Scheduling for parallel dedicated machines with a single server

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is NP-hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst-case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two-machine flow shop and the open shop problems with a single server are also shown to be NP-hard in the strong sense. However, we reduce the two-machine flow shop no-wait problem with a single server to the Gilmore-Gomory traveling salesman problem and solve it in polynomial time. (c) 2000 John Wiley & Sons, Inc.

Fictitious toponyms in the responsa: Bashan's ruleset revisited

Fictitious personal names and toponyms are not infrequent in legal casenotes as used for didactic purposes nowadays. There is a long tradition of fictitious names being used in the legal literature. The problem with medieval or early modern legal (here, rabbinical) responsa is that if they are used as evidence for historical purposes, as though they were chronicles, confusion may occurs. Historian Eliezer Bashan showed that this is the case, indeed, with particular reference to rabbinical responsa from the Ottoman empire where Holy Land toponyms occur. He set forth several tentative rules to decide whether a toponym is there to literally refer to the place it names, or whether, instead, the name is used fictitiously. This paper formalizes the ruleset.

X-ray crystallographic structures of two lamotrigine analogues: (I) 3,5-diamino-6-(2-chlorophenyl)-1,2,4-triazine water solvate and (II) 3,5-diamino-6-(3,6-dichlorophenyl)-1,2,4-triazine methanol solvate

The X-ray crystal structures of two lamotrigine derivatives (I) 3,5-diamino-6-(2-chlorophenyl)-1,2,4-triazine, C9H8ClN5, (465BL) as a hydrate, and (II) 3,5-diamino-6-(3,6-dichlorophenyl)-1,2,4-triazine, C9H7Cl2N5, (469BR) as a methanol solvate, have been carried out at liquid nitrogen temperature and room temperature, respectively. A detailed comparison of the two structures is given. Both are centrosymmetric with (I) in the orthorhombic space group Pbca, a = 12.2507(3), b = 15.7160(6), c = 21.71496(9) angstrom, Z = 16, and (II) in the monoclinic space group C2/c, a = 38.553(3), b = 4.9586(2), c = 14.546(2) angstrom, beta = 111.59(1)degrees, Z = 8. Final R indices [I > 2sigma(I)] for (I) are R1 = 0.0670, wR2 = 0.1515 and for (II) R1 = 0.0434, wR2 = 0.1185. Structure (I) has water of crystallization in the lattice and (II) includes a solvated CH3OH. Structure (I) is characterized by having two crystallographically independent molecules, A and B, of 465BL, per asymmetric unit. Molecule B has a very unusual feature in that the 2-chlorophenyl ring is statistically disordered, occupying site (1) in 87.5% of the structure and site (2) in 12.5% of the structure. Sites (1) and (2) are related by an exact 180 degrees pivot of the phenyl ring about the ring linkage bond. The presence of two independent molecules per asymmetric unit provides an ideal opportunity for the conformational flexibility of the molecule 465BL to be studied. Structure (I) also includes a further unusual feature in that the lattice contains one fully occupied water molecule and an additional solvated water which is only 33% occupied.