Singular Sturm comparison theorems

Sturm's comparison theorem is discussed for differential equations whose coefficients are continuous in an open, finite or infinite interval, but the coefficients cannot necessarily be extended continuously to the boundary points of the interval.     

THE VECTORIAL PHOTO-EXCITATION IN SOLAR-TRACKING LEAVES OF Lavatera cretica (MALVACEAE)*,†

Abstract— The diaphototropic responses of the solar-tracking leaves of Lavatera cretica were studied under constant levels of vectorial photo-excitation (negligible variations in angle of incidence and fluence rates). The results showed the following:
(a) The photoreceptors, that are associated with the (major) veins, can equally perceive vectorial excitation (by an oblique light-beam in the plane of symmetry of the vein), directed either towards its tip (tip-oriented: TO), or towards its base (base-oriented: BO).
(b) The mechanism of photo-perception is apparently qualitatively the same for TO and BO excitation.
(c) The response to TO and BO vectorial excitation, which takes place in a circular sheath of motor-cell tissue in the pulvinus (a2–3 mm long segment at the top of the petiole), is also highly directional and results in bending in the vertical plane of the oblique beam. Each sector of the motor tissue can expand longitudinally in response to TO excitation, presumably by influx of solutes, and contract longitudinally in response to BO excitation of the same vein, presumably by efflux of solutes.
(d) The angular velocity of the vectorial response to a constant level of vectorial excitation remains constant over large angular displacements and long periods, and was similar for TO and BO over a wide range of fluence rates (30-400 μmol m⁻²s⁻¹) of white light (400-700 nm).
(e) Reversal of the direction of vectorial excitation (TO to BO, and vice versa) results in reversal of the direction of the vectorial response (laminar reorientation). The change in the direction of laminar reorientation involved a larger overshoot in the original direction when the change was from BO to TO, than in the reverse case.     

Reverse pulse voltammetry in ec2 reactions: Electrochemistry of 1-alkyl-4-t-butylpyridinium ions

The applications of the reverse pulse method are extended in order to distinguish between different paths of electrodimerization. The method for determination of rate constants of the chemical reaction coupled with charge transfer (ec₂) is further developed. Measurements of K′_d vs. t_p provide valuable information for the determination of rate constants.The reverse pulse method is applied in the study of the electrodimerization of 1-alkyl-4-t-butylpyridinium ions (1-alkyl=?CH₃; ?CH₂CH₃; ?CH(CH ₃)₂) in acetonitrile. It is found that the electrodimerization mechanism is consistent with the sequence: Py⁺ + e = Py ? $\text{1}\text{2}$ Py₂. The formal potential E^o′ is measured directly for 1-CH(CH₃)₂, and indirectly for the other pyridium ions. All values are identical within experimental error (E^o′ = ?1.835 V vs. Ag/Ag⁺).The values of k_d and k_m are measured. With an increase in the size of the l-alkyl group, k_d decreases and k_m increases. This is consistent with the expected “stabilization” of the radicals due to the increase of the l-alkyl group size which hinders the dimerization site (2- and 6-positions).