Article
Mathematics, Applied
Saul Ancari, Xu Cheng
Summary: This paper extends the results on self-expanders obtained in Ancari and Cheng (2022) to lambda-self-expanders and proves some results characterizing hyperplanes, spheres, and cylinders as lambda-self-expanders.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Mathematics, Applied
Semra Kaya Nurkan, Ibrahim Gurgil, Murat Kemal Karacan
Summary: This paper presents the elementary theorems of geometric calculus to build the geometry on geometric space. It introduces the notions of geometric determinant and geometric vector product and studies their properties. The definitions of the circle, the plane, and the sphere are given and visualized along with a line in geometric space. Lastly, the paper discusses the Gram-Schmidt process in geometric space.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Theory & Methods
Hongjun Zhou, Xinxin Yan
Summary: This paper focuses on studying the migrativity properties of overlap functions over uninorms, which are a newly-born subclass of nonassociative aggregation functions. The main results include characterizations of solutions to migrative functional equations for overlap functions over uninorms in various classes, along with supporting examples for positive solutions and illustrating remarks for negative results.
FUZZY SETS AND SYSTEMS
(2021)
Article
Mathematics
Ana Khukhro, Kang Li, Federico Vigolo, Jiawen Zhang
Summary: The paper studies analytic and graph-theoretic properties of asymptotic expanders, characterizing them through their uniform Roe algebra and providing new counterexamples to the coarse Baum-Connes conjecture. It also shows that vertex-transitive asymptotic expanders are actually expanders, giving a C*-algebraic characterization for expanders in vertex-transitive graphs.
ADVANCES IN MATHEMATICS
(2021)
Article
Computer Science, Artificial Intelligence
Junsheng Qiao
Summary: This paper focuses on discrete overlap functions on finite chains and their properties, including idempotent property, Archimedean property, and cancellation law. Unlike overlap functions on other truth values sets, discrete overlap functions on finite chains take the greatest element on the chain as the neutral element. Furthermore, the results obtained in this paper provide a theoretical basis and possibilities for the potential applications of overlap functions in other fields.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Mechanics
Benlong Su, Shouyao Liu, Peng Zhang, Jian Wu, Youshan Wang
Summary: This study compared the experimental and simulation results of the mechanical properties of overlap structure in cord-rubber composite, introducing a cohesion zone model to analyze the failure mechanism. The errors in simulating the limit load of the overlap structure were found to be about 5%. Interlaminar damage evolution was identified as key in the strength of the overlap structure, providing a theoretical basis for design of cord-rubber composites.
COMPOSITE STRUCTURES
(2021)
Article
Computer Science, Artificial Intelligence
Junsheng Qiao, Bin Zhao
Summary: This paper investigates the unique property of overlap functions, namely the alpha-cross-migrativity, and explores and classifies the overlap functions that possess this property. The research findings contribute to the improvement of the application of overlap functions in various fields.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Computer Science, Information Systems
Rui Paiva, Regivan Santiago, Benjamin Bedregal, Eduardo Palmeira
Summary: Overlap functions, an important class of aggregation operators, were first introduced in 2009 for applications in image processing. Quasi-overlaps, a weakened version, on lattices were discussed without continuity, exploring properties like convex sum, migrativity, homogeneity, idempotency, and cancellation law. Properties related to continuity, such as Archimedean and limiting, were also studied.
INFORMATION SCIENCES
(2021)
Article
Mathematics, Applied
Andrei D. Werkhausen, Igor M. L. Lopes, Heyder Hey
Summary: This paper reviews the usage and applications of Lie Group in numerical methods for ordinary differential equations. A comparison is made between the midpoint symplectic method and the usual Runge-Kutta method for different dynamical behaviors, ranging from integrable to chaotic regimes. The simulation results demonstrate that the midpoint symplectic method has better precision in the regular region of the phase space, as indicated by a statistical indicator defined in this work. However, its performance sharply degrades near the homoclinic crossing.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Theory & Methods
Kuanyun Zhu, Jingru Wang, Yongwei Yang
Summary: The study focuses on the alpha-migrativity of overlap and grouping functions over uninorms and nullnorms, clarifying errors in previous propositions and presenting updated results. It also explores the alpha-migrativity of overlap functions over uninorms and t-norms, as well as the relationship between the alpha-migrativity of uninorms over overlap functions. Ultimately, the (alpha, U)-migrativity equation for grouping functions is discussed using a similar approach.
