Fréchet-valued meromorphic extension along a pencil of complex lines

The aim of paper is to find the condition under which a Fréchet-valued function [Formula: see text] admitting meromorphic extension along some pencil of complex lines can be meromorphically extended to a neighborhood of [Formula: see text] Some auxiliary results concerning the domains of existence for Fréchet-valued meromorphic functions, Rothstein’s theorem, Levi extension theorem for meromorphic functions with values in a locally complete space, convergence of formal power series of Fréchet-valued homogeneous polynomials are also proved in this work.

The threat of thinking in threats: reframing global health during and after COVID-19

Narratives and metaphors shape how actors perceive the world around them and how policymakers frame the range of policy choices they think of as feasible. The metaphor of war and the narrative of how to tackle the unprecedented threat of COVID-19 are effective mechanisms to convey urgency. However, they also bear serious implications: Thinking in terms of health threats works with a logic of exceptionalism, which supports images of “us” vs. an “enemy” thereby shortening complex lines of causality and responsibility and privileging national answers. It fails to provide for a normative framework for drafting long-term systemic approaches. In this contribution, we critically engage with existing narratives of global health security and show how the logic of exceptionalism is limiting the current responses to the pandemic. We conceptualize an alternative narrative that is based on the logic of solidarity and argue that within this alternative framing a more sustainable and ultimately more just way of coping with infectious diseases will be possible.

Hyperbolicity of the complement of arrangements of non complex lines

The goal of this paper is twofold. We study holomorphic curves f:C ? C3 avoiding four complex hyperplanes and a real subspace of real dimension five in C3 where we study the cases where the projection of f into the complex projective space CP2 is constant. On the other hand, we investigate the kobayashi hyperbolicity of the complement of five perturbed lines in CP2.

SIC-POVMs and the Stark Conjectures

The existence of $d^2$ pairwise equiangular complex lines [equivalently, a symmetric informationally complete positive operator-valued measure (SIC-POVM)] in $d$-dimensional Hilbert space is known only for finitely many dimensions $d$. We prove that, if there exists a set of real units in a certain ray class field (depending on $d$) satisfying certain algebraic properties, a SIC-POVM exists, when $d$ is an odd prime congruent to 2 modulo 3. We give an explicit analytic formula that we expect to yield such a set of units. Our construction uses values of derivatives of zeta functions at $s=0$ and is closely connected to the Stark conjectures over real quadratic fields. We verify numerically that our construction yields SIC-POVMs in dimensions 5, 11, 17, and 23, and we give the first exact SIC-POVM in dimension 23.

Auguste Rodin Draws Blind: An Art and Psychology Study

Late in his life Rodin produced many thousand “instant drawings.” He asked models to make natural energetic movements, and he would draw them at high speed without looking at his hand or paper. To help understand his “blind drawing” process, the authors tracked the eye and hand movements of art students while they drew blind, copying complex lines presented to them as static images. The study found that line shape was correctly reproduced, but scaling could show major deficiencies not seen in Rodin's sketches. The authors propose that Rodin's direct vision-to-motor strategy, coupled with his high expertise, allowed him to accurately depict in one sweep the entire model, without “thoughts arresting the flow of sensations.”

Functions with the One-dimensional Holomorphic Extension Property

In this paper we consider different families of complex lines, sufficient for holomorphic extension the functions f, defined on the boundary of a domain D Cn, n > 1, into this domain, and possessing the one-dimensional holomorphic extension property along this complex lines