A property of entire transcendental functions
A property of the class of functions whose derivative has a positive real part.
A pseudo-trigonometry related to Ptolemy's theorem and the hyperbolic geometry of punctured spheres
A hyperbolic geodesic joining two punctures on a Riemann surface has infinite length. To obtain a useful distance-like quantity we define a finite pseudo-length of such a geodesic in terms of the hyperbolic length of its surrounding geodesic loop. There is a well defined angle between two geodesics meeting at a puncture, and our pseudo-trigonometry connects these angles with pseudo-lengths. We state and prove a theorem resembling Ptolemy's classical theorem on cyclic quadrilaterals and three general...
A pure smoothness condition for Radó’s theorem for -analytic functions
Let be a bounded, simply connected -convex domain. Let and let be a function on which is separately -smooth with respect to (by which we mean jointly -smooth with respect to , ). If is -analytic on , then is -analytic on . The result is well-known for the case , , even when a priori is only known to be continuous.
A purely number theoretic attempt to prove Picard's theorems
A p-Valent Function with a Non-Normal Derivative.
A question of Gross and weighted sharing of a finite set by meromorphic functions.
-weighted Caccioppoli-type and Poincaré-type inequalities for -harmonic tensors.
-weighted Caccioppoli-type and Poincaré-type inequalities for -harmonic tensors. Erratum.
A Radical Cluster Set Uniqueness Theorem for Holomorphic Functions.
A Radó type theorem for -harmonic functions in the plane.
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
A reducibility problem for the classical residue formula
A reduction for asymptotic Teichmüller spaces.
A Region whose Prime Ends All Have the Same Impression.
A relationship between a Hankel matrix of Markov parameters and the associated matrix polynomial with some applications
A Reliable Argument Principle Algorithm to Find the Number of Zeros of an Analytic Function in a Bounded Domain.
A remark on Abel's Theorem and the mapping of linear series.
A remark on certain analytic class by using Ruscheweyh derivatives.
A remark on certain close-to-convex functions