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

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

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

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

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 $\beta$--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