Further results on nearly Kirkman triple systems with subsystems

AbstractIn this paper we further discuss the embedding problem for nearly Kirkman triple systems and get the result that: (1) For u≡v≡0(mod6), v⩾78, and u⩾3.5v, there exists an NKTS(u) containing a sub-NKTS(v). (2) For v=18,24,30,36,42,48,54,60,66 or 72, there exists an NKTS(u) containing a sub-NKTS(v) if and only if u≡0(mod6) and u⩾3v

On the minisymposium problem

The generalized Oberwolfach problem asks for a factorization of the complete graph $K_v$ into prescribed $2$-factors and at most a $1$-factor. When all $2$-factors are pairwise isomorphic and $v$ is odd, we have the classic Oberwolfach problem, which was originally stated as a seating problem: given $v$ attendees at a conference with $t$ circular tables such that the $i$th table seats $a_i$ people and ${\sum_{i=1}^t a_i = v}$, find a seating arrangement over the $\frac{v-1}{2}$ days of the conference, so that every person sits next to each other person exactly once. In this paper we introduce the related {\em minisymposium problem}, which requires a solution to the generalized Oberwolfach problem on $v$ vertices that contains a subsystem on $m$ vertices. That is, the decomposition restricted to the required $m$ vertices is a solution to the generalized Oberwolfach problem on $m$ vertices. In the seating context above, the larger conference contains a minisymposium of $m$ participants, and we also require that pairs of these $m$ participants be seated next to each other for $\left\lfloor\frac{m-1}{2}\right\rfloor$ of the days. When the cycles are as long as possible, i.e.\ $v$, $m$ and $v-m$, a flexible method of Hilton and Johnson provides a solution. We use this result to provide further solutions when $v \equiv m \equiv 2 \pmod 4$ and all cycle lengths are even. In addition, we provide extensive results in the case where all cycle lengths are equal to $k$, solving all cases when $m\mid v$, except possibly when $k$ is odd and $v$ is even.Comment: 25 page

Computing the chromatic number of t-(v,k,[lambda]) designs

Colouring t-designs has previously been shown to be an NP-complete problem; heuristics and a practical algorithm for this problem were developed for this thesis; the algorithm was then employed to find the chromatic numbers of the sixteen non- isomorphic 2-(25, 4, 1) designs and the four cyclic 2-(19, 3, 1) designs. This thesis additionally examines the existing literature on colouring and finding chromatic numbers of t-designs

Combinatorial designs and their automorphism groups

This thesis concerns the automorphism groups of Steiner triple systems and of cycle systems. Although most Steiner triple systems have trivial automorphism groups [2], it is widely known that for every abstract group, there exists a Steiner triple system whose automorphism is isomorphic to that group [16]. The well-known Bose construction [4] for Steiner triple systems, which has a number of variants, has a particularly nice structure, which makes it possible to say much about the automorphism group, and in the case of the construction based on an Abelian group, to derive the full automorphism group. The thesis contains a full analysis of these matters. Some of these results have been published by the author in [14]. The thesis also proves new results concerning the automorphism group for Steiner triple systems constructed using the tripling construction. An m-cycle system is a decomposition of a complete graph into cycles of length m. A Steiner triple system is thus a 3-cycle system. The thesis proves the result that for all m > 3, and for each abstract finite group, there exists an m-cycle system whose automorphism group is isomorphic to that group. In addition, the thesis contains a collection of new results concerning the conjecture by Furedi that every Steiner triple system is decomposable into triangles. Although this conjecture is expected to remain open for some time, it is possible to prove it for a number of standard constructions. It is further shown that for sufficiently large v, the number of Steiner triple systems of order v that are decomposable into triangles is at least vv2(1/54-0(1))

A study of low cost approaches to scientific experiment implementation for shuttle launched and serviced automated spacecraft

Cost reductions that can be obtained in experiment instrumentation by the use of standardized electronics and by the relaxation of instrument reliability requirements are studied. The feasibility of using standardized equipment for experiment instrumentation is assessed and a system design approach that most effectively incorporates standardized equipment is developed. The level and form of modularization that is appropriate for the standardized equipment is determined. Mission assurance aspects of instrument development are examined to determine the cost reductions that might be derived from the relaxation of reliability requirements and to formulate a systematic approach to the optimization of mission assurance cost reductions. The results of the analyses are applied to a representative model HEAO payload in order to provide a concrete example of the cost reductions that can be achieved by a standardized approach to the instrument electronics

Sustainable Development: The Nature of Change and the Influence of Cultural Traits

It is only in the last few years that researchers have started to investigate the impact of cultural characteristics on the approach nations take to addressing the demands of sustainable development. The basis of such work tends to resort to the use of frameworks that were developed by Hofstede and the GLOBE project. Rogge, Dessein, and and Verhoeve (2013) argue that research into subjects as complex as this should commence with work of a more exploratory nature. This thesis is multidisciplinary, and uses a variety of methods to provide that first exploration into the nature of this relationship. My review of literature reveals that there is general acceptance that paradigmatic change is necessary but that decision making, behaviour and politics all tend to “safer” incremental steps. Using systems theory to examine the nature of paradigm change I identify the potential scope of government influence. The remainder of my work concentrates on the development of case studies of Japan, Denmark, Sweden and the United Kingdom, focussing on the manner in which the governments concerned support small to medium sized enterprises (SMEs) within the country in developing more sustainable practices. I use these case studies to identify the impact of culture. I find that the cultural dimension as defined in classic frameworks is not the pertinent issue, but the nation is likely to be sensitive to environmental demands if the environmental damage impinges on areas of their life that they value. If there are characteristics within the nation that provide for care and support then action is more likely to be taken. The other characteristics necessary to see through financing such action are perserverence and a long-term view. My other finding is that the use of statistical analysis and frameworks of cultural characteristics is problematic in that they both simplify a subject that should be understood in all its complexity