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Articles de revues sur le sujet « Finite fields (Algebra) Geometry »

Auteur : Grafiati
Publié le 4 juin 2021
Mis à jour le 5 février 2022

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1

Dadarlat, Marius. « Fiberwise KK-equivalence of continuous fields of C*-algebras ». Journal of K-Theory 3, no 2 (28 mai 2008) : 205–19. http://dx.doi.org/10.1017/is008001012jkt041.

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AbstractLet A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element σ of the parametrized Kasparov group KKX(A,B) is invertible if and only all its fiberwise components σx ∈ KK(A(x),B(x)) are invertible. This criterion does not extend to infinite dimensional spaces since there exist nontrivial unital separable continuous fields over the Hilbert cube with all fibers isomorphic to the Cuntz algebra . Several applications to continuous fields of Kirchberg algebras are given. It is also shown that if each fiber of a separable nuclear continuous C(X)-algebra A over a finite dimensional locally compact space X satisfies the UCT, then A satisfies the UCT.
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2

Bani-Ata, Mashhour, et Mariam Al-Rashed. « On certain finite dimensional algebras over finite fields ». Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 58, no 1 (19 août 2016) : 195–200. http://dx.doi.org/10.1007/s13366-016-0312-8.

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3

RAFIE-RAD, M. « SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE ». International Journal of Geometric Methods in Modern Physics 09, no 04 (6 mai 2012) : 1250034. http://dx.doi.org/10.1142/s021988781250034x.

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The collection of all projective vector fields on a Finsler space (M, F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most [Formula: see text]. Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.
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4

Lo, Catharine Wing Kwan, et Matilde Marcolli. « 𝔽ζ-geometry, Tate motives, and the Habiro ring ». International Journal of Number Theory 11, no 02 (mars 2015) : 311–39. http://dx.doi.org/10.1142/s1793042115500189.

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In this paper, we propose different notions of 𝔽ζ-geometry, for ζ a root of unity, generalizing notions of 𝔽1-geometry (geometry over the "field with one element") based on the behavior of the counting functions of points over finite fields, the Grothendieck class, and the notion of torification. We relate 𝔽ζ-geometry to formal roots of Tate motives, and to functions in the Habiro ring, seen as counting functions of certain ind-varieties. We investigate the existence of 𝔽ζ-structures in examples arising from general linear groups, matrix equations over finite fields, and some quantum modular forms.
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Feng, Rongquan, Liwei Zeng et Yang Zhang. « Constructions of 112-Designs from Unitary Geometry over Finite Fields ». Algebra Colloquium 24, no 03 (septembre 2017) : 381–92. http://dx.doi.org/10.1142/s1005386717000232.

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In this paper, we construct some [Formula: see text]-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the unitary space. Furthermore, these [Formula: see text]-designs yield six infinite families of directed strongly regular graphs.
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Gao, Suogang, Zengti Li, Weili Wu, Panos M. Pardalos et Dingzhu Du. « Group testing with geometry of classical groups over finite fields ». Journal of Algebraic Combinatorics 49, no 4 (6 juin 2018) : 381–400. http://dx.doi.org/10.1007/s10801-018-0828-0.

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7

Camenga, Kristin A., Brandon Collins, Gage Hoefer, Jonny Quezada, Patrick X. Rault, James Willson et Rebekah B. Johnson Yates. « On the geometry of numerical ranges over finite fields ». Linear Algebra and its Applications 628 (novembre 2021) : 182–201. http://dx.doi.org/10.1016/j.laa.2021.07.008.

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8

Koike, Masao. « Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields ». Hiroshima Mathematical Journal 25, no 1 (1995) : 43–52. http://dx.doi.org/10.32917/hmj/1206127824.

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9

LARSSON, T. A. « CONFORMAL FIELDS : A CLASS OF REPRESENTATIONS OF Vect(N) ». International Journal of Modern Physics A 07, no 26 (20 octobre 1992) : 6493–508. http://dx.doi.org/10.1142/s0217751x92002970.

