Relevant bibliographies by topics / Galois Fields

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Galois Fields'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 July 2025

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Journal articles on the topic "Galois Fields"

1

Dahoklory, Novita, and Henry W. M. Patty. "Galois Group Correspondence On Extension Fields Over Q." Pattimura Proceeding: Conference of Science and Technology 4, no. 1 (2023): 17–28. http://dx.doi.org/10.30598/pattimurasci.2023.knmxxi.17-28.

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Let be an extension field where denotes dimension of as a vector space over . Let be the group of all automorphism of that fixes where the order of is denoted by . Particularly, an extension field is called a Galois extension if . Moreover, we will give some properties of an extension field which is a Galois extension. Using the properties of Galois extension, we will show that there is an one-one correspondence between the set of all intermediate fields in and the set of all subgroups in . Furthermore, we will give some examples of Galois group correspondence using an extension field over .&#
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TOMAŠIĆ, IVAN. "TWISTED GALOIS STRATIFICATION." Nagoya Mathematical Journal 222, no. 1 (2016): 1–60. http://dx.doi.org/10.1017/nmj.2016.9.

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We prove a direct image theorem stating that the direct image of a Galois formula by a morphism of difference schemes is equivalent to a Galois formula over fields with powers of Frobenius. As a consequence, we obtain an effective quantifier elimination procedure and a precise algebraic–geometric description of definable sets over fields with Frobenii in terms of twisted Galois formulas associated with finite Galois covers of difference schemes.
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Thakuri, Sandesh, and Bishnu Hari Subedi. "Applications of Galois Theory." Journal of Nepal Mathematical Society 7, no. 2 (2024): 90–99. https://doi.org/10.3126/jnms.v7i2.73108.

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This paper gives an insight to the Galois theory and discusses its applications in both pure and applied mathematics. First, the Fundamental theorem of Galois theory is applied to compute the Galois groups of polynomials and to prove the non-existence of a formula for solving a polynomial equation in rational coefficients having degree n ≥ 5. Then the Galois fields which are finite fields are applied to the error-correcting codes and cryptography in computer science. There are no general rules to compute the Galois groups of polynomials of degree more than four. Two new examples of Galois grou
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Pedro Ricardo, López-Bautista, та Gabriel Daniel Villa-Salvador. "Integral Representation of P-Class Groups In ℤp-Extensions and the Jacobian Variety". Canadian Journal of Mathematics 50, № 6 (1998): 1253–72. http://dx.doi.org/10.4153/cjm-1998-061-8.

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AbstractFor an arbitrary finite Galois p-extension L/K of ℤp-cyclotomic number fields of CM-type with Galois group G = Gal(L/K) such that the Iwasawa invariants are zero, we obtain unconditionally and explicitly the Galois module structure of CL-(p), the minus part of the p-subgroup of the class group of L. For an arbitrary finite Galois p-extension L/K of algebraic function fields of one variable over an algebraically closed field k of characteristic p as its exact field of constants with Galois group G = Gal(L/K) we obtain unconditionally and explicitly the Galois module structure of the p-t
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Pritee, Pritee, and Manjeet Singh Jakhar. "Arithmetic Progression and Binary Recurrence." International Journal of Applied and Behavioral Sciences 02, no. 01 (2025): 109–21. https://doi.org/10.70388/ijabs250111.

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When it comes to Galois theory, the idea of a field extension is considered to be one of the most fundamental concepts. In Galois theory, the field that is now being explored is used as an input, and the features of extension fields are investigated in relation to the field that is currently being investigated. It focuses on something called "Galois extensions," which are simply fields that possess specific symmetry features. These fields are referred to as "Galois extensions." Because of these features, we are now in a position to identify a relationship between the structure of the Galois gr
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Boston, Nigel, and Melanie Matchett Wood. "Non-abelian Cohen–Lenstra heuristics over function fields." Compositio Mathematica 153, no. 7 (2017): 1372–90. http://dx.doi.org/10.1112/s0010437x17007102.

