DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory

We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions \gamma of twist-2 operators in the non-physical points j=0,-1,... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. Moreover, in the multi-color limit of the N=4 model the BFKL and DGLAP dynamics in the leading logarithmic approximation is integrable for an arbitrary number of particles. In the next-to-leading approximation the holomorphic separability of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter kernel has the property of a hermitian separability. The main singularities of anomalous dimensions \gamma at j=-r obtained from the BFKL and DGLAP equations in the next-to-leading approximation coincide but our accuracy is not enough to verify an agreement for residues of subleading poles.Comment: 45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> \mu+\mu- in the double-logarithmic approximation at QED is corrected and its derivation is given in the Appendix

The Relationship of Parental Knowledge to the Development of Extremely Low Birth Weight Infants

This study examined the relationship between parental experience, parental knowledge, and the development of extremely low birth weight infants. The subjects (N = 40) were extremely high-risk infants averaging 1000.0 grams birthweight and 28.1 weeks gestational age. The study found that mothers of preterm infants called upon the same types of experiences and sources of information about infancy as mothers of full-term infants. Further, ratings of maternal accuracy on the Knowledge of Infant Development Inventory accounted for 13% to 15% of the variation on the Mental Development Index (MDI) and Psychomotor Development Index (PDI) of the Bayley Scales of Infant Development at 8 months corrected age. The infants of mothers with greater than average knowledge about infancy scored approximately one standard deviation higher on both the MDI and the PDI than did the infants of mothers who had less than average knowledge about Infancy. Implications for intervention are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67695/2/10.1177_105381519201600302.pd