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Добірка наукової літератури з теми "Arithmetic applications"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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Статті в журналах з теми "Arithmetic applications"

1

de Figueiredo, Luiz Henrique, and Jorge Stolfi. "Affine Arithmetic: Concepts and Applications." Numerical Algorithms 37, no. 1-4 (December 2004): 147–58. http://dx.doi.org/10.1023/b:numa.0000049462.70970.b6.

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2

Milea, Suzana, Christopher D. Shelley, and Martin H. Weissman. "Arithmetic of arithmetic Coxeter groups." Proceedings of the National Academy of Sciences 116, no. 2 (December 26, 2018): 442–49. http://dx.doi.org/10.1073/pnas.1809537115.

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In the 1990s, J. H. Conway published a combinatorial-geometric method for analyzing integer-valued binary quadratic forms (BQFs). Using a visualization he named the “topograph,” Conway revisited the reduction of BQFs and the solution of quadratic Diophantine equations such as Pell’s equation. It appears that the crux of his method is the coincidence between the arithmetic group PGL2(Z) and the Coxeter group of type (3,∞). There are many arithmetic Coxeter groups, and each may have unforeseen applications to arithmetic. We introduce Conway’s topograph and generalizations to other arithmetic Coxeter groups. This includes a study of “arithmetic flags” and variants of binary quadratic forms.

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3

Wood, Eric F. "Applications: Self-Checking Codes—An Application of Modular Arithmetic." Mathematics Teacher 80, no. 4 (April 1987): 312–16. http://dx.doi.org/10.5951/mt.80.4.0312.

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In the teaching of mathematics or computer science in secondary school, it is sometimes difficult to find material to present to the students that is interesting, comprehensible, and, at the same time, representative of modern achievement in the discipline. In this article I present two very relevant applications of mathematics and computer science that all students can relate to: International Standard Book Numbers (ISBN) that appear in textbooks and universal product codes that appear on grocery products.

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4

Harris, Michael. "Arithmetic applications of the Langlands program." Japanese Journal of Mathematics 5, no. 1 (April 2010): 1–71. http://dx.doi.org/10.1007/s11537-010-0945-6.

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5

Polonsky, S. V., Jao Ching Lin, and A. V. Rylyakov. "RSFQ arithmetic blocks for DSP applications." IEEE Transactions on Appiled Superconductivity 5, no. 2 (June 1995): 2823–26. http://dx.doi.org/10.1109/77.403179.

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6

Audeh, Wasim. "Applications of Arithmetic Geometric Mean Inequality." Advances in Linear Algebra & Matrix Theory 07, no. 02 (2017): 29–36. http://dx.doi.org/10.4236/alamt.2017.72004.

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7

Marschall, Tobias, Inke Herms, Hans-Michael Kaltenbach, and Sven Rahmann. "Probabilistic Arithmetic Automata and Their Applications." IEEE/ACM Transactions on Computational Biology and Bioinformatics 9, no. 6 (November 2012): 1737–50. http://dx.doi.org/10.1109/tcbb.2012.109.

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8

Rodríguez-Villegas, E., M. J. Avedillo, J. M. Quintana, G. Huertas та A. Rueda. "νMOS-based Sorter for Arithmetic Applications". VLSI Design 11, № 2 (1 січня 2000): 129–36. http://dx.doi.org/10.1155/2000/57240.

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The capabilities of the conceptual link between threshold gates and sorting networks are explored by implementing some arithmetic demonstrators. In particular, both an (8 × 8)-multiplier and a (15, 4) counter which use a sorter as the main building block have been implemented. Traditional disadvantages of binary sorters such as their hardware intensive nature are avoided by using νMOS circuits. It allows both an improving of previous results for multipliers based on a similar architecture, and to obtain a new type of counter which shows a reduced delay when compared to a conventional implementation.

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9

Kim, Dae San, Taekyun Kim, Seog-Hoon Rim, and Sang Hun Lee. "Hermite Polynomials and their Applications Associated with Bernoulli and Euler Numbers." Discrete Dynamics in Nature and Society 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/974632.

