scholarly journals On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field

1977 ◽  
Vol 47 (2) ◽  
pp. 400-410 ◽  
Author(s):  
Giampaolo Menichetti
Keyword(s):  
Finite Field ◽  
Three Dimensional ◽  
Division Algebras ◽  
Kaplansky Conjecture

SPIN CORRELATIONS IN MAGNETIZED HALDANE CHAINS

2002 ◽  
Vol 16 (20n22) ◽  
pp. 3250-3250
Author(s):  
C. L. BROHOLM
Keyword(s):  
Finite Field ◽  
High Field ◽  
Energy Gap ◽  
Three Dimensional ◽  
Zero Field ◽  
Singlet Ground State ◽  
Field Phase ◽  
Effective Spin ◽  
Spin Correlations ◽  
Theoretical Predictions

Neutron scattering experiments have been carried out in high magnetic fields to understand the magnetized state of the uniform spin-1 antiferromagnetic chain. In zero field this system has a cooperative singlet ground state with a gap to a propagating triplet excitation. The quasi-one-dimensional uniform spin-1 antiferromagnets NENP (Ni(C2D8N2)2NO2CIO4) and NDMAP (Ni(C5D14N2)2N3PF6) were examined. NENP has an alternating g-tensor such that staggered magnetization is induced for arbitrarily small fields and there is no finite field phase transition. In the high field phase the lowest energy mode has a field dependent gap and an unusually small effective spin wave velocity. NDMAP has only one spin per unit cell and hence a uniform g-tensor. This system has a critical transition at a finite field. Surprisingly the high field phase has quasi-two-dimensional or three-dimensional long-range order depending on the direction of the applied field. In the paramagnetic high field phase immediately above the ordering transition of NDMAP, there are gapless magnetic excitations that are broader in Q than the higher energy gap mode. The data is compared to theoretical predictions of a gapless incommensurate phase above the critical field.

scholarly journals Principal indecomposable modules for some three-dimensional special linear groups

1980 ◽  
Vol 22 (3) ◽  
pp. 439-455 ◽  
Author(s):  
James Archer
Keyword(s):  
Finite Field ◽  
Linear Group ◽  
Three Dimensional ◽  
Special Linear Group ◽  
Linear Groups ◽  
Indecomposable Modules ◽  
Special Linear ◽  
Special Linear Groups ◽  
Irreducible Modules ◽  
Characteristic 2

Let k be a finite field of characteristic 2, and let G be the three dimensional special linear group over k. The principal indecomposable modules of G over k are constructed from tensor products of the irreducible modules, and formulae for their dimensions are given.

scholarly journals Three-dimensional division algebras

1976 ◽  
Vol 40 (2) ◽  
pp. 384-391 ◽  
Author(s):  
Irving Kaplansky
Keyword(s):  
Three Dimensional ◽  
Division Algebras

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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