Continuous Dependence on the Initial-time Geometry for a Parabolic Equation from Dynamo Theory with Different Prescribed Data

In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.

The Relationship between Students’Problem Posing and Problem Solving Abilities and Beliefs:A Small-Scale Study with Chinese Elementary School Children

The goal of the present study is to investigate the relationship between pupils’problem posing and problem solving abilities,their beliefs about problem posing and problem solving,and their general mathematics abilities,in a Chinese context.Five instruments,i.e.,a problem posing test,a problem solving test,a problem posing questionnaire,a problem solving questionnaire,and a standard achievement test,were administered to 69 Chinese fifth-grade pupils to assess these five variables and analyze their mutual relationships.Results revealed strong correlations between pupils’problem posing and problem solving abilities and beliefs,and their general mathematical abilities.

Pose optimization based on integral of the distance between line segments

In this paper, new solutions for the problem of pose estimation from correspondences between 3D model lines and 2D image lines are proposed. Traditional line-based pose estimation methods rely on the assumption that the noises(perpendicular to the line) for the two endpoints are statistically independent. However, these two noises are in fact negatively correlated when the image line segment is fitted using the least-squares technique. Therefore, we design a new error function expressed by the average integral of the distance between line segments. Three least-squares techniques that optimize both the rotation and translation simultaneously are proposed in which the new error function is exploited. In addition, Lie group formalism is utilized to describe the pose parameters, and then, the optimization problem can be solved by means of a simple iterative least squares method. To enhance the robustness to outliers existing in the match data, an M-estimation method is developed to convert the pose optimization problem into an iterative reweighted least squares problem. The proposed methods are validated through experiments using both synthetic and real-world data. The experimental results show that the proposed methods yield a clearly higher precision than the traditional methods.

Experimental research on mathematics teaching of“situated creation and problem-based instruction”in Chinese primary and secondary schools

This research tends to make the experimental study on the mathematics teaching model of“situated creation and problem-based instruction”(SCPBI),namely,the teaching process of“creating situations—posing problems—solving problems—applying mathematics”.It is aimed at changing the situation where students generally lack problem-based learning experience and problem awareness.Result shows that this teaching model plays a vital role in arousing students’interest in mathematics,improving their ability to pose problems and upgrading their mathematics learning ability as well.

CONTINUOUS DEPENDENCE ON VELOCITY FOR THE BACKWARD DYNAMO EQUATION ON AN EXTERIOR DOMAIN

In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the unbounded domain.