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Global Stein theorem on Hardy spaces 哈代空间上的全局斯坦因定理
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2024-09-05 DOI: 10.1007/s10476-024-00003-2
A. Bonami, S. Grellier, B. F. Sehba
{"title":"Global Stein theorem on Hardy spaces","authors":"A. Bonami, S. Grellier, B. F. Sehba","doi":"10.1007/s10476-024-00003-2","DOIUrl":"https://doi.org/10.1007/s10476-024-00003-2","url":null,"abstract":"<p>Let <span>(f)</span> be an integrable function which has integral <span>(0)</span> on <span>(mathbb{R}^n )</span>.\u0000What is the largest condition on <span>(|f|)</span> that guarantees that <span>(f)</span> is in the Hardy space\u0000<span>(mathcal{H}^1(mathbb{R}^n))</span>? When <span>(f)</span> is compactly supported, it is well-known that the largest condition\u0000on <span>(|f|)</span> is the fact that <span>(|f|in L log L(mathbb{R}^n) )</span>. We consider the same kind of\u0000problem here, but without any condition on the support. We do so for <span>(mathcal{H}^1(mathbb{R}^n))</span>,\u0000as well as for the Hardy space <span>(mathcal{H}_{log}(mathbb{R}^n))</span> which appears in the study of pointwise\u0000products of functions in <span>(mathcal{H}^1(mathbb{R}^n))</span> and in its dual BMO.</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Geometry of Quantum Spheres and Hyperboloids 论量子球和超球的几何学
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-07-13 DOI: 10.1007/s00006-024-01339-6
Giovanni Landi, Chiara Pagani
{"title":"On the Geometry of Quantum Spheres and Hyperboloids","authors":"Giovanni Landi, Chiara Pagani","doi":"10.1007/s00006-024-01339-6","DOIUrl":"https://doi.org/10.1007/s00006-024-01339-6","url":null,"abstract":"<p>We study two classes of quantum spheres and hyperboloids, one class consisting of homogeneous spaces, which are <span>(*)</span>-quantum spaces for the quantum orthogonal group <span>(mathcal {O}(SO_q(3)))</span>. We construct line bundles over the quantum homogeneous space associated with the quantum subgroup <i>SO</i>(2) of <span>(SO_q(3))</span>. The line bundles are associated to the quantum principal bundle via representations of <i>SO</i>(2) and are described dually by finitely-generated projective modules <span>(mathcal {E}_n)</span> of rank 1 and of degree computed to be an even integer <span>(-2n)</span>. The corresponding idempotents, that represent classes in the K-theory of the base space, are explicitly worked out and are paired with two suitable Fredhom modules that compute the rank and the degree of the bundles. For <i>q</i> real, we show how to diagonalise the action (on the base space algebra) of the Casimir operator of the Hopf algebra <span>({mathcal {U}_{q^{1/2}}(sl_2)})</span> which is dual to <span>(mathcal {O}(SO_q(3)))</span>.</p>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141602718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit constructions of NMDS self-dual codes NMDS 自偶码的显式构造
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-07-12 DOI: 10.1007/s10623-024-01450-6
Dongchun Han, Hanbin Zhang
{"title":"Explicit constructions of NMDS self-dual codes","authors":"Dongchun Han, Hanbin Zhang","doi":"10.1007/s10623-024-01450-6","DOIUrl":"https://doi.org/10.1007/s10623-024-01450-6","url":null,"abstract":"<p>Near maximum distance separable (NMDS) codes are important in finite geometry and coding theory. Self-dual codes are closely related to combinatorics, lattice theory, and have important application in cryptography. In this paper, we construct a class of <i>q</i>-ary linear codes and prove that they are either MDS or NMDS which depends on certain zero-sum condition. In the NMDS case, we provide an effective approach to construct NMDS self-dual codes which largely extend known parameters of such codes. In particular, we proved that for square <i>q</i>, almost <i>q</i>/8 NMDS self-dual <i>q</i>-ary codes can be constructed.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model. 无根三叶树的最大似然估计:CFN 模型的解析解
IF 2 4区 数学
Bulletin of Mathematical Biology Pub Date : 2024-07-12 DOI: 10.1007/s11538-024-01340-x
Max Hill, Sebastien Roch, Jose Israel Rodriguez
{"title":"Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model.","authors":"Max Hill, Sebastien Roch, Jose Israel Rodriguez","doi":"10.1007/s11538-024-01340-x","DOIUrl":"https://doi.org/10.1007/s11538-024-01340-x","url":null,"abstract":"<p><p>Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798-811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141589713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integral trees with diameter 6 直径为 6
IF 1 3区 数学
Discrete Applied Mathematics Pub Date : 2024-07-12 DOI: 10.1016/j.dam.2024.06.039
Fangxu Xi, Ligong Wang