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Vect (N), the algebra of vector fields in N dimensions, is studied. Some aspects of local differential geometry are formulated as Vect(N) representation theory. There is a new class of modules, conformal fields, whose restrictions to the subalgebra sl(N+1)⊂ Vect (N) are finite-dimensional sl (N+1) representations. In this regard they are simpler than tensor fields. Fock modules are also constructed. Infinities, which are unremovable even by normal ordering, arise unless bosonic and fermionic degrees of freedom match.
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10

Evans, Ron, et John Greene. « Evaluations of hypergeometric functions over finite fields ». Hiroshima Mathematical Journal 39, no 2 (juillet 2009) : 217–35. http://dx.doi.org/10.32917/hmj/1249046338.

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11

Farkas, Daniel R. « Birational invariants of crystals and fields with a finite group of operators ». Mathematical Proceedings of the Cambridge Philosophical Society 107, no 3 (mai 1990) : 417–24. http://dx.doi.org/10.1017/s0305004100068717.

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It is well known that an n-dimensional crystallographic group can be reconstructed from its point group, the integral representation of the point group which arises from its action on the translation lattice, and the 2-cocycle which glues the point group to the lattice ([2]). In practice, this constitutes a complicated list of invariants. When confronted with the classification of objects possessing a rich structure, the algebraic geometer first attempts to find more coarse birational invariants. We begin such a programme for torsion-free crystallographic groups. More precisely, if Γ is a torsion-free crystallographic group and k is a field then the group algebra k[Γ] is a non-commutative domain (see [6], chapter 13). It can be localized at its centre to yield a division algebra k(Γ) which is a crossed product; the Galois group is the point group and it acts on the rational function field generated by k and the lattice (regarded multiplicatively), which is a maximal subfield ([3]). What are thecommon invariants of Γ1 and Γ2 when k(Γ1) and k(Γ2) are isomorphic k-algebras?
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12

KHREBTOVA, EKATERINA S., et DMITRY MALININ. « ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS ». Journal of Algebra and Its Applications 07, no 06 (décembre 2008) : 773–83. http://dx.doi.org/10.1142/s0219498808003119.

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We prove the existence and finiteness theorems for integral representations stable under Galois operation. An explicit construction of the realization fields for representations of finite groups stable under the natural operation of the Galois group is given. We also compare the representations over fields and the rings of integers, and give a quantitative result on the rarity of integral Galois stable representations. There is a series of related conjectures and applications to arithmetic algebraic geometry, finite flat group schemes, positive definite quadratic lattices and Galois cohomology.
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13

CRANE, LOUIS. « RELATIONAL SPACETIME, MODEL CATEGORIES AND QUANTUM GRAVITY ». International Journal of Modern Physics A 24, no 15 (20 juin 2009) : 2753–75. http://dx.doi.org/10.1142/s0217751x0904614x.

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We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime manifold disappears. We replace the underlying point set topological space with several apparently different models, which are actually related by pairs of adjoint functors from rational homotopy theory. One is a discrete approximation to the causal null path space derived from the multiple images in the spacetime theory of gravitational lensing, described as an object in the model category of differential graded Lie algebras. Another of our models appears as a thickening of spacetime, which we interpret as a formulation of relational geometry. This model is produced from the finite dimensional differential graded algebra of differential forms which can be transmitted out of a finite region consistent with the Bekenstein bound by another functor, called geometric realisation. The thickening of spacetime, which we propose as a version of relational spacetime, has a surprizingly rich structure. Information which would make up a spin bundle over spacetime is contained in it, making it possible to include fermionic fields in a geometric state sum over it. Avenues toward constructing an actual quantum theory of gravity on our models are given a preliminary exploration.
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14

Koike, Masao. « Hypergeometric series over finite fields and Apéry numbers ». Hiroshima Mathematical Journal 22, no 3 (1992) : 461–67. http://dx.doi.org/10.32917/hmj/1206128497.

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15

Coons, Jane Ivy, Jack Jenkins, Douglas Knowles, Rayanne A. Luke et Patrick X. Rault. « Numerical ranges over finite fields ». Linear Algebra and its Applications 501 (juillet 2016) : 37–47. http://dx.doi.org/10.1016/j.laa.2016.03.024.

