All posts under category "Mathematics / Math.CV"
We introduce a new deterministic factoring algorithm, which could be described in the cryptographically fashionable term of 'factoring with hints': we show that, given the knowledge of the factorisations of $O(N^{1/3+epsilon})$ terms surrounding $N=pq$ product of two large primes, we can recover det
The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is twofold: a) it endeavors to provide a more rigorous presentation of
In the works of Darboux and Walsh it was remarked that a one to one self mapping of $rr^3$ which sends convex sets to convex ones is affine. It can be remarked also that a $calc^2$-diffeomorphism $F:Uto U^{'}$ between two domains in $cc^n$, $nge 2$, which sends pseudoconvex hypersurfaces to pseudoco
We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient functions contain the accessory parameters t,lamb
We give a necessary and sufficient condition so that a pair of disjoint Jordan regions in the sphere can be quasiconformally mapped to a pair of disks. As a consequence, we obtain a simple characterization that involves Lipschitz functions for the case that one of the Jordan regions is a half-plane.
Let $mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = prod_{j=1}^{n}(z-β_j)$, $|β_j|>1$ for $1leq jleq n$. In this work, we investigate the growth behavior of rational functions with prescribed poles by
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc., is known to be integrable and to exhibit a large number of exact solutions. In this work, the boun
Enter keywords to search articles