Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

The comparative characterization of structural heterogeneity of mesoporous activated carbon fibers (ACFs)

The comparative analysis of the most widely used methods of mesoporosity characterization of two activated carbon fibers is presented. Not only the older methods are used, i.e. Barrett, Joyner and Halenda (BJH), Dubinin (the so-called first variant-D-1ST and the so-called second variant-D-2ND), Dollimore and Heal (DH), and Pierce (P) but the recently developed ones, i.e. the method of Nguyen and Do (ND) and that developed by Do (Do) are also applied. Additionally, the method of the characterization of fractality is put to use (fractal analog of FHH isotherm). The results are compared and discussed. (C) 2002 Elsevier Science B.V. All fights reserved.

Cadence, war and security

An increased incidence of attack has been identified as a major characteristic of the new threat posed by terrorist groups such as al Qaeda. This article considers what such a change means for Western national security systems by examining bow different parts of the system change over time. It becomes evident that Western national security systems are structured on an assumption of comparatively slow state-based threats. In contrast, terrorist franchises operate at a faster pace, are more 'lightweight' and can adapt within the operational and capability cycles of Western governments. Neither network-centric warfare nor an improved assessment of the threat, called for by some, offers a panacea in this regard. Rather, it is clear that not only do Western governments need to adjust their operational and capability cycles, but that they also need a greater diversity of responses to increase overall national security resilience and offer more tools for policy-makers.

Changes in the properties of a Vertisol and responses of wheat after compaction with harvester traffic

Soil compaction has been recognised as the greatest problem in terms of damage to Australia's soil resource. Compaction by tractor and harvester tyres, related to trafficking of wet soil, is one source of the problem. In this paper an array of soil properties was measured before and immediately after the application of a known compaction force to a wet Vertisol, A local grain harvester was used on soil that was just trafficable; a common scenario at harvest. The primary aim was to determine the changes in various soil properties in order to provide a benchmark against which the effectiveness of future remedial treatments could be evaluated. A secondary aim was a comparison of the measurements' efficiency to assess a soil's structural degradation status. Also assessed was the subsequent effect of the applied compaction on wheat growth and yield in the following cropping season. Nine of the soil properties measured gave statistically significant differences as a result of the soil compaction. Differences were mostly restricted to the top 0.2 m of the soil. The greatest measured depth of effect was decreased soil porosity to 0.4 m measured from intact soil clods. There was 72% emergence of the wheat crop planted into the compact soil and 93% in the uncompact soil. Wheat yield, however, was not affected by the compaction. This may demonstrate that wheat, growing on a full profile of stored soil water as did the current crop, may be little affected by compaction, Also, wheat may have potential to facilitate rapid repair of the damage in a Vertisol such as the current soil by drying the topsoil between rainfall events so increasing shrinking and swelling cycles. If this is true, then sowing a suitable crop species in a Vertisol may be a better option than tillage for repairing compaction damage by agricultural traffic. (C) 2000 Elsevier Science B.V. All rights reserved.