{"title":"Integral trees with diameter 6","authors":"Fangxu Xi,&nbsp;Ligong Wang","doi":"10.1016/j.dam.2024.06.039","DOIUrl":"https://doi.org/10.1016/j.dam.2024.06.039","url":null,"abstract":"<div><p>A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. In this paper, two new classes of trees <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>•</mo><mi>T</mi><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><mo>•</mo><mi>T</mi><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>s</mi></mrow></msub><mo>•</mo><mi>T</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>•</mo><mi>T</mi><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><mo>•</mo><mi>T</mi><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> of diameter 6 are defined. We obtain their characteristic polynomials and give the necessary and sufficient conditions for them to be integral. We also present some sufficient conditions of such trees to be integral by computer search. We also prove that the problem of finding integral trees of diameter 6 is equivalent to the problem of solving some Diophantine equations. Finally, we propose two basic open problems about integral trees of diameter 6 for further study.</p></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141592701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-layer Bundling as a New Approach for Determining Multi-scale Correlations Within a High-Dimensional Dataset. 多层捆绑是确定高维数据集内多尺度相关性的新方法
IF 2 4区 数学
Bulletin of Mathematical Biology Pub Date : 2024-07-12 DOI: 10.1007/s11538-024-01335-8
Mehran Fazli, Richard Bertram, Deborah A Striegel
{"title":"Multi-layer Bundling as a New Approach for Determining Multi-scale Correlations Within a High-Dimensional Dataset.","authors":"Mehran Fazli, Richard Bertram, Deborah A Striegel","doi":"10.1007/s11538-024-01335-8","DOIUrl":"https://doi.org/10.1007/s11538-024-01335-8","url":null,"abstract":"<p><p>The growing complexity of biological data has spurred the development of innovative computational techniques to extract meaningful information and uncover hidden patterns within vast datasets. Biological networks, such as gene regulatory networks and protein-protein interaction networks, hold critical insights into biological features' connections and functions. Integrating and analyzing high-dimensional data, particularly in gene expression studies, stands prominent among the challenges in deciphering these networks. Clustering methods play a crucial role in addressing these challenges, with spectral clustering emerging as a potent unsupervised technique considering intrinsic geometric structures. However, spectral clustering's user-defined cluster number can lead to inconsistent and sometimes orthogonal clustering regimes. We propose the Multi-layer Bundling (MLB) method to address this limitation, combining multiple prominent clustering regimes to offer a comprehensive data view. We call the outcome clusters \"bundles\". This approach refines clustering outcomes, unravels hierarchical organization, and identifies bridge elements mediating communication between network components. By layering clustering results, MLB provides a global-to-local view of biological feature clusters enabling insights into intricate biological systems. Furthermore, the method enhances bundle network predictions by integrating the bundle co-cluster matrix with the affinity matrix. The versatility of MLB extends beyond biological networks, making it applicable to various domains where understanding complex relationships and patterns is needed.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141589644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Framework, Measurement, and Determinants of the Digital Divide in China 中国数字鸿沟的新框架、测量方法和决定因素
IF 2.4 3区 数学
Mathematics Pub Date : 2024-07-11 DOI: 10.3390/math12142171
Yuanren Zhou, Menggen Chen, Xiaojie Liu, Yun Chen
{"title":"A New Framework, Measurement, and Determinants of the Digital Divide in China","authors":"Yuanren Zhou, Menggen Chen, Xiaojie Liu, Yun Chen","doi":"10.3390/math12142171","DOIUrl":"https://doi.org/10.3390/math12142171","url":null,"abstract":"The digital divide (DD) reflects the inequality of the digital economy, while existing research lacks a comprehensive framework for investigating the measurement of DD and its determinants. This study constructs a new framework with a five-dimensional comprehensive index system. City-level data are used to measure China’s DD index from 2010 to 2020 at the national, regional, and provincial levels. Furthermore, this study investigates the decomposition of DD at both regional and provincial levels and the determinants of DD from the perspectives of physical, human, and social capital. The key results are: (1) China’s DD has generally exhibited a fluctuating downward trend. While it remains high in the eastern and western regions, it has shown a decline year by year. However, the DD within most provinces is on the rise. (2) The intra-regional and inter-provincial are the primary drivers of changes in national DD, with both intra-regional and intra-provincial contribution rates on the rise. (3) Economic growth, infrastructure, foreign trade, education, and online interaction significantly impact DD, and these determinants may change at different periods. This study intends to provide empirical support for bridging the DD, fostering the balanced development of the digital economy, and reducing social inequality.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Automated Magnetic Microrobot Control: From Mathematical Modeling to Machine Learning 自动磁性微型机器人控制:从数学建模到机器学习