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16

González-Avilés, Cristian D. « On K2 of varieties over number fields ». Journal of K-Theory 1, no 1 (7 janvier 2008) : 175–83. http://dx.doi.org/10.1017/is007011012jkt004.

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AbstractLet k be a number field and let X be a smooth, projective and geometrically integral k-variety. We show that, if the geometric Néron-Severi group of X is torsion-free, then the Galois cohomology group is finite. Previously this group was only known to have a finite exponent. We also obtain a vanishing theorem for this group, showing in particular that it is trivial if X belongs to a certain class of abelian varieties with complex multiplication. The interest in the above cohomology group stems from its connection to the torsion subgroup of the Chow group CH2(X) of codimension 2 cycles on X. In the last section of the paper we record certain results on curves which must be familiar to all specialists in this area but which we have not formerly seen in print.
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17

Chen, Shangdi, et Dawei Zhao. « Construction of Multi-receiver Multi-fold Authentication Codes from Singular Symplectic Geometry over Finite Fields ». Algebra Colloquium 20, no 04 (7 octobre 2013) : 701–10. http://dx.doi.org/10.1142/s1005386713000679.

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As an extension of the basic model of MRA-codes, multi-receiver multi-fold authentication codes can use a single key distribution phase for multiple message transmission. A multi-receiver multi-fold authentication code is constructed from the singular symplectic geometry over finite fields in this paper. The parameters and probabilities of success in impersonation and substitution attacks by malicious groups of receivers of this code are computed.
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18

Falcón, Óscar J., Raúl M. Falcón et Juan Núñez. « A computational algebraic geometry approach to enumerate Malcev magma algebras over finite fields ». Mathematical Methods in the Applied Sciences 39, no 16 (30 juin 2016) : 4901–13. http://dx.doi.org/10.1002/mma.4054.

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19

Letellier, Emmanuel. « Tensor products of unipotent characters of general linear groups over finite fields ». Transformation Groups 18, no 1 (3 février 2013) : 233–62. http://dx.doi.org/10.1007/s00031-013-9211-3.

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20

Vera-López, Antonio, et J. M. Arregi. « Computing in unitriangular matrices over finite fields ». Linear Algebra and its Applications 387 (août 2004) : 193–219. http://dx.doi.org/10.1016/j.laa.2004.02.008.

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21

Misiurewicz, Michał, John G. Stevens et Diana M. Thomas. « Iterations of linear maps over finite fields ». Linear Algebra and its Applications 413, no 1 (février 2006) : 218–34. http://dx.doi.org/10.1016/j.laa.2005.09.002.

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22

Anbar, Nurdagül, et Seher Tutdere. « Belyi’s Theorems in Positive Characteristic ». International Journal of Number Theory 16, no 06 (17 mars 2020) : 1355–68. http://dx.doi.org/10.1142/s1793042120500712.

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There are two types of Belyi’s Theorems for curves defined over finite fields of characteristic [Formula: see text], namely the Wild and the Tame [Formula: see text]-Belyi Theorems. In this paper, we discuss them in the language of function fields. In particular, we provide a constructive proof for the existence of a pseudo-tame element introduced in [Y. Sugiyama and S. Yasuda, Belyi’s theorem in characteristic two, Compos. Math. 156(2) (2020) 325–339], which leads to a self-contained proof for the Tame [Formula: see text]-Belyi Theorem. Moreover, we provide unified and simple proofs for Belyi’s Theorems unlike the known ones that use technical results from Algebraic Geometry.
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23

Saïdi, Mohamed, et Akio Tamagawa. « A refined version of Grothendieck’s anabelian conjecture for hyperbolic curves over finite fields ». Journal of Algebraic Geometry 27, no 3 (29 mars 2018) : 383–448. http://dx.doi.org/10.1090/jag/708.

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24

Huo, Yuan-Ji, et Zhe-Xian Wan. « Lattices generated by subspaces of the same dimension and rank in orthogonal geometry over finite fields of odd characteristic ». Communications in Algebra 21, no 11 (janvier 1993) : 4219–52. http://dx.doi.org/10.1080/00927879308824796.

