953 research outputs found
On a conjecture of Bennewitz, and the behaviour of the Titchmarsh-Weyl matrix near a pole
For any real limit- th-order selfadjoint linear differential
expression on , Titchmarsh- Weyl matrices
can be defined. Two matrices of particu lar interest are the
matrices and assoc iated respectively with
Dirichlet and Neumann boundary conditions at . These satisfy
. It is known that when these matrices
have poles (which can only lie on the real axis) the existence of valid HELP
inequalities depends on their behaviour in the neighbourhood of these poles. We
prove a conjecture of Bennewitz and use it, together with a new algorithm for
computing the Laurent expansion of a Titchmarsh-Weyl matrix in the
neighbourhood of a pole, to investigate the existence of HELP inequalities for
a number of differential equations which have so far proved awkward to analys
Fast algorithm for detecting community structure in networks
It has been found that many networks display community structure -- groups of
vertices within which connections are dense but between which they are sparser
-- and highly sensitive computer algorithms have in recent years been developed
for detecting such structure. These algorithms however are computationally
demanding, which limits their application to small networks. Here we describe a
new algorithm which gives excellent results when tested on both
computer-generated and real-world networks and is much faster, typically
thousands of times faster than previous algorithms. We give several example
applications, including one to a collaboration network of more than 50000
physicists.Comment: 5 pages, 4 figure
Quantum Singularities in Horava-Lifshitz Cosmology
The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from
the quantum cosmology point of view. By employing usual quantum cosmology
techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW)
universe filled with radiation in the context of HL gravity. We find that this
universe is quantum mechanically nonsingular in two different ways: the
expectation value of the scale factor never vanishes and, if we
abandon the detailed balance condition suggested by Horava, the quantum
dynamics of the universe is uniquely determined by the initial wave packet and
no boundary condition at is indeed necessary.Comment: 13 pages, revtex, 1 figure. Final version to appear in PR
Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces
The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established
On the time delay in binary systems
The aim of this paper is to study the time delay on electromagnetic signals
propagating across a binary stellar system. We focus on the antisymmetric
gravitomagnetic contribution due to the angular momentum of one of the stars of
the pair. Considering a pulsar as the source of the signals, the effect would
be manifest both in the arrival times of the pulses and in the frequency shift
of their Fourier spectra. We derive the appropriate formulas and we discuss the
influence of different configurations on the observability of gravitomagnetic
effects. We argue that the recently discovered PSR J0737-3039 binary system
does not permit the detection of the effects because of the large size of the
eclipsed region.Comment: 7 pages, 2 eps figures, RevTex, to appear in Physical Review
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