Mathematical Reports - Comptes rendus mathématiques

of the Academy of Science | de l'Académie des sciences

  • Home
  • Articles
  • News
  • Editorial Board
  • General Information
    • General Information
    • Preparation of Manuscripts
    • Subscription Information
    • FAQ
    • Help
 

Vol.39 (2) 2017 — 3 results found.

Show all abstractsHide all abstracts

Polynomial Power Residue Symbols and $q$-resultants
C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (2) 2017, pp. 60-66
Yoshinori Hamahata (Received: 2016/03/17, Revised: 2016/05/22)

[+ show]Hide Abstract

We establish a relation between polynomial power residue symbols and \(q\)-resultants of \(\mathbb{F}_q\)-linear polynomials. We then establish the \(q-1\)-st power reciprocity law.

On établit une relation entre le symbole de résidu de puissances en caractéristique \(p\) et le \(q\)-résultant de deux \(\mathbb{F}_q\)-polynômes linéaire. Alors on démontre la loi de réciprocité des puissances \(q-1\)-èmes.

Cauchy Problem on Two Characteristic Hypersurfaces for the Einstein-Vlasov Scalar Field Equations in Temporal Gauge
C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (2) 2017, pp. 45-59
Marcel Dossa; Jean Baptiste Patenou (Received: 2015/12/01, Revised: 2016/05/16)

[+ show]Hide Abstract

In this paper, we consider the initial value problem for the Einstein-Vlasov scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of some free data, the initial data constraints’s problem is solved globally, then the evolution problem relative to the deduced initial data is solved locally in time.

Dans cet article, on considère le problème de Cauchy pour les équations d’Einstein-Vlasov-Champ scalaire en jauge temporelle, dans le cas où les données initiales sont préscrites sur deux hypersurfaces caractéristiques régulières sécantes. A partir d’un choix judicieux de certaines données indépendantes, le problème des contraintes initiales est globalement résolu, et ensuite le problème de l’évolution relatif aux données initiales déduites est résolu localement dans le temps.

Further Remarks on Rational Albime Triangles
C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (2) 2017, pp. 67-76
Jasbir S. Chahal; Josselin Kooij; Jaap Top (Received: 2015/07/26, Revised: 2016/11/14)

[+ show]Hide Abstract

In this note we present further number theoretic properties of the rational albime triangles, in particular, the distribution of acute vs. obtuse rational albime triangles. The notion of albime triangle is extended to include the case of external angle bisector. The proportion of internal vs. external rational albime triangles is also computed.

Dans cette note, nous présentons des propriétés supplémentaires (concernant la théorie des nombres) des triangles rationnels ‘albimes’; en particulier, la distribution des triangles rationnels albimes aigus contre obtus. La notion de triangle albime est développé pour comprendre le cas d’extérieur bissectrice. On calcule aussi la proportion des triangles rationnels albimes internes contre externes.

 Volume / Issue

Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

Be notified of new issues

Copyright © 2023 · The Royal Society of Canada | La Société royale du Canada · Log in
ISSN: 2816-5810 (Online)