Cohomology operations and obstructions to extending continuous functions /

"Work supported in part by U.S. Air Force Contract AF 18 (600)-1494."

Cohomology theories.

Caption title.

Linear groups, with an exposition of the Galois field theory,

Available on demand as hard copy or computer file from Cornell University Library.

Ueber die Galois'sche Gruppe des Apollonischen Problems in der Ebene und im Raum.

Thesis (doctoral)--Kaiser-Wilhelms-Universitaet-Strassburg.

Die modulargleichungen der galois'schen moduln der 2. bis 5. st...

Thesis (doctoral)--

Die untergruppen der galois'schen gruppe der modulargleichungen...

Thesis (doctoral)--

Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)

2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.

Groups of Order 32 as Galois Groups

2000 Mathematics Subject Classification: 12F12.

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.

Galois lattice dynamics

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Galois lattice dynamics

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

De las matem?ticas cl?sicas a las matem?ticas modernas y contempor?neas: el caso de la teor?a de Galois como una adjunci?n

En este trabajo de grado se presentan algunos elementos a considerar en el estudio de la transici?n de las matem?ticas cl?sicas a las matem?ticas modernas y contempor?neas, a trav?s de un estudio hist?rico ? epistemol?gico y matem?tico de la obra de Galois. As?, nos concentraremos en la indagaci?n de la teor?a de Galois como una adjunci?n, lo cual ser? analizado desde dos perspectivas: una matem?tica que nos muestra el presente te?rico de la teor?a de Galois y las adjunciones, lo que nos permite comentar como la teor?a de Galois es un caso particular de una adjunci?n; y otra hist?rica que muestra la evoluci?n de la teor?a de Galois desde 1830 hasta la actualidad. Todo esto, porque consideramos la teor?a de Galois como un ejemplo paradigm?tico en la transici?n de las matem?ticas cl?sicas a las matem?ticas modernas y contempor?neas. Al final presentaremos una reflexi?n did?ctica y epistemol?gica vinculada directamente a la formaci?n inicial de profesores en el cuerpo de las matem?ticas.

A study on independent component analysis over galois fields

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2015.