505,446 research outputs found
On the stability of m-sequences
We study the stability of m-sequences in the sense of determining
the number of errors needed for decreasing the period of the
sequences, as well as giving lower bounds on the k-error linear complexity
of the sequences. For prime periods the results are straightforward
so we concentrate on composite periods. We give exact results for the
case when the period is reduced by a factor which is a Mersenne number
and for the case when it is reduced by a prime p such that the order
of 2 modulo p equals p 1. The general case is believed to be di cult
due to its similarity to a well studied problem in coding theory. We also
provide results about the relative frequencies of the di erent cases. We
formulate a conjecture regarding the minimum number of errors needed
for reducing the period at all. Finally we apply our results to the LFSR
components of several well known stream ciphers
General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem
We consider discrete self-adjoint Dirac systems determined by the potentials
(sequences) such that the matrices are positive definite and
-unitary, where is a diagonal matrix and has entries
and entries () on the main diagonal. We construct
systems with rational Weyl functions and explicitly solve inverse problem to
recover systems from the contractive rational Weyl functions. Moreover, we
study the stability of this procedure. The matrices (in the potentials)
are so called Halmos extensions of the Verblunsky-type coefficients .
We show that in the case of the contractive rational Weyl functions the
coefficients tend to zero and the matrices tend to the indentity
matrix .Comment: This paper is a generalization and further development of the topics
discussed in arXiv:math/0703369, arXiv:1206.2915, arXiv:1508.07954,
arXiv:1510.0079
Stable scalable control of soliton propagation in broadband nonlinear optical waveguides
We develop a method for achieving scalable transmission stabilization and
switching of colliding soliton sequences in optical waveguides with
broadband delayed Raman response and narrowband nonlinear gain-loss. We show
that dynamics of soliton amplitudes in -sequence transmission is described
by a generalized -dimensional predator-prey model. Stability and bifurcation
analysis for the predator-prey model are used to obtain simple conditions on
the physical parameters for robust transmission stabilization as well as on-off
and off-on switching of out of soliton sequences. Numerical simulations
for single-waveguide transmission with a system of coupled nonlinear
Schr\"odinger equations with show excellent agreement with the
predator-prey model's predictions and stable propagation over significantly
larger distances compared with other broadband nonlinear single-waveguide
systems. Moreover, stable on-off and off-on switching of multiple soliton
sequences and stable multiple transmission switching events are demonstrated by
the simulations. We discuss the reasons for the robustness and scalability of
transmission stabilization and switching in waveguides with broadband delayed
Raman response and narrowband nonlinear gain-loss, and explain their advantages
compared with other broadband nonlinear waveguides.Comment: 37 pages, 7 figures, Eur. Phys. J. D (accepted
Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models
We show that the mass-radius relation corresponding to the stiffest
equation of state (EOS) does not provide the necessary and sufficient condition
of dynamical stability for the equilibrium configurations, since such
configurations can not satisfy the `compatibility criterion'. In this
connection, we construct sequences composed of core-envelope models such that,
like the stiffest EOS, each member of these sequences satisfy the extreme case
of causality condition, , at the centre. We, thereafter, show that
the relation corresponding to the said core-envelope model sequences can
provide the necessary and sufficient condition of dynamical stability only when
the `compatibility criterion' for these sequences is `appropriately' satisfied.
However, the fulfillment of `compatibility criterion' can remain satisfied even
when the relation does not provide the necessary and sufficient condition
of dynamical stability for the equilibrium configurations.
In continuation to the results of previous study, these results explicitly
show that the `compatibility criterion' {\em independently} provides, in
general, the {\em necessary} and {\em sufficient} condition of hydrostatic
equilibrium for any regular sequence. Beside its fundamental feature, this
study can also explain simultaneously, both (the higher as well as lower)
values of the glitch healing parameter observed for the Crab and the Vela-like
pulsars respectively, on the basis of starquake model of glitch generation.Comment: 14 pages (including 6 figures and 5 tables), accepted for publication
in MNRA
Fast integer merging on the EREW PRAM
We investigate the complexity of merging sequences of small integers on the EREW PRAM. Our most surprising result is that two sorted sequences of bits each can be merged in time. More generally, we describe an algorithm to merge two sorted sequences of integers drawn from the set in time using an optimal number of processors. No sublogarithmic merging algorithm for this model of computation was previously known. The algorithm not only produces the merged sequence, but also computes the rank of each input element in the merged sequence. On the other hand, we show a lower bound of on the time needed to merge two sorted sequences of length each with elements in the set , implying that our merging algorithm is as fast as possible for . If we impose an additional stability condition requiring the ranks of each input sequence to form an increasing sequence, then the time complexity of the problem becomes , even for . Stable merging is thus harder than nonstable merging
Gravitational Radiation From and Instabilities in Compact Stars and Compact Binary Systems.
