The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Abstract In this paper, we give a generalization and improvement of the Pavlović result on characterization continuously differentiable functions in Bloch space unit ball $\mathbb {R}^{m}$ . Then, derive Holland–Walsh type theorem for analytic normal mappings disk.

Most automated theorem provers suuer from the problem that the resulting proofs are diicult to understand even for experienced mathematicians. An eeective communication between the system and its users, however, is crucial for many applications, such as in a mathematical assistant system. Therefore, eeorts have been made to transform machine generated proofs (e.g. resolution proofs) into natura...

HOL-TestGen is a test environment for specification-based unit testing built upon the proof assistant Isabelle/HOL. While there is considerable skepticism with regard to interactive theorem provers in testing communities, we argue that they are a natural choice for (automated) symbolic computations underlying systematic tests. This holds in particular for the development of non-trivial formal t...

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Connected choice is the operation that finds a point in a non-empty connected closed set given by ne...