Early Pulmonary Interstitial Emphysema in Preterm Neonates-Respiratory Management and Case Report in Nonventilated Very Low Birth Weight Twins

Early pulmonary interstitial emphysema in extreme preterm neonates is closely linked with respiratory distress syndrome and exposure to mechanical ventilation. In severe cases, maintaining adequate gas exchange aiming to avoid further lung damage and other neonatal morbidities associated with systemic/pulmonary hypoperfusion, prolonged hypoxia, and respiratory acidosis can be challenging and requires in-depth knowledge into the pathophysiology of the disease. Herein, we report on very low birth weight twins who developed early pulmonary interstitial emphysema during noninvasive respiratory support. We further review the current evidence from the literature, specifically addressing on possible preventive measures and the respiratory management options of this acute pulmonary disease in high-risk neonates

Some Implications of the WP-Bailey Tree

We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs (αn(a, k), βn(a, k)), in which αn(a, k) is independent of k, for generalizations of identities of the Rogers-Ramanujan type

Some Applications of a Bailey-type Transformation

If k is set equal to aq in the definition of a WP Bailey pair, βn(a, k) = Xn j=0 (k/a)n−j (k)n+j (q)n−j (aq)n+j αj (a, k), this equation reduces to βn = Pn j=0 αj . This seemingly trivial relation connecting the αn’s with the βn’s has some interesting consequences, including several basic hypergeometric summation formulae, a connection to the Prouhet-Tarry-Escott problem, some new identities of the Rogers-Ramanujan-Slater type, some new expressions for false theta series as basic hypergeometric series, and new transformation formulae for poly-basic hypergeometric series

General WP-Bailey Chains

Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains