Depth-profiling of organic layers on microparticles with SNMS

Summary Previous work on the quantification and localization of organically bound elements with plasma-based SNMS for the characterization of microparticles has been continued. Relative detection factors for 10 elements have been determined. Except for lead and bromine a principle proportionality to atomic ionization probabilities is shown. A moderate matrix dependence of less than 40% variation was found even when inorganic and organic materials are included. For depth calibration, erosion rates of organic materials were determined from the time interval necessary to sputter through planar single-layers and Langmuir-Blodgett multi-layer systems with known thickness, as well as from gravimetric powder measurements. Depth propagation rates were 0.7 nm·sec^–1 for polymers and 2.3 nm·sec^–1 for aromatic compounds, when 400 eV argon ion bombardment with 0.7 mA·cm^–2 was used. A depth resolution of 30 nm has been obtained. Model particles of 5 m size have been coated with fluoranthene. Inspection with SNMS revealed an incomplete coating covering only 20% of the microparticle surface with an average thickness of the partial coating of 300 nm. Subsequent characterization using laser-induced fluorimetry confirmed the amount of fluoranthene coating measured by SNMS.     

On two methods of determining the ellipses and ellipsoids of positioning accuracy of robot manipulators

Summary When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Zwei Methoden zur Bestimmung der Ellipsen und Ellipsoide der Positioniergenauigkeit von Handhabungsrobotern

Übersicht Bei der Untersuchung der Positioniergenauigkeit von Handhabungsrobotern ist es wichtig, die Größe zufälliger Abweichungen des Greifers von der erstrebten Position zu kennen, wenn die Lagefehler der Verbindungen eine Normalverteilung besitzen. Es werden zwei Methoden zur Bestimmung der Ellipsen bzw. Ellipsoide der Wahrscheinlichkeitsdichte verglichen. Die erste beruht auf dem Standardverfahren der Wahrscheinlichkeitsrechnung. Die zweite Näherungsmethode besteht darin, daß zunächst das Polygon bzw. Polyeder der Positioniergenauigkeit bestimmt wird und danach die Ellipse bzw. das Ellipsoid mit den Hauptachsen und Momenten zweiter Ordnung wie das Polygon oder Polyeder. Beispiele zeigen, daß beide Methoden zu sehr ähnlichen Ergebnissen führen.

     

A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

On the construction and calculation of optimal nonlifting critical airfoils

Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM for a given thickness ratio and tail angle _t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM and for various _t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM 1, 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding and _t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.     

On PP-rings

A ringR is called a leftPP-ring if every principal left ideal is projective, equivalently if the left annihilatorl(a) is generated by an idempotent for allaR. These rings seem first to have been discussed by Hattori [2] and examples include (von Neumann) regular rings and domains (possibly noncommutative). In this note we give a new characterization of leftPP-rings, use that to give an elementary proof of a result of Xue [4] characterizing triangularPP-rings, and then determine when the ringT _n (R) of upper triangular matrices overR is a leftPP-ring. Throughout the paper all rings have a unity and all modules are unitary.This research was supported by NSERC Grant A8075     

On depth first search strees inm-out digraphs

We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let _i be thei ^th vertex encountered by DFS andL(i, m, n) be the height of _i in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree.     

Modular curves and Poncelet polygons

Parts of the results and the essential techniques of this note are taken from the Erlangen thesis (1991) of the second author. They were circulated as Nr. 122 of Schriftenreihe Komplexe Mannigfaltigkeiten. Our research was supported by DFG grant Ba 423/3-3 and the European Science Project Geometry of Algebraic Varieties SCI-0398-C(A)     

Two-Arc Transitive Graphs and Twisted Wreath Products

The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x ^–1 for all x F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given.