Relevant bibliographies by topics / Farey sequence

Academic literature on the topic 'Farey sequence'

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Published: 4 June 2021
Last updated: 30 January 2023

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Journal articles on the topic "Farey sequence"

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Ripan Saha. "On Some Special Property of The Farey Sequence." Mathematical Journal of Interdisciplinary Sciences 7, no. 2 (March 6, 2019): 121–23. http://dx.doi.org/10.15415/mjis.2019.72016.

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In this paper, some special property of the Farey sequence is discussed. We prove in each term of the Farey sequence, the sum of elements in the denominator is two times of the sum of elements in the numerator. We also prove that the Farey sequence contains a palindrome structure.
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Setyati, Endang, and Raymond Sugiarto. "Pengenalan Tulisan Pada Iklan Pinggir Jalan yang Melengkung Menggunakan Shape Context." Journal of Intelligent System and Computation 3, no. 2 (October 1, 2021): 78–84. http://dx.doi.org/10.52985/insyst.v3i2.202.

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Membaca sebuah tulisan yang sama di bidang melengkung berbeda dengan di bidang datar, karena tulisan pada bidang melengkung bergantung pada permukaan bidang lengkungnya. Pada saat ini, banyak sekali tulisan pada iklan pinggir jalan yang ditempel pada bidang melengkung di sepanjang jalan. Tulisan yang digunakan berupa huruf dan angka, dengan berbagai macam background, bentuk dan warna yang diambil di pinggir jalan dengan menggunakan Farey Shape Context. Fitur Farey ini bergantung pada DSS (Digital Straight Line Segment) endpoint dan menggunakan pecahan Augmented Farey sequence. DSS endpoint ini dijadikan sebagai titik fitur atau feature point untuk menemukan shape context dari citra. DSS endpoint tersebut digunakan sebagai acuan bounding box yang akan digunakan sebagai object boundary yang dimana setiap sudutnya merupakan reference point. Untuk melakukan Binning Farey Rank, Augmented Farey Table (AFT) harus dibentuk terlebih dahulu berdasarkan Augmented Farey Sequence yang merupakan pengembangan dari Farey Sequence. Farey Sequence hanya meliputi pecahan dengan pembilang dan penyebut yang positif, sedangkan Augmented Farey Sequence meliputi pecahan dengan pembilang dan penyebut positif serta negatif. Pada penelitian ini digunakan 500 data iklan di pinggir jalan yang melengkung, dimana 70% digunakan sebagai data sample. Dari 70% data sample tersebut didapatkan ribuan karakter berupa huruf dan angka yang dijadikan data sample. Berdasarkan hasil uji coba penelitian yang dilakukan pada 500 Gambar dimana 30% sebagai data testing, maka hasil Farey Shape Context untuk mengenali tulisan berupa huruf dan angka pada iklan pinggir jalan yang melengkung mencapai akurasi benar 74.94% dan salah 25.06%.
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Shiu, Peter, and R. R. Hall. "The index of a Farey sequence." Michigan Mathematical Journal 51, no. 1 (April 2003): 209–23. http://dx.doi.org/10.1307/mmj/1049832901.

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Li, Junxian, Albert Tamazyan, and Alexandru Zaharescu. "Ducci iterates and similar ordering of visible points in convex regions." International Journal of Number Theory 16, no. 01 (July 25, 2019): 1–28. http://dx.doi.org/10.1142/s1793042120500013.

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Hardy et al. first introduced the notion of similar ordering of pairs of rationals, and Mayer proved that pairs of Farey fractions in [Formula: see text] are similarly ordered when [Formula: see text] is large enough. We generalize Mayer’s result to Ducci iterates of Farey sequence and visible points in certain regions in the plane. We also study the distribution of values of generalized indices of these sequences.
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Tou, Erik R. "The Farey Sequence: From Fractions to Fractals." Math Horizons 24, no. 3 (February 2017): 8–11. http://dx.doi.org/10.4169/mathhorizons.24.3.8.

