Relevant bibliographies by topics / Frobenius index

Academic literature on the topic 'Frobenius index'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Frobenius index"

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Castillo-Guillén, C. A., and C. Rentería-Márquez. "Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4." Analele Universitatii "Ovidius" Constanta - Seria Matematica 28, no. 2 (July 1, 2020): 67–91. http://dx.doi.org/10.2478/auom-2020-0020.

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AbstractThe family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given. And the number and structure of γ-constacyclic codes over those rings, of length relatively prime to the characteristic of the residue field of the ring, are determined.
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YAMAGAMI, SHIGERU. "A NOTE ON OCNEANU'S APPROACH TO JONES' INDEX THEORY." International Journal of Mathematics 04, no. 05 (October 1993): 859–71. http://dx.doi.org/10.1142/s0129167x9300039x.

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Some of the basic facts in the Ocneanu's approach to Jones' index theory are proved. Among other things the biunitarity of connections in paragroups is proved generally by making use of Frobenius reciprocity.
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Al Baidani, Mashael, and Judi McDonald. "On the Block Structure and Frobenius Normal Form of Powers of Matrices." Electronic Journal of Linear Algebra 35 (February 1, 2019): 297–306. http://dx.doi.org/10.13001/1081-3810.3955.

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The Frobenius normal form of a matrix is an important tool in analyzing its properties. When a matrix is powered up, the Frobenius normal form of the original matrix and that of its powers need not be the same. In this article, conditions on a matrix $A$ and the power $q$ are provided so that for any invertible matrix $S$, if $S^{-1}A^qS$ is block upper triangular, then so is $S^{-1}AS$ when partitioned conformably. The result is established for general matrices over any field. It is also observed that the contributions of the index of cyclicity to the spectral properties of a matrix hold over any field. The article concludes by applying the block upper triangular powers result to the cone Frobenius normal form of powers of a eventually cone nonnegative matrix.
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Wei, X. B., W. B. Guo, D. V. Lytkina, V. D. Mazurov, and A. Kh Zhurtov. "Solubility of Finite Generalized Frobenius with the Kernel of Odd Index." Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 55, no. 1 (January 2020): 67–70. http://dx.doi.org/10.3103/s1068362320010082.

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Boje, Edward, and Osita D. I. Nwokah. "Quantitative Feedback Design Using Forward Path Decoupling1." Journal of Dynamic Systems, Measurement, and Control 123, no. 1 (February 24, 1997): 129–32. http://dx.doi.org/10.1115/1.1343463.

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The Perron-Frobenius root is used to measure the level of interaction in MIMO quantitative feedback design (QFT). A design approach to reduce interaction in uncertain plants via a precompensator is presented. A decentralized stability result applies if the interaction index can be made less than unity by design.
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Castillo-Guillén, C. A., and C. Álvarez-García. "DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4." Analele Universitatii "Ovidius" Constanta - Seria Matematica 30, no. 1 (February 1, 2022): 89–108. http://dx.doi.org/10.2478/auom-2022-0006.

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Abstract A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over these rings is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.
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Yildiz, Bahattin, and Ismail Kelebek. "The homogeneous weight for Rk, related gray map and new binary quasi-cyclic codes." Filomat 31, no. 4 (2017): 885–97. http://dx.doi.org/10.2298/fil1704885y.

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Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family Rk, a recently introduced family of Frobenius rings which have been used extensively in coding theory. We find an associated Gray map for the homogeneous weight using first order Reed-Muller codes and we describe some of the general properties of the images of codes over Rk under this Gray map. We then discuss quasi-twisted codes over Rk and their binary images under the homogeneous Gray map. In this way, we find many optimal binary codes which are self-orthogonal and quasi-cyclic. In particular, we find a substantial number of optimal binary codes that are quasi-cyclic of index 8, 16 and 24, nearly all of which are new additions to the database of quasi-cyclic codes kept by Chen.
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DAHMANI, FRANÇOIS, DAVID FUTER, and DANIEL T. WISE. "Growth of quasiconvex subgroups." Mathematical Proceedings of the Cambridge Philosophical Society 167, no. 3 (June 28, 2018): 505–30. http://dx.doi.org/10.1017/s0305004118000440.

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AbstractWe prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron–Frobenius theory.We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel and Osin on rotating families.
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Castillo-Guillén, C. A., and C. Álvarez-García. "Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4." Analele Universitatii "Ovidius" Constanta - Seria Matematica 29, no. 2 (June 1, 2021): 25–50. http://dx.doi.org/10.2478/auom-2021-0017.

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Abstract Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.
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Castillo-Guillén, C. A., C. Rentería-Márquez, and H. Tapia-Recillas. "Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3." Finite Fields and Their Applications 43 (January 2017): 1–21. http://dx.doi.org/10.1016/j.ffa.2016.08.004.

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Dissertations / Theses on the topic "Frobenius index"

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García-Cobián, Jáuregui Ramón. "Diferenciabilidad de la raíz de Perron-Frobenius de matrices innegativas e indescomponibles." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96383.

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Luego de establecer el que las matrices innegativas e indescomponibles nxn forman un subconjunto abierto y denso en el espacio de las innegativas nxn se demuestra la diferenciablidad de la función que a cada matriz tal le asigna su raíz de Perron - Frobenius.
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Pierrot, Cécile. "Le logarithme discret dans les corps finis." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066495/document.