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We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. LetPn={p(x)∈ℚ[x]∣deg p(x)≤n}be the(n+1)-dimensional vector space overℚ. Then we show that{H0(x),H1(x),…,Hn(x)}is a good basis for the spacePnfor our purpose of arithmetical and combinatorial applications.

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10

Wu, X. M., Gui Xian Li, De Bin Shan, and G. B. Yu. "RBF Neural Network Arithmetic and Applications in Surface Interpolation Reconstruction." Key Engineering Materials 460-461 (January 2011): 575–80. http://dx.doi.org/10.4028/www.scientific.net/kem.460-461.575.

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Aiming at problems such as: surface interpolation reconstruction of points cloud data，surface hole filling and two simple surface connection, a neural network arithmetic was employed. Based on radial basis function neural network, simulated annealing was employed to adjust the network weights. The new arithmetic can approach any nonlinear function by arbitrary precision, and also keep the network from getting into local minimum for global optimization feature of simulated annealing. MATLAB program was compiled, experiments on points cloud data have been done employing this arithmetic, the result shows that this arithmetic can efficiently approach the surface with 10-4 mm error precision, and also the learning speed is quick and reconstruction surface is smooth.

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Дисертації з теми "Arithmetic applications"

1

Hanss, Michael. "Applied fuzzy arithmetic : an introduction with engineering applications /." Berlin [u.a.] : Springer, 2005. http://www.loc.gov/catdir/enhancements/fy0662/2004117177-d.html.

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2

Lee, Peter. "Hybrid-logarithmic arithmetic and applications." Thesis, University of Kent, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.633518.

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This thesis is a contribution to the existing body of research on logarithmic arithmetic and signal processing. The implementation of log2 arithmetic circuits using modem digital hardware has been an area of active research for over 40 years. In this time over 400 academic papers in journals and conferences have been published and more than 40 patent applications submitted. At the time of writing there are at least 6 different research groups around the world actively working on new algorithms for conversion to and from the logarithmic domain and using logarithmic arithmetic and logarithmic signal processing in a wide range of academic, industrial, consumer and scientific applications. This thesis is separated into two sections. The first section deals with algorithms for logarithmic and anti-logarithmic conversion. It includes an overview and comparison of existing conversion algorithms before presenting two new conversion architectures which are more computationally efficient and suitable for implementation in both ASIC and VLSI technologies. The second section presents material published by the author on two specific applications of logarithmic signal processing where a Hybrid-Logarithmic Number System (Hybrid-LNS or Hybrid-Log) approach has been used. The first is the analysis, design· and implementation of a Discrete Cosine Transform (and its inverse) architecture which has been optimised for use in image compression applications such as JPEG and MPEG. The second describes the TOTEM neural network processor before discussing its implementation in both full-custom IC and FPGA technologies. The concentration. on Hybrid-LNS solutions indicates that this thesis does not discuss in any significant detail the problem of performing addition and subtraction in the logarithnlic domain. There has been extensive research into this problem in recent years and it · is beyond the scope of this thesis. This work is intended to add to the continued debate about the advantages/disadvantages of Hybrid-LNS architectures over "pure" logarithmic or LNS processors.

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3

Taïbi, Olivier. "Two arithmetic applications of Arthur's work." Palaiseau, Ecole polytechnique, 2014. https://tel.archives-ouvertes.fr/pastel-01066463/document.