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HEERSINK, BYRON. "Equidistribution of Farey sequences on horospheres in covers of and applications." Ergodic Theory and Dynamical Systems 41, no. 2 (October 7, 2019): 471–93. http://dx.doi.org/10.1017/etds.2019.71.

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We establish the limiting distribution of certain subsets of Farey sequences, i.e., sequences of primitive rational points, on expanding horospheres in covers $\unicode[STIX]{x1D6E5}\backslash \text{SL}(n+1,\mathbb{R})$ of $\text{SL}(n+1,\mathbb{Z})\backslash \text{SL}(n+1,\mathbb{R})$, where $\unicode[STIX]{x1D6E5}$ is a finite-index subgroup of $\text{SL}(n+1,\mathbb{Z})$. These subsets can be obtained by projecting to the hyperplane $\{(x_{1},\ldots ,x_{n+1})\in \mathbb{R}^{n+1}:x_{n+1}=1\}$ sets of the form $\mathbf{A}=\bigcup _{j=1}^{J}\mathbf{a}_{j}\unicode[STIX]{x1D6E5}$, where for all $j$, $\mathbf{a}_{j}$ is a primitive lattice point in $\mathbb{Z}^{n+1}$. Our method involves applying the equidistribution of expanding horospheres in quotients of $\text{SL}(n+1,\mathbb{R})$ developed by Marklof and Strömbergsson, and more precisely understanding how the full Farey sequence distributes in $\unicode[STIX]{x1D6E5}\backslash \text{SL}(n+1,\mathbb{R})$ when embedded on expanding horospheres as done in previous work by Marklof. For each of the Farey sequence subsets, we extend the statistical results by Marklof regarding the full multidimensional Farey sequences, and solutions by Athreya and Ghosh to Diophantine approximation problems of Erdős–Szüsz–Turán and Kesten. We also prove that Marklof’s result on the asymptotic distribution of Frobenius numbers holds for sets of primitive lattice points of the form $\mathbf{A}$.
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Mihaila, Ioana. "Farey Sums and Understanding Ratios." Mathematics Teacher 98, no. 3 (October 2004): 158–62. http://dx.doi.org/10.5951/mt.98.3.0158.

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Ringland, John, Naoum Issa, and Mark Schell. "From U sequence to Farey sequence: A unification of one-parameter scenarios." Physical Review A 41, no. 8 (April 1, 1990): 4223–35. http://dx.doi.org/10.1103/physreva.41.4223.

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PRATIHAR, SANJOY, PARTHA BHOWMICK, SHAMIK SURAL, and JAYANTA MUKHOPADHYAY. "SKEW CORRECTION OF DOCUMENT IMAGES BY RANK ANALYSIS IN FAREY SEQUENCE." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 07 (November 2013): 1353004. http://dx.doi.org/10.1142/s0218001413530042.

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Skew correction of a scanned document page is an important preprocessing step in document image analysis. We propose here a fast and robust skew estimation algorithm based on rank analysis in Farey sequence. Our target document class comprises two major Indian scripts with headlines, namely Devnagari and Bangla. At the beginning, straight edge segments from the edge map of the document page are detected by our algorithm using properties of digital straightness. Straight edges derived in this manner are binned by Farey ranks in correspondence with their slopes. The principal bin, identified from these bins using the strength of accumulated edge points, represents the principal direction along the direction of headlines, from which the gross skew angle is estimated. A fast refinement algorithm is then applied with a finer tuning of Farey ranks, to detect the skew up to the desired level of precision. The algorithm has been tested on a diverse set of document images, containing Bangla and Devnagari scripts. Experimental results are quite encouraging in terms of accuracy, sensitivity to non-textual objects, effectiveness in dealing with unrestricted layouts, and computational efficiency.
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Poornima, M., S. Jagannathan, R. Chandrasekhar, and S. T Kumara. "Farey Sequence for Error Correcting Codes and Medical Images." International Journal of Engineering & Technology 7, no. 3.1 (August 4, 2018): 118. http://dx.doi.org/10.14419/ijet.v7i3.1.16812.

