Phytochrome (far red form) alone can mediate anthocyanin synthesis in the mustard seedling (Sinapis alba L.). Complete photoreversibility and reciprocity, for both red and far red light exposures over a period of at least 5 minutes, demonstrate this phytochrome involvement.The duration of the initial lag-phase is constant (about 3 hours at 25 C) for seedlings more than 30 hours old and is specific for the system, being independent of the dose or quality of light. Since a complete reversal by far red of a red light induction is possible only during a 5 minute period, phytochrome (far red form) obviously mediates anthocyanin synthesis during the lag-phase although the actual synthesis of pigment can proceed only after the lag-phase is overcome. We suggest that phytochrome (far red form) exerts a double function during the initial lag-phase. It mediates both the build up of a biosynthetic potential ("capacity") and anthocyanin synthesis.However, the sequence of events leading to anthocyanin is arrested at some intermediate stage until this "capacity" is built up after 3 hours. Once "capacity" is achieved it does not decay readily. Therefore, no significant "secondary lag-phase" occurs if the seedling, under appropriate conditions, is reirradiated after an intervening dark period. The rate or extent of synthesis for both anthocyanin and lipoxygenase, previously reported (32), are functions of the amount of phytochrome (far red form). No "phytochrome paradoxes," i.e., nonrational relationships between the amount of phytochrome (far red form) and rate or extent of response, were detected. This fact suggests that the mustard seedling is especially well suited for investigating the biophysical and molecular mechanisms of phytochrome action.Since the well known report by Arthur (1), the effect of light on anthocyanin synthesis has attracted the attention of many plant physiologists (5, 21, 37). However, the general mechanism of this light effect has not yet been formulated. This failure is due partly to the descriptive nature of many reports and, in the main, because light appears to exert its influence through different photochemical mechanisms which probably are mixed in the usual experimental approaches. Recently, (e.g.,2,6,7,9,10,11,35,40) anin synthesis be mediated exclusively without the interference of any other photochemical mechanism? These advantages are that (24) anthocyanin synthesis by light is predominantly controlled by phytochrome without the requirement of any prolonged "high energy pretreatment" (e.g., 2, 6, 10, 35), and the mustard seedling does not produce significant amounts of anthocyanin in complete darkness. Seedlings can easily be handled under standardized conditions, and a great amount of information, including spectrophotometric measurements of P,, is available on this system (26). While the mustard seedling forms five anthocyanins, the aglycon is always cyanidin (17). At 25 C the stored fat and protein of the cotyledons allow development in total darkness without any indications of ...
We prove global existence and uniqueness of classical solutions of the Wigner-Poisson and SchrodingerPoisson systems of equations for both repulsive and attractive potentials. In the repulsive case, we prove decay estimates for the particle density, the potential and the solutions.
This paper is concerned with the one-dimensional stationary linear Wigner equation, a kinetic formulation of quantum mechanics. Specifically, we analyze the well-posedness of the boundary value problem on a slab of the phase space with given inflow data for a discrete-velocity model. We find that the problem is uniquely solvable if zero is not a discrete velocity. Otherwise one obtains a differential-algebraic equation of index 2 and, hence, the inflow data make the system overdetermined.
Abstract.We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical "No-go" result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control (E(t) · x)u is not controllable in finite or infinite time. Finally, in Section 3, we give criteria for additive controllability of linear Schrödinger equations, and we give a distributed additive controllability result for the nonlinear Schrödinger equation if the data are small.Mathematics Subject Classification. 35Q40, 35Q55, 81Q99, 93B05.
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