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Nous proposons deux applications à l'arithmétique des travaux récents de James Arthur sur la classification endoscopique du spectre discret des groupes symplectiques et orthogonaux. La première consiste à ôter une hypothèse d'irréductibilité dans un résultat de Richard Taylor décrivant l'image des conjugaisons complexes par les représentations galoisiennes p-adiques associées aux représentations automorphes cuspidales algébriques régulières essentiellement autoduales pour le groupe GL_{2n+1} sur un corps totalement réel. Nous l'étendons également au cas de GL_{2n}, sous une hypothèse de parité du caractère multiplicatif. Nous utilisons un résultat de déformation p-adique. Plus précisément, nous montrons l'abondance de points correspondant à des représentations galoisiennes (quasi-)irréductibles sur les variétés de Hecke pour les groupes symplectiques et orthogonaux pairs. La classification d'Arthur est utilisée à la fois pour définir les représentations galoisiennes et pour transférer des représentations automorphes autoduales (pas nécessairement cuspidales) de groupes linéaires aux groupes symplectiques et orthogonaux. La deuxième application concerne le calcul explicite de dimensions d'espaces de formes automorphes ou modulaires. Notre contribution principale est un algorithme calculant les intégrales orbitales aux éléments de torsion des groupes classiques p-adiques non ramifiés, pour l'unité de l'algèbre de Hecke non ramifiée. Cela permet le calcul du côté géométrique de la formule des traces d'Arthur, et donc celui de la caractéristique d'Euler du spectre discret en niveau un. La classification d'Arthur permet l'analyse fine de cette caractéristique d'Euler, jusqu'à en déduire les dimensions des espaces de formes automorphes. De là il n'est pas difficile d'apporter une réponse à un problème plus classique: déterminer les dimensions des espaces de formes modulaires de Siegel à valeurs vectorielles
We present two arithmetic applications of James Arthur's endoscopic classification of the discrete automorphic spectrum for symplectic and orthogonal groups. The first one consists in removing the irreducibility assumption in a theorem of Richard Taylor describing the image of complex conjugations by p-adic Galois representations associated with regular, algebraic, essentially self-dual, cuspidal automorphic representations of GL_{2n+1} over a totally real number field. We also extend it to the case of representations of GL_{2n} whose multiplicative character is ''odd''. We use a p-adic deformation argument, more precisely we prove that on the eigenvarieties for symplectic and even orthogonal groups, there are ''many'' points corresponding to (quasi-)irreducible Galois representations. Arthur's endoscopic classification is used to define these Galois representations, and also to transfer self-dual automorphic representations of the general linear group to these classical groups. The second application concerns the explicit computation of dimensions of spaces of automorphic or modular forms. Our main contribution is an algorithm computing orbital integrals at torsion elements of an unramified p-adic classical group, for the unit of the unramified Hecke algebra. It allows to compute the geometric side in Arthur's trace formula, and thus the Euler characteristic of the discrete spectrum in level one. Arthur's endoscopic classification allows to analyse precisely this Euler characteristic, and deduce the dimensions of spaces of level one automorphic forms. The dimensions of spaces of vector-valued Siegel modular forms, which constitute a more classical problem, are easily derived

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4

Cheng, Lo Sing. "Efficient finite field arithmetic with cryptographic applications." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/26871.

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Finite field multiplication is one of the most useful arithmetic operations and has applications in many areas such as signal processing, coding theory and cryptography. However, it is also one of the most time consuming operations in both software and hardware, which makes it pertinent to develop a fast and efficient implementation. We propose four improved FPGA multiplication implementations using the Karatsuba and Fast Fourier Transform algorithms over GF (2n). We also implement the hyperelliptic curve coprocessor and compare the results of our finite field arithmetics on the ring arithmetics. Three of our implementations are based on the Karatsuba algorithm which has a running time of O (n1.585). Our final implementation is based on Fast Fourier Transform algorithm who's running time is O (nlog(n)). They are a significant increase from the classical schoolbook algorithm which has a running time of O (n2). We then approximate the ring arithmetic's performance in our hyperelliptic curve coprocessor by applying our finite field implementations. We had improvements of up to 96 percent over the classical multiplier. We conclude that we have the most efficient ring arithmetic FPGA implementation with regards to area and speed.

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5

Göbel, Benjamin [Verfasser], and Ulf [Akademischer Betreuer] Kühn. "Arithmetic Local Coordinates and Applications to Arithmetic Self-Intersection Numbers / Benjamin Göbel. Betreuer: Ulf Kühn." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2015. http://d-nb.info/1075317495/34.

