3,887 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
On the Number of Unbordered Factors
We illustrate a general technique for enumerating factors of k-automatic
sequences by proving a conjecture on the number f(n) of unbordered factors of
the Thue-Morse sequence. We show that f(n) = 4 and that f(n) = n
infinitely often. We also give examples of automatic sequences having exactly 2
unbordered factors of every length
Effect of physical aging on the low-frequency vibrational density of states of a glassy polymer
The effects of the physical aging on the vibrational density of states (VDOS)
of a polymeric glass is studied. The VDOS of a poly(methyl methacrylate) glass
at low-energy (<15 meV), was determined from inelastic neutron scattering at
low-temperature for two different physical thermodynamical states. One sample
was annealed during a long time at temperature lower than Tg, and another was
quenched from a temperature higher than Tg. It was found that the VDOS around
the boson peak, relatively to the one at higher energy, decreases with the
annealing at lower temperature than Tg, i.e., with the physical aging.Comment: To be published in Europhys. Let
Raman scattering from fractals. Simulation on large structures by the method of moments
We have employed the method of spectral moments to study the density of
vibrational states and the Raman coupling coefficient of large 2- and 3-
dimensional percolators at threshold and at higher concentration. We first
discuss the over-and under-flow problems of the procedure which arise when
-like in the present case- it is necessary to calculate a few thousand moments.
Then we report on the numerical results; these show that different scattering
mechanisms, all {\it a priori} equally probable in real systems, produce
largely different coupling coefficients with different frequency dependence.
Our results are compared with existing scaling theories of Raman scattering.
The situation that emerges is complex; on the one hand, there is indication
that the existing theory is not satisfactory; on the other hand, the
simulations above threshold show that in this case the coupling coefficients
have very little resemblance, if any, with the same quantities at threshold.Comment: 26 pages, RevTex, 8 figures available on reques
Polymer Sensors for the Quantification of Waterborne Uranium
Clandestine activities involving the separation, concentration or manipulation of special nuclear material for the express purpose of developing a weapon of mass destruction is likely to result in the contamination of environmental water sources. The capability to conduct isotopic analyses for waterborne special nuclear material, like uranium, would be a powerful nuclear forensics tool. Despite widespread interest, there currently is no on-line or field-able measurement system available for low-level quantification of uranium in aqueous solutions. A recent development in environmental sensing is a portable, flow cell detector that utilizes extractive scintillating (ES) resin. The ES resin serves the dual purpose of (1) concentrating the radionuclide of interest and (2) serving as a radiation transducer. Currently, such resins are produced by physically absorbing organic extractants and fluors into a polymer matrix. Unfortunately, this approach yields resins with poor stability as the active components leach from the resin over time. This contribution describes our work to increase resin stability by synthesizing ES resin in which the active components are bound covalently within the polymer matrix. The extraction and fluorescence properties of the resin were studied separately before the resin was applied in flow cell detector where detection efficiencies of 40% were achieved
Natural and projectively equivariant quantizations by means of Cartan Connections
The existence of a natural and projectively equivariant quantization in the
sense of Lecomte [20] was proved recently by M. Bordemann [4], using the
framework of Thomas-Whitehead connections. We give a new proof of existence
using the notion of Cartan projective connections and we obtain an explicit
formula in terms of these connections. Our method yields the existence of a
projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant
quantization exists in the flat situation in the sense of [18], thus solving
one of the problems left open by M. Bordemann.Comment: 13 page
A lower bound for nodal count on discrete and metric graphs
According to a well-know theorem by Sturm, a vibrating string is divided into
exactly N nodal intervals by zeros of its N-th eigenfunction. Courant showed
that one half of Sturm's theorem for the strings applies to the theory of
membranes: N-th eigenfunction cannot have more than N domains. He also gave an
example of a eigenfunction high in the spectrum with a minimal number of nodal
domains, thus excluding the existence of a non-trivial lower bound. An analogue
of Sturm's result for discretizations of the interval was discussed by
Gantmacher and Krein. The discretization of an interval is a graph of a simple
form, a chain-graph. But what can be said about more complicated graphs? It has
been known since the early 90s that the nodal count for a generic eigenfunction
of the Schrodinger operator on quantum trees (where each edge is identified
with an interval of the real line and some matching conditions are enforced on
the vertices) is exact too: zeros of the N-th eigenfunction divide the tree
into exactly N subtrees. We discuss two extensions of this result in two
directions. One deals with the same continuous Schrodinger operator but on
general graphs (i.e. non-trees) and another deals with discrete Schrodinger
operator on combinatorial graphs (both trees and non-trees). The result that we
derive applies to both types of graphs: the number of nodal domains of the N-th
eigenfunction is bounded below by N-L, where L is the number of links that
distinguish the graph from a tree (defined as the dimension of the cycle space
or the rank of the fundamental group of the graph). We also show that if it the
genericity condition is dropped, the nodal count can fall arbitrarily far below
the number of the corresponding eigenfunction.Comment: 15 pages, 4 figures; Minor corrections: added 2 important reference
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