Linear Filtering for Time-Delay Systems

A linear filtering problem is studied in which the signal process(x(t):t 0) is described by a stochastic differential equationwhere time delays are present in both the noise input and thex variable. By means of a transformation new to the filteringliterature, we reduce the signal equation to a delay-free stochasticevolution equation; this permits us to solve the problem byapplication of the theory of infinite-dimensional linear filtering.     

FIBER-OPTIC PLANT TISSUES: SPECTRAL DEPENDENCE IN DARK-GROWN AND GREEN TISSUES*

Abstract— The fiber-optic properties of etiolated plant tissues can be used to detect and characterize pigment absorption in vivo. Transmission spectra of light guided through several monocot and dicot etiolated tissues show a decreasing red/far red ratio with increasing tissue length. Absorption bands attributable both to vacuolar pigments such as anthocyanins and to chloroplast pigments lead to the conclusion that the guided light passes through both vacuole and cytoplasm. As etiolated tissue becomes green under white light treatment, the red/far red ratio also changes, the nature of the change depending upon the tissue involved. The blue/red ratio also changes both with increasing length of etiolated tissue and during the greening process, with the changes again dependent on the tissue involved. The spectral dependence of the light-guiding phenomenon in dark grown and green plants may have implications for physiological responses mediated by phytochrome.     

Budget-constrained maintenance in the building industry

Given records of building component renewals which occurredduring the year and also theage profile of the building stock,the theory of alternating renewal processes in discrete timeis used to deduce the underlying probability mass functionsof the natural lifespan of building components and of delaydue to limited resource. In an investigation into the economicsof renewal delay, the expected number of component renewalsin each year of the life of a building is deduced from the convolutionsof the probability mass function of natural lifespan: theseexpected numbers depend on the chosen delay. The nett presentvalue of the expected cost associated with each specified delayis calculated, so that a judgement can be made as to the optimumdelay (if any). These calculations are conveniently performedusing a spreadsheet macro.