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6

Göbel, Benjamin Verfasser], and Ulf [Akademischer Betreuer] [Kühn. "Arithmetic Local Coordinates and Applications to Arithmetic Self-Intersection Numbers / Benjamin Göbel. Betreuer: Ulf Kühn." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2015. http://nbn-resolving.de/urn:nbn:de:gbv:18-74739.

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7

Handley, W. G. "Some machine characterizations of classes close to #DELTA#0Ì²'IN." Thesis, University of Manchester, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375068.

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8

Dyer, A. K. "Applications of sieve methods in number theory." Thesis, Bucks New University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384646.

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9

Viale, Matteo. "Applications of the proper forcing axiom to cardinal arithmetic." Paris 7, 2006. http://www.theses.fr/2006PA07A003.

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10

Zhu, Dalin. "Residue number system arithmetic inspired applications in cellular downlink OFDMA." Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/2070.

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Книги з теми "Arithmetic applications"

1

Aubry, Yves, Everett Howe, and Christophe Ritzenthaler, eds. Arithmetic Geometry: Computation and Applications. Providence, Rhode Island: American Mathematical Society, 2019. http://dx.doi.org/10.1090/conm/722.

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2

Schwab, Emil. Arithmetic convolution. Applications in combinatorics. Romania: Universtatea Din Timisoara, 1988.

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3

N, Aufmann Richard, and Lockwood Joanne S, eds. Essential mathematics with applications. 5th ed. Boston: Houghton Mifflin, 1999.

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4

Christensen, Chris, Avinash Sathaye, Ganesh Sundaram, and Chandrajit Bajaj, eds. Algebra, Arithmetic and Geometry with Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18487-1.

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5

Petković, Miodrag. Complex interval arithmetic and its applications. Berlin: Wiley-VCH, 1998.

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6

Akst, Geoffrey. Developmental mathematics through applications. Boston: Pearson, 2014.

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7

Akst, Geoffrey. Developmental mathematics through applications. Boston: Pearson, 2014.

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8

M, Gupta Madan, ed. Introduction to fuzzy arithmetic: Theory and applications. New York: Van Nostrand Reinhold, 1991.

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9

M, Gupta Madan, ed. Introduction to fuzzy arithmetic: Theory and applications. New York, N.Y: Van Nostrand Reinhold Co., 1985.

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10

Sarnak, Peter. Some applications of modular forms. Cambridge: Cambridge University Press, 1990.

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Частини книг з теми "Arithmetic applications"

1

Fried, Michael D., and Moshe Jarden. "Examples and Applications." In Field Arithmetic, 268–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-07216-5_19.

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2

Mortensen, Chris. "Arithmetic Starred." In Paraconsistency: Logic and Applications, 309–14. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4438-7_16.

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3

Kundu, Satyabrota, and Sypriyo Mazumder. "Arithmetic Functions." In Number Theory and its Applications, 113–44. London: CRC Press, 2021. http://dx.doi.org/10.1201/9781003275947-6.

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4

Shparlinski, Igor. "Arithmetic Functions." In Cryptographic Applications of Analytic Number Theory, 67–81. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8037-4_6.

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5

Yoshida, Ruriko. "Matrix Arithmetic." In Linear Algebra and Its Applications with R, 85–148. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003042259-2.

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6

Maclachlan, Colin, and Alan W. Reid. "Applications." In The Arithmetic of Hyperbolic 3-Manifolds, 165–95. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-1-4757-6720-9_6.

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7

Buhler, Joe. "Elliptic curves, modular forms, and applications." In Arithmetic Algebraic Geometry, 5–81. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/pcms/009/02.

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8

Gustafsson, Oscar, and Lars Wanhammar. "Basic Arithmetic Circuits." In Arithmetic Circuits for DSP Applications, 1–32. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119206804.ch1.

