Phase relations between a circadian rhythm and its zeitgeber within the range of entrainment

The regular day-night changes in tissues, physiologic functions, and behavior of organisms are based on endogenous rhythmic processes which under constant conditions continue with periods slightly deviating from 24h. These ‘arcadian’ rhythms have properties of self-sustained oscillators. Under natural conditions, circadian rhythms are synchronized (entrained) to 24 h by periodic factors in the environment, the so-called ‘Zeitgebers’. In the laboratory, circadian rhythms can also be entrained to periods other than 24 h within certain limits. Data on the phase relationship between the circadian rhythm and an entraining light-dark cycle for vertebrates, insects, plants, and unicellular organisms are reviewed.     

Transport of particulate matter in natural waters — modelling and in situ-measurements

The significant processes controlling the fate of particulates are convection an dispersion on one hand, and sedimentation on the other hand. Due to inteparticulated reactions, larger aggregates can be formed from smaller units thus changing the sedimentation characteristics. These phenomena are summarized in a mathematical model whereby hydrodynamic effects as well as the control mechanisms of the dissolved phase are included. A relationship was derived on the basis of energy considerations leading to the formulation of a critical sedimentation velocity of the suspensa, which determines the transport capacity of the flowing system. The sedimentation term is calculated from the above discussed transport capacity, hydro-dynamic parameters and suspending media properties. Aggregation effects are taken into account as an increase of sedimentation velocities of the particles. The equations are solved in a particular computational routine such that the horizontal distribution of suspended solids in a natural system can be describe as function of the above discussed phenomena. The model was tested with in situ-measurements. It was found that the observed processes are described satisfactorily by this model.     

Threshold and dose response estimation using the “filter model”

The “filter model” has been developed to explain the biologic effects of radiation and chemicals. We have examined nearly 300 sets of dose response data, of which 50 are presented here. Responses (induced by radiation and chemicals) which have been examined include in vitro survival studies on animal and plant tissues, induction of cellular aberrations and time to tumor or death. Similar data from in vivo studies has also been examined. All of the data appear to fit the model R = a lnD + b(lnD)² + c, where R is the response, a and b are parameters fitted by regression to a particular set of data, and c is the response at zero (or lowest) dose. By writing this model in exponential form, it can be seen that the response R results from multistage filtering (by net amounts a and b) of the initial dose, D. The threshold is obtained from this model as the point, $\text{D}\text{?}{}_{\mathrm{T}}$, at which the second derivative becomes zero. This is given by $\text{D}\text{?}{}_{\mathrm{T}}\text{=}\text{exp}\text{(1 ?}\text{a}\text{2b}\text{)}$ when a and b are oppositelt signed.     

A note on the allocation of investment

It is shown by example that the results obtained by Gruver [11 concerning specialization of investment in either directly productive or pollution control capital arise because of an implicit linearity assumption on the underlying technology. Utilizing a strictly concave “eighth sphere” technology, results are obtained which imply joint investment in the two types of capital except in “rare” instances. The results indicate the need for incorporating more general technologies into the analysis of such problems.