Brazilian Society of Computational and Applied Mathematics

The exterior derivative and the mean value equality in $$\mathbb {R}^n$$

Abstract This survey revisits classical results in vector calculus and analysis by exploring a generalised perspective on the exterior derivative, interpreting it as a measure of “infinitesimal flux”. This viewpoint leads to a higher-dimensional analogue of the Mean Value Theorem...

Ground states of the defocusing nonlinear Schrödinger equation with a point interaction in dimensions 2 and 3

Abstract This paper is concerned with ground states of the defocusing nonlinear Schrödinger equation with a point interaction, $$ \textrm{i} \partial _t \psi = -\Delta _\alpha \psi + \psi |\psi |^{p - 2} \quad \text {in} \quad \mathbb {R} \times \mathbb {R}^N, $$ i ∂ t ψ = - Δ α...

Fractional counterpart of a higher-order abstract Cauchy problem

Abstract In this paper, we consider the fractional powers of a linear operator associated with a higher-order abstract Cauchy problem defined by a linear parabolic equation. We also characterize the domain of the fractional powers and discuss the solvability of the fractional equ...

Artificial intelligence for Amazonian health: validation is the price of entry

At the AI as Catalyst meeting in Manaus (July 28–29, 2026; https://ia-como-catalisadora-manaus.netlify.app), participants ran a simple exercise. Working in teams, they wrote about ten clinical cases and put each one to widely used general-purpose chatbots twice: first in standard...

Characterisations of finite groups by subsets of commutators

Abstract Given a finite group 𝐺 and an element 𝑥 of 𝐺, let K x ⁢ ( G ) K_{x}(G) denote the set of commutators [ x , g ] [x,g] as 𝑔 varies through 𝐺. We prove that various group theoretical properties of 𝐺, for instance, nilpotency of several subgroups of 𝐺 and the existence of a...

An angular-momentum-preserving dissipative model for the point-mass N-body problem

Abstract A simple mathematical model emulating energy dissipation due to tidal effects is proposed. In this model, forces acting between masses remove energy but preserve the total angular momentum of the system. We study the effect of such forces on the particular family of orbi...

The Fourier transform in variable exponent Lebesgue spaces

Abstract In this work we define a Fourier transform for each $$f\in L^{p(\cdot )}({{\,\mathrm{\mathbb {R}}\,}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>p</mml:mi>...