Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Very intense pulse in the groundwater flow in fissurized-porous stratum

An asymptotic solution is obtained corresponding to a very intense pulse: a sudden strong increase and fast subsequent decrease of the water level at the boundary of semi-infinite fissurized-porous stratum. This flow is of practical interest: it gives a model of a groundwater flow after a high water period or after a failure of a dam around a collector of liquid waste. It is demonstrated that the fissures have a dramatic influence on the groundwater flow, increasing the penetration depth and speed of fluid penetration into the stratum. A characteristic property of the flow in fissurized-porous stratum is the rapid breakthrough of the fluid at the first stage deeply into the stratum via a system of cracks, feeding of porous blocks by the fluid in cracks, and at a later stage feeding of advancing fluid flow in fissures by the fluid, accumulated in porous blocks.

Cocaine: mechanism of inhibition of a muscle acetylcholine receptor studied by a laser-pulse photolysis technique.

Effects of cocaine on the muscle nicotinic acetylcholine receptor were investigated by using a chemical kinetic technique with a microsecond time resolution. This membrane-bound receptor regulates signal transmission between nerve and muscle cells, initiates muscle contraction, and is inhibited by cocaine, an abused drug. The inhibition mechanism is not well understood because of the lack of chemical kinetic techniques with the appropriate (microsecond) time resolution. Such a technique, utilizing laser-pulse photolysis, was recently developed; by using it the following results were obtained. (i) The apparent cocaine dissociation constant of the closed-channel receptor form is approximately 50 microM. High carbamoylcholine concentration and, therefore, increased concentrations of the open-channel receptor form, decrease receptor affinity for cocaine approximately 6-fold. (ii) The rate of the receptor reaction with cocaine is at least approximately 30-fold slower than the channel-opening rate, resulting in a cocaine-induced decrease in the concentration of open receptor channels without a concomitant decrease in the channel-opening or -closing rates. (iii) The channel-closing rate increases approximately 1.5-fold as the cocaine concentration is increased from 20 to 60 microM but then remains constant as the concentration is increased further. The results are consistent with a mechanism in which cocaine first binds rapidly to a regulatory site of the receptor, which can still form transmembrane channels. Subsequently, a slow step (t1/2 approximately 70 ms) leads to a receptor form that cannot form transmembrane channels, and acetylcholine receptor-mediated signal transmission is, therefore, blocked. Implications for the search for therapeutic agents that alleviate cocaine poisoning are mentioned.

Estradiol and the inhibition of hypothalamic gonadotropin-releasing hormone pulse generator activity in the rhesus monkey.

In mammals, gonadal function is controlled by a hypothalamic signal generator that directs the pulsatile release of gonadotropin-releasing hormone (GnRH) and the consequent pulsatile secretion of luteinizing hormone. In female rhesus monkeys, the electrophysiological correlates of GnRH pulse generator activity are abrupt, rhythmic increases in hypothalamic multiunit activity (MUA volleys), which represent the simultaneous increase in firing rate of individual neurons. MUA volleys are arrested by estradiol, either spontaneously at midcycle or after the administration of the steroid. Multiunit recordings, however, provide only a measure of total neuronal activity, leaving the behavior of the individual cells obscure. This study was conducted to determine the mode of action of estradiol at the level of single neurons associated with the GnRH pulse generator. Twenty-three such single units were identified by cluster analysis of multiunit recordings obtained from a total of six electrodes implanted in the mediobasal hypothalamus of three ovariectomized rhesus monkeys, and their activity was monitored before and after estradiol administration. The bursting of all 23 units was arrested within 4 h of estradiol administration although their baseline activity was maintained. The bursts of most units reappeared at the same time as the MUA volleys, the recovery of some was delayed, and one remained inhibited for the duration of the study (43 days). The results indicate that estradiol does not desynchronize the bursting of single units associated with the GnRH pulse generator but that it inhibits this phenomenon. The site and mechanism of action of estradiol in this regard remain to be determined.