We have examined three types of compact astrophysical systems that are possible sources of detectable gravitational wave radiation (GWR): nonaxisymmetric pulsars; rapidly rotating compact stars undergoing the bar-mode instability; and coalescing compact binaries. Our analysis of nonaxisymmetric pulsars, based on the assumption that any equatorial asymmetries present in these objects were rotationally induced, indicates that nearby millisecond pulsars are generally better candidates for the detection of GWR than the Crab pulsar, which has been the object of an ongoing search for GWR (Tsubono 1991). Our finite difference hydrodynamics (FDH) simulation of an object encountering the rotationally induced bar-mode instability results in an ellipsoidal final configuration which, although gradually becoming more axisymmetric, persists for several orbits, continuously emitting GWR. We also have examined the stability and coalescence of equal mass binaries with polytropic, white dwarf (WD), and neutron star (NS) equations of state (EOS). In order for our explicit FDH code to be able to follow the coalescence of a binary system, it must proceed on a dynamical timescale. Hence, we began our investigation by performing FDH tests of the dynamical stability of individual models constructed along equilibrium sequences of binaries with the same total mass M\sb{T} and EOS but decreasing separation, in order to determine if any models on these sequences were unstable to merger on a dynamical timescale. Our simulations indicate that no points of instability exist on the WD EOS sequences with M\sb{T} =.500 M\sb{\odot} and 2.03 M\sb\odot or on the polytropic EOS sequences with polytropic indices n = 1.5 and 1.0. However, binary models on the n = 0.5 polytropic sequence and on two realistic NS EOS sequences were dynamically unstable to merger. Again using our FDH code, we followed the evolution of the binary with the minimum total energy and angular momentum on the n = 0.5 sequence through coalescence. At the end of the simulation, the ellipsoidal central object is encircled by spiral arms, ejected from the system during the merger, that have wrapped around on themselves and is continuing to emit low amplitude GWR
Strange stars with different quark mass scalings
We investigate the stability of strange quark matter and the properties of
the corresponding strange stars, within a wide range of quark mass scaling. The
calculation shows that the resulting maximum mass always lies between 1.5 solor
mass and 1.8 solor mass for all the scalings chosen here. Strange star
sequences with a linear scaling would support less gravitational mass, and a
change (increase or decrease) of the scaling around the linear scaling would
lead to a larger maximum mass. Radii invariably decrease with the mass scaling.
Then the larger the scaling, the faster the star might spin. In addition, the
variation of the scaling would cause an order of magnitude change of the strong
electric field on quark surface, which is essential to support possible crusts
of strange stars against gravity and may then have some astrophysical
implications.Comment: 5 pages, 6 figures, 1 table. accepted by M
Complexity measures for classes of sequences and cryptographic apllications
Pseudo-random sequences are a crucial component of cryptography, particularly
in stream cipher design. In this thesis we will investigate several measures of
randomness for certain classes of finitely generated sequences.
We will present a heuristic algorithm for calculating the k-error linear complexity
of a general sequence, of either finite or infinite length, and results on the
closeness of the approximation generated.
We will present an linear time algorithm for determining the linear complexity
of a sequence whose characteristic polynomial is a power of an irreducible element,
again presenting variations for both finite and infinite sequences. This algorithm
allows the linear complexity of such sequences to be determined faster than was
previously possible.
Finally we investigate the stability of m-sequences, in terms of both k-error
linear complexity and k-error period. We show that such sequences are inherently
stable, but show that some are more stable than others
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