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Boston, Bush and Hajir have developed heuristics, extending the Cohen–Lenstra heuristics, that conjecture the distribution of the Galois groups of the maximal unramified pro-$p$extensions of imaginary quadratic number fields for$p$an odd prime. In this paper, we find the moments of their proposed distribution, and further prove there is a unique distribution with those moments. Further, we show that in the function field analog, for imaginary quadratic extensions of$\mathbb{F}_{q}(t)$, the Galois groups of the maximal unramified pro-$p$extensions, as$q\rightarrow \infty$, have the moments pred
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BARTEL, ALEX. "Large Selmer groups over number fields." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 1 (2009): 73–86. http://dx.doi.org/10.1017/s0305004109990132.

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AbstractLet p be a prime number and M a quadratic number field, M ≠ ℚ() if p ≡ 1 mod 4. We will prove that for any positive integer d there exists a Galois extension F/ℚ with Galois group D2p and an elliptic curve E/ℚ such that F contains M and the p-Selmer group of E/F has size at least pd.
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Nithya, B., and V. Ramadoss. "Extension fields and Galois Theory." International Journal of Mathematics Trends and Technology 65, no. 7 (2019): 41–47. http://dx.doi.org/10.14445/22315373/ijmtt-v65i7p507.

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Somodi, Marius. "Galois theory for fuzzy fields." Fuzzy Sets and Systems 117, no. 3 (2001): 413–18. http://dx.doi.org/10.1016/s0165-0114(98)00397-2.

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LEV, FELIX M. "QUANTUM THEORY AND GALOIS FIELDS." International Journal of Modern Physics B 20, no. 11n13 (2006): 1761–77. http://dx.doi.org/10.1142/s0217979206034273.

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We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one.
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Dissertations / Theses on the topic "Galois Fields"

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McGown, Kevin Joseph. "Norm-Euclidean Galois fields." Diss., [La Jolla] : University of California, San Diego, 2010. http://wwwlib.umi.com/cr/fullcit?p3407998.

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Thesis (Ph. D.)--University of California, San Diego, 2010.<br>Title from first page of PDF file (viewed June 23, 2010). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (leaves 86-90).
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Heiderich, Florian. "Galois Theory of Module Fields." Doctoral thesis, Universitat de Barcelona, 2010. http://hdl.handle.net/10803/674.

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This thesis is about Galois theory.<br/><br/>The development of a Galois theory for differential equations analogous to the classical Galois theory for polynomial equations was already an aim of S. Lie in the 19th century. The first step in this direction was the development of a Galois theory for linear differential equations due to E. Picard and E. Vessiot. Later, B.H. Matzat and M. van der Put created a theory for iterative differential equations in positive characteristic. H. Umemura constructed a Galois theory for algebraic differential equations in characteristic zero.<br/><br/>There als
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Alabdali, Ali Abdulqader Bilal. "Hopf-Galois structures on Galois extensions of fields of squarefree degree." Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/33782.

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Hopf-Galois extensions were introduced by Chase and Sweedler [CS69] in 1969, motivated by the problem of formulating an analogue of Galois theory for inseparable extensions. Their approach shed a new light on separable extensions. Later in 1987, the concept of Hopf-Galois theory was further developed by Greither and Pareigis [GP87]. So, as a problem in the theory of groups, they explained the problem of finding all Hopf-Galois structures on a finite separable extension of fields. After that, many results on Hopf-Galois structures were obtained by N. Byott, T. Crespo, S. Carnahan, L. Childs, an
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Huczynska, Sophie. "Primitive free elements of Galois fields." Thesis, University of Glasgow, 2002. http://theses.gla.ac.uk/5533/.

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The key result linking the additive and multiplicative structure of a finite field is the Primitive Normal Basis Theorem; this was established by Lenstra and Schoof in 1987 in a proof which was heavily computational in nature. In this thesis, a new, theoretical proof of the theorem is given, and new estimates (in some cases, exact values) are given for the number of primitive free elements. A natural extension of the Primitive Normal Basis Theorem is to impose additional conditions on the primitive free elements; in particular, we may wish to specify the norm and trace of a primitive free elem
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Morita, Kazuma. "On Galois representations of local fields with imperfect residue fields." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124384.

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Bailey, Daniel V. "Computation in optimal extension fields." Link to electronic version, 2000. http://www.wpi.edu/Pubs/ETD/Available/etd-0428100-133037/.

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Mattman, Thomas W. "The computation of Galois groups over function fields /." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56944.

