1,272 research outputs found
On the (2,3)-generation of the finite symplectic groups
This paper is a new important step towards the complete classification of the
finite simple groups which are -generated. In fact, we prove that the
symplectic groups are -generated for all . Because
of the existing literature, this result implies that the groups
are -generated for all , with the exception of and
Scott's formula and Hurwitz groups
This paper continues previous work, based on systematic use of a formula of
L. Scott, to detect Hurwitz groups. It closes the problem of determining the
finite simple groups contained in for which are Hurwitz,
where is an algebraically closed field. For the groups , ,
and the Janko groups and it provides explicit -generators
More on regular subgroups of the affine group
This paper is a new contribution to the study of regular subgroups of the
affine group , for any field . In particular we associate to any
partition of abelian regular subgroups in such a
way that different partitions define non-conjugate subgroups. Moreover, we
classify the regular subgroups of certain natural types for . Our
classification is equivalent to the classification of split local algebras of
dimension over . Our methods, based on classical results of linear
algebra, are computer free
The -generation of the finite unitary groups
In this paper we prove that the unitary groups are
-generated for any prime power and any integer . By
previous results this implies that, if , the groups and
are -generated, except when
.Comment: In this version, we obtained a complete classification of the finite
simple unitary groups which are (2,3)-generated; some proofs have been
semplifie
The simple classical groups of dimension less than 6 which are (2,3)-generated
In this paper we determine the classical simple groups of dimension r=3,5
which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are
PSL_3(q), q 4, and PSU_3(q^2), q^2 9, 25. If r = 5 they are PSL_5(q), for
all q, and PSU_5(q^2), q^2 >= 9. Also, the soluble group PSU_3(4) is not
(2,3)-generated. We give explicit (2,3)-generators of the linear preimages, in
the special linear groups, of the (2,3)-generated simple groups.Comment: 12 page
Method to measure off-axis displacements based on the analysis of the intensity distribution of a vortex beam
We study the properties of the Fraunhofer diffraction patterns produced by
Gaussian beams crossing spiral phase plates. We show, both analytically and
numerically, that off-axis displacements of the input beam produce asymmetric
diffraction patterns. The intensity profile along the direction of maximum
asymmetry shows two different peaks. We find that the intensity ratio between
these two peaks decreases exponentially with the off-axis displacement of the
incident beam, the decay being steeper for higher strengths of the optical
singularity of the spiral phase plate. We analyze how this intensity ratio can
be used to measure small misalignments of the input beam with a very high
precision.Comment: 8 pages, 4 figures. Accepted for publication in PR
The (2,3)-generation of the special unitary groups of dimension 6
In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^
2), for all q. They fit into a uniform sequence of likely (2,3)-generators for
all n>= 6
Effect of farming system changes on life cycle assessment indicators for dairy farms in the Italian Alps.
In some Alpine areas dairy farming is going through a process of intensification with significant changes in farming systems. The aim of this study was to investigate environmental performance of a sample of 31 dairy farms in an Alpine area of Lombardy with different levels of intensification. A cradle to farm gate life cycle assessment was performed including the following impact categories: land use, non-renewable energy use, climate change, acidification and eutrophication. From a cluster analysis it resulted that the group of farms with lowest environmental impacts were characterized by low stocking density and production intensity; farms that combined good environmental performances with medium gross margins were characterized also by high feed self-sufficiency and lowland availability. Environmental impacts of dairy farms in the mountain areas could be mitigated by the improvement of forage production and quality and by the practice of summer highland grazing, that significantly reduced eutrophication per kg of milk of the less self-sufficient farms
Improved local-constant-field approximation for strong-field QED codes
The local-constant-field approximation (LCFA) is an essential theoretical
tool for investigating strong-field QED phenomena in background electromagnetic
fields with complex spacetime structure. In our previous work
[Phys.~Rev.~A~\textbf{98}, 012134 (2018)] we have analyzed the shortcomings of
the LCFA in nonlinear Compton scattering at low emitted photon energies for the
case of a background plane-wave field. Here, we generalize that analysis to
background fields, which can feature a virtually arbitrary spacetime structure.
In addition, we provide an explicit and simple implementation of an improved
expression of the nonlinear Compton scattering differential probability that
solves the main shortcomings of the standard LCFA in the infrared region, and
is suitable for background electromagnetic fields with arbitrary spacetime
structure such as those occurring in particle-in-cell simulations. Finally, we
carry out a systematic procedure to calculate the probability of nonlinear
Compton scattering per unit of emitted photon light-cone energy and of
nonlinear Breit-Wheeler pair production per unit of produced positron
light-cone energy beyond the LCFA in a plane-wave background field, which
allows us to identify the limits of validity of this approximation
quantitatively.Comment: 15 pages, 3 figure
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