3139598 documents found, page 313960 of 313960
Dual compatibility for measure-driven function space scales
Caetano, A. M.; Gomes, B.We address a basic but recurring functional-analytic issue: given a continuous linear operator acting between nested scales of spaces, its dual and the dual of its restriction typically act on non-comparable abstract dual spaces, so that a naive “restriction” statement is ill-posed. While one can, if appropriate conditions are met, resolve this difficulty on a case-by-case basis by introducing concrete identifi...
Designing with Generative AI: ethical and creative redesign of visual assets in...
Pais, Sónia; Hall, AndreiaIn game-based learning, visual elements play a crucial role, particularly in mathematics education, where they often represent numerical information and support conceptual understanding. Nevertheless, copyright constraints may limit the reuse and adaptation of educational games outside their original context, posing both practical and ethical challenges for teachers and researchers. This paper presents the rede...
Symmetry in urban ornament: a mathematical trail through the historic centre of...
Ambrósio, Helena; Hall, Andreia; Pais, SóniaMathematical trails provide a way of experiencing mathematics in direct connection with urban space, cultural heritage, and artistic expression. In this paper we present a mathematical trail through the city of Leiria (Portugal), designed to invite inhabitants and visitors to observe, analyse, and appreciate mathematical structures embedded in the built environment. The proposed route highlights decorative elem...
From Rosettes to Flexagons: exploring symmetry and antisymmetry with Truchet tiles
Hall, Andreia; Bastos, NunoThis workshop explores symmetry and antisymmetry in planar rosettes through hands-on artistic creation with Truchet tiles. Participants explore the concepts by designing coloured patterns with prescribed properties. Activities alternate between paper-and-pencil challenges and interactive GeoGebra applets, using Truchet tiles as the basic motif. The session concludes with the construction of a personalised hexa-...
On the periodic orbits of C0-typical impulsive semiflows
Bessa, M.; Siqueira, J.; Torres, M. J.; Varandas, P.Impulsive semiflows modeled by continuous flows and continuous impulsive functions, defined over an impulsive region, are piecewise continuous semiflows with piecewise smooth trajectories. In this paper we contribute to the topological description of typical impulsive semiflows, parameterized by both vector fields and impulses. We prove that C 0-generic continuous flows generate impulsive semiflows with densene...
Very-well-behaved epireflections for categories of models of sketches
Xarez, João J.We study reflections obtained from other adjunctions by factorizing the unit of the adjunction. The objective is to provide some conditions which ensure that such reflections have stable units, and induce a monotone-light factorization system. In particular, we consider the cases where the adjunction is induced by a left and right Kan extension (respectively). In last section, the case of right Kan extensions f...
Piecewise rational aiffine maps, multidimensional generalized shifts, and compu...
Graça, Daniel S.In this paper we study the computational power of certain classes of dynamical systems defifined by the iteration of piecewise rational affine maps on the compact set [0,1]nas a model of computation over the real numbers. To achieve this aim we use symbolic dynamics to study the dynamics of this class of piecewise rational aiffine maps and in the process introduce multidimensional generalized shifts, which are ...
Existence of weak solutions for parabolic equations involving the p(x, t)-Lapla...
Bae, Hyeong-Ohk; Oliveira, Hermenegildo Borges de; Wolf, JörgWe consider a parabolic equation involving the p(x, t)-Laplacian as a prime term in a time-space cylinder QT := Ω × (0,T) ⊂ Rd × R,d ≥ 2. We assume that p(x, t): QT → (1, +∞) is a continuous function, except in a closed set of zero measure. Under the assumption that p is unbounded, such that 1 < infK×(δ,T ) p(x, t) ≤ supK×(δ,T ) p(x, t) < ∞ for every compact set K ⊂ Ω and δ ∈ (0,T), we prove the existence of a ...