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Practical computational techniques are described to determine the Galois group of a degree 8 polynomial over a function field of the form Q($t sb1$, ...,$t sb{r}$). Each transitive permutation group of degree 8 is realized as a Galois group over the rationals. The techniques of Soicher and McKay (SM) for rational polynomials of degree less than 8 are also extended to function fields. Timing and efficiency of a MAPLE V implementation are discussed.
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Gill, Philip Geoffrey. "Galois isomorphisms between ideals in P-acidic fields." Thesis, University of Exeter, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264602.

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Sutherland, Nicole. "Algorithms for Galois extensions of global function fields." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/13364.

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In this thesis we consider the computation of integral closures in cyclic Galois extensions of global function fields and the determination of Galois groups of polynomials over global function fields. The development of methods to efficiently compute integral closures and Galois groups are listed as two of the four most important tasks of number theory considered by Zassenhaus. We describe an algorithm each for computing integral closures specifically for Kummer, Artin--Schreier and Artin--Schreier--Witt extensions. These algorithms are more efficient than previous algorithms because they com
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Nöcker, Michael. "Data structures for parallel exponentiation in finite fields." [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=962689777.

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Books on the topic "Galois Fields"

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(Firm), Red Charming, ed. Galois fields. Red Charming, 2004.

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Larned, Emily K. Galois fields. Red Charming Press, 2004.

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Hachenberger, Dirk, and Dieter Jungnickel. Topics in Galois Fields. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60806-4.

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Morandi, Patrick. Field and Galois theory. Springer, 1996.

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Lin, Shu. Serial-parallel multiplication in Galois fields. National Aeronautics and Space Administration, 1987.

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Borceux, Francis. Galois Theories of Fields and Rings. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58460-2.

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Malle, Gunter. Inverse Galois theory. Springer, 1999.

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A, Thas J., ed. General Galois geometries. Clarendon Press, 1991.

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1912-, Milgram Arthur N., ed. Galois theory. Dover Publications, 1998.

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Hélou, Charles. Non Galois ramification theory of local fields. Verlag Reinhard Fischer, 1990.

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Book chapters on the topic "Galois Fields"

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Gazi, Orhan. "Galois Fields." In Forward Error Correction via Channel Coding. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33380-5_5.

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Schroeder, Manfred R. "Galois Fields." In Number Theory in Science and Communication. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-22246-1_25.

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Vourdas, Apostolos. "Galois Fields." In Quantum Science and Technology. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59495-8_8.

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Schroeder, Manfred R. "Galois Fields." In Number Theory in Science and Communication. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03430-9_25.

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Stewart, Ian. "Finite fields." In Galois Theory. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-0839-0_16.

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Stewart, Ian. "Finite Fields." In Galois Theory, 5th ed. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003213949-19.

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Stewart, Ian. "Algebraically Closed Fields." In Galois Theory, 5th ed. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003213949-23.

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Stewart, Ian. "Abstract Rings and Fields." In Galois Theory, 5th ed. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003213949-16.

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Hachenberger, Dirk, and Dieter Jungnickel. "Field Extensions and the Basic Theory of Galois Fields." In Topics in Galois Fields. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60806-4_3.

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Knapp, Anthony W. "Fields and Galois Theory." In Basic Algebra. Birkhäuser Boston, 2006. http://dx.doi.org/10.1007/978-0-8176-4529-8_9.

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Conference papers on the topic "Galois Fields"

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Song, Zefeng, Yetong Li, Yuyao Zhao, Qun Ding, Hai Cheng, and Chunguang Huang. "A Word-oriented Code on Galois Field with Accurate Period." In 2024 3rd International Joint Conference on Information and Communication Engineering (JCICE). IEEE, 2024. http://dx.doi.org/10.1109/jcice61382.2024.00018.

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Herr, Laurent. "Φ–Γ–modules and Galois cohomology". У Higher local fields. Mathematical Sciences Publishers, 2000. http://dx.doi.org/10.2140/gtm.2000.3.263.

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Erez, Boas. "Galois modules and class field theory." In Higher local fields. Mathematical Sciences Publishers, 2000. http://dx.doi.org/10.2140/gtm.2000.3.299.

