Search results for "equation"

Multimodal Communication and Peer Interaction during Equation-Solving Sessions with and without Tangible Technologies

2023

Despite the increasing use of technologies in the classroom, there are concerns that technology-enhanced learning environments may hinder students’ communication and interaction. In this study, we investigated how tangible technologies can enhance students’ multimodal communication and interaction during equation-solving pair work compared to working without such technologies. A tangible app for learning equation solving was developed and tested in fourth and fifth-grade classrooms with two class teachers and 24 students. Video data of the interventions were analysed using deductive and inductive content analysis. Coded data were also quantified for quantitative analysis. Additionally, teac…

Asymptotic Hölder regularity for the ellipsoid process

2020

We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.

Euler Characteristics of Moduli Spaces of Curves

2005

Let ${mathcal M}_g^n$ be the moduli space of n-pointed Riemann surfaces of genus g. Denote by ${\bar {\mathcal M}}_g^n$ the Deligne-Mumford compactification of ${mathcal M}_g^n$. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of ${\bar {\mathcal M}}_g^n$ for any g and n such that n>2-2g.

Exact solutions of the Zakharov equations

2009

APROXIMACIÓN CONCEPTUAL Y PRÁCTICA A LOS MODELOS DE ECUACIONES ESTRUCTURALES

2017

En el presente trabajo se expone una aproximación conceptual y práctica a los Modelos de Ecuaciones Estructurales o Structural Equation Modeling (SEM). Los SEM están considerados entre las herramientas más potentes para el estudio de relaciones causales en datos no experimentales. Son una combinación del análisis factorial y la regresión múltiple y están compuestos por dos componentes: el modelo de medida y el modelo estructural. El modelo de medida describe la relación existente entre una serie de variables observables; mientras que en el modelo estructural se especifican las relaciones hipotetizadas entre las variables, es decir, se describen las relaciones entre las variables latentes me…

Soliton solutions for an higher order nonlinear Schroedinger equation in optical fiber

2008

The new improvements to increase the bit rate in optical fiber require the propagation of pulse whose temporal width is always lesser. This causes the presence of further terms, linear and nonlinear, in the evolution equation of the pulse. The analysis on the complete integrability of the evolution equation, in a fiber optics with local properties and achieved in a previous paper, is improved dealing with the normal dispersion case, which allows the dark soliton propagation. In the last section special efforts are made to propose some interesting soliton solutions both bright and dark.

Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

1984

The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given. peerReviewed

Inverse problems and invisibility cloaking for FEM models and resistor networks

2013

In this paper we consider inverse problems for resistor networks and for models obtained via the finite element method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of Calderón. We characterize FEM models corresponding to a given triangulation of the domain that are equivalent to certain resistor networks, and apply the results to study nonuniqueness of the discrete inverse problem. It turns out that the degree of nonuniqueness for the discrete problem is larger than the one for the partial differential equation. We also study invisibility cloaking for FEM models, and show how an arbitrary body can be surrounded with a layer …

An optimal local active noise control method based on stochastic finite element models

2013

A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A leas…

On FE-grid relocation in solving unilateral boundary value problems by FEM

1992

We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed