John's Theorem for an Arbitrary Pair of Convex Bodies

We provide a generalization of John's representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in ⁿ . From this representation we obtain Banach–Mazur distance and volume ratio estimates.     

Dynamic K-L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic flows

Earlier work [1, 2], using Karhunen-Loeve (K-L) analysis, demonstrated a dramatic enhancement of the importance of large scale motions with increased viscoelasticity and an equally dramatic decrease in the K-L dimension of the flow (an order of magnitude) as viscoelasticity increases versus similar Newtonian results. In this work we look into dynamics of viscoelastic turbulent flows by projecting the DNS data in time into a selected set of K-L modes. The dynamics of the coherent structures embedded in turbulent flows were investigated through calculations of mode auto and cross correlations. This allows for a more systematic examination of the role of large-scale structures in turbulence and drag reduction. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rheological characterization of polyethylene terephthalate resins using a multimode Phan-Tien-Tanner constitutive relation

Linear viscoelastic, shear, and extensional rheological characterization of linear and branched Poly(Ethylene Terephthalate) resins (PET) was carried out by means of both a parallel-plate and capillary rheometers. Before loading into the rheometers, the polymer pellets were thoroughly dried at well-characterized conditions long enough to obtain consistent and reproducible results. Continuing polymer degradation and poly-condensation reactions in the relatively open environment of the parallel-plate rheometer were accounted for by correcting the data using material-time super-position. The rheological data obtained were used to fit by nonlinear optimization, the linear relaxation spectrum and nonlinear parameters of a multi-mode Phan-Thien and Tanner (PTT) constitutive relation. It was found that this model can represent rheological data for PET resins very well and as a result may be used in relevant processing flow simulations, i.e. film casting.     

Possibility of CP violation in the cascade non-leptonic decays

There is more than one parameter expressing CP violation in the non-leptonic hyperon decays. The recent experimental results provide us with indications that CP conservation may not be valid for the Ξ decays. Especially for the Ξ dacays this is not due to the deviations from the exact ΔI=1/2 rule.     

Symplectic Methods for the Numerical Solution of the Radial Shrödinger Equation

In this paper new symplectic-schemes for the numerical solution of the radial Shrödinger equation are proposed. In particular, symplectic integrators for Hamiltonian systems have been developed. Based on this approach, second- and third-order methods are proposed. These methods are more accurate than the existing ones. We compare these methods not only with the existing symplectic methods, but also with a classical Runge–Kutta–Nyström method.     

Organic residue analysis of Neolithic pottery from North Greece

Organic residues associated with Neolithic pottery from two Late Neolithic sites, Paliambela and Makriyalos (Northern Greece), were analyzed by gas chromatography-mass spectrometry. The study aimed at identifying the origin of the tar used for waterproofing and gluing broken pots. Reference tars were prepared in laboratory conditions by pyrolysis of the bark from three tree species, namely from Betula pendula (silver birch), Ostrya carpinifolia (hop hornbeam) and Carpinus orientalis (Eastern hornbeam). The results suggest that mostly birch bark tar was used as glue for fixing broken pieces of the pots as well as for waterproofing close-shaped vessels. None of the archaeological tars derived from the two hornbeams. The analysis shows certain variability in the composition of birch bark tar, which is related to the production technique and to the re-use of tar. Of particular interest is the presence of characteristic diterpenoid biomarkers in several samples, which indicates that pine pitch was used for gluing and pine resin for waterproofing vessels for liquids. Correspondence: Sophia Mitkidou, Department of Science, School of Technological Applications, Technological Institute of Kavala, Greece     

Combined effect of temperature and organic modifier concentration on the retention under single mode gradient conditions in reversed-phase HPLC

The combined effect of temperature, T, and organic modifier concentration, phi, on the retention under gradient conditions in RPLC is studied by considering, both theoretically and experimentally gradients, of phi at constant T and gradients of T at constant phi. Two approaches are examined: in the first approach the prediction of the elution time of a sample solute is based on the isocratic/isothermal properties of this solute. The second approach is based on a direct fitting procedure of a proper retention model to 2-D isocratic/T-gradient or isothermal/phi-gradient retention data. These approaches were tested using alkylbenzes in eluting systems modified by ACN. We found that both approaches can give excellent predictions under certain prerequisites. However, the first approach exhibits the notable advantage that it can be used effectively to predict retention times under any kind of phi-gradients at constant T or T-gradients at constant phi. The second approach has the advantage that it is relatively simple but its applicability is very restricted since its predictions are satisfactory only if the gradients are of the same kind with those used in the fitting procedure and the conditions lie within those used for fitting.     

On the average volume of sections of convex bodies

The average section functional as(K) of a star body in Rn is the average volume of its central hyperplane sections: \(as\left( k \right) = \int_{{S^{n - 1}}} {\left| {K \cap {\xi ^ \bot }} \right|} d\sigma \left( \xi \right)\). We study the question whether there exists an absolute constantC > 0 such that for every n, for every centered convex body K in R ⁿ and for every 1 ≤ k ≤ n ? 2,

$$as\left( K \right) \leqslant {C^k}{\left| K \right|^{\frac{k}{n}}}\mathop {\max }\limits_{|E \in G{r_{n - k}}} {\kern 1pt} as\left( {K \cap E} \right)$$

. We observe that the case k = 1 is equivalent to the hyperplane conjecture. We show that this inequality holds true in full generality if one replaces C by CL _K orCd_ovr(K, BP _k ⁿ ), where L _K is the isotropic constant of K and dovr(K, BP _k ⁿ ) is the outer volume ratio distance of K to the class BP _k ⁿ of generalized k-intersection bodies. We also compare as(K) to the average of as(K ∩ E) over all k-codimensional sections of K. We examine separately the dependence of the constants on the dimension when K is in some classical position. Moreover, we study the natural lower dimensional analogue of the average section functional.