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Koscielny, C. "Spurious Galois fields (coding theory applications)." In Conference Proceeding IEEE Pacific Rim Conference on Communications, Computers and Signal Processing. IEEE, 1989. http://dx.doi.org/10.1109/pacrim.1989.48390.

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Scripcariu, Luminita, Petre-Daniel Matasaru, and Felix Diaconu. "Extended DES algorithm to Galois Fields." In 2017 International Symposium on Signals, Circuits and Systems (ISSCS). IEEE, 2017. http://dx.doi.org/10.1109/isscs.2017.8034875.

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Petra, Nicola, Davide De Caro та Antonio G. M. Strollo. "High Speed Galois Fields GF(2𝓂) Multipliers". У 2007 18th European Conference on Circuit Theory and Design (ECCTD '07). IEEE, 2007. http://dx.doi.org/10.1109/ecctd.2007.4529634.

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Pradhan, Dhiraj K. "Application of Galois Fields to Logic Synthesis." In 2008 IEEE Region 10 and the Third international Conference on Industrial and Information Systems (ICIIS). IEEE, 2008. http://dx.doi.org/10.1109/iciinfs.2008.4798327.

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Rodriguez, Sergio. "Quantum Fourier Transform (QFT) over Galois fields." In SPIE Defense, Security, and Sensing, edited by Eric Donkor, Andrew R. Pirich, and Howard E. Brandt. SPIE, 2013. http://dx.doi.org/10.1117/12.2015194.

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Efrat, Ido. "Recovering higher global and local fields from Galois groups – an algebraic approach." In Higher local fields. Mathematical Sciences Publishers, 2000. http://dx.doi.org/10.2140/gtm.2000.3.273.

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Ronyai, L. "Galois groups and factoring polynomials over finite fields." In 30th Annual Symposium on Foundations of Computer Science. IEEE, 1989. http://dx.doi.org/10.1109/sfcs.1989.63462.

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Reports on the topic "Galois Fields"

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Waisner, Scott, Victor Medina, Charles Ellison, et al. Design, construction, and testing of the PFAS Effluent Treatment System (PETS), a mobile ion exchange–based system for the treatment of per-, poly-fluorinated alkyl substances (PFAS) contaminated water. Engineer Research and Development Center (U.S.), 2022. http://dx.doi.org/10.21079/11681/43823.

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Poly-,Per-fluorinated alkyl substances (PFAS) are versatile chemicals that were incorporated in a wide range of products. One of their most important use was in aqueous film-forming foams for fighting liquid fuel fires. PFAS compounds have recently been identified as potential environmental contaminants. In the United States there are hundreds of potential military sites with PFAS contamination. The ERDC designed and constructed a mobile treatment system to address small sites (250,000 gallons or less) and as a platform to field test new adsorptive media. The PFAS Effluent Treatment System (PE
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Dudley, Lynn M., Uri Shani, and Moshe Shenker. Modeling Plant Response to Deficit Irrigation with Saline Water: Separating the Effects of Water and Salt Stress in the Root Uptake Function. United States Department of Agriculture, 2003. http://dx.doi.org/10.32747/2003.7586468.bard.

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Standard salinity management theory, derived from blending thermodynamic and semi- empirical considerations leads to an erroneous perception regarding compensative interaction among salinity stress factors. The current approach treats matric and osmotic components of soil water potential separately and then combines their effects to compute overall response. With deficit water a severe yield decrease is expected under high salinity, yet little or no reduction is predicted for excess irrigation, irrespective of salinity level. Similarly, considerations of competition between chloride and nitrat
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Galili, Naftali, Roger P. Rohrbach, Itzhak Shmulevich, Yoram Fuchs, and Giora Zauberman. Non-Destructive Quality Sensing of High-Value Agricultural Commodities Through Response Analysis. United States Department of Agriculture, 1994. http://dx.doi.org/10.32747/1994.7570549.bard.

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The objectives of this project were to develop nondestructive methods for detection of internal properties and firmness of fruits and vegetables. One method was based on a soft piezoelectric film transducer developed in the Technion, for analysis of fruit response to low-energy excitation. The second method was a dot-matrix piezoelectric transducer of North Carolina State University, developed for contact-pressure analysis of fruit during impact. Two research teams, one in Israel and the other in North Carolina, coordinated their research effort according to the specific objectives of the proj
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