A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

On the Neighbour-Distinguishing Index of a Graph

A proper edge colouring of a graph G is neighbour-distinguishing provided that it distinguishes adjacent vertices by sets of colours of their incident edges. It is proved that for any planar bipartite graph G with Δ(G)≥12 there is a neighbour-distinguishing edge colouring of G using at most Δ(G)+1 colours. Colourings distinguishing pairs of vertices that satisfy other requirements are also considered.     

Estimation of the aggregation number and core radius of microemulsions

Summary A simple working method for the estimation of the aggregation numbers and core radii from weight measurements of sodium bis-2-ethylhexylsulphosuccinate (aerosol-OT orAOT)/decane/water microemulsions of several compositions is proposed.Starting out from the hypotheses that (i) the density of the water inside the droplets is the same as that of free water, (ii) all the surfactant is localized as interface, and (iii) the penetration of the organic phase into the interface is negligible, values for the aggregation number and core radii comparable to those determined using more sophisticated methods were obtained.The results/methodological simplicity ratio may be of great advantage in kinetic work on reaction mechanisms in microemulsions.

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Abschätzung von Aggregationszahl und Radius von Mikroemulsionen

Zusammenfassung Es wird eine einfache Methode zur Abschätzung von Aggregationszahl und Core-Radius von Mikroemulsionen aus Gewichtsmessungen von Natriumbis-2-ethylhexylsulphosuccinat (aerosol-OT oderAOT)/Decan/Wasser-Mikroemulsionen verschiedener Zusammensetzung vorgeschlagen. Unter den Annahmen, daß (i) die Dichte von Wasser innerhalb der Aggregationen die gleiche als bei freiem Wasser ist, (ii) das ganze Emulsionsmittel in der Grenzfläche vorliegt und (iii) das Eindringen der organischen Phase in die Grenzfläche vernachlässigbar ist, können Werte für Aggregationszahlen und Core-Radien erhalten werden, die durchaus mit entsprechenden Werten aus aufwendigeren Methoden vergleichbar sind. Das Leistungsverhältnis (Ergebnisse/geringer Aufwand) ist sehr vorteilhaft und macht die Methode für kinetische Arbeiten zur Bestimmung von Reaktionsmechanismen in Mikroemulsionen interessant.

     

Low noise optical receiver with multi-octave bandwidth

Optical and Quantum Electronics - A new approach for the design and construction of low noise broadband optical receivers is presented utilizing distributed amplification based on hybrid integrated...     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.     

Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.