Integrable systems from inelastic curve flows in 2-and 3-dimensional Minkowski space

Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2-and 3- dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrodinger (NLS) equation in 2- and 3- dimensional Euclidean space, respectively. In 2-dimensional Minkowski space, time-like/space-like inelastic curve flows are shown to yield the defocusing mKdV equation and its bi-Hamiltonian integrability structure, while inelastic null curve flows are shown to give rise to Burgers' equation and its symmetry integrability structure. In 3-dimensional Minkowski space, the complex defocusing mKdV equation and the NLS equation along with their bi-Hamiltonian integrability structures are obtained from timelike inelastic curve flows, whereas spacelike inelastic curve flows yield an interesting variant of these two integrable equations in which complex numbers are replaced by hyperbolic (split-complex) numbers

Benefits Of Caffeine: Birth Weigth Over 1250 g Infants With Respiratuar Distress

INTRODUCTION: Prophylactic caffeine therapy, reduces the frequency of apnea in premature babies. Moreover, its effect has been well established in reducing the intermittent hypoxemia, and the need for additional ventilator support of infants with a birthweight of <1.250 g. The aim of this study is to determine the effects of prophylactic caffeine use on neonatal outcomes in preterm babies with a birthweight of >1.250 g and respiratory distress. METHODS: Sixty-eight infants with birthweight of 1.250 to 2.000 g with respiratory distress and born at 32-34 GA and intubated with the indication of respiratory distress who also needed nasal ventilation for at least 48 hours were included in this prospective randomized controlled study, starting from birth one group received prophylactic caffeine citrate at loading dose of 20 mg/kg, and maintenance dose of 5 mg/kg in addition to respiratory support, long term neurological and developmental outcomes were recorded with Bayley-II. RESULTS: There was no difference in weight or gestational age at birth between the groups. Also, the groups were smilar in respiratory states. The caffeine group, was associated with a significant reduction in intubation requirement within the first 72 hr and shorter duration of mechanical and nasal ventilation, while there was no difference between the groups in total duration of oxygen therapy, and frequency of apneic episodes (respectively p=0.03, p=0.00, p=0.02, p>0.05). Any differences were not detected in terms of prematurity morbidities (p>0.05). Any significant intergroup differences were not detected as for PDA, NEC, IVC, laser-requiring ROP, and BPD (p>0.05). While the study was continuing regarding long-term neurodevelopmental outcomes Bayley neurodevelopmental tests were applied to 15 infants in the caffeine and 18 infants in the caffeine group at 12. and 18. months, and test results were csimilar in both groups (p>0.05). DISCUSSION AND CONCLUSION: The prophylactic use of caffeine in older preterm babies with respiratory distress, have short term benefits as lesser requirement for ntubation within the first 72 hours and decreased duration of ventilatory support without any advers side effects. Therefore if symptoms of respiratory distress are seen in preterm babies with a birthweight of >1.250 g, then initiation of prophylactic treatment may be considered. Larger scale randomized kontrollü studies are needed regarding this issue