3,040 research outputs found
Relative unitary commutator calculus and applications
This note revisits localisation and patching method in the setting of
generalised unitary groups. Introducing certain subgroups of relative
elementary unitary groups, we develop relative versions of the conjugation
calculus and the commutator calculus in unitary groups, which are both more
general, and substantially easier than the ones available in the literature.
For the general linear group such relative commutator calculus has been
recently developed by the first and the third authors. As an application we
prove the mixed commutator formula, for two form ideals of a form ring. This
answers two problems posed in a paper by Alexei Stepanov and the second author.Comment: polishe
Calculation of intensity of high energy muon groups observed deep underground
The intensity of narrow muon groups observed in Kolar Gold Field (KGF) at the depth of 3375 m.w.e. was calculated in terms of quark-gluon strings model for high energy hadron - air nuclei interactions by the method of direct modeling of nuclear cascade in the air and muon propagation in the ground for normal primary cosmic ray composition. The calculated intensity has been found to be approx. 10 to the 4 times less than one observed experimentally
The yoga of commutators
In the present paper we discuss some recent versions of localisation methods
for calculations in the groups of points of algebraic-like and classical-like
groups. Namely, we describe relative localisation, universal localisation, and
enhanced versions of localisation-completion. Apart from the general strategic
description of these methods, we state some typical technical results of the
conjugation calculus and the commutator calculus. Also, we state several recent
results obtained therewith, such as relative standard commutator formulae,
bounded width of commutators, with respect to the elementary generators, and
nilpotent filtrations of congruence subgroups. Overall, this shows that
localisation methods can be much more efficient, than expected
Interplay between magnetism and superconductivity in Fe-pnictides
We consider phase transitions and potential co-existence of spin-density-wave
(SDW) magnetic order and extended s-wave () superconducting order within a
two-band itinerant model of iron pnictides, in which SDW magnetism and
superconductivity are competing orders. We show that depending on parameters,
the transition between these two states is either first order, or involves an
intermediate phase in which the two orders co-exist. We demonstrate that such
co-existence is possible when SDW order is incommensurate.Comment: 5 pages, 3 figure
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