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, ...

We develop a closed loop subspace identification method based on stochastic realization theory. Using the preliminary orthogonal decomposition of (Picci and Katayama, 1996b) we show that, under the assumption that the exogenous input is feedback-free and persistently exciting (PE), the identification of closed loop systems is divided into two subproblems: the deterministic identification of the...

However, in many infections the effect on the lymphatics may be both consistent and clinically marked. The lymphadenopathy may be local or generalized and lymphadenopathy is or can be a significant feature of acute HIV infection, primary Herpes simplex, some rickettsial infections, tularaemia, plague, cat-scratch fever due to Bartonella henselae, primary syphilis, lymphogranuloma venereum, chan...