11,428 research outputs found
Bounding the Čebyšev Functional for the Riemann-Stieltjes Integral via a Beesack Inequality and Applications
Lower and upper bounds of the Čebyšev functional for the Riemann-
Stieltjes integral are given. Applications for the three point quadrature rules
of functions that are n-time differentiable are also provided
Approximating the Riemann-Stieltjes Integral via Some Moments of the Integrand
Error bounds in approximating the Riemann-Stieltjes integral in
terms of some moments of the integrand are given. Applications for p-convex
functions and in approximating the Finite Foureir Transform are pointed out
as well
Integrability of Supergravity Black Holes and New Tensor Classifiers of Regular and Nilpotent Orbits
In this paper we apply in a systematic way a previously developed integration
algorithm of the relevant Lax equation to the construction of spherical
symmetric, asymptotically flat black hole solutions of N=2 supergravities with
symmetric Special Geometry. Our main goal is the classification of these
black-holes according to the H*-orbits in which the space of possible Lax
operators decomposes, H* being the isotropy group of scalar manifold
originating from time-like dimensional reduction of supergravity from D=4 to
D=3 dimensions. The main result of our investigation is the construction of
three universal tensors, extracted from quadratic and quartic powers of the Lax
operator, that are capable of classifying both regular and nilpotent H* orbits
of Lax operators. Our tensor based classification is compared, in the case of
the simple one-field model S^3, to the algebraic classification of nilpotent
orbits and it is shown to provide a simple and practical discriminating method.
We present a detailed analysis of the S^3 model and its black hole solutions,
discussing the Liouville integrability of the corresponding dynamical system.
By means of the Kostant-representation of a generic Lie algebra element, we
were able to develop an algorithm which produces the necessary number of
hamiltonians in involution required by Liouville integrability of generic
orbits. The degenerate orbits correspond to extremal black-holes and are
nilpotent. We analyze these orbits in some detail working out different
representatives thereof and showing that the relation between H* orbits and
critical points of the geodesic potential is not one-to-one. Finally we present
the conjecture that our newly identified tensor classifiers are universal and
able to label all regular and nilpotent orbits in all homogeneous symmetric
Special Geometries.Comment: Analysis of nilpotent orbits in terms of tensor classifiers in
section 8.1 corrected. Table 1 corrected. Discussion in section 11 extende
Some Remarks on the Trapezoid Rule In Numerical Integration
In this paper, by the use of some classical results from the Theory of Inequalities, we point out quasi-trapezoid quadrature formulae for which the error of approximation is smaller than in the classical case. Examples are given to demonstrate that the bounds obtained within this paper may be tighter than the classical ones. Some applications for special means are also given
On the Topology of the Inflaton Field in Minimal Supergravity Models
We consider global issues in minimal supergravity models where a single field
inflaton potential emerges. In a particular case we reproduce the Starobinsky
model and its description dual to a certain formulation of R+R^2 supergravity.
For definiteness we confine our analysis to spaces at constant curvature,
either vanishing or negative. Five distinct models arise, two flat models with
respectively a quadratic and a quartic potential and three based on the
SU(1,1)/U(1) space where its distinct isometries, elliptic, hyperbolic and
parabolic are gauged. Fayet-Iliopoulos terms are introduced in a geometric way
and they turn out to be a crucial ingredient in order to describe the de Sitter
inflationary phase of the Starobinsky model.Comment: 31 pages, LaTex, 7 eps figures, 2 table
Studies of a weak polyampholyte at the air-buffer interface: The effect of varying pH and ionic strength
We have carried out experiments to probe the static and dynamic interfacial
properties of --casein monolayers spread at the air-buffer interface,
and analysed these results in the context of models of weak polyampholytes.
Measurements have been made systematically over a wide range of ionic strength
and pH. In the semi-dilute regime of surface concentration a scaling exponent,
which can be linked to the degree of chain swelling, is found. This shows that
at pH close to the isoelectric point, the protein is compact. At pH away from
the isoelectric pH the protein is extended. The transition between compact and
extended states is continuous. As a function of increasing ionic strength, we
observe swelling of the protein at the isoelectric pH but contraction of the
protein at pH values away from it. These behaviours are typical of a those
predicted theoretically for a weak polyampholyte. Dilational moduli
measurements, made as a function of surface concentration exhibit maxima that
are linked to the collapse of hydrophilic regions of the protein into the
subphase. Based on this data we present a configuration map of the protein
configuration in the monolayer. These findings are supported by strain (surface
pressure) relaxation measurements and surface quasi-elastic light scattering
(SQELS) measurements which suggest the existence of loops and tails in the
subphase at higher surface concentrations.Comment: Submitted to J. Chem. Phy
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