Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body

Detailed studies of anomalous conductors in otherwise homogeneous media have been modelled. Vertical contacts form common geometries in galvanic studies when describing geological formations with different electrical conductivities on either side. However, previous studies of vertical discontinuities have been mainly concerned with isotropic environments. In this paper, we deal with the effect on the electric potentials, such as mise-`a-la-masse anomalies, due to a conductor near a vertical contact between two anisotropic regions. We also demonstrate the interactive effects when the conductive body is placed across the vertical contact. This problem is normally very difficult to solve by the traditional numerical methods. The integral equations for the electric potential in anisotropic half-spaces are established. Green’s function is obtained using the reflection and transmission image method in which five images are needed to fit the boundary conditions on the vertical interface and the air-earth surface. The effects of the anisotropy of the environments and the conductive body on the electric potential are illustrated with the aid of several numerical examples.

Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x.

A review of mathematical equations to assign individual marks from a team mark

BACKGROUND : Team-based learning is an integral part of engineering education today. Development of team skills is now a part of the curriculum at universities as employers demand these skills on graduates. Higher education institutions enforce academic staff to teach, practise and assess team skills, and at the same time, they ask academic staff to supply individual marks and/or grades. Allocating individual marks from a team mark is a very complex and sensitive task that may adversely affect both individual and team performance. A number of both qualitative and quantitative methods are available to address this issue. Quantitative mathematical methods are favoured over qualitative subjective methods as they are more straightforward to explain to the students and they may help minimise conflicts between assessors and students. PURPOSE : This study presents a review of commonly used mathematical equations to allocate individual marks from a team mark. Quantitative analytical equations are favoured over qualitative subjective methods because they are more straightforward to explain to the students and if explained to the students in advance, they may help minimise conflicts between assessors and students. Some of these analytical equations focus primarily on the assessment of the quality of teamwork product (product assessment) while the others put greater emphasis on the assessment of teamwork performance (process assessment). The remaining equations try to strike a balance between product assessment and process assessment. The primary purpose of this study is to discuss the qualitative aspects of quantitative equations. DESIGN/METHOD : This study simulates a set of scenarios of team marks and individual contributions that collectively cover all possible teamwork assessment environments. The available analytical equations are then applied to each case to examine their relative merits with respect to a set of evaluation criteria with exhaustive graphical plots. RESULTS : Although each analytical equations discussed and analysed in this study has its own merits for a particular application scenario, the recent methods such as knee formula in SPARKPLUS and cap formula, are relatively better in terms of a number of evaluation criteria such as fairness, teamwork attitude, balance between process and product assessments etc. In addition to having all favourable properties of knee formula, cap formula explicitly considers the quality of teamwork (i.e., team mark) while allocating individual marks. Cap formula may, however, be difficult to explain to the students due to relatively complex mathematical equations involved. CONCLUSIONS : Not all existing analytical equations that allocate individual marks from a team mark have similar characteristics. Recent methods, knee formula and cap formula, are advantageous in terms of a number of evaluation criteria and are recommended to apply in practice. However, it is important to examine these equations with respect to enhancing students’ learning achievements rather than the students and academic staff’s preferences.