On Transformations Of Functional-Differential Equations

. The paper contains applications of Schroder's equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity y = x can be transformed into an equation with a deviation of the form ø(x) = x. Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory and asymptotic properties of the considered equation. 1. Introduction and notation In this article the transformations of functional-differential equations with one deviating argument are studied. These transformations are supposed to be global, i.e., they are defined on the whole definition intervals of corresponding equations. The case where the deviating argument of a considered equation is a sufficiently smooth function with a positive derivative and which does not intersect..

Response of linden tree to nocturnal simulation of daylight conditions

Although the importance of the internal clock for plant development and fitness was extensively studied in the last few decades, the majority of work was conducted in laboratory conditions using some small plants as model species. The objective of this study was to determine the response of sap flow to the circadian regulation physiological state of the entire tree. Monitoring a variety of relevant parameters and sap flow in different tree organs, we illuminated the crown of a linden tree, Tilia cordata, with artificial daylight mimicking solar conditions during three consecutive nights. The patterns of stimulated nocturnal sap flow were compared to sap flow patterns observed during daytime. The response of sap flow to light stimuli was weak compared to daytime and diminished further as night progresses. Light induced sap flow during the night was very low and the responses to changes in light intensity were highly non linear and sluggish. While sap flow correlated directly with changes in VPD during the day, it did not respond to occasional fluctuations in VPD at night. The results convincingly demonstrated the effectiveness of the internal regulation at the level of the entire large tree through gating of external stimul