Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

First human administration of MR04A3: a novel water-soluble nonbenzodiazepine sedative.

BACKGROUND: JM-1232(-), (-)-3-[2-(4-methyl-1-piperazinyl)-2-oxoethyl]-2-phenyl-3,5,6,7-tetrahydrocyclopenta [f]isoindol-1(2H)-one, molecular formula, C(24)H(27)N(3)O(2); molecular weight, 389.49, is a novel isoindoline water-soluble benzodiazepine receptor agonist with favorable anesthetic/sedative properties in animals. MR04A3 is a 1% aqueous presentation of JM-1232(-). METHODS: In Step 1, healthy male volunteers received 10-min infusions of MR04A3, 0.05, 0.1, 0.2, 0.4, and 0.8 mg/kg, with three MR04A3 subjects and one placebo subject per dose concentration. In Step 2, doses were 0.025, 0.05, 0.075, 0.1, 0.2, 0.3, and 0.4 mg/kg over 1 min with six MR04A3 subjects and one placebo subject per dose concentration. RESULTS: Hypnotic effects of MR04A3 were seen at all dose concentrations in Step 1 and at doses of 0.075 mg/kg or more in Step 2. Central nervous system effect was seen at all dose concentrations with larger doses of MR04A3 producing a deeper and longer reduction in bispectral index. Ramsay sedation scores were increased with higher doses causing sedation and then unresponsiveness. The adverse event profile of subjects receiving MR04A3 was similar to that of subjects given placebo except that some subjects receiving MR04A3 developed upper airway obstruction while sedated. This responded to simple maneuvers (i.e., chin lift). Changes in systolic arterial blood pressure and heart rate were minimal. CONCLUSIONS: MR04A3 is hypnotic in man with a satisfactory hemodynamic and safety profile