IF 2.4 3区 数学
Mathematics Pub Date : 2024-07-11 DOI: 10.3390/math12142180
Yamei Li, Yingxin Huo, Xiangyu Chu, Lidong Yang
{"title":"Automated Magnetic Microrobot Control: From Mathematical Modeling to Machine Learning","authors":"Yamei Li, Yingxin Huo, Xiangyu Chu, Lidong Yang","doi":"10.3390/math12142180","DOIUrl":"https://doi.org/10.3390/math12142180","url":null,"abstract":"Microscale robotics has emerged as a transformative field, offering unparalleled opportunities for innovation and advancement in various fields. Owing to the distinctive benefits of wireless operation and a heightened level of safety, magnetic actuation has emerged as a widely adopted technique in the field of microrobotics. However, factors such as Brownian motion, fluid dynamic flows, and various nonlinear forces introduce uncertainties in the motion of micro/nanoscale robots, making it challenging to achieve precise navigational control in complex environments. This paper presents an extensive review encompassing the trajectory from theoretical foundations of the generation and modeling of magnetic fields as well as magnetic field-actuation modeling to motion control methods of magnetic microrobots. We introduce traditional control methods and the learning-based control approaches for robotic systems at the micro/nanoscale, and then these methods are compared. Unlike the conventional navigation methods based on precise mathematical models, the learning-based control and navigation approaches can directly learn control signals for the actuation systems from data and without relying on precise models. This endows the micro/nanorobots with high adaptability to dynamic and complex environments whose models are difficult/impossible to obtain. We hope that this review can provide insights and guidance for researchers interested in automated magnetic microrobot control.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Improved Method for Calculating Wave Velocity Fields in Fractured Rock Based on Wave Propagation Probability 基于波传播概率的断裂岩中波速场计算改进方法
IF 2.4 3区 数学
Mathematics Pub Date : 2024-07-11 DOI: 10.3390/math12142177
Jing Zhou, Lang Liu, Yuan Zhao, Dengdeng Zhuang, Zhizhen Liu, Xuebin Qin
{"title":"An Improved Method for Calculating Wave Velocity Fields in Fractured Rock Based on Wave Propagation Probability","authors":"Jing Zhou, Lang Liu, Yuan Zhao, Dengdeng Zhuang, Zhizhen Liu, Xuebin Qin","doi":"10.3390/math12142177","DOIUrl":"https://doi.org/10.3390/math12142177","url":null,"abstract":"Ultrasonic velocity field imaging offers a robust tool for characterizing and analyzing damage and its evolution within fractured rock masses. The combined application of ultrasonic first arrival waves and coda waves can significantly enhance the accuracy and range of velocity field imaging. This manuscript introduces an improved imaging method that integrates the propagation probability distribution of the first arrival and coda waves to calculate the velocity field. The proposed method was applied to the velocity field imaging of a medium with multiple scatterers and varying degrees of fracturing. The overall error and calculation unit error of the proposed method were analyzed, and its improvement in calculation accuracy and applicable scope was verified. Additionally, this method was employed to image the velocity field during the damage process of fractured rock masses. The imaging results were compared against digital speckle patterns to confirm the method’s suitability. Finally, we discussed the impact of measurement errors and sensor missing on the accuracy of the computational outcomes presented in this method. These two situations will affect the calculation results, and the influence of reducing the number of sensors is smaller than that of measuring time shifts with error.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computational methods for fast Bayesian model assessment via calibrated posterior p-values 通过校准后p值快速评估贝叶斯模型的计算方法
IF 2.4 2区 数学
Journal of Computational and Graphical Statistics Pub Date : 2024-07-11 DOI: 10.1080/10618600.2024.2374585
Sally Paganin, Perry de Valpine
{"title":"Computational methods for fast Bayesian model assessment via calibrated posterior p-values","authors":"Sally Paganin, Perry de Valpine","doi":"10.1080/10618600.2024.2374585","DOIUrl":"https://doi.org/10.1080/10618600.2024.2374585","url":null,"abstract":"Posterior predictive p-values (ppps) have become popular tools for Bayesian model assessment, being general-purpose and easy to use. However, interpretation can be difficult because their distribut...","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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