The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

How model sets can be determined by their two-point and three-point correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

Four types of special functions of G_2 and their discretization

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the other two (S^L- and S^S-functions) are not found elsewhere in the literature. It is shown explicitly that all four families have similar properties. In particular, they are orthogonal when integrated over a finite region F of the Euclidean space, and they are discretely orthogonal when their values, sampled at the lattice points F_M \subset F, are added up with a weight function appropriate for each family. Products of ten types among the four families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S, S^LS^S and S^LS^L, are completely decomposable into the finite sum of the functions. Uncommon arithmetic properties of the functions are pointed out and questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table

Affine extension of noncrystallographic Coxeter groups and quasicrystals

Unique affine extensions H^{\aff}_2, H^{\aff}_3 and H^{\aff}_4 are determined for the noncrystallographic Coxeter groups $H_2$, $H_3$ and $H_4$. They are used for the construction of new mathematical models for quasicrystal fragments with 10-fold symmetry. The case of H^{\aff}_2 corresponding to planar point sets is discussed in detail. In contrast to the cut-and-project scheme we obtain by construction finite point sets, which grow with a model specific growth parameter.Comment: (27 pages, to appear in J. Phys. A

Interactions between organic friction modifier additives

The interactions of different additives in engine oils can create synergistic or antagonistic effects. This paper studies how mixing different organic friction modifier additives affects friction reducing properties of lubricants in the boundary lubrication regime. Amines of different degree of saturation were mixed with either glycerol monooleate (GMO) or oleic acid in hexadecane. The model lubricants thus formed were characterised with Fourier-transform infrared spectroscopy. Friction tests in reciprocating motion using ball-on-disc steel-steel contacts were conducted to examine the tribological performance of these lubricants. Worn surfaces were examined using X-ray photoelectron spectroscopy. Oleic acid and oleylamine, a primary amine. Were found to form a partial ionic liquid, providing synergistic friction reduction. This positive interaction reduces with increasing degree of saturation of the amine. No synergistic effect was observed between GMO and oleylamine,suggesting that GMO does not hydrolyse into a carboxylic acid within a rubbing contact in the presence of amine. Keywords: Boundary Lubrication, Additives, Friction Abbreviations: organic friction modifier (OFM); glycerol monooleate (GMO); ionic liquid (IL); oleylamine (OA); diocylamine (DA); trihexylamine (TA); dimethylhexadecaylamine (DM16); high frequency reciprocating rig (HFRR); X-ray photoelectron spectroscopy (XPS)

Bundling of actin filaments by aorta caldesmon is not related to its regulatory function

AbstractCa2+-sensitive thin filaments from vascular smooth muscle were disassembled into their constituent proteins, actin, tropomyosin and caldesmon. Caldesmon bound to both actin and to actin-tropomyosin and inhibited actin-tropomyosin activation of skeletal muscle myosin MgATPase. It also promoted the aggregation of actin or actin-tropomyosin into parallel aligned bundles. Quantitative electron microscopy measurements showed that with 1.1 μM actin-tropomyosin, 1.6 ± 0.5% (n = 3) of the filaments were in bundles. At 0.073 μM, caldesmon inhibited MgATPase activity by 50%, whereas bundling was 3.0 ± 1.3% (n = 4). At 0.37 μM caldesmon, MgATPase inhibition was 83% while 28.1 ± 6.9% (n = 4) of filaments were in bundles. Experiments at 4.4 μM in which MgATPase and bundling were measured in the same samples gave similar results. Small bundles of 2–3 filaments showed the most frequent occurrence at 1.1 μM actin. At 4.4 μM actin the most common bundle size was 3-5 filaments, with the occasional occurrence of large bundles consisting of up to 120 filaments. The incidence of bundling was the same in the presence and absence of tropomyosin. Thus caldesmon can induce the formation of actin bundles but this property bears no relationship to its inhibition of MgATPase activity

Final design proposal: Delta Group-Nood Rider 821(tm)

The Nood Rider 821 (trademark) twin-engine, prop passenger aircraft is described. It is argued that the aircraft is very economical to operate and maintain, offering competitive advantages in the air travel marketplace. The aircraft was designed to operate in 'Aeroworld', a fictional world where the passengers are ping pong balls and the distances between cites are on the order of thousands of feet

The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general Lie algebras and superalgebras, and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.Comment: Many improvements in the redaction for pedagogical purposes. Latex, 11 page