The eigentime identity for one-dimensional diffusion processes on the halfline with an entrance boundary at ∞ is obtained by using the trace of the deviation kernel. For the case of an exit boundary at ∞, a similar eigentime identity is presented with the aid of the Green function. Explicit equivalent statements are also listed in terms of the strong ergodicity or the uniform decay for diffusion processes.

A data file on 36396 lactations was used to determine the strength of the phenotypic relationship between productive, reproductive and lifespan traits for 7935 Spanish Churra ewes. These ewes first lambed between 1989 and 1997 and belonged to 23 flocks. The study took into account four lifespan traits (lifetime, productive life, useful life and lifetime score), three productive traits (total milk yield produced during lifetime, lambs weaned during ewe lifetime and total revenues from sold milk and weaned lambs during lifetime) and two reproductive traits (age at first lambing and mean interval between successive lambings). Moreover, milk yield and revenues from sold milk and weaned lambs were calculated per day of lifetime, productive life and useful life. Partial lifespan traits were considered for the first three parities. The model included flock, birth year within flock and season of birth of the ewe as fixed effects. The first two effects contributed significantly to variation in all traits, while season significantly affected lifespan traits, productive traits and age at first lambing. Milk production level was added to the model for lifespan traits only. It significantly contributed to explaining the variation in all lifespan traits with high percentage of variance explained averaging 14·91%. Lifetime averaged 2324 d. Productive life accounted for 57% of lifetime while useful life represented 50% of productive life. Age at first lambing averaged 622 d and average days dry during lifetime was 560. During lifetime, ewes gave an average of 4·6 parities, 6·5 weaned lambs and 636 l of milk. Average revenue from milk and lambs during lifetime was €673. Milk/day of lifetime, productive life and useful life averaged 0·26, 0·51 and 0·93 l, respectively. The corresponding per-day revenues from sold milk and weaned lambs were, €0.27, €0.55 and €1.01, respectively. Lifespan and productive traits had strong relationships (rp among these traits ranged between 0·75 and 0·95). Two-parity and three-parity per-day milk yield had moderately high correlation (0·70–0·83) with total lifetime per-day milk yield traits. Therefore, good use of these traits would be helpful in determining best individuals early in life.

This paper examines four specific themes relating to older carers' experience: care-giving in the context of particular roles and relationships embedded in biographical histories; care in the context of dementia; care involving skilled or complex health care-tasks; and care of an intimate/personal nature. In each case, we look at the nature of support provided by health care professionals. Analysis of the data suggests several conclusions. Older carers are carrying out a range of tasks including complex health care tasks, many of which were once part of a nurse's remit and role. Nurses approach older carers as a unique but not homogeneous group and acknowledge many of their distinct needs as well as their right to choice concerning the extent of their involvement in care-giving. However, this approach conceals several implicit assumptions and expectations about the role of older carers. In particular, professionals' emphasis on older people's individual choice jars with the latter's own experience of reciprocity existing within the context of lifetime relationships. The paper suggests that modifications have to be made in professionals' approach if older people are to be presented with choice and support in the care-giving they perform.

The ability to observe the behavior of living cells and tissues provides unparalleled access to information regarding the organization and dynamics of complex cellular structures. While great strides have been made over the past 30 to 40 years in the design and application of a variety of novel optical microscopic techniques, until recently, it has not been possible to image biological phenomena that occur over very short time periods (nanosecond to millisecond) or over short distances (10 to 1000 Å). However, the recent combination of (1) very rapidly gated and sensitive image intensifiers and (2) the ability to deliver fluorescence excitation energy to intact living biological specimens in a pulsed or sinusoidally modulated fashion has allowed such measurements to become a reality through the imaging of the lifetimes of fluorescent molecules. This capability has resulted in the ability to observe the dynamic organization and interaction of cellular components on a spatial and temporal scale previously not possible using other microscopic techniques. This paper discusses the implementation of a fluorescence lifetime imaging microscope (FLIM) and provides a review of some of the applications of such an instrument. These include measurements of receptor topography and subunit interactions using fluorescence resonance energy transfer (FRET), fluorescence anisotropy of phospholipids in cell membranes, cytosolic free calcium (Ca2+)i and the detection of human papillomavirus (HPV) infection in clinical cervicovaginal smears.

We develop a theory of semiregenerative phenomena. These may be viewed as a family of linked regenerative phenomena, for which Kingman [6], [7] developed a theory within the framework of quasi-Markov chains. We use a different approach and explore the correspondence between semiregenerative sets and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete-time case). We use techniques based on results from Markov renewal theory.

The paper presents an extension of the classical Cramér–Lundberg ruin theory: the famous upper bound for the ruin probability with an infinite time horizon can be extended in a certain sense to the short and middle term case. Furthermore, a relation between the average values of lifetime and ruin amount is given.

Aging, of biological and mechanical systems, is well described as ‘deterioration of the power to withstand destruction.’ The failure-rate concept is the mathematical way of describing aging. Failure rates have been defined for discrete and continuous time and used extensively, particularly in actuarial science and reliability. This paper assumes an arbitrary scale on which an object encounters stress, and develops a theory of failure rate with respect to ‘stress-time’ in analogy with the discrete- and continuous-time cases.