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25

Huo, Yuan-ji, et Zhe-xian Wan. « Lattices generated by subspaces of the same dimension and rank in orthogonal geometry over finite fields of even characteristic ». Communications in Algebra 22, no 6 (janvier 1994) : 2015–37. http://dx.doi.org/10.1080/00927879408824953.

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26

Lima, J. B., et R. M. Campello de Souza. « Fractional cosine and sine transforms over finite fields ». Linear Algebra and its Applications 438, no 8 (avril 2013) : 3217–30. http://dx.doi.org/10.1016/j.laa.2012.12.021.

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27

Reese, Tyler M., Joseph D. Fehribach, Randy C. Paffenroth et Brigitte Servatius. « Matrices over finite fields and their Kirchhoff graphs ». Linear Algebra and its Applications 547 (juin 2018) : 128–47. http://dx.doi.org/10.1016/j.laa.2018.02.020.

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28

Price, Geoffrey, et Myles Wortham. « On sequences of Toeplitz matrices over finite fields ». Linear Algebra and its Applications 561 (janvier 2019) : 63–80. http://dx.doi.org/10.1016/j.laa.2018.09.013.

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29

Ballico, E. « Numerical range over finite fields : Restriction to subspaces ». Linear Algebra and its Applications 571 (juin 2019) : 1–13. http://dx.doi.org/10.1016/j.laa.2019.02.013.

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30

Shparlinski, Igor E. « Geometric progressions in vector sumsets over finite fields ». Finite Fields and Their Applications 68 (décembre 2020) : 101747. http://dx.doi.org/10.1016/j.ffa.2020.101747.

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31

Miyatani, Kazuaki, et Makoto Sano. « An exponential sum and higher-codimensional subvarieties of projective spaces over finite fields ». Hiroshima Mathematical Journal 44, no 3 (novembre 2014) : 327–40. http://dx.doi.org/10.32917/hmj/1419619750.

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32

Legendre, Eveline. « Existence and non-uniqueness of constant scalar curvature toric Sasaki metrics ». Compositio Mathematica 147, no 5 (27 juillet 2011) : 1613–34. http://dx.doi.org/10.1112/s0010437x1100529x.

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AbstractWe study compatible toric Sasaki metrics with constant scalar curvature on co-oriented compact toric contact manifolds of Reeb type of dimension at least five. These metrics come in rays of transversal homothety due to the possible rescaling of the Reeb vector fields. We prove that there exist Reeb vector fields for which the transversal Futaki invariant (restricted to the Lie algebra of the torus) vanishes. Using an existence result of E. Legendre [Toric geometry of convex quadrilaterals, J. Symplectic Geom. 9 (2011), 343–385], we show that a co-oriented compact toric contact 5-manifold whose moment cone has four facets admits a finite number of rays of transversal homothetic compatible toric Sasaki metrics with constant scalar curvature. We point out a family of well-known toric contact structures on S2×S3 admitting two non-isometric and non-transversally homothetic compatible toric Sasaki metrics with constant scalar curvature.
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33

LAAMARA, RACHID AHL, ADIL BELHAJ, LUIS J. BOYA, LEILA MEDARI et ANTONIO SEGUI. « ON F-THEORY QUIVER MODELS AND KAC–MOODY ALGEBRAS ». International Journal of Geometric Methods in Modern Physics 07, no 06 (septembre 2010) : 989–99. http://dx.doi.org/10.1142/s0219887810004671.

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We discuss quiver gauge models with bi-fundamental and fundamental matter obtained from F-theory compactified on ALE spaces over a four-dimensional base space. We focus on the base geometry which consists of intersecting F0 = CP1 × CP1 Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds of Kac–Moody (KM) algebras: ordinary, i.e. finite-dimensional, affine and indefinite, in particular hyperbolic. We interpret the equations defining these three classes of generalized Lie algebras as the anomaly cancelation condition of the corresponding N = 1 F-theory quivers in four dimensions. We analyze in some detail hyperbolic geometries obtained from the affine [Formula: see text] base geometry by adding a node, and we find that it can be used to incorporate fundamental fields to a product of SU-type gauge groups and fields.
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34

Fiorani, Emanuele, Sandra Germani et Andrea Spiro. « Lie algebras of conservation laws of variational partial differential equations ». Advances in Geometry 18, no 2 (25 avril 2018) : 207–28. http://dx.doi.org/10.1515/advgeom-2018-0004.

