We first introduce a generic model for discrete cost multicommodity network optimization, together with several variants relevant to telecommunication networks such as: the case where discrete node cost functions (accounting for switching equipment) have to be included in the objective; the case where survivability constraints with respect to single-link and/or single-node failure have to be ta...

The weekly maintenance schedule specifies when maintenance activities should be performed on the equipment, taking into account the availability of workers and maintenance bays, and other operational constraints. The current approach to generating this schedule is labour intensive and requires coordination between the maintenance schedulers and operations staff to minimise its impact on the ope...

The purpose of this paper is to solve the 0-1 k-item quadratic knapsack problem (kQKP ), a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we st...

Exact numerical methods and stochastic simulation methods are developed to study the force stretching single RNA issue on the secondary structure level in equilibrium. By computing the force-extension curves on the constant force and the constant extension ensembles, we find the two independent methods agree with each other quite well. To show the precision of our methods in predicting unfoldin...

Expanding upon an observation of Hou [Math. Comp., submitted], exact desingularizations are presented of the Euler equations in two and three dimensions for which the singularity within the Biot-Savart integrand is reduced by one order. The reformulated equations are then solved numerically using either the point vortex method or the vortex blob method. The increased smoothness of the Biot-Sava...

This paper points out that the treatment of utility maximization in current textbooks on microeconomic theory is deficient in at least three respects: breadth of coverage, completeness-cumcoherence of solution methods and mathematical correctness. Improvements are suggested in the form of a Kuhn-Tucker type theorem that has been customized for microeconomics. The role of the domain of different...

Statistical parameters of Ivan Franko's novel Perekhresni stežky (The Cross-Paths) 39 Solomija Buk and Andrij Rovenchak Some remarks on the generalized Hermite and generalized Gegen-bauer probability distributions and their applications 49 Mario Cortina-Borja New approaches to cluster analysis of typological indices 61 Michael Cysouw

The mathematical method of fractional or continuous iteration can be used to model a dynamical system exactly from limited experimental data. However, mathematics is complicated and exact solutions even if proven to exist can rarely be found analytically. We have shown previously that neural networks can be utilized to numerically compute fractional iterates of mathematical functions. In this p...

A vital task facing government agencies and commercial organizations that report data is to represent the data in a meaningful way and simultaneously to protect the confidentiality of critical components of this data. The challenge is to organize and disseminate data in a form that prevents such critical components from being inferred by groups bent on corporate espionage, to gain competitive a...