A characterization of dual quermassintegrals and the roots of dual steiner polynomials

For any $I\subset\mathbb{R}$ finite with $0\in I$, we provide a characterization of those tuples $(\omega_i)_{i\in I}$ of positive numbers which are dual querma\ss integrals of two star bodies. It turns out that this problem is related to the moment problem. Based on this relation we also get new inequalities for the dual querma\ss integrals. Moreover, the above characterization will be the key tool in order to investigate structural properties of the set of roots of dual Steiner polynomials of star bodies

The isodiametric problem with lattice-point constraints

In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is shown that the intersection of a suitable ball with the Dirichlet-Voronoi cell of 2L is extremal, i.e., it has minimum diameter among all bodies with the same volume. It is conjectured that these sets are the only extremal bodies, which is proved for all three dimensional and several prominent lattices.Comment: 12 pages, 4 figures, (v2) referee comments and suggestions incorporated, accepted in Monatshefte fuer Mathemati

The histidine phosphocarrier kinase/phosphorylase from bacillus subtilis is an oligomer in solution with a high thermal stability

The histidine phosphocarrier protein (HPr) kinase/phosphorylase (HPrK/P) modulates the phosphorylation state of the HPr protein, and it is involved in the use of carbon sources by Gram-positive bacteria. Its X-ray structure, as concluded from crystals of proteins from several species, is a hexamer; however, there are no studies about its conformational stability, and how its structure is modified by the pH. We have embarked on the conformational characterization of HPrK/P of Bacillus subtilis (bsHPrK/P) in solution by using several spectroscopic (namely, fluorescence and circular dichroism (CD)) and biophysical techniques (namely, small-angle X-ray-scattering (SAXS) and dynamic light-scattering (DLS)). bsHPrK/P was mainly a hexamer in solution at pH 7.0, in the presence of phosphate. The protein had a high conformational stability, with an apparent thermal denaturation midpoint of ~70¿ C, at pH 7.0, as monitored by fluorescence and CD. The protein was very pH-sensitive, precipitated between pH 3.5 and 6.5; below pH 3.5, it had a molten-globule-like conformation; and it acquired a native-like structure in a narrow pH range (between pH 7.0 and 8.0). Guanidinium hydrochloride (GdmCl) denaturation occurred through an oligomeric intermediate. On the other hand, urea denaturation occurred as a single transition, in the range of concentrations between 1.8 and 18 µM, as detected by far-UV CD and fluorescence

On mean outer radii of random polytopes

In this paper we introduce a new sequence of quantities for random polytopes. Let KN = conv{X1, . . . ,XN} be a random polytope generated by independent random vectors uniformly distributed in an isotropic convex body K of Rn. We prove that the so-called k-th mean outer radius e Rk(KN) has order max{ pk,plogN}LK with high probability if n2 N epn. We also show that this is also the right order of the expected value of e Rk(KN) in the full range n N epn

Bounding the integral of powered i-th mean curvatures

We get estimates for the integrals of powered i-th mean curvatures, 1 = i = n - 1, of compact and convex hypersurfaces, in terms of the quermaßintegrals of the corresponding C 2 + convex bodies. These bounds will be obtained as consequences of a most general result for functions defined on a general probability space. From this result, similar estimates for the integrals of any convex transformation of the elementary symmetric functions of the radii of curvature of C 2 + convex bodies will be also proved, both, in terms of the quermaßintegrals, and of the roots of their Steiner polynomials. Finally, the radial function is considered, and estimates of the corresponding integrals are obtained in terms of the dual quermaßintegrals

An isodiametric problem with lattice-point constraints

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