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Abstract We establish a version of Noether’s first Theorem according to which the (equivalence classes of) conserved quantities of given Euler–Lagrange equations in several independent variables are in one-to-one correspondence with the (equivalence classes of) vector fields satisfying an appropriate pair of geometric conditions, namely: (a) they preserve the class of vector fields tangent to holonomic submanifolds of a jet space; (b) they leave invariant the action from which the Euler–Lagrange equations are derived, modulo terms identically vanishing along holonomic submanifolds. Such a bijective correspondence Φ͠ between equivalence classes comes from an explicit (non-bijective) linear map Φ from vector fields into conserved differential operators, and not from a map into divergences of conserved operators as it occurs in other proofs of Noether’s Theorem. Where possible, claims are given a coordinate-free formulation and all proofs rely just on basic differential geometric properties of finite-dimensional manifolds.
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35

Abdollahi, Alireza. « Commuting graphs of full matrix rings over finite fields ». Linear Algebra and its Applications 428, no 11-12 (juin 2008) : 2947–54. http://dx.doi.org/10.1016/j.laa.2008.01.036.

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36

Morrow, Matthew. « Continuity of the norm map on MilnorK-theory ». Journal of K-theory 9, no 3 (21 novembre 2011) : 565–77. http://dx.doi.org/10.1017/is011011005jkt166.

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AbstractThe norm map on the MilnorK-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.
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37

Nopendri, Nopendri, Intan Muchtadi-Alamsyah, Djoko Suprijanto et Aleams Barra. « Cyclic Codes from a Sequence over Finite Fields ». European Journal of Pure and Applied Mathematics 14, no 3 (5 août 2021) : 685–94. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3907.

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A cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have efficient encoding and decoding algorithms. This paper explains the construction of a family of cyclic codes from sequences generated by a trace of a monomial over finite fields of odd characteristics. The parameter and some examples of the codes are presented in this paper.
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38

Price, Geoffrey, et Myles Wortham. « Corrigendum to : “ On sequences of Toeplitz matrices over finite fields” [Linear Algebra Appl. 561 (2019) 63–80] ». Linear Algebra and its Applications 590 (avril 2020) : 330–32. http://dx.doi.org/10.1016/j.laa.2020.01.008.

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39

Huang, Li-Ping, Zejun Huang, Chi-Kwong Li et Nung-Sing Sze. « Graphs associated with matrices over finite fields and their endomorphisms ». Linear Algebra and its Applications 447 (avril 2014) : 2–25. http://dx.doi.org/10.1016/j.laa.2013.12.030.

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40

Entin, Alexei. « On the Bateman–Horn conjecture for polynomials over large finite fields ». Compositio Mathematica 152, no 12 (21 septembre 2016) : 2525–44. http://dx.doi.org/10.1112/s0010437x16007570.

