Difference Sturm–Liouville problems in the imaginary direction

The Quasi-Normal Direction (QND) Method: An Efficient Method for Finding the Pareto Frontier in Multi-Objective Optimization Problems

In managerial and economic applications, there appear problems in which the goal is to simultaneously optimize several criteria functions (CFs). However, since the CFs are in conflict with each other in such cases, there is not a feasible point available at which all CFs could be optimized simultaneously. Thus, in such cases, a set of points, referred to as 'non-dominate' points (NDPs), will be...

Difference Problems and Differential Problems

We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a significant contribution to the understanding of the foundations of differential and integral calculus. AMS subject classification: 14A25, 39A12, 39A13, 46S10...

Regularized Discriminative Direction for Shape Difference Analysis

The "discriminative direction" has been proven useful to reveal the subtle difference between two anatomical shape classes. When a shape moves along this direction, its deformation will best manifest the class difference detected by a kernel classifier. However, we observe that such a direction cannot maintain a shape's "anatomical" correctness, introducing spurious difference. To overcome this...

Significant Error Propagation in the Finite Difference Solution of Non-Linear Magnetostatic Problems Utilizing Boundary Condition of the Third Kind

This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite di...

The Class of Functions Convex in the Negative Direction of the Imaginary Axis of Order (α,β)