1,176 research outputs found
Quasi-exactly solvable quartic: elementary integrals and asymptotics
We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where
p, h and P are polynomials in one variable. For the case when h is an odd cubic
polynomial, we found an interesting identity which is used to describe the
spectral locus. We also establish some asymptotic properties of the QES
spectral locus.Comment: 20 pages, 1 figure. Added Introduction and several references,
corrected misprint
Permutable entire functions and multiply connected wandering domains
Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f)=J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set
Connectedness properties of the set where the iterates of an entire function are unbounded
We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded
Magnetoelastic Coupling and Possibility of Spintronic Electromagnetomechanical Effects
Nanoelectromangetomechanical systems (NEMMS) open up a new path for the
development of high speed autonomous nanoresonators and signal generators that
could be used as actuators, for information processing, as elements of quantum
computers etc. Those NEMMS that include ferromagnetic layers could be
controlled by the electric current due to effects related with spin transfer.
In the present paper we discuss another situation when the current-controlled
behaviour of nanorod that includes an antiferro- (instead of one of ferro-)
magnetic layer. We argue that in this case ac spin-polarized current can also
induce resonant coupled magneto-mechanical oscillations and produce an
oscillating magnetization of antiferromagnetic (AFM) layer. These effects are
caused by \emph{i}) spin-transfer torque exerted to AFM at the interface with
nonmagnetic spacer and by \emph{ii}) the effective magnetic field produced by
the spin-polarized free electrons due to -exchange.The described nanorod
with an AFM layer can find an application in magnetometry and as a
current-controlled high-frequency mechanical oscillator.Comment: 8 pages, 2 figures, submitted to Low Temp. Physic
Rigidity of escaping dynamics for transcendental entire functions
We prove an analog of Boettcher's theorem for transcendental entire functions
in the Eremenko-Lyubich class B. More precisely, let f and g be entire
functions with bounded sets of singular values and suppose that f and g belong
to the same parameter space (i.e., are *quasiconformally equivalent* in the
sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to
the set of points which remain in some sufficiently small neighborhood of
infinity under iteration. Furthermore, this conjugacy extends to a
quasiconformal self-map of the plane.
We also prove that this conjugacy is essentially unique. In particular, we
show that an Eremenko-Lyubich class function f has no invariant line fields on
its escaping set.
Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f
and g which belong to the same parameter space are conjugate on their sets of
escaping points.Comment: 28 pages; 2 figures. Final version (October 2008). Various
modificiations were made, including the introduction of Proposition 3.6,
which was not formally stated previously, and the inclusion of a new figure.
No major changes otherwis
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