137 research outputs found
On some first-order differential subordination
AbstractLet A denote the class of functions f that are analytic in the unit disc D and normalized by f(0)=f′(0)−1=0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex, and convex. To obtain this, we first estimate ∣Arg{f′(z)}∣ which improves the earlier results
On the thin-shell limit of branes in the presence of Gauss-Bonnet interactions
In this paper we study thick-shell braneworld models in the presence of a
Gauss-Bonnet term. We discuss the peculiarities of the attainment of the
thin-shell limit in this case and compare them with the same situation in
Einstein gravity. We describe the two simplest families of thick-brane models
(parametrized by the shell thickness) one can think of. In the thin-shell
limit, one family is characterized by the constancy of its internal density
profile (a simple structure for the matter sector) and the other by the
constancy of its internal curvature scalar (a simple structure for the
geometric sector). We find that these two families are actually equivalent in
Einstein gravity and that the presence of the Gauss-Bonnet term breaks this
equivalence. In the second case, a shell will always keep some non-trivial
internal structure, either on the matter or on the geometric sectors, even in
the thin-shell limit.Comment: 17 pages, 2 figures, RevTeX 4. Revised version accepted for
publication in Physical Review
Certain subclasses of multivalent functions defined by new multiplier transformations
In the present paper the new multiplier transformations
\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq
0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent
functions is defined. Making use of the operator two new subclasses and \textbf{\ }of multivalent analytic
functions are introduced and investigated in the open unit disk. Some
interesting relations and characteristics such as inclusion relationships,
neighborhoods, partial sums, some applications of fractional calculus and
quasi-convolution properties of functions belonging to each of these subclasses
and
are
investigated. Relevant connections of the definitions and results presented in
this paper with those obtained in several earlier works on the subject are also
pointed out
Brane Universes with Gauss-Bonnet-Induced-Gravity
The DGP brane world model allows us to get the observed late time
acceleration via modified gravity, without the need for a ``dark energy''
field. This can then be generalised by the inclusion of high energy terms, in
the form of a Gauss-Bonnet bulk. This is the basis of the
Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and
late time modifications to the cosmological evolution. Recently the simplest
GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of
the three possible branches in these models start with a finite density
``Big-Bang'' and with late time acceleration. Here we present a comprehensive
analysis of more general models where we include a bulk cosmological constant
and brane tension. We show that by including these factors it is possible to
have late time phantom behaviour.Comment: 12 pages, 19 figures. Minor modifications to text, comments on
phantom behaviour added. References added. As submitted to JCA
Measuring geometric phases of scattering states in nanoscale electronic devices
We show how a new quantum property, a geometric phase, associated with
scattering states can be exhibited in nanoscale electronic devices. We propose
an experiment to use interference to directly measure the effect of the new
geometric phase. The setup involves a double path interferometer, adapted from
that used to measure the phase evolution of electrons as they traverse a
quantum dot (QD). Gate voltages on the QD could be varied cyclically and
adiabatically, in a manner similar to that used to observe quantum adiabatic
charge pumping. The interference due to the geometric phase results in
oscillations in the current collected in the drain when a small bias across the
device is applied. We illustrate the effect with examples of geometric phases
resulting from both Abelian and non-Abelian gauge potentials.Comment: Six pages two figure
High-resolution Ce 3d-edge resonant photoemission study of CeNi_2
Resonant photoemission (RPES) at the Ce 3d -> 4f threshold has been performed
for alpha-like compound CeNi_2 with extremely high energy resolution (full
width at half maximum < 0.2 eV) to obtain bulk-sensitive 4f spectral weight.
The on-resonance spectrum shows a sharp resolution-limited peak near the Fermi
energy which can be assigned to the tail of the Kondo resonance. However, the
spin-orbit side band around 0.3 eV binding energy corresponding to the f_{7/2}
peak is washed out, in contrast to the RPES spectrum at the Ce 3d -> 4f RPES
threshold. This is interpreted as due to the different surface sensitivity, and
the bulk-sensitive Ce 3d -> 4f RPES spectra are found to be consistent with
other electron spectroscopy and low energy properties for alpha-like
Ce-transition metal compounds, thus resolves controversy on the interpretation
of Ce compound photoemission. The 4f spectral weight over the whole valence
band can also be fitted fairly well with the Gunnarsson-Schoenhammer
calculation of the single impurity Anderson model, although the detailed
features show some dependence on the hybridization band shape and (possibly) Ce
5d emissions.Comment: 4 pages, 3 figur
Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
In spacetimes of dimension greater than four it is natural to consider higher
order (in R) corrections to the Einstein equations. In this letter generalized
Israel junction conditions for a membrane in such a theory are derived. This is
achieved by generalising the Gibbons-Hawking boundary term. The junction
conditions are applied to simple brane world models, and are compared to the
many contradictory results in the literature.Comment: 4 page
Scalar brane backgrounds in higher order curvature gravity
We investigate maximally symmetric brane world solutions with a scalar field.
Five-dimensional bulk gravity is described by a general lagrangian which yields
field equations containing no higher than second order derivatives. This
includes the Gauss-Bonnet combination for the graviton. Stability and
gravitational properties of such solutions are considered, and we particularily
emphasise the modifications induced by the higher order terms. In particular it
is shown that higher curvature corrections to Einstein theory can give rise to
instabilities in brane world solutions. A method for analytically obtaining the
general solution for such actions is outlined. Genericaly, the requirement of a
finite volume element together with the absence of a naked singularity in the
bulk imposes fine-tuning of the brane tension. A model with a moduli scalar
field is analysed in detail and we address questions of instability and
non-singular self-tuning solutions. In particular, we discuss a case with a
normalisable zero mode but infinite volume element.Comment: published versio
Brane cosmology with curvature corrections
We study the cosmology of the Randall-Sundrum brane-world where the
Einstein-Hilbert action is modified by curvature correction terms: a
four-dimensional scalar curvature from induced gravity on the brane, and a
five-dimensional Gauss-Bonnet curvature term. The combined effect of these
curvature corrections to the action removes the infinite-density big bang
singularity, although the curvature can still diverge for some parameter
values. A radiation brane undergoes accelerated expansion near the minimal
scale factor, for a range of parameters. This acceleration is driven by the
geometric effects, without an inflaton field or negative pressures. At late
times, conventional cosmology is recovered.Comment: RevTex4, 8 pages, no figures, minor change
Brane World Cosmology with Gauss-Bonnet Interaction
We study a Randall-Sundrum model modified by a Gauss-Bonnet interaction term.
We consider, in particular, a Friedmann-Robertson-Walker metric on the brane
and analyse the resulting cosmological scenario. It is shown that the usual
Friedmann equations are recovered on the brane. The equation of state relating
the enery density and the pressure is uniquely determined by the matching
conditions. A cosmological solution with negative pressure is found.Comment: 9 pages, revtex styl
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