Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.

Preparation, properties and applications of colloidal microgels

This chapter contains sections titled: - Introduction - Microgel preparation - Characterisation of microgels - Properties and applications - Conclusions

Applications of DNP-NMR for the measurement of heteronuclear T1 relaxation times

Measurement of heteronuclear spin-lattice relaxation times is hampered by both low natural abundance and low detection sensitivity. Combined with typically long relaxation times, this results in extended acquisition times which often renders the experiment impractical. Recently a variant of dynamic nuclear polarisation has been demonstrated in which enhanced nuclear spin polarisation, generated in the cryo-solid state, is transferred to the liquid state for detection. Combining this approach with small flip angle pulse trains, similar to the FLASH-T(1) imaging sequence, allows the rapid determination of spin-lattice relaxation times. In this paper we explore this method and its application to the measurement of T(1) for both carbon-13 and nitrogen-15 at natural abundance. The effects of RF inhomogeneity and the influence of proton decoupling in the context of this experiment are also investigated.

The determinants of business performance of estate agency in England and Wales

Purpose: This paper seeks to investigate the factors influencing the business performance of estate agency in England and Wales. Design/methodology/approach: The paper investigates the effect of housing market, company size and pricing policy on business performance in the estate agency sector in England and Wales. The analysis uses the survey data of Woolwich Cost of Moving Survey (a survey of transactions costs sponsored by the Woolwich/Barclays Bank) from 2003 to 2005 to test the hypothesis that the business performance of estate agency is affected by industry characteristics and firm factors. Findings: The empirical analysis indicates that the business performance of estate agency is subject to market environment volatility such as market uncertainty, housing market liquidity and house price changes. The firm factors such as firm size and the level of agency fee have no explanatory power in explaining business performance. The level of agency fee is positively associated with firm size, market environment and liquidity. Research limitations/implications: The research is limited to the data received and is based on a research project on transaction costs designed prior to this analysis. Originality/value: There is little other research that investigates the factors determining the business performance of estate agency, using consecutive data of three years across England and Wales. The findings are useful for practitioners and/or managers to allocate resources and adjust their business strategy to enhance business performance in the estate agency sector.