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9

Holz, M., K. Steffens, and E. Weitz. "Applications of pcf-Theory." In Introduction to Cardinal Arithmetic, 249–68. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0346-0330-0_9.

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10

Bhargava, Manjul, and Benedict H. Gross. "Arithmetic invariant theory." In Symmetry: Representation Theory and Its Applications, 33–54. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1590-3_3.

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Тези доповідей конференцій з теми "Arithmetic applications"

1

TSIMERMAN, JACOB. "FUNCTIONAL TRANSCENDENCE AND ARITHMETIC APPLICATIONS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0062.

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2

Hough, D., B. Hay, J. Kidder, J. Riedy, G. Steele, and J. Thomas. "Arithmetic Interactions: From Hardware to Applications." In Proceedings. 17th IEEE Symposium on Computer Arithmetic. IEEE, 2005. http://dx.doi.org/10.1109/arith.2005.10.

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3

Han, Jie. "Approximate Arithmetic Circuits and Their Applications." In 2018 Twelfth IEEE/ACM International Symposium on Networks-on-Chip (NOCS). IEEE, 2018. http://dx.doi.org/10.1109/nocs.2018.8512174.

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4

Gennat, Marc, and Bernd Tibken. "Sensitivity Analysis Using Interval Arithmetic." In Communication Technologies: from Theory to Applications (ICTTA). IEEE, 2008. http://dx.doi.org/10.1109/ictta.2008.4530369.

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5

Modarressi, Mehdi, Seyyed Hossein Nikounia, and Amir-Hossein Jahangir. "Low-power arithmetic unit for DSP applications." In 2011 International Symposium on System-on-Chip - SOC. IEEE, 2011. http://dx.doi.org/10.1109/issoc.2011.6089696.

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6

D'Hoe, M., M. Pierre, Ph Deleuze, A. Vandemeulebroecke, P. Jespers, and M. Davio. "CASBA : Cryptographic Applications using Signed Binary Arithmetic." In 11th European Solid State Circuits Conference. IEEE, 1985. http://dx.doi.org/10.1109/esscirc.1985.5468162.

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7

Marshall, Alan, Tony Stansfield, Igor Kostarnov, Jean Vuillemin, and Brad Hutchings. "A reconfigurable arithmetic array for multimedia applications." In the 1999 ACM/SIGDA seventh international symposium. New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/296399.296444.

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8

Bajard, J. C., and N. El Mrabet. "Pairing in cryptography: an arithmetic point of view." In Optical Engineering + Applications, edited by Franklin T. Luk. SPIE, 2007. http://dx.doi.org/10.1117/12.733789.

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9

Jaafar, Sayuthi, Azizah A. Manaf, and Akram M. Zeki. "Steganography technique using modulus arithmetic." In 2007 9th International Symposium on Signal Processing and Its Applications (ISSPA). IEEE, 2007. http://dx.doi.org/10.1109/isspa.2007.4555443.

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10

Dimond, Rob, Sebastien Racanière, and Oliver Pell. "Accelerating Large-Scale HPC Applications Using FPGAs." In 2011 IEEE 20th Symposium on Computer Arithmetic (ARITH). IEEE, 2011. http://dx.doi.org/10.1109/arith.2011.34.

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Звіти організацій з теми "Arithmetic applications"

1

Saltus, Christina, Todd Swannack, and S. McKay. Geospatial Suitability Indices Toolbox (GSI Toolbox). Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41881.

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Habitat suitability models are widely adopted in ecosystem management and restoration, where these index models are used to assess environmental impacts and benefits based on the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). Here, we present a geospatial toolbox for assessing habitat suitability. The Geospatial Suitability Indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python® 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the Suitability Index Calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices based on user-specified habitat relationships. Second, the Overall Suitability Index Calculator combines multiple parameter suitability indices into one overarching index using one or more options, including: arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The resultant output is a raster layer representing habitat suitability values from 0.0 to 1.0, where zero is unsuitable habitat and one is ideal suitability. This report documents the model purpose and development as well as provides a user’s guide for the GSI toolbox.

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