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La cryptologie consiste en l’étude des techniques utilisées par deux entités pour communiquer en secret en présence d’une troisième. Les propriétés mathématiques qui sous-tendent ces techniques garantissent que leur attaque reste infaisable en pratique par un adversaire malveillant. Ainsi, les protocoles s’appuient sur diverses hypothèses, comme la di fficulté présumée de factoriser des entiers ou de calculer le logarithme discret d’un élément arbitraire dans certains groupes. Cette thèse qui porte sur le problème du logarithme discret dans les corps finis s’articule autour de trois volets.Nous exposons les résultats théoriques associés au problème sans considération du groupe cible, détaillant ainsi les classes de complexité auxquelles il appartient ainsi que di fférentes approches pour tenter de le résoudre.L’étude du problème dans les corps finis commence en tant que telle par les corps présentant une caractéristique de petite taille relativement à l’ordre total du corps en question. Cette seconde partie résulte sur l’exposition d’un algorithme par représentation de Frobenius dont une application a aboutit au record actuel de calcul de logarithme discret en caractéristique 3.Pour les corps de moyenne ou grande caractéristiques, une autre méthode est requise. Le crible par corps de nombres (NFS) multiples obtient les complexités asymptotiques les plus basses pour un corps arbitraire. Un dernier chapitre introduit la notion de matrice presque creuse. L’élaboration d’un nouvel algorithme spécifique qui explicite le noyau d’une telle matrice facilite en pratique l’étape d’algèbre sous-jacente à toute variante de NFS
Cryptography is the study of techniques for secure communication in the presence of third parties, also called adversaries. Such techniques are detailed in cryptosystems, explaining how to securely encode and decode messages. They are designed around computational hardness assumptions related to mathematical properties, making such algorithms hard to break in practice by any adversary. These protocols are based on the computational difficulty of various problems which often come from number theory, such as integer factorization or discrete logarithms computations. This manuscript focuses on the discrete logarithm problem in finite fields and revolves around three axes.First we detail classical results about the problem without any consideration to the target group. We deal with complexity classes and some general methods that do not need any information on the group.The study of the discrete logarithm problem in finite fields starts with small characteristic ones. The aim is to present a Frobenius representation algorithm that leads to the current discrete logarithm record in characteristic 3.For medium or large characteristics finite fields, another approach is required. The multiple number field sieve reaches the best asymptotic heuristic complexities for this double range of characteristics. We also introduce the notion of nearly sparse matrices. Designing a new algorithm dedicated to explicitly give the kernel of such a matrix eases in practice the linear algebra step of any variant of the number field sieve
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Sorge, Joshua. "On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators." Thesis, 2008. http://hdl.handle.net/1828/1257.

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The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In this paper, it is verified directly that the peripheral point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic.
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Hsieh, Li-Yu Shelley. "Ergodic theory of mulitidimensional random dynamical systems." Thesis, 2008. http://hdl.handle.net/1828/1253.

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Given a random dynamical system T constructed from Jablonski transformations, consider its Perron-Frobenius operator P_T. We prove a weak form of the Lasota-Yorke inequality for P_T and thereby prove the existence of BV- invariant densities for T. Using the Spectral Decomposition Theorem we prove that the support of an invariant density is open a.e. and give conditions such that the invariant density for T is unique. We study the asymptotic behavior of the Markov operator P_T, especially when T has a unique absolutely continuous invariant measure (ACIM). Under the assumption of uniqueness, we obtain spectral stability in the sense of Keller. As an application, we can use Ulam's method to approximate the invariant density of P_T.
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Books on the topic "Frobenius index"

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(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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Book chapters on the topic "Frobenius index"

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Caenepeel, Stefaan, Gigel Militaru, and Shenglin Zhu. "Index." In Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations, 353–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-48042-6_10.

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"INDEX TERMINOLOGIQUE." In Déformations isomonodromiques et variétés de Frobenius, 285–90. EDP Sciences, 2002. http://dx.doi.org/10.1051/978-2-7598-0268-5.c013.

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"INDEX DES NOTATIONS." In Déformations isomonodromiques et variétés de Frobenius, 283–84. EDP Sciences, 2002. http://dx.doi.org/10.1051/978-2-7598-0268-5.c012.

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Conference papers on the topic "Frobenius index"

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Rehman, A. U., J. A. Rongong, and K. Worden. "Detection of Damage in Repeating Structures." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23351.

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Repeating structures in the form of multiple-bladed rotors are used widely in turbomachinery. Damage to blades can have significant consequences but can be difficult to identify in normal operation. This paper introduces an approach for identifying small defects such as cracks in a repeating structure that may be applicable to the limited data obtainable from developing techniques such as blade tip-timing. In order to understand the key issues involved, this initial work involves a numerical study of a simple comb-like repeating structure rather than a bladed rotor. Changes to the system modeshapes and mode order arising from damage are related to the location and severity of damage. Damage, in the form of small, open cracks, is modelled using different techniques such as material removal, periodic reduction in modulus of elasticity of selected elements at the required location and mass modification. Damage indices based on differences in the Modal Assurance Criterion (MAC) that give a measure of the change in the modeshapes are introduced. MAC matrices are obtained using a reduced number of data points. The damage index is obtained from the Frobenius norm of MAC matrix subtracted from (1) the AutoMAC of reference model without crack and (2) the identity matrix. A clear correlation between the damage indices and crack depth / location is shown. In order to account for mistuning in real repeating structures, the performance when the assembly is subjected to inhomogeneous temperature distributions is also considered.
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