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Examples and Counterexamples最新文献

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A family of asymptotically bad wild towers of function fields 函数域的渐近野塔族
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-04-25 DOI: 10.1016/j.exco.2025.100186
M. Chara , R. Toledano
{"title":"A family of asymptotically bad wild towers of function fields","authors":"M. Chara ,&nbsp;R. Toledano","doi":"10.1016/j.exco.2025.100186","DOIUrl":"10.1016/j.exco.2025.100186","url":null,"abstract":"<div><div>In Chara and Toledano (2015) general conditions were given to prove the infiniteness of the genus of certain towers of function fields over a perfect field. It was shown that many examples where particular cases of those general results. In this paper the genus of a family of wild towers of function fields will be considered together with a result with less restrictive sufficient conditions for a wild tower to have infinite genus.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100186"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 uniqueness of collections of pennies and marbles 论便士和弹珠收藏的独特性
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-02-14 DOI: 10.1016/j.exco.2025.100181
Sean Dewar , Georg Grasegger , Kaie Kubjas , Fatemeh Mohammadi , Anthony Nixon
{"title":"On the uniqueness of collections of pennies and marbles","authors":"Sean Dewar ,&nbsp;Georg Grasegger ,&nbsp;Kaie Kubjas ,&nbsp;Fatemeh Mohammadi ,&nbsp;Anthony Nixon","doi":"10.1016/j.exco.2025.100181","DOIUrl":"10.1016/j.exco.2025.100181","url":null,"abstract":"<div><div>In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit <span><math><mi>d</mi></math></span>-spheres that may touch but not overlap. Given the existence of such a collection, one may analyse the contact graph of the collection. In particular we consider the uniqueness of the collection arising from the contact graph. Using the language of graph rigidity theory, we prove a precise characterisation of uniqueness (global rigidity) in dimensions 2 and 3 when the contact graph is additionally chordal. We then illustrate a wide range of examples in these cases. That is, we illustrate collections of marbles and pennies that can be perturbed continuously (flexible), are locally unique (rigid) and are unique (globally rigid). We also contrast these examples with the usual generic setting of graph rigidity.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100181"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Automation of image processing through ML algorithms of GRASS GIS using embedded Scikit-Learn library of Python 利用嵌入式Python Scikit-Learn库实现GRASS GIS的ML算法图像处理自动化
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-02-03 DOI: 10.1016/j.exco.2025.100180
Polina Lemenkova
{"title":"Automation of image processing through ML algorithms of GRASS GIS using embedded Scikit-Learn library of Python","authors":"Polina Lemenkova","doi":"10.1016/j.exco.2025.100180","DOIUrl":"10.1016/j.exco.2025.100180","url":null,"abstract":"<div><div>Image processing using Machine Learning (ML) and Artificial Neural Network (ANN) methods was investigated by employing the algorithms of Geographic Resources Analysis Support System (GRASS) Geographic Information System GIS with embedded Scikit-Learn library of Python language. The data are obtained from the United States Geological Survey (USGS) and include the Landsat 8 Operational Land Imager/Thermal Infrared Sensor (OLI/TIRS) multispectral satellite images. The images were collectedon 2013 and 2023 to evaluate land cover categories in each of the year. The study area covers the region of Nile Delta and the Faiyum Oasis, Egypt. A series of modules for raster image processing was applied using scripting language of GRASS GIS to process the remote sensing data. The satellite images were classified into raster maps presenting the land cover types. These include ‘i.cluster’ and ‘i.maxlik’ for non-supervised classification used as training dataset of random pixel seeds, ‘r.random’, ‘r.learn.train’, ‘r.learn.predict’ and ‘r.category’ for ML part of image processing. The consequences of various ML parameters on the cartographic outputs are analysed, such as speed and accuracy, randomness of nodes, analytical determination of the output weights, and dependence distribution of pixels for each algorithm. Supervised learning models of GRASS GIS were tested and compared including the Gaussian Naive Bayes (GaussianNB), Multi-layer Perceptron classifier (MLPClassifier), Support Vector Machines (SVM) Classifier, and Random Forest Classifier (RF). Though each algorithms was developed to serve different objectives of ML applications in RS data processing, their technical implementation and practical purposes present valuable approaches to cartographic data processing and image analysis. The results shown that the most time-consuming algorithms was noted as SVM classification, while the fastest results were achieved by the GaussianNB approach to image processing and the best results are achieved by RF Classifier.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100180"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving change of basis from Bernstein to Chebyshev polynomials 求解Bernstein多项式到Chebyshev多项式的基变换
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-02-02 DOI: 10.1016/j.exco.2025.100178
D.A. Wolfram
{"title":"Solving change of basis from Bernstein to Chebyshev polynomials","authors":"D.A. Wolfram","doi":"10.1016/j.exco.2025.100178","DOIUrl":"10.1016/j.exco.2025.100178","url":null,"abstract":"<div><div>We provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. The first solution uses orthogonality properties of the Chebyshev polynomials. The second is “modular” which enables separately verified sub-problems to be composed and re-used in other basis transformations. These results have applications in change of basis of orthogonal, and non-orthogonal polynomials.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100178"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Meta-analytic functions with derivative not in a Hardy space 非Hardy空间中导数的元解析函数
