We use a payment pattern of the type {1k,2k,3k,…} to generalize standard level and increasing annuity polynomial patterns. derive explicit formulas for present value an n-year annuity, m-monthly continuous annuity. also idea extend annuities patterns derived from analytic functions, as well {1r,2r,3r,…}, with r being arbitrary real number. In process, we develop possible approximations k! gamma...

Abstract Inflationary ? -attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as n s = 1 - 2/ N e , assuming that the potential terms of original geometric variables, well its derivatives, are not singular at boundary disk, or half-plane. In these models, canonically normalized inflaton field ? has a plateau, ...

OBJECTIVE Cerebral oedema is a potentially devastating complication of diabetic ketoacidosis (DKA). The relationship between osmolar changes, acid-base changes and development of cerebral oedema during therapy is unclear. DESIGN Retrospective cohort study on 53 children with severe DKA (mean pH at presentation 6.92±0.08). Cerebral oedema was diagnosed using neurological status, response to os...

background: multiple sclerosis (ms) is one of the most prevalent of nerves system disease. ms is a chronic neurodegenerative disorder. nutrition and diet are effective factors for prevention and treatment in ms, however finding are controversial. the aim of this study was investigation of dietary pattern of fat consumption and its relationship with lipid profiles crp level in ms patient.  metho...