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We prove an analogue of the classical Bateman–Horn conjecture on prime values of polynomials for the ring of polynomials over a large finite field. Namely, given non-associate, irreducible, separable and monic (in the variable$x$) polynomials$F_{1},\ldots ,F_{m}\in \mathbf{F}_{q}[t][x]$, we show that the number of$f\in \mathbf{F}_{q}[t]$of degree$n\geqslant \max (3,\deg _{t}F_{1},\ldots ,\deg _{t}F_{m})$such that all$F_{i}(t,f)\in \mathbf{F}_{q}[t],1\leqslant i\leqslant m$, are irreducible is$$\begin{eqnarray}\displaystyle \biggl(\mathop{\prod }_{i=1}^{m}\frac{\unicode[STIX]{x1D707}_{i}}{N_{i}}\biggr)q^{n+1}(1+O_{m,\,\max \deg F_{i},\,n}(q^{-1/2})), & & \displaystyle \nonumber\end{eqnarray}$$where$N_{i}=n\deg _{x}F_{i}$is the generic degree of$F_{i}(t,f)$for$\deg f=n$and$\unicode[STIX]{x1D707}_{i}$is the number of factors into which$F_{i}$splits over$\overline{\mathbf{F}}_{q}$. Our proof relies on the classification of finite simple groups. We will also prove the same result for non-associate, irreducible and separable (over$\mathbf{F}_{q}(t)$) polynomials$F_{1},\ldots ,F_{m}$not necessarily monic in$x$under the assumptions that$n$is greater than the number of geometric points of multiplicity greater than two on the (possibly reducible) affine plane curve$C$defined by the equation$$\begin{eqnarray}\displaystyle \mathop{\prod }_{i=1}^{m}F_{i}(t,x)=0 & & \displaystyle \nonumber\end{eqnarray}$$(this number is always bounded above by$(\sum _{i=1}^{m}\deg F_{i})^{2}/2$, where$\deg$denotes the total degree in$t,x$) and$$\begin{eqnarray}\displaystyle p=\text{char}\,\mathbf{F}_{q}>\max _{1\leqslant i\leqslant m}N_{i}, & & \displaystyle \nonumber\end{eqnarray}$$where$N_{i}$is the generic degree of$F_{i}(t,f)$for$\deg f=n$.
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41

Hutchinson, Kevin. « A Bloch-Wigner complex for SL2 ». Journal of K-Theory 12, no 1 (22 avril 2013) : 15–68. http://dx.doi.org/10.1017/is013003031jkt13222.

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AbstractWe introduce a refinement of the Bloch-Wigner complex of a field F. This refinement is complex of modules over the multiplicative group of the field. Instead of computing K2(F) and Kind3(F) - as the classical Bloch-Wigner complex does - it calculates the second and third integral homology of SL2(F). On passing to F× -coinvariants we recover the classical Bloch-Wigner complex. We include the case of finite fields throughout the article.
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42

BANKS, TOM. « HOLOGRAPHIC SPACETIME ». International Journal of Modern Physics D 21, no 11 (octobre 2012) : 1241004. http://dx.doi.org/10.1142/s0218271812410040.

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The theory of holographic spacetime (HST) generalizes both string theory and quantum field theory (QFT). It provides a geometric rationale for supersymmetry (SUSY) and a formalism in which super-Poincare invariance follows from Poincare invariance. HST unifies particles and black holes, realizing both as excitations of noncommutative geometrical variables on a holographic screen. Compact extra dimensions are interpreted as finite-dimensional unitary representations of super-algebras, and have no moduli. Full field theoretic Fock spaces, and continuous moduli are both emergent phenomena of super-Poincare invariant limits in which the number of holographic degrees of freedom goes to infinity. Finite radius de Sitter (dS) spaces have no moduli, and break SUSY with a gravitino mass scaling like Λ1/4. In regimes where the Covariant Entropy Bound is saturated, QFT is not a good description in HST, and inflation is such a regime. Following ideas of Jacobson, the gravitational and inflaton fields are emergent classical variables, describing the geometry of an underlying HST model, rather than "fields associated with a microscopic string theory". The phrase in quotes is meaningless in the HST formalism, except in asymptotically flat and AdS spacetimes, and some relatives of these.
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43

Antieau, Benjamin, et Ben Williams. « Godeaux–Serre varieties and the étale index ». Journal of K-Theory 11, no 2 (avril 2013) : 283–95. http://dx.doi.org/10.1017/is013003003jkt220.

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AbstractWe use Godeaux–Serre varieties of finite groups, projective representation theory, the twisted Atiyah–Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α ∈ Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux–Serre varieties in terms of projective representation theory.
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Berrick, A. J., M. Karoubi et P. A. Østvær. « Periodicity of hermitianK-groups ». Journal of K-theory 7, no 3 (16 mai 2011) : 429–93. http://dx.doi.org/10.1017/is011004009jkt151.

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AbstractBott periodicity for the unitary and symplectic groups is fundamental to topologicalK-theory. Analogous to unitary topologicalK-theory, for algebraicK-groups with finite coefficients, similar results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraicK-groups for any ring implies periodicity for the hermitianK-groups, analogous to orthogonal and symplectic topologicalK-theory.The proofs use in an essential way higherKSC-theories, extending those of Anderson and Green. They also provide an upper bound for the higher hermitianK-groups in terms of higher algebraicK-groups.We also relate periodicity to étale hermitianK-groups by proving a hermitian version of Thomason's étale descent theorem. The results are illustrated in detail for local fields, rings of integers in number fields, smooth complex algebraic varieties, rings of continuous functions on compact spaces, and group rings.
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Castro, Francis N., et Luis A. Medina. « Hadamard matrices and the spectrum of quadratic symmetric polynomials over finite fields ». Linear Algebra and its Applications 549 (juillet 2018) : 153–75. http://dx.doi.org/10.1016/j.laa.2018.03.013.

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Chistov, Alexander, Hervé Fournier, Pascal Koiran et Sylvain Perifel. « On the construction of a family of transversal subspaces over finite fields ». Linear Algebra and its Applications 429, no 2-3 (juillet 2008) : 589–600. http://dx.doi.org/10.1016/j.laa.2008.03.014.

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47

Rvachev, V. L., et T. I. Sheiko. « R-Functions in Boundary Value Problems in Mechanics ». Applied Mechanics Reviews 48, no 4 (1 avril 1995) : 151–88. http://dx.doi.org/10.1115/1.3005099.

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Described are the concepts and applications of the R-functions theory in continuum mechanics boundary value problems which model fields of different physical natures. With R-functions there appears the possibility of creating a constructive mathematical tool which incorporates the capabilities of classical continuous analysis and logic algebra. This allows one to overcome the main obstacle which hinders the use of variational methods when solving boundary value problems in domains of complex shape with complex boundary conditions, this obstacle being connected with the construction of so-called coordinate sequences. In contrast to widely used methods of the network type (finite difference, finite and boundary elements), in the R-functions method all the geometric information present in the boundary value problem statement is reduced to analytical form, which allows one to search for a solution in the form of formulae called solution structures containing some indefinite functional components. A method of constructing solution structures satisfying the required conditions of completeness has been developed. The structural formulae include the left-hand sides of the normalized equations of the boundaries of the domains or their regions being considered, thus allowing one to change the solution structure expeditiously when changing the geometric shape. Given in the work is a definition of the basic class of R-functions, solution with their help of the inverse problem of analytical geometry (construction of equations of specified configurations); generalization of the Taylor-Hermite formulae for functional spaces in which points are represented by lines and surfaces; and construction of solution structures of some types of boundary value problems. Shown are the solutions of a number of concrete problems in these application fields with the use of the RL language and POLYE system.
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Mofrad, Asieh A., M. R. Sadeghi et D. Panario. « Solving sparse linear systems of equations over finite fields using bit-flipping algorithm ». Linear Algebra and its Applications 439, no 7 (octobre 2013) : 1815–24. http://dx.doi.org/10.1016/j.laa.2013.05.016.

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Bach, Eric, et Andrew Bridy. « On the number of distinct functional graphs of affine-linear transformations over finite fields ». Linear Algebra and its Applications 439, no 5 (septembre 2013) : 1312–20. http://dx.doi.org/10.1016/j.laa.2013.04.014.

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Chandoul, Amara, et Alanod M. Sibih. « Note on Irreducible Polynomials over Finite Field ». European Journal of Pure and Applied Mathematics 14, no 1 (31 janvier 2021) : 265–67. http://dx.doi.org/10.29020/nybg.ejpam.v14i1.3898.

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In this note we extend an irreducibility criterion of polynomial over finite fields. Weprove the irreducibility of the polynomial P(Y ) = Yn + λn−1Y n−1 + λn−2Y n−2 + · · · + λ1Y + λ0, such that λ0 6= 0, deg λn−2 = 2 deg λn−1 + l > deg λi, for all i 6= n − 2 and odd integer l.
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