Optimization of the Ambulance Fleet Location and Relocation

Journal of Applied and Industrial Mathematics - We study the problem of optimal location of the ambulance fleet at the base stations. The objective is to minimize the average waiting time for...     

Special Issue: 18th International conference on mathematical optimization theory and operations research (MOTOR 2019)

Journal of Global Optimization -     

Gradings on Modules Over Lie Algebras of E Types

For any grading by an abelian group G on the exceptional simple Lie algebra \(\mathcal {L}\) of type E ₆ or E ₇ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple finite-dimensional modules, thus completing the computation of these invariants for simple finite-dimensional Lie algebras. This yields the classification of finite-dimensional G-graded simple \(\mathcal {L}\)-modules, as well as necessary and sufficient conditions for a finite-dimensional \(\mathcal {L}\)-module to admit a G-grading compatible with the given G-grading on \(\mathcal {L}\).     

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.     

Study of the glow discharge in inert gases with water vapor

The behavior of the water vapor concentrations and fragments in wet plasma is studied. The results of plasma-chemical modeling are compared with the results of direct measurements of water molecule dissociation in plasma.     

Ionization process in the humid air of the lower troposphere

This paper analyzes the local processes of ionization and electron loss in the early stages of an electric discharge in humid air at altitudes of 0–12 km. The processes of ionization in an external electric field, background ionization, attachment and detachment of electrons from atomic and molecular oxygen, charge transfer, and the conversion of negative ions are considered. The dependences of the rate constants on the pressure are taken into account. It is shown that the electric field strength at which the effective ionization of air begins decreases with increasing altitude.     

Identifying Symmetry Classes of Elasticity Tensors Using Monoclinic Distance Function

We present a method to identify the symmetry class of an elasticity tensor whose components are given with respect to an arbitrarily oriented coordinate system. The method is based on the concept of distance in the space of tensors, and relies on the monoclinic or transversely isotropic distance function. Since the orientation of a monoclinic or transversely isotropic tensor depends on two Euler angles only, we can plot the corresponding distance functions on the unit sphere in ℝ³ and observe the symmetry pattern of the plot. In particular, the monoclinic distance function vanishes in the directions of the normals of the mirror planes, so the number and location of the zeros allows us to identify the symmetry class and the orientation of the natural coordinate system. Observing the approximate locations of the zeros on the plot, we can constrain a numerical algorithm for finding the exact orientation of the natural coordinate system.     

Complexity of local search for the p-median problem

We study the complexity of finding local minima for the p-median problem. The relationship between Swap local optima, 0–1 local saddle points, and classical Karush–Kuhn–Tucker conditions is presented. It is shown that the local search problems with some neighborhoods are tight PLS-complete. Moreover, the standard local descent algorithm takes exponential number of iterations in the worst case regardless of the tie-breaking and pivoting rules used. To illustrate this property, we present a family of instances where some local minima may be hard to find. Computational results with different pivoting rules for random and Euclidean test instances are discussed. These empirical results show that the standard local descent algorithm is polynomial in average for some pivoting rules.