The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches

In this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities that are open need not be the same in different time periods. It is also assumed that at each period there is a minimum number of customers that can be assigned to the facilities that are open. The decisions to be made include not only the facilities to open at each time period and the time period in which each customer will be served, but also the allocation of customers to open facilities in their service period.     

Extensive facility location problems on networks: an updated review

Location problems with extensive facilities represent a challenging field of research. According to the specialized literature, a facility is called extensive if, for purposes of location, it is too large in relation to its environment to be considered a point. There are many examples of this type of structures that appear in real-world applications both in the continuous space (straight lines, circles, strips) and in networks (paths, cycles, trees). There exists a recent literature review on the location of dimensional facilities on continuous space (Díaz-Báñez et al. in TOP 154:22–44, 2004; Schöbel in Location of dimensional facilities in a continuous space, 2015) that does not cover similar problems on networks. The goal of this paper is to review the location of dimensional facilities in networks. We mainly concentrate on the location of paths and trees considering the most common objective functions in the location literature, namely median and center. However, we also consider some other alternative criteria generalizing them, as the ordered median objective function, or related to equity, reliability, and robustness. We include the basic tools and techniques that are applicable to develop algorithms for this kind of problems. Moreover, we present the best known complexity results for each of the considered problems. Finally, some suggestions are also made for possible directions of future research.     

1‐(6‐Amino‐1,3‐benzodioxol‐5‐yl)‐3‐(2‐oxo‐1,2‐dihydroquinolin‐3‐yl)prop‐2‐enone: a sheet built by π‐stacking of hydrogen‐bonded chains of rings

The bond distances in the molecule of the title compound, C₁₉H₁₄N₂O₄, provide evidence for electronic polarization in the aminoarylpropenone fragment and for bond fixation in the quinolinone unit. Molecules are linked by N—H...O and C—H...O hydrogen bonds into chains in which centrosymmetric rings of R₂²(8) and R₂²(18) types alternate, and these chains are linked into sheets by a single aromatic π–π stacking interaction.     

1‐(2‐Aminophenyl)‐3‐(4‐pyridyl)prop‐2‐en‐1‐one: a three‐dimensional framework structure built from N—H...N,C—H...O and C—H...π(arene) hydrogen bonds

The intramolecular dimensions of the title compound, C₁₄H₁₂N₂O, provide evidence for a polarized electronic structure. The molecule, which is almost completely planar, contains an intramolecular N—H...O hydrogen bond, and the molecules are linked by a combination of N—H...N, C—H...O and C—H...π(arene) hydrogen bonds to form a three‐dimensional framework structure.     

(E)‐N‐{[6‐Chloro‐4‐(4‐chlorophenyl)‐3‐methyl‐1‐phenyl‐1H‐pyrazolo[3,4‐b]pyridin‐5‐yl]methylene}benzene‐1,2‐diamine: a three‐dimensional framework structure built from only two hydrogen bonds

The molecules of the title compound, C₂₆H₁₉Cl₂N₅, are conformationally chiral, with none of the aryl groups coplanar with the pyrazolo[3,4‐b]pyridine core of the molecule. A single unique N—H...N hydrogen bond links the molecules into two symmetry‐related sets of C(11) chains running parallel to the [011] and [01] directions, respectively, and these two sets of chains are linked into a continuous three‐dimensional framework structure by a single unique C—H...N hydrogen bond which forms a chain parallel to the [100] direction.     

4‐Hydroxy‐2‐vinyl‐2,3,4,5‐tetrahydro‐1‐benzazepine and its 7‐fluoro and 7‐chloro analogues are isomorphous but not strictly isostructural

4‐Hydroxy‐2‐vinyl‐2,3,4,5‐tetrahydro‐1‐benzazepine, C₁₂H₁₅NO, (I), and its 7‐fluoro and 7‐chloro analogues, namely 7‐fluoro‐4‐hydroxy‐2‐vinyl‐2,3,4,5‐tetrahydro‐1‐benzazepine, C₁₂H₁₄FNO, (II), and 7‐chloro‐4‐hydroxy‐2‐vinyl‐2,3,4,5‐tetrahydro‐1‐benzazepine, C₁₂H₁₄ClNO, (III), are isomorphous, but with variations in the unit‐cell dimensions which preclude in compound (III) one of the weaker intermolecular interactions found in compounds (I) and (II). Thus the compounds are not strictly isostructural in terms of the structurally significant intermolecular interactions, although the corresponding atomic coordinates are very similar. The azepine rings adopt chair conformations. The molecules are linked by a combination of N—H...O and O—H...N hydrogen bonds into chains of edge‐fused R³₃(10) rings, which in compounds (I) and (II) are further linked into sheets by a single C—H...π(arene) hydrogen bond. The significance of this study lies in its observation of isomorphism in compounds (I)–(III), and its observation of a sufficient variation in one of the cell dimensions effectively to alter the range of significant hydrogen bonds present in the crystal structures.     

Direct determination of 226Ra in NORM/TENORM matrices by gamma-spectrometry

Summary The main shortcoming with the procedure to determine ²²⁶Ra in a gamma spectrum of an environmental sample by means of the ²¹⁴Bi and ²¹⁴Pb photopeaks is the likelihood of ²²²Rn leakage from the sample counting vial. An option to make such determination is to disregard the ²²⁶Ra gamma-contributions to the spectrum, other than 186.2 keV (3.5%), subtracting the ²³⁵U contribution to the ²²⁶Ra+²³⁵U peak at 186 keV. The use of this option to determine directly ²²⁶Ra activity concentrations in environmental samples and in NORM/TENORM matrices will be presented and discussed.     

Redetermination of 6‐amino‐5‐formyl‐1,3‐dimethyluracil monohydrate at 120 K: a polarized molecular structure and two interwoven hydrogen‐bonded frameworks

The title compound [systematic name: 6‐amino‐5‐formyl‐1,3‐dimethylpyrimidine‐2,4(1H,3H)‐dione monohydrate], C₇H₉N₃O₃·H₂O, has been reexamined at 120 K. The improved precision of the intramolecular dimensions provides evidence for a polarized molecular–electronic structure, and the molecular components are linked by one N—H...O and two O—H...O hydrogen bonds into two interwoven three‐dimensional frameworks, which are weakly linked by the longer component of a three‐centre N—H...(O)₂ hydrogen bond.