Existence and exponential stability of periodic solutions of Nicholson-type systems with nonlinear density-dependent mortality and linear harvesting

In this work we study a Nicholson-type periodic system with variable delay, density-dependent mortality and linear harvesting rate. Using the topological degree and Lyapunov stability theories, we obtain sufficient conditions that allow us to demonstrate the existence of periodic solutions for the Nicholson-type system and, under suitable conditions, the uniqueness and local exponential stability of the periodic solution is established. We illustrate our results with an example and numerical simulations

WhatsApp and audio misinformation during the Covid-19 pandemic

Given user choices and the commercial offerings of internet providers, WhatsApp has increasingly become established as a new standard for communication by audio, image, and text. This paper explores the role of misinformation during the Covid-19 pandemic by using content disseminated through WhatsApp, thereby making three main contributions: a discussion about the potential shift toward nontextual and nonvisual forms of misinformation; the new social role of audio, namely related to the critique of policies and political actors during the early stage of the Covid-19 pandemic; and the questioning of the First Draft News disinformation conceptual model by proposing a complementary approach that focuses only on factuality. Conclusions were drawn after conducting a content analysis of 988 units of Covid-19-related audio files, images, videos, and texts shared via WhatsApp during the early stage of the pandemic. A typology was identified to address distinct claims that focus on five different topics (society, policy and politics, health science, pandemic, and other), as well as audio messaging trending as a novel format for spreading misinformation. The results help us to contextualize and discuss a potential shift toward nontextual and nonvisual forms of misinformation, reflecting the increasing adoption of the audio format among WhatsApp users and making WhatsApp a fertile environment for the circulation and dissemination of misinformation regarding Covid-19-related themes. In a society characterized by the rapid consumption of information, the idea that content must have a degree of falsehood to mislead is an indicator of the distance between theoretical models and social reality. This indicator is important to identify true content as potential misinformation on the basis of its factuality

Non-Lipschitz differentiable functions on slit domains

It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free algebras– inside the family of non-Lipschitz differentiable real functions with bounded gradient defined on special non-convex plane domains. In particular, this yields that there are many differentiable functions on plane domains that do not satisfy the Mean Value Theorem.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ

Bounded and unbounded polynomials and multilinear forms: Characterizing continuity

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only if it transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the \emph{lineability} of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.Comment: 8 page

Universality of sequences of operators related to Taylor series

In this note, the universality of a sequence of operators associated to the partial sums of the Taylor series of a holomorphic function is investigated. The emphasis is put on the fact that the Taylor series are evaluated at a prescribed point and the variable is the center of the expansion. The dynamics of the sequence of operators linked to the partial sums of a power series that is not generated by an entire function is also studied.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