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British Educational Research Journal, EarlyView.Abstract Parents of children with special educational needs and disabilities (SEND) increasingly seek information and support through online discussions, yet little is known about how architectural features of digital platforms shape the interactions and support that parents encounter. The paper makes two contributions: First, it develops and applies a
Alan Shaw, Patricia A. Shaw
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An Introduction to Predictive Processing Models of Perception and Decision‐Making
Topics in Cognitive Science, EarlyView., 2023 Abstract The predictive processing framework includes a broad set of ideas, which might be articulated and developed in a variety of ways, concerning how the brain may leverage predictive models when implementing perception, cognition, decision‐making, and motor control.
Mark Sprevak, Ryan Smith
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International Journal of Mathematics and Mathematical Sciences, 2012 The Dirichlet problem for the 2D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral
P. A. Krutitskii
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Demonstratio Mathematica, 2023 We investigate the existence and nonexistence of nonnegative radial solutions to exterior problems of the form ΔHmu(q)+λψ(q)K(r(q))f(r2−Q(q),u(q))=0{\Delta }_{{{\mathbb{H}}}^{m}}u\left(q)+\lambda \psi \left(q)K\left(r\left(q))f\left({r}^{2-Q}\left(q),u ...
Jleli Mohamed
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The Canadian Journal of Chemical Engineering, EarlyView.A perturbative Graetz model describes coupled heat and mass transfer in reactive Couette–Poiseuille flow between parallel plates. Viscous dissipation and heat of reaction produce a small temperature rise, which enhances Arrhenius reaction rates and modestly accelerates axial species conversion in the small‐Brinkman‐number regime.
Leonardo Damián Soria Rodríguez +1 more
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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Bruno Pini Mathematical Analysis Seminar, 2016 For every bounded open set Ω in RN+1, we study the first boundary problem for a wide class of hypoelliptic evolution operators. The operators are assumed to be endowed with a well behaved global fundamental solution that allows us to construct a ...
Alessia E. Kogoj
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Exterior Dirichlet and Neumann Problems and the Linked Ergodic Inverse Problems in the Entire Space
Journal of Fourier Analysis and Applications, 2022 AbstractThe paper is mainly concerned with the interconnection of the boundary behaviour of the solutions of the exterior Dirichlet and Neumann problems of harmonic analysis for the unit disk in $${\mathbb {R}}^2$$ R 2
Paul L. Butzer, Rudolf L. Stens
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, 2022 In this paper, we study the exterior Dirichlet problem for the fully nonlinear elliptic equation $f(\lambda(D^{2}u))=1$. We obtain the necessary and sufficient conditions of existence of radial solutions with prescribed asymptotic behavior at ...
Wang, Bo, Bao, Jiguang, Dai, Limei
core
A Geometric Characterization of Steady Laminar Flow
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
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