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A new scheme for Error Correcting Codes and the coding of medical images through Farey Sequence is brought in the paper. It brings out the reduced real point representations and more of integer point representations. The test case and outcomes are explained in the section 4 and 5.
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Dissertations / Theses on the topic "Farey sequence"

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Tolmie, Julie, and julie tolmie@techbc ca. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." The Australian National University. School of Mathematical Sciences, 2000. http://thesis.anu.edu.au./public/adt-ANU20020313.101505.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. ¶ The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. ¶ The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.
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Tolmie, Julie. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." Phd thesis, 2000. http://hdl.handle.net/1885/6969.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.
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Books on the topic "Farey sequence"

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A motif of mathematics: [history and application of the mediant and the Farey sequence]. Boston: Docent Press, 2011.

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Farey Sequences: Duality and Maps Between Subsequences. de Gruyter GmbH, Walter, 2017.

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Matveev, Andrey O. Farey Sequences: Duality and Maps Between Subsequences. de Gruyter GmbH, Walter, 2017.

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Matveev, Andrey O. Farey Sequences: Duality and Maps Between Subsequences. de Gruyter GmbH, Walter, 2017.

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Bird, Alexander. Scientific Progress. Edited by Paul Humphreys. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199368815.013.29.

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What constitutes scientific progress? This article considers and evaluates three competing answers to this question. These seek to understand scientific progress in terms of problem-solving, of truthlikeness/verisimilitude, and of knowledge, respectively. How does each fare, taking into consideration the fact that the history of science involves disruptive change, not merely the addition of new beliefs to old beliefs, and the fact that sometimes the history of such changes involves a sequence of theories, all of which are believed to be false, even by scientific realists? The three answers are also evaluated with regard to how they assess certain real and hypothetical scientific changes. Also considered are the three views of the goal of science implicit in the three answers. The view that the goal of science is knowledge and that progress is constituted by the accumulation of knowledge is argued to be preferable to its competitors.
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Book chapters on the topic "Farey sequence"

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Pǎtraşcu, Corina E., and Mihai Pǎtraşcu. "Computing Order Statistics in the Farey Sequence." In Lecture Notes in Computer Science, 358–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24847-7_27.

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Marklof, Jens. "Fine-Scale Statistics for the Multidimensional Farey Sequence." In Limit Theorems in Probability, Statistics and Number Theory, 49–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36068-8_3.

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Boenn, Georg. "The Farey Sequence as a Model for Musical Rhythm and Meter." In Computational Models of Rhythm and Meter, 83–112. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76285-2_7.

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Burger, Edward. "Building the rationals via Farey sequences." In The Student Mathematical Library, 11–15. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/stml/008/03.

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Hulin, Jérôme, and Édouard Thiel. "Farey Sequences and the Planar Euclidean Medial Axis Test Mask." In Lecture Notes in Computer Science, 82–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10210-3_7.

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Pratihar, Sanjoy, and Partha Bhowmick. "On Applying the Farey Sequence for Shape Representation in Z2." In Speech, Image, and Language Processing for Human Computer Interaction, 172–90. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-0954-9.ch009.

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Describing the shape of an object is a well-studied, yet ever-engrossing problem, because an appropriate description can improve the efficiency of a shape matching algorithm, thereby enriching subsequent applications. The authors propose a novel boundary-based shape description using the Farey sequence to capture an object shape represented as a sequence of discrete straight line segments. The straight edges are extracted directly from a gray-scale image without resorting to any edge map detection, and without using any thinning procedure. Then we merge the straight pieces, which are almost collinear but usually small in length, by employing the novel idea of an Augmented Farey Table (AFT). An AFT is a preprocessed data structure that provides us the Farey indices based on which the amount of linearity of three consecutive vertices of a polygon in the digital plane, is decided. Using the final straight pieces after AFT-based merging, the authors build a shape description using the Farey indices of the merged/larger pieces. In particular, the method would be computationally attractive for polygonal approximation and shape description of a large database of gray-scale images. Experimental results demonstrate its usefulness, efficiency, and elegance.
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"Farey sequences and collective decision making." In Farey Sequences, 1–4. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110547665-001.

