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The Arithmetic of Points on a Conic and Projectivities 二次曲线上点的算术与投影
The Mathematica journal Pub Date : 2019-01-01 DOI: 10.3888/TMJ.21-2
H. Coxeter, G. Beck
{"title":"The Arithmetic of Points on a Conic and Projectivities","authors":"H. Coxeter, G. Beck","doi":"10.3888/TMJ.21-2","DOIUrl":"https://doi.org/10.3888/TMJ.21-2","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962562","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
From Discrete to Continuous Spectra 从离散光谱到连续光谱
The Mathematica journal Pub Date : 2019-01-01 DOI: 10.3888/tmj.21-3
C. Winfield
{"title":"From Discrete to Continuous Spectra","authors":"C. Winfield","doi":"10.3888/tmj.21-3","DOIUrl":"https://doi.org/10.3888/tmj.21-3","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962584","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
Peak Response of Single-Degree-of-Freedom Systems to Swept-Frequency Excitation 单自由度系统对扫频激励的峰值响应
The Mathematica journal Pub Date : 2019-01-01 DOI: 10.3888/tmj.21-1
Christopher H. Reed, A. Kabe
{"title":"Peak Response of Single-Degree-of-Freedom Systems to Swept-Frequency Excitation","authors":"Christopher H. Reed, A. Kabe","doi":"10.3888/tmj.21-1","DOIUrl":"https://doi.org/10.3888/tmj.21-1","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962503","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: 2
Computational Aspects of Quaternionic Polynomials - Part I: Manipulating, Evaluating and Factoring 四元数多项式的计算方面——第一部分：操作、评估和因子分解
The Mathematica journal Pub Date : 2018-05-01 DOI: 10.3888/TMJ.20-4
I. Falcão, Fernando Miranda, R. Severino, Joana Soares
{"title":"Computational Aspects of Quaternionic Polynomials - Part I: Manipulating, Evaluating and Factoring","authors":"I. Falcão, Fernando Miranda, R. Severino, Joana Soares","doi":"10.3888/TMJ.20-4","DOIUrl":"https://doi.org/10.3888/TMJ.20-4","url":null,"abstract":"Research at the Centre of Mathematics at the University of Minho was financed by Portuguese Funds \u0000through FCT - Fundacao para a Ciencia e a Tecnologia, within the Project UID/MAT/00013/2013. Research \u0000at the Economics Politics Research Unit was carried out within the funding with COMPETE \u0000reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC’s \u0000(Fundacao para a Ciencia e a Tecnologia, I.P.) financial support through national funding and by the \u0000European Regional Development Fund through the Operational Programme on “Competitiveness and \u0000Internationalization - COMPETE 2020” under the PT2020 Partnership Agreement.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42504197","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: 1
Improving the Kruskal–Katona Bounds for Complete Subgraphs of a Graph 改进图的完全子图的Kruskal-Katona界
The Mathematica journal Pub Date : 2018-01-01 DOI: 10.3888/TMJ.20-6
R. Cowen
{"title":"Improving the Kruskal–Katona Bounds for Complete Subgraphs of a Graph","authors":"R. Cowen","doi":"10.3888/TMJ.20-6","DOIUrl":"https://doi.org/10.3888/TMJ.20-6","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962375","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: 2
A Beginner’s Guide to Solving Sudoku Puzzles by Computer 用电脑解决数独的初学者指南
The Mathematica journal Pub Date : 2018-01-01 DOI: 10.3888/tmj.20-1
R. Cowen
{"title":"A Beginner’s Guide to Solving Sudoku Puzzles by Computer","authors":"R. Cowen","doi":"10.3888/tmj.20-1","DOIUrl":"https://doi.org/10.3888/tmj.20-1","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962340","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
The Modular Group 模块组
The Mathematica journal Pub Date : 2018-01-01 DOI: 10.3888/TMJ.20-3
P. Mccreary, Teri Jo Murphy, Christan Carter
{"title":"The Modular Group","authors":"P. Mccreary, Teri Jo Murphy, Christan Carter","doi":"10.3888/TMJ.20-3","DOIUrl":"https://doi.org/10.3888/TMJ.20-3","url":null,"abstract":"The modular group Γ is the set of all 2 × 2 matrices with integral elements and determinant 1. That is, Γ is the special linear group of 2 × 2 matrices over the integers, Γ = SL(2, Z). It forms a group under matrix multiplication. If M = a b c d ∈ Γ Then M defines a map f M (z) = az + b cz + d of the extended complex plane to itself. Here f M (−d/c) = ∞, and f M (∞) = a/c. Suppose that N = α β γ δ. Then by direct calculation we find that f N (f M (z)) = (αa + βc)z + (αb + βd) (γa + δc)z + (γb + δd) = f N M (z). While it might seem surprising that the composition of one such rational function with another would be connected with matrix multiplication, the mystery can be dispelled by considering how M and N transform the 2-dimensional vectors C 2. Suppose that M z 1 z 2 = w 1 w 2 , N w 1 w 2 = t 1 t 2. Then N M z 1 z 2 = t 1 t 2. Now suppose we consider these vectors in terms of projective geometry. Two vectors are then considered to be the same if their coordinates are proportional (i.e., the vectors are colinear). In other words, if c is a non-zero complex number, then z 1 z 2 and cz 1 cz 2 are considered to be the same. Thus a projective point z 1 : z 2 is determined by the ratio z = z 1 /z 2 if its coordinates, and the image w 1 : w 2 is determined by the ratio w = w 1 /w 2 of its coordinates. But then w = w 1 w 2 = az 1 + bz 2 cz 1 + dz 2 = az 1 /z 2 + b cz 1 /z 2 + d = az + b cz + d , so the map from z to w reflects a linear transformation in projective coordinates.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"9 1","pages":"564-582"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962348","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: 9
A Wolfram Language Approach to Real Numerical Algebraic Plane Curves 实际数值代数平面曲线的Wolfram语言方法
The Mathematica journal Pub Date : 2018-01-01 DOI: 10.3888/tmj.20-7
Barry H. Dayton
{"title":"A Wolfram Language Approach to Real Numerical Algebraic Plane Curves","authors":"Barry H. Dayton","doi":"10.3888/tmj.20-7","DOIUrl":"https://doi.org/10.3888/tmj.20-7","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962388","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
Pseudo-Dynamic Approach to the Numerical Solution of Nonlinear Stationary Partial Differential Equations 非线性平稳偏微分方程数值解的伪动力方法
The Mathematica journal Pub Date : 2018-01-01 DOI: 10.3888/TMJ.20-8
A. Boulbitch
{"title":"Pseudo-Dynamic Approach to the Numerical Solution of Nonlinear Stationary Partial Differential Equations","authors":"A. Boulbitch","doi":"10.3888/TMJ.20-8","DOIUrl":"https://doi.org/10.3888/TMJ.20-8","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962486","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: 1
Aspects of Input Shaping Control of Flexible Mechanical Systems 柔性机械系统输入成形控制的几个方面
The Mathematica journal Pub Date : 2017-01-01 DOI: 10.3888/TMJ.19-3
D. Adair, M. Jaeger
{"title":"Aspects of Input Shaping Control of Flexible Mechanical Systems","authors":"D. Adair, M. Jaeger","doi":"10.3888/TMJ.19-3","DOIUrl":"https://doi.org/10.3888/TMJ.19-3","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962731","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: 3
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