Explore the vast range of titles available.

The mass and centroid of rolling rings are the key factors affecting the mass and centroid detection of large launch vehicles. However, at present, the detection of rolling ring mass and centroid stays in the use of theoretical parameters or specially designed measuring tables, and the method used is time-consuming and laborious, and the compatibility is poor. To solve this problem, this paper proposes a flexible measurement method for rolling ring mass and centroid. This method does not need a special measuring platform and has the characteristics of strong universality and high precision. Finally, the feasibility of this method is verified by experiments.

To address challenges associated with the traditional drill positioning method, which demands manual walking tracking and imposes stringent environmental conditions, this paper introduces an improved weighted centroid localization (WCL) algorithm based on multiple magnetic beacons. This algorithm alleviates the environmental requirements. Initially, a magnetic beacon measurement model immune to sensor attitude is formulated, followed by the development of a positioning model based on multiple magnetic beacons. The WCL algorithm is then introduced and refined for positioning with multiple magnetic beacons. Finally, the effectiveness of the proposed approach is validated through simulation experiments, revealing an average error of 0.632 m in large-scale positioning. This demonstrates clear advantages over traditional methods, making it highly applicable.

To achieve high-speed and high-precision measurements, this study introduces a height measurement system based on LCCD and optical triangulation that utilizes a gray-scale centroid algorithm for sub-pixel positioning. Ultimately, the system achieves a resolution of 10 nm, a repeatability of 15 nm, and a stability of 7.8 nm, by setting up an experimental system in the laboratory.

The efficient segmentation of customers of an enterprise is categorized into groups of similar behavior based on the RFM (Recency, Frequency and Monetary) values of the customers. The transactional data of a company over is analyzed over a specific period. Segmentation gives a good understanding of the need of the customers and helps in identifying the potential customers of the company. Dividing the customers into segments also increases the revenue of the company. It is believed that retaining the customers is more important than finding new customers. For instance, the company can deploy marketing strategies that are specific to an individual segment to retain the customers. This study initially performs an RFM analysis on the transactional data and then extends to cluster the same using traditional K-means and Fuzzy C- Means algorithms. In this paper, a novel idea for choosing the initial centroids in K- Means is proposed. The results obtained from the methodologies are compared with one another by their iterations, cluster compactness and execution time.

The objective of this article is to establish a condition by which we are able to state that an ellipsoidal fragment formed by a plane cutting the ellipsoid can always contain a sphere in any position inside in it. A method to construct a chain of mutually tangent spheres inscribed in the ellipsoidal segment has been proposed. The locus of the centroid as well as the radii of the mutually tangent spheres have been computed. The prime concern of our work is to explore some geometrical properties of such a chain of spheres which includes the condition of inscribability of a sphere in any position inside the ellipsoid along with the computation of points of tangency between consecutive spheres.

We prove an analogue of Grünbaum's inequality on the sphere. Let \\(n 3\\) and let \\(K\\) be a convex body on \\( S^n-1 R^n\\) with centroid at \\(ın S^n-1\\). Then for any \\(uın S^n-1\\) that is orthogonal to \\(\\) we have$$\\sigma(K\\cap u^+) \\ge \\left(1-\\frac{1}{n}\\right)^{n-1} \\sigma(K),$$where \\(\\) denotes the spherical measure. The constant in this inequality is optimal.

We study the formation of ring-like structures in interacting active particle systems in two dimensions. The emergent structure shows signatures of both spatial and orientational organization. The spatial organization is characterized by the radial distance of a tagged particle from the centroid of the assembly, while orientational organization is characterized by the radial alignment of its self-propulsion direction. We derive exact analytical expressions for the radial and polarization distributions for systems of active Brownian particles and run-and-tumble particles. While both models exhibit annular steady states, we show that their spatial and orientational organization differ qualitatively in the strongly active regime. A direct comparison of the two models reveals how the nature of the propulsion mechanism leads to the distinction in both the structure of the annulus and the statistics of particle orientations. Our results provide a unified analytical framework for characterizing emergent annular states in active matter and identify robust signatures that distinguish persistent active dynamics with continuous and discrete reorientation.

In a classical paper [20] in 2000, Lutwak-Yang-Zhang established the \\(L^p\\) analog of the Petty projection inequality and the \\(L^p\\) analog of the Busemann-Petty centroid inequality. In Section 7 of [20], Lutwak-Yang-Zhang proposed the important \\(L^p\\) projection centroid conjecture. We give a positive solution to the \\(L^p\\) projection centroid conjecture in this work.

The conventional K‐Means clustering algorithm is widely used for grouping similar data points by initially selecting random centroids. However, the accuracy of clustering results is significantly influenced by the initial centroid selection. Despite different approaches, including various K‐Means versions, suboptimal outcomes persist due to inadequate initial centroid choices and reliance on common normalization techniques like min‐max normalization. In this study, we propose an improved algorithm that selects initial centroids more effectively by utilizing a novel formula to differentiate between instance attributes, creating a single weight for differentiation. We introduce a preprocessing phase for dataset normalization without forcing values into a specific range, yielding significantly improved results compared to unnormalized datasets and those normalized using min‐max techniques. For our experiments, we used five real datasets and five simulated datasets. The proposed algorithm is evaluated using various metrics and an external benchmark measure, such as the Adjusted Rand Index (ARI), and compared with the traditional K‐Means algorithm and 11 other modified K‐Means algorithms. Experimental evaluations on these datasets demonstrate the superiority of our proposed methodologies, achieving an impressive average accuracy rate of up to 95.47% and an average ARI score of 0.95. Additionally, the number of iterations required is reduced compared to the conventional K‐Means algorithm. By introducing innovative techniques, this research provides significant contributions to the field of data clustering, particularly in addressing modern data‐driven clustering challenges.

The cevian triangle corresponding to an interior point \\(M\\) of a triangle is the triangle determined by the feet of the three cevians concurrent at \\(M\\). It is known that the area of the cevian triangle for an interior point \\(M\\) of a triangle is at most \\(14\\) of the area of the triangle, with maximum attained when \\(M\\) is the triangle's centroid. This can be generalized from triangles to \\(n\\)-dimensional simplices, with \\(14\\) replaced by \\(1n^n\\), using barycentric coordinates. We also use this method to solve two optimization problems about the parts of this simplex.