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"1. Basic properties of Farey sequences." In Farey Sequences, 5–68. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110547665-002.

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"2. Farey duality." In Farey Sequences, 69–142. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110547665-003.

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"3. Monotone maps between Farey subsequences." In Farey Sequences, 143–56. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110547665-004.

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Conference papers on the topic "Farey sequence"

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Pratihar, Sanjoy, and Partha Bhowmick. "Shape decomposition using Farey sequence and saddle points." In the Seventh Indian Conference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1924559.1924570.

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Pratihar, Sanjoy, and Partha Bhowmick. "Vectorization of thick digital lines using Farey sequence and geometric refinement." In the Seventh Indian Conference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1924559.1924629.

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Poornima, M., S. Jagannathan, and R. Chandrasekhar. "Farey sequences and image processing of brain images." In 2016 International conference on Signal Processing, Communication, Power and Embedded System (SCOPES). IEEE, 2016. http://dx.doi.org/10.1109/scopes.2016.7955780.

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Thomas, Terry M., Micky C. Marine, Jeffrey L. Wirth, and Brian W. Peters. "Emergency-Locking Retractor Performance in Rollover Accidents." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39101.

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Generally accepted accident statistical analyses indicate that seat belted occupants involved in automobile accidents fare far better than those that are not belted. This is especially true for rollover accidents, with the primary reason being that seat belts help prevent ejection of the occupant from the vehicle. Ejected occupants are far more likely to incur serious or fatal injuries than those that remain inside the vehicle occupant compartment. Nonetheless, even belted occupants can be seriously or fatally injured in rollovers. The excursion of belted occupants during rollover accidents has been a topic of research over the past several years. Much work has been reported on the effects of belt anchor geometry. More recently published analyses have looked at the performance of the seat belt retractor in rollover accidents as well as other accident scenarios. One theory, put forth by various analysts, is that the seat belt webbing can “spool-out” from vehicle-sensitive emergency-locking retractors (ELR’s). According to this theory, the “spool-out” mechanism occurs because the retractor may cycle between a locked condition to an unlocked condition as the vehicle is overturning. Seat belt webbing can then be spooled-out from the retractor if the occupant engages the seat belt at a time that the retractor is in an unlocked condition. The added webbing introduced into the seat belt system mitigates the effectiveness of the seat belt during the subsequent roll motion. In this paper, we specifically address the performance of ELR’s in rollover accidents. A detailed analysis of the various phases of a multiple-roll rollover sequence, with an emphasis on vehicle dynamics and occupant kinematics as they relate to the physics of the sensing mass and operation of the retractor spool and locking mechanism(s), is presented. Additionally, the results of full-scale rollover testing are analyzed. The conditions to effect a retractor “spool-out” require that the sensing mass of the ELR must move to a neutral position, and the occupant must move in such a way to release tension in the seat belt thereby allowing webbing to retract back onto the spool. This retraction motion is necessary to release the ELR lockup components from a locked position. After conditions have been achieved, the sensing mass must then remain in a neutral position while occupant moves sufficiently, relative to the vehicle, to withdraw seat belt webbing from the The analysis presented in this paper and the results of testing indicate that the circumstances necessary for retractor spool-out to occur are not present in rollover accidents. A condition where sensing mass of the ELR will remain in a neutral position long enough and coincident with the occupant moving relative to the vehicle in such a manner to withdraw appreciable webbing from the does not occur. The external inputs to the vehicle that induce occupant motion also induce mass motion. The sensing mass need only move fractions of an inch to activate the retractor mechanisms. As a result, the retractor will be locked before webbing can be extracted from webbing spool.
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