terrain model. To allow it to be applied more effectively to land management, a map with K terrain values for the entire Czech Republic was created with a resolution of 10 m.

Land degradation is accelerating in the Himalayan ecosystem, resulting in the loss of soil nutrients due to severe erosion. Soil erosion presents a significant environmental challenge, resulting in both on-site and off-site consequences, such as reduced soil productivity and siltation in reservoirs. Soil erodibility (K factor), an inherent soil property, determines the susceptibility of soils to erosion. Sampling across hilly and mountainous terrain pose challenges due to its complex landscape. Despite these challenges, it is essential to study K factor variations in different land use/land cover types to comprehend the threat of erosion. Digital soil mapping offers an opportunity to overcome this limitation by providing spatial predictions of soil properties. The objective of our study is to map the spatial distribution of soil erodibility using the Random Forest (RF) model, a machine learning method based on sampled in situ soil data and environmental covariates. We collected 556 surface soil samples from the mountainous catchment (Tehri dam catchment) using the stratified random sampling approach. The model performed satisfactorily in both training ( r 2  = 0.91; RMSE = 0.00185) and testing ( r 2  = 0.45; RMSE = 0.00318) phases. Subsequently, we generated a digital map with a resolution of 12.5 m to depict the distribution of the K factor. Our analysis revealed that key environmental variables influencing the prediction of the K factor included geology, mean NDVI, and climatic factors. The average K factor value was estimated at 0.0304 and ranging from 0.0251 to 0.0400 t ha h ha −1  MJ −1  mm −1 . A higher K factor was observed in the barren land (0.0344) primarily located in the higher and trans-Himalayan region of seasonally snow-covered areas. These areas typically feature young soils with weak soil formation and unstable soil aggregates. Subsequently cropland/cultivated soils (0.0307) exhibited higher K factor values due to the breakdown of soil aggregates by ploughing activities and exposing carbon to decomposition. The average K factor value of evergreen (0.0294) and deciduous (0.0295) forests were the lowest compared to other land use/land cover types indicating the role of forests in resisting soil erosion. By assessing and predicting soil erodibility, land planners and farmers can implement erosion control measures to protect soil health, prevent sedimentation in water bodies, and sustain agricultural productivity in the Himalayas.

A graph G of order n is said to be k -factor-critical for integers 1 ≤ k < n , if the removal of any k vertices results in a graph with a perfect matching. 1- and 2-factor-critical graphs are the well-known factor-critical and bicritical graphs, respectively. A k -factor-critical graph G is called minimal if for any edge e ∈ E ( G ) , G - e is not k -factor-critical. In 1998, O. Favaron and M. Shi conjectured that every minimally k -factor-critical graph of order n has the minimum degree k + 1 and confirmed it for k = 1 , n - 2 , n - 4 and n - 6 . In this paper, we use a simple method to reprove the above results. As a main result, the further use of this method enables us to prove the conjecture to be true for k = n - 8 . We also obtain that every minimally ( n - 6 ) -factor-critical graph of order n has at most n - Δ ( G ) vertices with the maximum degree Δ ( G ) for Δ ( G ) ≥ n - 4 .

The study of soil erodibility, i.e., its ability to resist the destructing action of water flow and raindrops, is one of the important challenges in erosion science. The values of soil erodibility are used in erosion models and make it possible to calculate the rate of soil matter loss/accumulation. The purpose of this study is to assess soil erodibility and its variation on plots of different areas in the northern forest-steppe of the Central Russian Upland. It has been established that the calculated parameter of soil erodibility ( K -factor) is mainly determined by the soil organic matter content. The mean K -factor for gray forest soils is more than 1.5 times higher than that for noneroded chernozems. The K -factor increases with an increase in the degree of soil erosion. For example, in a series of noneroded and slightly, moderately, and strongly eroded chernozems, it reaches 38, 42, 44, and 57 kg h/(MJ mm), respectively. Gray forest soils are much more susceptible to the risk of degradation from erosion than chernozems because of their higher erodibility and lower thickness of the humus layer, other factors being equal. The use of different methods of K -factor interpolation exerts little effect on changes in the mean soil erosion rates calculated by the WaTEM/SEDEM model, even under conditions of the highly contrasting soil cover. With a change in the scale of soil erosion estimates (the transition from a medium to a large scale, or from a large to a medium scale), the deviation of calculated mean soil erosion rates is less than 15%.

For any integer k ≥ 1 , a graph G is said to be k -factor-critical if G - S has a perfect matching for each S ⊆ V ( G ) with | S | = k . In this paper, we present a sufficient condition in terms of the number of r -cliques to guarantee a graph with minimum degree at least δ to be k -factor-critical, which improves the result of Fan and Lin (Spectral conditions for k -extendability and k -factors of bipartite graphs, arXiv: 2211.09304 ). For any integer k ≥ 2 , a spanning k -tree of a connected graph G is a spanning tree in which every vertex has degree at most k . Neumann–Lara and Rivera–Campo (Combinatorica 11:55–61, 1991) proved that, for an m -connected graph G with m ≥ 2 , if its independence number α ( G ) ≤ ( k - 1 ) m + 1 , then G contains a spanning k -tree. Motivated by the above result, we provide tight spectral conditions for an m -connected graph to contain a spanning k -tree.

The applicability of the stress–strain formulations in Eurocode 2 (BS EN 1992-1-1:2004 and British Standard (BS 8110-2:1985)) for modeling the compressive behavior of concrete in non-linear structural analysis is investigated. Both codes employ similar expressions governed by a key parameter–k-factor. The current formulation incorporates an empirically calibrated constant to align the theoretical tangent modulus with the secant modulus obtained from experimental data. However, this constant remains fixed and does not account for variations in concrete properties, resulting in mathematical inconsistency within certain strength ranges. A modified equation for determining the k-factor is derived to overcome this limitation. Comparative and validation analyses demonstrate that the proposed formulation provides a more reliable prediction of the stress–strain response, particularly for low- and normal-strength concrete.

Opsariichthys uncirostris uncirostris (Hasu fish), a vulnerable potamodromous fish, is the only piscivorous cyprinid fish in Japan and endemic as a subspecies to Lake Biwa. The species population is on a continued decline for the past 70 years. This study aimed at developing a portfolio on the species during its reproductive migration to Shiotsuo River, a Lake Biwa tributary, by using a combination of biometric measurements and stable isotope ratios in its tissues. Hasu fish were collected monthly, from May to September 2019, using cast nets. The biometric measurements: wet weight, standard length, gonad weight and gut content were collected and used to calculate the gonado-somatic index (GSI) and Fulton’s condition constant (K) and determine the feeding habits of Hasu fish. Carbon and nitrogen isotope ratios (δ13C and δ15N) in slow-changing muscle and fast-changing mucus tissues of Hasu fish were also used to determine recent diet change. At the beginning of the reproductive season, fewer females than males were caught; however, the number of females increased as the season progressed. On average, males were larger than females. Migrating individuals were healthy (K > 1) and over 37% larger in length than those in the 1960s. Gut content analysis revealed, for the first time, Hasu fish feeding in the rivers, primarily on Ayu fish, during the reproductive migration. δ13C and δ15N in muscle and mucus indicated a recent change in diet, i.e., from Lake Biwa to Shiotsuo River, with differences in the onset of feeding (and consequently upstream migration) between sexes and individuals. For the effective conservation of Hasu fish in the other tributaries where Ayu fish traps block other fishes’ migration, we recommend having the rivers open from June to September to cover its variable timing in the recruitment of reproductive individuals.