Steiner trade spectra of complete partite graphs

The Steiner trade spectrum of a simple graph G is the set of all integers t for which there is a simple graph H whose edges can be partitioned into t copies of G in two entirely different ways. The Steiner trade spectra of complete partite graphs were determined in all but a few cases in a recent paper by Billington and Hoffman (Discrete Math. 250 (2002) 23). In this paper we resolve the remaining cases. (C) 2004 Elsevier B.V. All rights reserved.

1H-1,3-Diazepines, 5H-1,3-diazepines, 1,3-diazepinones, and 2,4-diazabicyclo[3.2.0]heptenes

Tetrazolo[1,5-a] pyridines/ 2-azidopyridines 1 undergo photochemical nitrogen elimination and ring expansion to 1,3-diazacyclohepta-1,2,4,6-tetraenes 3, which react with alcohols to afford 2-alkoxy-1H-1,3-diazepines 4 (5), with secondary amines to 2-dialkylamino-5H-1,3-diazepines 16, sometimes via isolable 2-dialkylamino-1H-1,3-diazepines 15, and with water to 1,3-diazepin-2-ones 19. The latter are also obtained by elimination of isobutene or propene from 2-tert-butoxy- or 2-isopropoxy-1H-1,3-diazepines 4 or 5. 1,3-Diazepin-2-one 22B and 1,3-diazepin-4-one 24 were obtained from hydrolysis of the corresponding 4-chlorodiazepines. Diazepinones 19 undergo photochemical ring closure to diazabicycloheptenones 25 in high yields. The 2-alkoxy-1H-1,3-diazepines 4 and 5 interconvert by rapid proton exchange between positions N1 and N3. The free energies of activation for the proton exchange were measured by the Forsen - Hoffman method as DeltaGdouble dagger(298) = 16.2 +/- 0.6 kcal mol(-1) as an average for 4a - c in CD2Cl2, acetone-d(6), and methanol-d(4), and 14.1 +/- 0.6 kcal mol(-1) for 4c in acetone/D2O. The structures of 2-methoxy-5,6-bis( trifluoromethyl)-1H-1,3-diazepine 4k, 1,2-dihydro-4-diethylamino-5H-1,3-diazepin-2-one 22bB, and diazabicycloheptanone 26 were determined by X-ray crystallography. The former represents the first reported X-ray crystal structure of any monocyclic N-unsubstituted 1H-azepine.

Use of the Vector (TM) scaling unit in supportive periodontal therapy: a subjective patient evaluation

Background: Patient discomfort is one reason for poor compliance with supportive periodontal therapy (SPT). The aim of this study was to compare the levels of discomfort during SPT, using the Vector (TM) system and treatment with a conventional ultrasonic scaler. Methods: Forty-six patients with an SPT programme were debrided using both the Vector (TM) system and a conventional piezo-electric scaler (Sirona (TM)) in a split mouth design. A visual analogue scale was used to evaluate of pain scores upon completion of treatment. A verbal response scale(VRS) was used to assess discomfort, vibration and noise associated with the scaling system, as well as the volume and taste of the coolant used by these systems. Results: Patients instrumented with the Vector (TM) system experienced approximately half the amount of pain compared with the conventional ultrasonic scaling system. The VRS showed that the Vector (TM) system caused less discomfort than the conventional ultrasonic scaling system when assessed for pain, vibration, noise and volume of coolant. These findings were all statistically significant. There was, however, no statistically significant difference between the two systems when assessed for taste. Conclusion: During SPT the Vector (TM) system caused reduced discomforting sensations compared with conventional methods and may be useful in improving compliance with SPT programmes.

Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.

Tool support for executable documentation of Java class hierarchies

While object-oriented programming offers great solutions for today's software developers, this success has created difficult problems in class documentation and testing. In Java, two tools provide assistance: Javadoc allows class interface documentation to be embedded as code comments and JUnit supports unit testing by providing assert constructs and a test framework. This paper describes JUnitDoc, an integration of Javadoc and JUnit, which provides better support for class documentation and testing. With JUnitDoc, test cases are embedded in Javadoc comments and used as both examples for documentation and test cases for quality assurance. JUnitDoc extracts the test cases for use in HTML files serving as class documentation and in JUnit drivers for class testing. To address the difficult problem of testing inheritance hierarchies, JUnitDoc provides a novel solution in the form of a parallel test hierarchy. A small controlled experiment compares the readability of JUnitDoc documentation to formal documentation written in Object-Z. Copyright (c) 2005 John Wiley & Sons, Ltd.

Tool support for generating passive C++ test oracles from object-z specifications

A test oracle provides a means for determining whether an implementation behaves according to its specification. A passive test oracle checks that the correct behaviour has been implemented, but does not implement the behaviour itself. In previous work, we have presented a method that allows us to derive passive C++ test oracles from formal specifications written in Object-Z. We describe the "Warlock" prototype tool that supports the method. Warlock is built on top of an existing Object-Z type checker and generates oracle code for a substantial subset of the Object-Z language. We describe the architecture of Warlock and its application to a number of Object-Z specifications. We also discuss its current limitations.