In the early 1980’s an elementary algorithm for computing conformal maps was discovered by R. Kühnau and the first author. The algorithm is fast and accurate, but convergence was not known. Given points z0, . . . , zn in the plane, the algorithm computes an explicit conformal map of the unit disk onto a region bounded by a Jordan curve γ with z0, . . . , zn ∈ γ. We prove convergence for Jordan ...

A local normal form is obtained for geodesics in the space Λ = {Γ} of analytic Jordan curves in the extended complex plane with symmetric space multiplication Γ1 · Γ2 defined by Schwarzian reflection of Γ2 in Γ1. Local geometric features of (Λ, ·) will be seen to reflect primarily the structure of the Witt algebra, while issues of global behavior of the exponential map will be viewed in the con...

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 2 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 3 The Jordan Curve Theorem and the concept of a curve . . . . . . . . . . . . . . . . . 707 4 Local connectedness; plane continua.. . . . . ....

Certain categorial calculi exhibit a property that is known as count invariance (Van Benthem 1986). In these grammars, it is true that if a proposition Y ⇒ z is derivable, the string to the left of ⇒ and the type to its right share the results of a particular way of counting occurrences of basic types. This count protocol discriminates between positive occurences (heads) and negative occurrence...

Let F be a Jordan curve in the plane, i.e. the image of the unit circle C = {(x,y);x + y = 1} under an injective continuous mapping y into R. The Jordan curve theorem [1] says that / ? 2 \ F is disconnected and consists of two components. (We shall use the original definition whereby two points are in the same component if and only if they can be joined by a continuous path (image of [0,1]).) A...

1. Given any associative ring A one can construct from its operations and elements a new ring, the Jordan ring of A, by defining the product in this ring to be a o b = ab+ba for all a, b^A, where the product ab signifies the product of a and b in the associative ring A itself. If R is any ring, associative or otherwise, by a derivation of R we shall mean a function, ', mapping R into itself so ...

A relatively simple proof is given for Haimo’s theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo’s criterion, which is now shown to be sharp. It is proved that Haimo’s functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presenc...

A recommendation of: Shinichi Nakagawa, Malgorzata Lagisz, Roxane Francis, Jessica Tam, Xun Li, Andrew Elphinstone, Neil R. Jordan, Justine K. O’Brien, Benjamin J. Pitcher, Monique Van Sluys, Arcot Sowmya, Richard T. Kingsford Rapid literature mapping on the recent use of machine learning for wildlife imagery https://doi.org/10.32942/X2H59D

We will extend in this paper some results about commutativity of Jordan ideals proved [2] and [6]. However, we consider left derivations instead derivations, which is enough to get good relation the structure near-rings. also show that conditions imposed cannot be removed.