A General Vehicle Routing Problem

In this paper, we study a rich vehicle routing problem incorporating various complexities found in real-life applications. The General Vehicle Routing Problem (GVRP) is a combined load acceptance and generalised vehicle routing problem. Among the real-life requirements are time window restrictions, a heterogeneous vehicle fleet with different travel times, travel costs and capacity, multi-dimensional capacity constraints, order/vehicle compatibility constraints, orders with multiple pickup, delivery and service locations, different start and end locations for vehicles, and route restrictions for vehicles. The GVRP is highly constrained and the search space is likely to contain many solutions such that it is impossible to go from one solution to another using a single neighbourhood structure. Therefore, we propose iterative improvement approaches based on the idea of changing the neighbourhood structure during the search.     

On quantitative aspects of the unit sum number problem

We investigate the function u _K,S (n; q) which counts the number of representations of algebraic integers α with |N_{K/\mathbb Q}(a)| ￡ q{|N_{K/{\mathbb Q}}(\alpha)| \leq q} for some real positive q that can be written as sums of exactly n S-units of the number field K.     

Elaborate treatment of retention in chemoselective chromatography—The retention increment approach and non-linear effects

The retention increment approach is described which quantifies the association equilibria of a selectand and a selector in complexation and inclusion chromatography. A thermodynamic treatment of enantioselectivity based on retention phenomena in chromatography including entropy/enthalpy compensation and the isoenantioselective temperature is advanced. Kinetic parameters of enantiomerization are discussed. Non-linear effects, both existent and elusive, are described and proposed, respectively. The enantioselectivity pertaining to catalysis vs. chromatography is compared and a unified nomenclature is proposed. Through an educational effort, this account is aimed at providing a deeper insight into chemoselective aspects of chromatography thereby stimulating further research of both established and speculative phenomena of the most intriguing manifestation of chemoselectivity, that is, of enantioselectivity.     

On the Conformation of a Sterically Congested Amide Group in the Crystalline State and in Solution

The conformation in the crystalline state and in solution of the sterically congested tetramethylpiperidinederived amide group of the symmetric diamide I formed from 2,2,6,6-tetramethylpiperidine ( b ) and 1,2,5-thiadiazole-3,4-dicarbonyl dichloride ( c ), and of the mixed diamide II derived from b , c , and piperidine ( a ) has been investigated. In crystals, as observed with II , this group is strongly bent out-of-plane at both the N-atom and the carbonyl C-atom, and there is also a sizable twisting around the amide bond. Furthermore, the amide bond is abnormally long (1.37 Å). In CD₂Cl₂ (or CDCl₃) solution, the group is apparently planar in its ground-state conformation, but the energy barrier to rotation around the amide bond is low. This conclusion is based on low-temperature ¹H-NMR measurements on I , II , and on the symmetric diamide III derived from a and c .