New saponins from Sechium mexicanum

The chemical study of Sechium mexicanum roots led to the isolation of the two new saponins {3‐O‐β‐D ‐glucopyranosyl (1 → 3)‐β‐D ‐glucopyranosyl‐2β,3β,16α,23‐tetrahydroxyolean‐12‐en‐28‐oic acid 28‐O‐α‐L ‐rhamnopyranosyl‐(1 → 3)‐β‐D ‐xylopyranosyl‐(1 → 4)‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐α‐L ‐arabinopyranoside} (1) and {3‐O‐β‐D ‐glucopyranosyl (1 → 3)‐β‐D ‐glucopyranosyl‐2β,3β,16α,23‐tetrahydroxyolean‐12‐en‐28‐oic acid 28‐O‐α‐L ‐rhamnopyranosyl‐(1 → 3)‐β‐D ‐xylopyranosyl‐(1 → 4)‐[β‐D ‐apiosyl‐(1 → 3)]‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐α‐L ‐arabinopyranoside} (2), together with the known compounds {3‐O‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐2β,3β,6β,16α,23‐pentahydroxyolean‐12‐en‐28‐oic acid 28‐O‐α‐L ‐rhamnopyranosyl‐(1 → 3)‐β‐D ‐xylopyranosyl‐(1 → 4)‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐α‐L ‐arabinopyranoside} (3), tacacosides A₁ (4) and B₃ (5). The structures of saponins 1 and 2 were elucidated using a combination of ¹H and ¹³C 1D‐NMR, COSY, TOCSY, gHMBC and gHSQC 2D‐NMR, and FABMS of the natural compounds and their peracetylated derivates, as well as by chemical degradation. Compounds 1–3 are the first examples of saponins containing polygalacic and 16‐hydroxyprotobasic acids found in the genus Sechium, while 4 and 5, which had been characterized partially by NMR, are now characterized in detail. Copyright © 2009 John Wiley & Sons, Ltd.     

NMR assignments and histone specificity of the ING2 PHD finger

The ING2 plant homeodomain (PHD) finger is recruited to the nucleosome through specific binding to histone H3 trimethylated at lysine 4 (H3K4me3). Here, we describe backbone and side chain assignments of the ING2 PHD finger, analyze its binding to the unmodified and modified histone and p53 peptides, and map the histone H3 and H3K4me3 binding sites based on chemical shift perturbation analysis. Copyright © 2009 John Wiley & Sons, Ltd.     

The Assembly of Macrocyclic Bis‐ and Tetra‐β‐lactams with Embedded Platinum or Palladium Square‐Planar Centers

The synthesis, isolation, and full characterization of different types of stable, metal‐assembled macrocyclic β‐lactams are reported. By using adequately functionalized bis‐β‐lactams with defined stereochemistry as building blocks, a series of mono‐ and bimetallic Pd and Pt macrocycles has been prepared in good to quantitative yields. These novel structures combine the β‐lactam moiety with transition‐metal fragments with cis‐square‐planar geometry and constitute a new class of metal‐assembled cavities involving molecules with biological relevance as building blocks. By combining the adequate ligands, metallic fragments, and tuning the reaction conditions, different mono‐ and bimetallic macrocyclic β‐lactam cavities can be selectively obtained. Macrocycles with Pt–ethynyl groups are suitable to form host–silver triflate guest complexes in a tweezer fashion.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

Measurements of electrostatic potentials and electric fields in some industrial applications: Basic principles

Electrostatic potentials or electric fields are often measured in order to characterize materials or to make a diagnostic of an industrial installation. Electrostatic probes or field mills are widely used and sometimes considered equivalent. However, experimental configurations must be carefully analyzed to make a valid interpretation. Depending on the instrument, results and influence on the analyzed system are very different. An analysis of different situations shows the electrostatic conditions imposed by each instrument and the concept of unperturbed surface potential. This paper analyses from an electrostatic point of view some measurement cases representative of industrial situations or described in standards.     

Periodic solutions of second order non-autonomous singular dynamical systems

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray-Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder's fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions. Recent results in the literature are generalized and significantly improved.     

Boundaries of cocompact proper CAT(0) spaces

A proper CAT(0) metric space X is cocompact if it has a compact generating domain with respect to its full isometry group. Any proper CAT(0) space, cocompact or not, has a compact metrizable boundary at infinity ∂_∞X; indeed, up to homeomorphism, this boundary is arbitrary. However, cocompactness imposes restrictions on what the boundary can be. Swenson showed that the boundary of a cocompact X has to be finite-dimensional. Here we show more: the dimension of ∂_∞X has to be equal to the global ?ech cohomological dimension of ∂_∞X. For example: a compact manifold with non-empty boundary cannot be ∂_∞X with X cocompact. We include two consequences of this topological/geometric fact: (1) The dimension of the boundary is a quasi-isometry invariant of CAT(0) groups. (2) Geodesic segments in a cocompact X can “almost” be extended to geodesic rays, i.e. X is almost geodesically complete.     

Job scheduling, cooperation, and control

This paper studies one machine job scheduling situations where clients can have more than one job to be processed and where a job can be of interest for different players. Corresponding cooperative games are introduced and a result on balancedness is provided.