Modified Logarithmic Potential Theory and Applications

Logarithmic Potential Theory with Applications to Approximation Theory

We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete points, logarithmic capacity, and Chebyshev constant through a variety of examples and exercises. Many of the fundamental theorems of potential theory, such as Fr...

Large deviation principle in logarithmic potential theory

Some logarithmic function spaces, entropy numbers, applications to spectral theory

In [18] and [19] we have studied compact embeddings of weighted function spaces on Rn, id : Hs q (w(x),Rn) −→ Lp(R), s > 0, 1 < q ≤ p < ∞, s − n/q + n/p > 0, with, for example, w(x) = 〈x〉α, α > 0, or w(x) = logβ〈x〉, β > 0, and 〈x〉 = (2 + |x|2)1/2. We have determined the behaviour of their entropy numbers ek(id). Now we are interested in the limiting case 1/q = 1/p + s/n. Let w(x) = logβ〈x〉, β >...

Genetically modified mice- Methods, applications and outlook

Background & Aim: Transgenic mice, of tengenerated by random integration of foreign genes into the mouse genome or by targeted mutation in a particular gene, have demonstrated to be a very effective tool for studying gene function in living things. In this review article, we discussed on the current methods of generating genetically-modified mice and their related problems and then investigated...

Logarithmic Jet Bundles and Applications

Hyperbolic complex manifolds have been studied extensively during the last 30 years (see, for example, [10], [11]). However, it is still an important problem in hyperbolic geometry to understand the algebro-geometric and the differential-geometric meaning of hyperbolicity. The use of jet bundles has become a powerful tool to attack this problem. For example, Green and Griffiths ([5]) explained ...