661 research outputs found
Bond relaxation, electronic and magnetic behavior of 2D metals structures Y on Li(110) surface
We investigated the bond, electronic and magnetic behavior of adsorption
Yttrium atoms on Lithium (110) surface using a combination of
Bond-order-length-strength(BOLS) correlation and density-functional
theory(DFT). We found that adsorption Y atoms on Li(110) surfaces form
two-dimensional (2D) geometric structures of hexagon, nonagon, solid hexagonal,
quadrangle and triangle. The consistent with the magnetic moment are
6.66{\mu}B, 5.54{\mu}B, 0.28{\mu}B, 1.04{\mu}B, 2.81{\mu}B, respectively. In
addition, this work could pave the way for design new 2D metals electronic and
magnetic properties
New constructions of two slim dense near hexagons
We provide a geometrical construction of the slim dense near hexagon with
parameters . Using this construction, we construct
the rank 3 symplectic dual polar space which is the slim dense near
hexagon with parameters . Both the near hexagons are
constructed from two copies of a generalized quadrangle with parameters (2,2)
On hyperovals of polar spaces
We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon E-3 has up to isomorphism a unique full embedding into the dual polar space DH(5, 4)
Characterizations of the Suzuki tower near polygons
In recent work, we constructed a new near octagon from certain
involutions of the finite simple group and showed a correspondence
between the Suzuki tower of finite simple groups, , and the tower of near polygons, . Here we characterize
each of these near polygons (except for the first one) as the unique near
polygon of the given order and diameter containing an isometrically embedded
copy of the previous near polygon of the tower. In particular, our
characterization of the Hall-Janko near octagon is similar to an
earlier characterization due to Cohen and Tits who proved that it is the unique
regular near octagon with parameters , but instead of regularity
we assume existence of an isometrically embedded dual split Cayley hexagon,
. We also give a complete classification of near hexagons of
order and use it to prove the uniqueness result for .Comment: 20 pages; some revisions based on referee reports; added more
references; added remarks 1.4 and 1.5; corrected typos; improved the overall
expositio
Unitary reflection groups for quantum fault tolerance
This paper explores the representation of quantum computing in terms of
unitary reflections (unitary transformations that leave invariant a hyperplane
of a vector space). The symmetries of qubit systems are found to be supported
by Euclidean real reflections (i.e., Coxeter groups) or by specific imprimitive
reflection groups, introduced (but not named) in a recent paper [Planat M and
Jorrand Ph 2008, {\it J Phys A: Math Theor} {\bf 41}, 182001]. The
automorphisms of multiple qubit systems are found to relate to some Clifford
operations once the corresponding group of reflections is identified. For a
short list, one may point out the Coxeter systems of type and (for
single qubits), and (for two qubits), and (for three
qubits), the complex reflection groups and groups No 9 and 31 in
the Shephard-Todd list. The relevant fault tolerant subsets of the Clifford
groups (the Bell groups) are generated by the Hadamard gate, the phase
gate and an entangling (braid) gate [Kauffman L H and Lomonaco S J 2004 {\it
New J. of Phys.} {\bf 6}, 134]. Links to the topological view of quantum
computing, the lattice approach and the geometry of smooth cubic surfaces are
discussed.Comment: new version for the Journal of Computational and Theoretical
Nanoscience, focused on "Technology Trends and Theory of Nanoscale Devices
for Quantum Applications
On the order of a non-abelian representation group of a slim dense near hexagon
We show that, if the representation group of a slim dense near hexagon
is non-abelian, then is of exponent 4 and ,
, where is the near polygon
embedding dimension of and is the dimension of the universal
representation module of . Further, if , then
is an extraspecial 2-group (Theorem 1.6)
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