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Let $${\mu}$$ be a probability measure with an infinite compact support on $${\mathbb{R}}$$ . Let us further assume that $${F_n:=f_n\circ\dots\circ f_1}$$ is a sequence of orthogonal polynomials for $${\mu}$$ where $${{(f_n)}_{n=1}^\infty}$$ is a sequence of nonlinear polynomials. We prove that if there is an $${s_0\in\mathbb{N}}$$ such that 0 is a root of f′ for each $${n > s_0}$$ then the distance between any two zeros of an orthogonal polynomial for $${\mu}$$ of a given degree greater than 1 has a lower bound in terms of the distance between the set of critical points and the set of zeros of some F. Using this, we find sharp bounds from below and above for the infimum of distances between the consecutive zeros of orthogonal polynomials for singular continuous measures. [ABSTRACT FROM AUTHOR]

Presents a study that developed a method which combines the advantages of Petri nets (PN) and the supervisory controller design based on Formal Language Theory (FLT). Synthesis of a combined plant and controller model; Conflicts that arise in the equivalence of the PN model and a controller; Limitations of FLT.

In an earlier paper, the authors (1997) developed a technique called "relative temporal analysis" to study the performance of timed Petri nets, where depending on the temporal constraints imposed on the transitions, conflict was possible between the processes modelled by the Petri net. The essence of the technique focused on the transformation of the real time trajectory of the processes into a time domain where only their relative shifts were considered. Within this domain the shifts are limited to a bounded and well defined region. Here, we extend this technique to more complex systems where structural conflict is also possible. Within a regenerative cycle of the system, each and every path should be followed according to a set of prespecified frequencies. We use the relative temporal technique to synthesize an optimal sequential controller to schedule these paths. [ABSTRACT FROM PUBLISHER]

There are several techniques for the analysis of the dynamics of timed Petri nets. When the net is not decision free, the existing methods come short of an efficient analysis. In this paper, we present a method, we call "relative temporal analysis", to analyze the dynamics of a system with two processes and a shared resource. It is possible to find the resource utilization sequence, the waiting time period for each process and identify possible conflicts through this technique. Based on this technique we also build control charts which can be used for control purposes such as obtaining "optimal" conflict resolution schemes. [ABSTRACT FROM PUBLISHER]

Objective:To determine the effects of sodium bicarbonate (NaHCO3) correction of metabolic acidosis on cardiopulmonary, laboratory, and cerebral, renal and splanchnic regional oxygen saturation (rSO2) and fractional tissue oxygen extraction (FTOE) in extremely premature neonates during the first postnatal week.Study Design:Observational cohort data were collected from 500 to 1250 g neonates who received NaHCO3 'half' corrections (0.3 * Weight (kg) * Base Deficit (mmol l−1)) for presumed renal losses.Result:Twelve subjects with normal blood pressure and heart rate received 17 NaHCO3 corrections. Mean (±s.d.) gestational age was 27±2 week and birth weight was 912±157 g. NaHCO3 corrections provided a mean (±s.d.) 4.5±1.0 ml kg−1 fluid bolus, shifted mean (±s.d.) base deficit from 7.6±1.8 to 3.4±2.1 mmol l−1 (P<0.05), and increased median (±s.d.) pH from 7.23±0.06 to 7.31±0.05 (P<0.05). No significant changes in blood pressure, pulse oximetry, PCO2, lactate, sodium, blood urea nitrogen, creatinine or hematocrit were observed. Cerebral, renal and splanchnic rSO2 (74%, 66% and 44%, respectively, at baseline) and FTOE (0.21, 0.29 and 0.52, respectively, at baseline) were unchanged following NaHCO3 correction.Conclusion:NaHCO3 infusions decreased base deficits and increased pH though produced no discernible effects or benefits on cardiopulmonary parameters including rSO2 and FTOE. These findings warrant further prospective evaluation in larger populations with more significant metabolic acidosis to determine the utility of tissue oxygenation monitoring in differentiating metabolic acidosis due to oxygen delivery/consumption imbalance versus renal bicarbonate losses. [ABSTRACT FROM AUTHOR]

OBJECTIVE: In extremely premature neonates, data concerning the normal baseline variability of near-infrared spectroscopy (NIRS)-derived regional oxygen saturation (rSO2) are lacking. We sought to determine: 1) the quiescent variability of cerebral, renal, and splanchnic rSO2 in clinically stable, undisturbed very low birth weight neonates and 2) the effects of different data averaging epochs on site-specific variability. STUDY DESIGN: In this prospective, observational study, neonates between 500 and 1250 g underwent seven days of continuous, real-time cerebral, renal, and splanchnic NIRS monitoring starting within the first seventy-two postnatal hours. Demographic, cardiopulmonary, bedside care, and rSO2 data were collected. rSO2 variability was analyzed utilizing data from quiescent periods identified using pre-specified stability criteria. Between- and within-monitoring site comparisons of data averaging methods were made utilizing ANOVA. RESULT: Twenty-four subjects (GA 27 ± 0.3 wk, birth weight 988 ± 34 g; mean ± SEM) were monitored. Coefficients of variation (CoVar = SD/mean) were calculated for each monitoring site using varied data averaging epochs. CoVar was lowest for cerebral, intermediate for renal, and highest for splanchnic rSO2 (P < 0.01). For renal and splanchnic sites, shorter epochs (5- and 15-min) resulted in significantly smaller CoVars [P < 0.01 and P < 0.05, respectively]. Splanchnic variability was highly dependent on epoch length, ranging from 16% over 5 min to 23% over 60 min. CONCLUSION: 1) rSO2 variability differs significantly between monitoring sites and 2) shorter data sampling epochs decrease rSO2 variability. These observations may assist clinicians in operationally defining minimally significant departures to enable medical decision making utilizing this monitoring technique. [ABSTRACT FROM AUTHOR]

OBJECTIVE: We sought to characterize the effects of 'booster' packed red blood cell transfusions on multisite regional oxygen saturation in very low birth weight neonates during the first postnatal week and to examine the utility of fractional tissue oxygen extraction as an estimate of tissue oxygenation adequacy. STUDY DESIGN: Data were collected in an observational near-infrared spectroscopy (NIRS) pilot survey of 500-1250 g neonates during the first postnatal week. A before-after analysis of 'booster' transfusions, defined as empiric 15 mL/kg transfusion following 10 mL/kg cumulative phlebotomy losses, was conducted upon cardiopulmonary, laboratory, and spectroscopy data. RESULT: Ten neonates (gestational age 26 ± 0 wk; birth weight 879 ± 49 g) received 14 transfusions at 3 ± 0 postnatal days. Mean hematocrit increased from 35.2 ± 1.2 to 38.5 ± 1.2 % (P < 0.05) following transfusion; pH, base deficit, lactate, creatinine, and cardiopulmonary parameters were unchanged. Cerebral, renal, and splanchnic tissue oxygenation increased 10, 18, and 16%, with concomitant decreases in calculated oxygen extraction of 27, 30, and 9% (all P < 0.05), consistent with enhanced tissue oxygenation. These findings were not observed in a non-transfused comparison group of nine patients. CONCLUSION: 'Booster' transfusions improved indices of regional tissue oxygenation while no departures were observed in conventional cardiovascular assessments. We speculate that NIRS-derived oxygenation parameters can provide an objective, graded, and continuous estimate of oxygen delivery-consumption balance not evident using standard monitoring techniques. [ABSTRACT FROM AUTHOR]