The open shop scheduling problem with a given sequence of jobs on one machine

The paper considers the open shop scheduling problem to minimize the make-span, provided that one of the machines has to process the jobs according to a given sequence. We show that in the preemptive case the problem is polynomially solvable for an arbitrary number of machines. If preemption is not allowed, the problem is NP-hard in the strong sense if the number of machines is variable, and is NP-hard in the ordinary sense in the case of two machines. For the latter case we give a heuristic algorithm that runs in linear time and produces a schedule with the makespan that is at most 5/4 times the optimal value. We also show that the two-machine problem in the nonpreemptive case is solvable in pseudopolynomial time by a dynamic programming algorithm, and that the algorithm can be converted into a fully polynomial approximation scheme. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 705–731, 1998

[Book Review] Vardah Shiloh, Millon 'Ivri-'Arami-'Aššuri bs-Lahag Yihude Zaxo (A New Neo-Aramaic Dictionary: Jewish Dialect of Zakho). Volume I: 'alef—nun\ Volume II: samex-tav. V. Shilo (16 Ben-Gamla Street), Jerusalem 1995. Pp. xiv + 488 (Vol. I); 489-963 (Vol. II). (Modern Hebrew, Zakho Jewish Neo-Aramaic).

Review of: Vardah Shiloh, Millon 'Ivri-'Arami-'Aššuri bs-Lahag Yihude Zaxo (A New Neo-Aramaic Dictionary: Jewish Dialect of Zakho). Volume I: 'alef—nun\ Volume II: samex-tav. V. Shilo (16 Ben-Gamla Street), Jerusalem 1995. Pp. xiv + 488 (Vol. I); 489-963 (Vol. II). (Modern Hebrew, Zakho Jewish Neo-Aramaic). Hbk.

Identification and doing without it, V: A formal mathematical analysis for a case of mix-up of individuals, and of recovery from failure to attain identification

Identification, when sought, is not necessarily obtained. Operational guidance that is normatively acceptable may be necessary for such cases. We proceed to formalize and illustrate modes of exchanges of individual identity, and provide procedures of recovery strategies in specific prescriptions from an ancient body of law for such situations when, for given types of purposes, individuals of some relevant kind had become intermixed and were undistinguishable. Rules were devised, in a variety of domains, for coping with situations that occur if and when the goal of identification was frustrated. We propose or discuss mathematical representations of such recovery procedures.

[Book review] Piero della Francesca: A Mathematician's art by J.V. Field, Yale University Press.

Review of the book 'Piero della Francesca: A Mathematician’s Art' by J.V. Field, Yale University Press, 420 pp, £35 ISBN 0300103425.

Joint ownership and beneficial entitlement: Stack v Dowden.

Explores the issue of the share of beneficial entitlement to the family home where the legal title is jointly owned, but where there has not been an express declaration of a beneficial joint tenancy. Discusses the House of Lords judgment in Stack v Dowden which addressed this point. Explains how the judges moved the focus away from the court imposing its own sense of fairness on the parties or imputing an intention based on the circumstances to one where the concentration will be on the parties' relevant conduct. Outlines three other points of interest referred to in the judgment: (1) whether an indirect financial contribution could support a constructive trust; (2) whether proprietary estoppel and common intention constructive trusts should be assimilated; and (3) whether a mortgage liability is equivalent to a financial contribution.

Jackson v JH Watson Property Investment Ltd.

Comments on the Chancery Division decision in Jackson v JH Watson Property Investment Ltd on whether a landlord was liable in nuisance to a long leaseholder in respect of damage caused to the demised property by a building defect which pre-dated the grant of the lease or whether the principle of caveat lessee applied. Considers whether the defect amounted to "disrepair" within the meaning of the landlord's repairing covenant.

Horsham Properties Group Ltd v Clark: possession - mortgagee's right or discretionary remedy?

Comments on the Chancery Division decision in Horsham Properties Group Ltd v Clark on whether a mortgagee's exercise of its contractual right, on the mortgagor falling into arrears, to appoint receivers such that the property could be sold and possession obtained without triggering the court's discretionary powers pursuant to the Administration of Justice Act 1970 s.36 infringed the mortgagor's rights under the European Convention on Human Rights 1950 Protocol 1 art.1. Considers the implications of proposed reforms recasting the mortgagee's right to possession as a discretionary remedy. [From Legal Journals Index]

Marginal adaptation and performance of bioactive dental restorative materials in deciduous and young permanent teeth

Objective: The aim of this study was to investigate the adaptation of different types of restorations towards deciduous and young permanent teeth. Materials and Methods: Class V cavities were prepared in deciduous and young permanent teeth and filled with different materials (a conventional glass-ionomer, a resin-modified glass-ionomer, a poly-acid-modified composite resin and a conventional composite resin). Specimens were aged in artificial saliva for 1, 6, 12 and 18 months, then examined by SEM. Results: The composite resin and the polyacid-modified composite had better marginal adaptation than the glass-ionomers,though microcracks developed in the enamel of the tooth. The glass-ionomers showed inferior marginal quality and durability, but no microcracking of the enamel. The margins of the resin-modified glass-ionomer were slightly superior to the conventional glass-ionomer. Conditioning improved the adaptation of the composite resin, but the type of tooth made little or no difference to the performance of the restorative material. All materials were associated with the formation of crystals in the gaps between the filling and the tooth; the quantity and shape of these crystals varied with the material. Conclusions: Resin-based materials are generally better at forming sound, durable margins in deciduous and young permanent teeth than cements, but are associated with microcracks in the enamel. All fluoride-releasing materials give rise to crystalline deposits.