FUZZY SETS AND SYSTEMS
(2021)
Article
Surgery
Zhezhen Xiong, Yahong Chen, Peng Xu, Chuhsin Chen, Yun Xie, Yu Chang, Tingrui Pan, Kai Liu
Summary: The regional-controlled expansion technique allows targeted expansion of skin and soft tissues for defect repair. Thickened regions have larger skin area and thickness, but lower cell proliferation and higher vascular density.
PLASTIC AND RECONSTRUCTIVE SURGERY
(2022)
Article
Statistics & Probability
Yeganeh Alimohammadi, Christian Borgs, Amin Saberi
Summary: We study random digraphs on sequences of expanders with a bounded average degree which converge locally in probability. We prove that the relative size and the threshold for the existence of a giant strongly connected component as well as the asymptotic fraction of nodes with giant fan-in or nodes with giant fan-out are local, in the sense that they are the same for two sequences with the same local limit. The digraph has a bow-tie structure, with all but a vanishing fraction of nodes lying either in the unique strongly connected giant and its fan-in and fan-out or in sets with small fan-in and small fan-out. All local quantities are expressed in terms of percolation on the limiting rooted graph, without any structural assumptions on the limit, allowing, in particular, for nontree-like graphs. In the course of establishing these results, we generalize previous results on the locality of the size of the giant to expanders of bounded average degree with possibly nontree-like limits. We also show that, regardless of the local convergence of a sequence, the uniqueness of the giant and convergence of its relative size for unoriented percolation imply the bow-tie structure for directed percolation. An application of our methods shows that the critical threshold for bond percolation and random digraphs on preferential attachment graphs is pc = 0 with an infinite order phase transition at pc.
ANNALS OF PROBABILITY
(2023)
Review
Chemistry, Multidisciplinary
Lichao Sun, Yunlong Tao, Guizeng Yang, Chuang Liu, Xuehao Sun, Qingfeng Zhang
Summary: Intrinsically chiral plasmonic nanomaterials, which combine plasmonic features with geometric chirality, exhibit intriguing geometry-dependent chiroptical properties. These nanomaterials have become promising candidates for applications in biosensing, asymmetric catalysis, biomedicine, and photonics. Recent advances in geometric control and optical tuning have further expanded the potential applications of these nanomaterials in various emerging technological areas. This review focuses on the recent developments in the geometric control of chiral plasmonic nanomaterials and the quantitative understanding of the structure-property relationship. It also discusses important optical spectroscopic tools for characterizing the optical chirality of these nanomaterials and highlights three emerging applications in enantioselective sensing, enantioselective catalysis, and biomedicine. These advanced studies in chiral plasmonic nanomaterials are expected to pave the way for the rational design of chiral nanomaterials with desired optical properties for diverse emerging technological applications.
ADVANCED MATERIALS
(2023)
Article
Materials Science, Multidisciplinary
Jie Ji, Chenbo Xie, Jianfeng Chen, Ming Zhao, Hao Yang, Kunming Xing, Bangxin Wang
Summary: This study explores the effects of different factors on the results and accuracy of aerosol optical property measurements made in overlap factor regions using scanning lidar, simulation calculations, and aerosol detection experiments. The proposed method effectively solves the problem of unavailability of optical properties of aerosols in the overlap factor region of lidar.
RESULTS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Hyunseok Lee, Jeff Gore, Kirill S. Korolev
Summary: This article explores the competition dynamics of biological populations during spatial growth. The study finds that slower-growing mutants can still win in competition, especially in local competitions. By conducting experiments and simulations, the researchers develop a theory that can explain different sector shapes and validate its accuracy. These findings are important for understanding the evolutionary and ecological dynamics in expanding populations.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)