On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups

Let G be a finite group and (G) the set of the numbers of conjugates of noncyclic proper subgroups of G. We prove that (1) if |(G)|≤2, then G is solvable, and (2) G is a nonsolvable group with |(G)|=3 if and only if G≅PSL(2,5) or PSL(2,13) or SL(2,5) or SL(2,13)

Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures.

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures

A Framework and Classification for Fault Detection Approaches in Wireless Sensor Networks with an Energy Efficiency Perspective

Wireless Sensor Networks (WSNs) are more and more considered a key enabling technology for the realisation of the Internet of Things (IoT) vision. With the long term goal of designing fault-tolerant IoT systems, this paper proposes a fault detection framework for WSNs with the perspective of energy efficiency to facilitate the design of fault detection methods and the evaluation of their energy efficiency. Following the same design principle of the fault detection framework, the paper proposes a classification for fault detection approaches. The classification is applied to a number of fault detection approaches for the comparison of several characteristics, namely, energy efficiency, correlation model, evaluation method, and detection accuracy. The design guidelines given in this paper aim at providing an insight into better design of energy-efficient detection approaches in resource-constraint WSNs

Persistence versus extinction for two competing species under a climate change

This paper considers effects of a climate-induced range shift on outcomes of two competitive species, which is modeled by a reaction–diffusion system with the increasing growth rates of species along a shifting habitat gradient. Analytical conditions are established for the coexistence or competitive exclusion of two-competitors under the climate change, which present the control strategies to maintain the persistence of species

Player detection method based on scale attention and scale equalization algorithm

IntroductionObject detection methods for team ball games players often struggle due to their reliance on dataset scale statistics, resulting in missed detections for players with smaller bounding boxes and reduced accuracy for larger bounding boxes.MethodsThis study introduces a two-fold approach to address these challenges. Firstly, a novel multi-scale attention mechanism is proposed, aiming to reduce reliance on scale statistics by utilizing a specially created SIoU (Similar to Intersection over Union) label that explicitly represents multi-scale features. This label guides the training of multi-scale attention network modules at two granularity levels. Secondly, an integrated scale equalization algorithm within SIoU labels enhances the detection ability of multi-scale targets in imbalanced samples.Results and discussionComparative experiments conducted on basketball, volleyball, and ice hockey datasets validate the proposed method. The relative optimal approach demonstrated improvements in the detection accuracy of players with smaller and larger scale bounding boxes by 11%, 7%, 15%, 8%, 9%, and 4%, respectively