Let $J \in C(\mathbb{R})$, $J\ge 0$, $\int_{\tiny$\mathbb{R}$} J = 1$ and consider the nonlocal diffusion operator $\mathcal{M}[u] \star u - u$. We study equation $\mathcal{M} + f(x,u) $u \ge in $\mathbb{R}$, where $f$ is a KPP-type nonlinearity, periodic $x$. show that principal eigenvalue of linearization around zero well defined nontrivial solution nonlinear problem exists if only this negative. prove if, additionally, $J$ symmetric, then unique.

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, is, distributions where all individuals have equal fitness and there is no net movement at equilibrium. find property producing necessary often sufficient for stability. Our results extend those already developed discrete diffusion models on finite patch networks to case based integrodifferential equations. The analysis use comparison methods construction sub- supersolutions.

Consider an expanding map T:A contained in Rn to with TA contains/implies A strictly. Pianigiani and Yorke have shown that under some suitable conditions there exists a conditionally invariant probability measure mu f, density f satisfying Pf= alpha for the Perron-Frobenius operator P. We prove conditional of staying when evolution occurs i.e. f(B intersection T-nA mod T-nA) n infinity nu (B) any Borel set B in/implied by A, is T-invariant on limit Cantor K= n>or=0T-nA which Gibbsian...

In this paper we study the asymptotic behavior of following nonlocal inhomogeneous dispersal equation$$u_t(x,t) = \int_{\mathbb{R}} J\left(\frac{x-y}{g(y)}\right) \frac{u(y,t)}{g(y)} dy -u(x,t)\qquad x\in \mathbb{R},\ t>0,$$where $J$ is an even, smooth, probability density, and $g$, which accounts for a distance, continuous positive.We prove that if $g(|y|)\sim |y|$ as $|y|\to + \infty$ some $0 2$ there are no positivestationary solutions. We also establish solutions evolution problem in both cases.

La modalidad de enseñanza que adoptan los formadores influye en el aprendizaje la profesores formación. Para avanzar una mejor comprensión este fenómeno, es fundamental comenzar a investigar cómo y sus estudiantes pedagogía configuran proceso dentro del aula, profundizando intercambios establecen. Este estudio analizó las prácticas discursivas e interacciones pedagógicas tres matemáticas carrera Pedagogía Enseñanza Básica. A cada formador se le videograbaron cuatro clases, cuales fueron...

For educators, identifying and characterising problems in their teaching practice is essential for triggering inquiries into practice. Knowing what educators consider problematic generating strategies situated approaches to help teacher manage promote professional learning. In this study, we report on qualitative research with the aim of types that 43 Chilean mathematics identified teaching. We adopted an ecological data collection approach investigate practices. The source was a set open...

In this article we study the existence and asymptotic profiles of high-energy rotation type solutions singularly perturbed forced pendulum equation We prove that profile these is described in terms an energy function which satisfy integro-differential equation. Also show given a suitable E satisfying equation, family above exists having as profile, when ε → 0.

Considering the relevance of preservice teachers possessing positive beliefs their future efficacy as and absence validated instruments to measure this construct in Chile, research generated a convergent factorial validation Escala de Creencias Eficacia en la Enseñanza Matemática (ECEEM), adapted version Spanish Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), United States, 2000. The sample was comprised 945 elementary school studying 14 universities from 5 regions corresponding...

An online activity provides instructional strategies that can help students engage in mathematical modeling and autonomous learning.