We use generalized power series to construct algebraically a nonstandard model of the theory of the real eld with exponentiation. This model enables us to show the undeenability of the zeta function and certain non-elementary and improper integrals. We also use this model to answer a question of Hardy by showing that the compositional inverse to the function (log x)(log log x) is not asymptotic...

Shannon's entropy has been characterized in several ways. Kaminski and Mikusihski [5] simplified Fadeev's [3] approach by considering, what they called the entropy equation: (1.1) H(x, y, z) = H(x + y, 0, z) + H(x, y, 0) , (x ^ 0 , y ^ 0 , z > 0 , xy + yz + zx > 0) . A general continuous symmetric solution of (1.1) given by (1.2) H(x, y, z) = (x + y + z) log (x + y + z) — x log x y log y — z lo...

It is shown that, if ν ≥ 1/2 then the generalized Marcum Q function Qν(a, b) is log-concave in b ∈ [0,∞). This proves a conjecture of Sun, Baricz and Zhou (2010). We also point out relevant results in the statistics literature.

We consider the generalized network flow problem. Each arc e in the network has a gain factor y (e ) . If f ( e ) units of flow enter arc e , then f ( e ) r ( e ) units arrive at the other end of e. The generalized network flow problem is to maximize the net flow into one specific node, the sink. -We give an algorithm which solves this problem in O(m2 (m + n log log B ) log B ) time, where B is...

This work presents a study of how log-polar images can be combined with a generalized least squares-based technique in order to get an accurate and fast parametric motion estimation algorithm. The possibility of replacing the classical hierarchical algorithm —based on using a pyramid of multiple resolution— by an algorithm which gets a good aproximation of the motion parameters using log-polar ...