scholarly journals Rational points and derived equivalence

2021 ◽  
Vol 157 (5) ◽  
pp. 1036-1050
Author(s):  
Nicolas Addington ◽  
Benjamin Antieau ◽  
Katrina Honigs ◽  
Sarah Frei
Keyword(s):  
Rational Point ◽  
Source Code ◽  
Rational Points ◽  
The Other ◽  
Online Version ◽  
Hasse Principle ◽  
Derived Equivalence ◽  
Derived Equivalences ◽  
Closed Fields ◽  
Supplementary Material

We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors over Jacobians of curves over $\mathbb {Q}$ and $\mathbb {F}_q(t)$ , and conclude with a pair of hyperkähler 4-folds over $\mathbb {Q}$ . The latter is independently interesting as a new example of a transcendental Brauer–Manin obstruction to the Hasse principle. The source code for the various computations is supplied as supplementary material with the online version of this article.

Some cubic surfaces with no rational points

1978 ◽  
Vol 84 (2) ◽  
pp. 219-223 ◽  
Author(s):  
Andrew Bremner
Keyword(s):  
Rational Point ◽  
Rational Points ◽  
Hasse Principle ◽  
Cubic Surfaces ◽  
Image Position

Selmer(1) conjectured that the Hasse principle holds for all cubic surfaces of the typethat is, such a surface has a rational point whenever it has points defined over every p-adic field Qp; and he proved this assertion in the case that ab = cd.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

The Roman Fort at Bainbridge, Wensleydale: Excavations by B.R. Hartley on the Principia and a Summary Account of Other Excavations and Surveys

Britannia ◽  
2012 ◽  
Vol 43 ◽  
pp. 45-113 ◽  
Author(s):  
Paul Bidwell
Keyword(s):  
Detailed Analysis ◽  
Tenth Century ◽  
Roman Period ◽  
The Other ◽  
Main Text ◽  
Commanding Officer ◽  
Supplementary Material

AbstractOccupation at Bainbridge began in the governorship of Agricola. Little is known of the first fort; the visible remains represent a successor fort, established in c.a.d. 85 at the earliest, abandoned under Hadrian and Antoninus Pius, and reoccupied in c. a.d. 160. In the early Severan period, the size of the unit at the fort seems to have been greatly reduced in numbers, and a suite of rooms for an officer was inserted in the principia. Extensive work by cohors VI Nerviorum which took place in c. a.d. 205–7 included the building of new principia, the relocation of the east gate, and probably the addition of an annexe, its wall described in an inscription from the site as a bracchium. The fort was held until the end of the Roman period, by which time the principia had been partly demolished to provide space for a timber building probably accommodating the commanding officer. The aedes and part of the rear range seem to have stood until the ninth or tenth century, when the former was possibly converted into a church. Knowledge of this sequence of occupation depends largely on the results of Brian Hartley's excavations which are published here. The main focus of the report is on the remarkable series of principia, but a review of what is known of the overall archaeology of the fort is also included in the main text. The Supplementary Material (http://journals.cambridge.org/bri) contains a more detailed analysis of some of the other excavations together with various specialist reports.

Erratum: Fibers of word maps and the multiplicities of non-abelian composition factors

2021 ◽  
Vol 31 (01) ◽  
pp. 201-204
Author(s):  
Alexander Bors
Keyword(s):  
Source Code ◽  
The Other ◽  
Title One ◽  
Composition Factors

We discuss two corrections concerning the paper mentioned in the title. One of them pertains to a slight error in a statement from a different paper that was used. For this statement, it is explained how to fix it and why this does not affect the correctness of our results. The other is concerned with an error in the original GAP source code used to verify some of our results. This error, which was subsequently fixed, did affect the correctness of one of our main theorems, which is now given in corrected (and stronger) form.

Plagiarism Detection Algorithm for Source Code in Computer Science Education

2015 ◽  
Vol 13 (4) ◽  
pp. 29-39 ◽  
Author(s):  
Xin Liu ◽  
Chan Xu ◽  
Boyu Ouyang
Keyword(s):  
Hash Function ◽  
Source Code ◽  
College Education ◽  
Detection Algorithm ◽  
Longest Common Subsequence ◽  
The Other ◽  
Plagiarism Detection ◽  
Detection Algorithms ◽  
Common Subsequence ◽  
Basic Concepts

Nowadays, computer programming is getting more necessary in the course of program design in college education. However, the trick of plagiarizing plus a little modification exists among some students' home works. It's not easy for teachers to judge if there's plagiarizing in source code or not. Traditional detection algorithms cannot fit this condition. The author designed an effective and complete method to detect source code plagiarizing according to the popular way of students' plagiarizing. There are two basic concepts of the algorithm. One is to standardize the source code via filtration against to remove the majority noises intentionally blended by plagiarists. The other one is an improved Longest Common Subsequence algorithm for text matching, using statement as the unit for matching. The authors also designed an appropriate HASH function to increase the efficiency of matching. Based on the algorithm, a system was designed and proved to be practical and sufficient, which runs well and meet the practical requirement in application.

scholarly journals Genus-2 curves and Jacobians with a given number of points

2015 ◽  
Vol 18 (1) ◽  
pp. 170-197 ◽  
Author(s):  
Reinier Bröker ◽  
Everett W. Howe ◽  
Kristin E. Lauter ◽  
Peter Stevenhagen
Keyword(s):  
Finite Field ◽  
Elliptic Curves ◽  
Polynomial Time ◽  
Rational Points ◽  
The Other ◽  
Base Field ◽  
Arbitrary Base ◽  
The Family ◽  
Genus 2 ◽  
Genus 2 Curves

AbstractWe study the problem of efficiently constructing a curve $C$ of genus $2$ over a finite field $\mathbb{F}$ for which either the curve $C$ itself or its Jacobian has a prescribed number $N$ of $\mathbb{F}$-rational points.In the case of the Jacobian, we show that any ‘CM-construction’ to produce the required genus-$2$ curves necessarily takes time exponential in the size of its input.On the other hand, we provide an algorithm for producing a genus-$2$ curve with a given number of points that, heuristically, takes polynomial time for most input values. We illustrate the practical applicability of this algorithm by constructing a genus-$2$ curve having exactly $10^{2014}+9703$ (prime) points, and two genus-$2$ curves each having exactly $10^{2013}$ points.In an appendix we provide a complete parametrization, over an arbitrary base field $k$ of characteristic neither two nor three, of the family of genus-$2$ curves over $k$ that have $k$-rational degree-$3$ maps to elliptic curves, including formulas for the genus-$2$ curves, the associated elliptic curves, and the degree-$3$ maps.Supplementary materials are available with this article.

Rational points on Fermat curves over finite fields

2017 ◽  
Vol 16 (03) ◽  
pp. 1750046
Author(s):  
Wei Cao ◽  
Shanmeng Han ◽  
Ruyun Wang
Keyword(s):  
Finite Fields ◽  
Rational Point ◽  
Rational Points ◽  
Fermat Curve ◽  
Fermat Curves ◽  
Curves Over Finite Fields

Let [Formula: see text] be the [Formula: see text]-rational point on the Fermat curve [Formula: see text] with [Formula: see text]. It has recently been proved that if [Formula: see text] then each [Formula: see text] is a cube in [Formula: see text]. It is natural to wonder whether there is a generalization to [Formula: see text]. In this paper, we show that the result cannot be extended to [Formula: see text] in general and conjecture that each [Formula: see text] is a cube in [Formula: see text] if and only if [Formula: see text].

Effects of nandrolone decanoate on time to consolidation of bone defects resulting from osteotomy for tibial tuberosity advancement

2017 ◽  
Vol 30 (05) ◽  
pp. 351-356 ◽  
Author(s):  
José Ibañez ◽  
Itallo Freitas ◽  
Ana Hespanha ◽  
Juliana Monteiro ◽  
Mayara Eggert ◽  
...  
Keyword(s):  
Visual Inspection ◽  
Bone Defects ◽  
Tibial Tuberosity ◽  
The Other ◽  
Meniscal Injury ◽  
Nandrolone Decanoate ◽  
Bone Consolidation ◽  
Significant Difference ◽  
Supplementary Material ◽  
Kappa Agreement

SummaryStudy design: Experimental study.Objective: The aim of this study was to evaluate the effect of nandrolone decanoate (ND) on the time taken for bone consolidation in dogs undergoing tibial tuberosity advancement surgery (TTA).Materials and methods: Seventeen dogs that underwent TTA surgery were randomly divided into two groups: group C (TTA; 9 stifles), and group TTA+ND (TTA and systemic administration of ND; 8 stifles). Three observers (two radiologists and an orthopaedic surgeon), assessed bone consolidation by visual inspection of serial radiographs at intervals of 21 days following surgery.Results: There were no differences in median weight and age between groups, nor between the medians of the variables right and left stifle. Only weight and age values were normally distributed. The other variables, right and left stifle and time to consolidation, showed non-normal distribution. Meniscal injury was present in all animals in group C and all animals in group TTA+ND. There was a significant difference between time to consolidation in groups C and TTA+ND (p <0.05). One animal in the group TTA+ND showed increased libido. Kappa agreement among observers on radiographs was 0.87.Conclusion: Administration of ND reduces time to bone consolidation in dogs undergoing TTA.Supplementary Material for this article is available online at https://doi.org/10.3415/VCOT-16-09-0130

Plagiarism Detection Algorithm for Source Code in Computer Science Education

2019 ◽  
pp. 354-365
Author(s):  
Xin Liu ◽  
Chan Xu ◽  
Boyu Ouyang
Keyword(s):  
Hash Function ◽  
Source Code ◽  
College Education ◽  
Detection Algorithm ◽  
Longest Common Subsequence ◽  
The Other ◽  
Plagiarism Detection ◽  
Detection Algorithms ◽  
Common Subsequence ◽  
Basic Concepts

Nowadays, computer programming is getting more necessary in the course of program design in college education. However, the trick of plagiarizing plus a little modification exists among some students' home works. It's not easy for teachers to judge if there's plagiarizing in source code or not. Traditional detection algorithms cannot fit this condition. The author designed an effective and complete method to detect source code plagiarizing according to the popular way of students' plagiarizing. There are two basic concepts of the algorithm. One is to standardize the source code via filtration against to remove the majority noises intentionally blended by plagiarists. The other one is an improved Longest Common Subsequence algorithm for text matching, using statement as the unit for matching. The authors also designed an appropriate HASH function to increase the efficiency of matching. Based on the algorithm, a system was designed and proved to be practical and sufficient, which runs well and meet the practical requirement in application.

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