4,910 research outputs found
On Maximal Unbordered Factors
Given a string of length , its maximal unbordered factor is the
longest factor which does not have a border. In this work we investigate the
relationship between and the length of the maximal unbordered factor of
. We prove that for the alphabet of size the expected length
of the maximal unbordered factor of a string of length~ is at least
(for sufficiently large values of ). As an application of this result, we
propose a new algorithm for computing the maximal unbordered factor of a
string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern
Matching (CPM 2015
Exotic galilean symmetry and the Hall effect
The ``Laughlin'' picture of the Fractional Quantum Hall effect can be derived
using the ``exotic'' model based on the two-fold centrally-extended planar
Galilei group. When coupled to a planar magnetic field of critical strength
determined by the extension parameters, the system becomes singular, and
``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne,
Jackiw, and Trugenberger. The reduced system moves according to the Hall law.Comment: Talk given by P. A. Horvathy at the Joint APCTP- Nankai Symposium.
Tianjin (China), Oct.2001. To appear in the Proceedings, to be published by
Int. Journ. Mod. Phys. B. 7 pages, LaTex, IJMPB format. no figure
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Let be an odd-dimensional Euclidean space endowed with a contact 1-form
. We investigate the space of symmetric contravariant tensor fields on
as a module over the Lie algebra of contact vector fields, i.e. over the
Lie subalgebra made up by those vector fields that preserve the contact
structure. If we consider symmetric tensor fields with coefficients in tensor
densities, the vertical cotangent lift of contact form is a contact
invariant operator. We also extend the classical contact Hamiltonian to the
space of symmetric density valued tensor fields. This generalized Hamiltonian
operator on the symbol space is invariant with respect to the action of the
projective contact algebra . The preceding invariant operators lead
to a decomposition of the symbol space (expect for some critical density
weights), which generalizes a splitting proposed by V. Ovsienko
Computing the Longest Unbordered Substring
International audienceA substring of a string is unbordered if its only border is the empty string. The study of unbordered substrings goes back to the paper of Ehrenfeucht and Silberger [7]. The main focus of [7] and of subsequent papers was to elucidate the relationship between the longest unbordered substring and the minimal period of strings. In this paper, we consider the algorithmic problem of computing the longest unbordered substring of a string. The problem was introduced recently in [12], where the authors showed that the average-case running time of the simple, border-array based algorithm can be bounded by O(n 2 /Ï 4) for Ï being the size of the alphabet. (The worst-case running time remained O(n 2).) Here we propose two algorithms, both presenting substantial theoretical improvements to the result of [12]. The first algorithm has O(n log n) average-case running time and O(n 2) worst-case running time, and the second algorithm has O(n 1.5) worst-case running time
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
Transverse Shifts in Paraxial Spinoptics
The paraxial approximation of a classical spinning photon is shown to yield
an "exotic particle" in the plane transverse to the propagation. The previously
proposed and observed position shift between media with different refractive
indices is modified when the interface is curved, and there also appears a
novel, momentum [direction] shift. The laws of thin lenses are modified
accordingly.Comment: 3 pages, no figures. One detail clarified, some misprints corrected
and references adde
Twist Deformation of Rotationally Invariant Quantum Mechanics
Non-commutative Quantum Mechanics in 3D is investigated in the framework of
the abelian Drinfeld twist which deforms a given Hopf algebra while preserving
its Hopf algebra structure. Composite operators (of coordinates and momenta)
entering the Hamiltonian have to be reinterpreted as primitive elements of a
dynamical Lie algebra which could be either finite (for the harmonic
oscillator) or infinite (in the general case). The deformed brackets of the
deformed angular momenta close the so(3) algebra. On the other hand, undeformed
rotationally invariant operators can become, under deformation, anomalous (the
anomaly vanishes when the deformation parameter goes to zero). The deformed
operators, Taylor-expanded in the deformation parameter, can be selected to
minimize the anomaly. We present the deformations (and their anomalies) of
undeformed rotationally-invariant operators corresponding to the harmonic
oscillator (quadratic potential), the anharmonic oscillator (quartic potential)
and the Coulomb potential.Comment: 20 page
Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect
Our previous ``exotic'' particle, together with the more recent anomalous
anyon model (which has arbitrary gyromagnetic factor ) are reviewed. The
non-relativistic limit of the anyon generalizes the exotic particle which has
to any .When put into planar electric and magnetic fields, the Hall
effect becomes mandatory for all , when the field takes some critical
value.Comment: A new reference added. Talk given by P. Horvathy at the International
Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli
(Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no
figure
Dynamics of semiclassical Bloch wave - packets
The semiclassical approximation for electron wave-packets in crystals leads
to equations which can be derived from a Lagrangian or, under suitable
regularity conditions, in a Hamiltonian framework. In the plane, these issues
are studied %in presence of external fields using the method of the coadjoint
orbit applied to the ``enlarged'' Galilei group.Comment: 15 pages, Talk given at Nonlinear Physics. Theory and Experiment.
IV,Gallipoli (Lecce), Italy - June 22 - July 1, 200
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