Here I sit, making men in my own image: how learning disorder labels affect teacher student’s expectancies

Teacher’s evaluation of students is sometimes negatively affected by diagnostic labels. We explored such negative effects caused by the labels “dyscalculia”, “dyslexia”, and “ADHD” in teacher students. In Experiment 1, we varied the presence of the dyscalculia and dyslexia label in vignettes between participants. The dyslexia but not the dyscalculia label had a negative effect on participant’s academic expectations. In our preregistered Experiment 2, the presence of the ADHD label in vignettes was manipulated within participants. To understand the cognitive mechanisms driving label effects, we explored participants’ attributions regarding the students’ problems. Furthermore, a short dissonance-based intervention for counteracting negative label effects was implemented. Unexpectedly, we found both negative and positive label effects. The label led to more positive performance expectations and to more negative ratings of problem stability and problem control. The dissonance-based intervention led to more positive evaluations regardless of whether the ADHD label was mentioned or not. Overall, our findings suggest that learning-disorder labels affect teachers’ expectations in different ways.

Inverse problem for a multi-term fractional differential equation

Inverse problem for a family of multi-term time fractional differential equation with non-local boundary conditions is studied. The spectral operator of the considered problem is non-self-adjoint and a bi-orthogonal set of functions is used to construct the solution. The operational calculus approach has been used to obtain the solution of the multi-term time fractional differential equations. Integral type over-determination condition is considered for unique solvability of the inverse problem. Different estimates of multinomial Mittag-Leffler functions alongside Banach fixed point theorem are used to prove the unique local existence of the solution of the inverse problem. Stability of the solution of the inverse problem on the given datum is established.

On Applying of Equilibrium Stability Criteria for Systems of Differential Equations with Two Cosymmetries in Critical Cases

Critical cases of equilibrium stability are considered for differential equations with two cosymmetries. Stability spectrum of such equilibrium consists of two spectral sets. The first is the non-trivial neutral spectrum that is on the imaginary axis. The second is a stable part of the spectrum that lies in the left half-plane. According to the general theory, research of the critical cases comes down to study of nonlinear model systems. To calculate the coefficients for such systems is a separate problem. Stability criteria for the model systems are described in the previous work of the authors. The purpose of given paper is to express the coefficients of Taylor’s series for model systems from such coefficients for the original equation. A usual algorithm constructing a model system consists of two coherent conversions of the original equation. The first is to form the reduction on the neutral surface for this equation. As a result its dimension is decreased to the neutral subspace’s dimension. Then the constriction is transformed to normal form to some finite order. The higher order terms are ignored. In this work the coefficients of the model systems are computed with the help of algorithm of V.I. Yudovich. It makes possible to unite both conversions into one. The obtained formulae for coefficients of model systems are independent of the original equation’s dimension. Thus it is applicable to systems of finite or infinite dimension and usable to realize using packages of analytical calculations.

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders α = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.

Analysis of the Generalized Inverse Polynomial Scheme to Initial Value Problems

In this paper, we study the analysis of the generalized inverse polynomial scheme for the numerical solution of initial value problems of ordinary differential equation. At first, we generalize the scheme up to the fifth stage using the Binomial expansion and Taylor’s series method towards its derivation. The trend shows the generalization to the kth term. The analysis demonstrates the efficiency and the effectiveness of the generalized scheme.Keywords— Taylor’s Series, Initial Value Problem, Stability, Consistency, Convergence.

Inverse Problem: Stability for the aligned magnetic field by the Dirichlet-to-Neumann map for the wave equation in a periodic quantum waveguide

International audience Dans ce papier, on a prouvé une estimation de stabilité pour le problème inverse de dé-termination du champ magnétique dans l'équation des ondes donné sur un domaine non borné à partir de l'opérateur de Dirichlet-to-Neumann. On a montré un résultat de stabilité pour ce problème inverse, dont la démonstration est basée sur la construction de solutions optique géométrique pour l'équation des ondes avec un potentiel magnétique 1-périodique. ABSTRACT. We consider the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic wave equation in a periodic quantum cylindrical waveguide from boundary observations. The observation is given by the Dirichlet to Neumann map associated to the wave equation. We prove by means of the geometrical optics solutions of the magnetic wave equation that the knowledge of the Dirichlet-to-Neumann map determines uniquely the aligned magnetic field induced by a time independent and 1-periodic magnetic potential. We establish a Hölder-type stability estimate in the inverse problem.