A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called euclidean rhythms in world music. We offer a method to easily calculate Euclid...
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A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called euclidean rhythms in world music. We offer a method to easily calculate Euclid's algorithm by hand as a modification of Bresenham's line-drawing algorithm. Notably, this modified algorithm is a nonrecursive matrix construction, using only modular arithmetic and combinatorics. This construction does not outperform the traditional divide-with-remainder method;it is presented for combinatorial interest and ease of hand computation.
We analyse the behaviour of the euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field $\mathbb{F}_{q}$ of q elements when the highest degree polynomial g is fixed. Consid...
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We analyse the behaviour of the euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field $\mathbb{F}_{q}$ of q elements when the highest degree polynomial g is fixed. Considering all the elements f of fixed degree, we establish asymptotically optimal bounds in terms of q for the number of elements f that are relatively prime with g and for the average degree of $\gcd(g,f)$ . We also exhibit asymptotically optimal bounds for the average-case complexity of the euclidean algorithm applied to pairs (g,f) as above.
Borrowing inspiration from Marcone and Montalban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed tree...
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Borrowing inspiration from Marcone and Montalban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an analogous correspondence with equimorphism classes of indecomposable finite rank discrete linear orders. We also introduce the class of finitely presented linear orders-the smallest subclass of finite rank linear orders containing 1, omega and omega* and closed under finite sums and lexicographic products. For this class we develop a generalization of the euclidean algorithm where the width of a linear order plays the role of the euclidean norm. Using this as a tool we classify the isomorphism classes of finitely presented linear orders in terms of an equivalence relation on their presentations using 3-signed trees.(c) 2023 Elsevier B.V. All rights reserved.
We introduce a generalization of the euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an o...
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We introduce a generalization of the euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution that admit such an algorithm. We give two applications: first, any order that admits such an algorithm has class number 1;second, we show how the existence of such an algorithm relates to the problem of constructing explicit Dirichlet domains for Kleinian subgroups of the isometry group of hyperbolic 4-space. (C) 2020 Elsevier Inc. All rights reserved.
Over-speeding is one of the problems that contribute to the causes of road accidents which leads to traffic. As many automated systems are currently emerging to detect the speed of the vehicles to prevent accidents, t...
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ISBN:
(纸本)9781450385930
Over-speeding is one of the problems that contribute to the causes of road accidents which leads to traffic. As many automated systems are currently emerging to detect the speed of the vehicles to prevent accidents, the growing number of vehicles puts itself as another factor that affects the improvement of our current systems which can affect both accuracy and performance. The proposed method aims to improve the classification model to handle a large input to further improve the speed estimation system. A YOLOv3 model was utilized to detect and classify vehicles which gained a 96.69% accuracy, and the application of the euclidean algorithm for speed estimation yielded a +/- 0.00286494m/s (0.010313784 km/h) margin of sampling error with a 95% level of confidence.
In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is e...
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In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. Mathematics is rife with the usage of some of its concepts in the study of other ones when these concepts belong to its very different branches. The article presents an example of such a surprising meeting-the use of the euclidean algorithm in geometric constructions with the help of just a straightedge. The article can be used to enrich mathematical activities in high school and by teachers and students of classical geometry in colleges and universities.
A novel method based on euclidean algorithm is proposed to solve the problem of blind recognition of binary Bose-Chaudhuri-Hocquenghem (BCH) codes in non-cooperative applications. By carrying out iterative euclidean d...
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A novel method based on euclidean algorithm is proposed to solve the problem of blind recognition of binary Bose-Chaudhuri-Hocquenghem (BCH) codes in non-cooperative applications. By carrying out iterative euclidean divisions on the demodulator output bit-stream, the proposed method can determine the codeword length and generator polynomial of unknown BCH code. The computational complexity is derived asO(n(3)). Simulation results show the efficiency of the proposed method.
Over-speeding is one of the problems that contribute to the causes of road accidents which leads to traffic. As many automated systems are currently emerging to detect the speed of the vehicles to prevent accidents, t...
详细信息
ISBN:
(纸本)9781450385930
Over-speeding is one of the problems that contribute to the causes of road accidents which leads to traffic. As many automated systems are currently emerging to detect the speed of the vehicles to prevent accidents, the growing number of vehicles puts itself as another factor that affects the improvement of our current systems which can affect both accuracy and performance. The proposed method aims to improve the classification model to handle a large input to further improve the speed estimation system. A YOLOv3 model was utilized to detect and classify vehicles which gained a 96.69% accuracy, and the application of the euclidean algorithm for speed estimation yielded a +/- 0.00286494m/s (0.010313784 km/h) margin of sampling error with a 95% level of confidence.
A profiling attack is a powerful variant among the noninvasive side channel attacks. In this work, we target RSA key generation relying on the binary version of the extended euclidean algorithm for modular inverse and...
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A profiling attack is a powerful variant among the noninvasive side channel attacks. In this work, we target RSA key generation relying on the binary version of the extended euclidean algorithm for modular inverse and GCD computations. To date, this algorithm has only been exploited by simple power analysis;therefore, the countermeasures described in the literature are focused on mitigating only this kind of attack. We demonstrate that one of those countermeasures is not effective in preventing profiling attacks. The feasibility of our approach relies on the extraction of several leakage vectors from a single power trace. Moreover, because there are known relationships between the secrets and the public modulo in RSA, the uncertainty in some of the guessed secrets can be reduced by simple tests. This increases the effectiveness of the proposed attack.
The article discusses the polynomial version of the euclidean algorithm and the solutions to the linear equation AX + BY = gcd (A,B) over a finite field. Topics include how the polynomial euclidean solution of linear ...
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The article discusses the polynomial version of the euclidean algorithm and the solutions to the linear equation AX + BY = gcd (A,B) over a finite field. Topics include how the polynomial euclidean solution of linear equation can lie closest to (0,0) based on the integer case, the radius q-times at each concentric circles of the polynomial euclidean solution, and the distances between the adjacent solutions.
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