System identification based on distribution theory and wavelet transform

A review of system identification based on distribution theory is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time--frequency information of kernel distributions are deduced. A new wavelet-based system identification method for health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform.     

The biogenetic law

We develop one criterion for the selection of the content of a mathematics syllabus. We advocate the importance of the biogenetic law and stress the importance of a historical perspective in mathematical education.     

Ergodic Control of Partially Degenerate Diffusions in a Compact Domain

The problem of ergodic control of a reflecting diffusion in a compact domain is analysed under the condition of partial degeneracy, i.e. when its transition kernel after some time is absolutely continuous with respect to the Lebesgue measure on a part of the state space. Existence of a value function and a “martingale dynamic programming principle” are established by mapping the problem to a discrete time control problem. Implications for existence of optimal controls are derived.     

Three Point Boundary Value Problems on Time Scales

This work formulates existence theorems for solutions to three-point boundary value problems on time scales. The ideas are based on a relationship between the three point boundary conditions, lower and upper solutions and topological degree theory.     

Creep mechanism of gas-pressure-sintered silicon nitride polycrystals I. Macroscopic and microscopic experimental study

The creep behaviour and microstructure of two silicon nitride ceramics have been investigated. Compressive creep tests were performed at temperatures between 1450 and 1700°C at stresses between 6 and 90?MPa in an Ar atmosphere. The creep behaviour was characterized by a stress exponent lower than one for both materials, with an average value n?≈?0.6 over the whole range of stresses and temperatures, and with apparent activation energies between 470 and 530?kJ?mol^?1. The study of the microstructural evolution revealed the absence of dynamic grain growth and, in some cases, evidence of grain rearrangement. Partial coalescence of cavities was observed only at the highest stress, but this did not result in accelerated creep.     

Indentation of elastic solids with rigid cones

Experimental investigations of the response of several elastic solids, carried out using an instrumented indentation machine, are described. These solids include a natural rubber compound, neoprene, and three different compositions of poly(dimethylsiloxane) (PDMS) when they were indented with tungsten carbide cones of included angles of 60°, 90°, 120° and 136°. It is shown that, except for the case of the 60° cone loading on to the blocks of PDMS (1?:?10) and PDMS (1?:?20), the indentation load versus indenter displacement behaviour of all the elastic solids corresponding to all the conical indenters is well fitted by the 1965 Sneddon theory for frictionless indentations. Video camera sequences of the process of indentation by cones of different included angles into the blocks of PDMS (1?:?10) and PDMS (1?:?20) have also been taken from which measurements of the elastic deformation of the indented surface have been made. It is shown that the magnitude of the elastic deformation of the indented surface closely agrees with the theory when the blocks are indented with cones of included angles of 90°, 120° and 136°. However, for the case of the 60° cone, there is again a discrepancy between experiment and theory; the magnitude of the deformation is significantly smaller than that predicted theoretically. It is suggested that the discrepancy between theory and experimental observations may be due to a non-zero coefficient of friction between the 60° conical indenter and the blocks of PDMS (1?:?10) and PDMS (1?:?20). It is also shown experimentally that, for indenter loading speeds in the range 0.2–200?mm?min^?1, no time-dependent effects were observed for the loading curves, thus justifying the use of the theory given by Love in and of the Sneddon theory of conical indentations of elastic solids. Finally, using the findings described in this work, a brief discussion is included to explain the discrepancy between the results obtained by Sabey in and those obtained by Greenwood and Tabor in the same year when tyre-tread rubber specimens obtained from a single source were indented with steel cones of different included angles.