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-05-14 DOI: 10.1016/j.exco.2025.100187
William L. Blair
{"title":"Meta-analytic functions with derivative not in a Hardy space","authors":"William L. Blair","doi":"10.1016/j.exco.2025.100187","DOIUrl":"10.1016/j.exco.2025.100187","url":null,"abstract":"<div><div>We show there exist solutions to higher-order Vekua equations that, along with their <span><math><mover><mrow><mi>z</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-derivatives, have finite Hardy space norm, but their <span><math><mi>z</mi></math></span>-derivatives do not.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100187"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hölder’s inequality for shifted quantum integral operator 位移量子积分算子的Hölder不等式
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-02-02 DOI: 10.1016/j.exco.2025.100179
Andrea Aglić Aljinović, Lana Horvat Dmitrović, Ana Žgaljić Keko
{"title":"Hölder’s inequality for shifted quantum integral operator","authors":"Andrea Aglić Aljinović,&nbsp;Lana Horvat Dmitrović,&nbsp;Ana Žgaljić Keko","doi":"10.1016/j.exco.2025.100179","DOIUrl":"10.1016/j.exco.2025.100179","url":null,"abstract":"<div><div>We show by two counterexamples that Hölder’s inequality for shifted quantum integral operator does not hold in general and we prove the case in which it is valid.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100179"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143240692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Counterexamples for your calculus course 微积分课的反例
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-02-03 DOI: 10.1016/j.exco.2025.100177
Jürgen Appell , Simon Reinwand
{"title":"Counterexamples for your calculus course","authors":"Jürgen Appell ,&nbsp;Simon Reinwand","doi":"10.1016/j.exco.2025.100177","DOIUrl":"10.1016/j.exco.2025.100177","url":null,"abstract":"<div><div>We present 2 theorems and 20 counterexamples illustrating the surprising behaviour of functions between metric spaces.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100177"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143240880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exceptional surgeries on hyperbolic knots arising from the 3-chain link 特殊手术对双曲节产生的3链
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-02-14 DOI: 10.1016/j.exco.2025.100182
Alberto Cavicchioli, Fulvia Spaggiari
{"title":"Exceptional surgeries on hyperbolic knots arising from the 3-chain link","authors":"Alberto Cavicchioli,&nbsp;Fulvia Spaggiari","doi":"10.1016/j.exco.2025.100182","DOIUrl":"10.1016/j.exco.2025.100182","url":null,"abstract":"<div><div>We study some closed connected orientable 3–manifolds obtained by Dehn surgery along the oriented components of the 3-chain link. For such manifolds, we describe exceptional surgeries related to some results from Audoux et al. (2018) and Martelli and Petronio (2006). Then we construct a related family of hyperbolic knots in the 3-sphere, which admit two consecutive Seifert fibered surgeries and two toroidal fillings at distance 3. Such additional examples are not mentioned in the quoted papers.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100182"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods 由有限差分方法导出的晶格Boltzmann格式的非唯一性
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2024-12-18 DOI: 10.1016/j.exco.2024.100171
Eliane Kummer, Stephan Simonis
{"title":"Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods","authors":"Eliane Kummer,&nbsp;Stephan Simonis","doi":"10.1016/j.exco.2024.100171","DOIUrl":"10.1016/j.exco.2024.100171","url":null,"abstract":"<div><div>Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1–40]. It is thus known that any lattice Boltzmann scheme can be expressed in terms of a corresponding multi-step finite difference scheme on the conserved variables. In the present work, we provide counterexamples for the conjecture that any multi-step finite difference scheme has a unique lattice Boltzmann formulation. Based on that, we indicate the existence of equivalence classes for discretized relaxation systems.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100171"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph 在具有图的Hilbert空间中，G-Tseng近似g变分不等式问题的提取方法
Examples and Counterexamples Pub Date : 2025-06-01 Epub Date: 2025-04-28 DOI: 10.1016/j.exco.2025.100185
Monika Swami , M.R. Jadeja
{"title":"G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph","authors":"Monika Swami ,&nbsp;M.R. Jadeja","doi":"10.1016/j.exco.2025.100185","DOIUrl":"10.1016/j.exco.2025.100185","url":null,"abstract":"<div><div>In this article, we introduce the <span><math><mi>G</mi></math></span>-Tseng’s extragradient method, inspired by the extragradient method defined by Korpelevich, for solving <span><math><mi>G</mi></math></span>-variational inequality problems in Hilbert space. We also address a fixed point problem in a Hilbert space endowed with a graph using the proposed <span><math><mi>G</mi></math></span>-Tseng’s extragradient method. In the context of Hilbert space, we establish weak and strong convergence theorems for the algorithm. Additionally, we provide numerical examples to support our findings.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100185"},"PeriodicalIF":0.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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