The extended metamorphosis of a complete bipartite design into a cycle system

A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.

The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

Certain Roman and flock generalized quadrangles have nonisomorphic elation groups

We prove that the elation groups of a certain infinite family of Roman generalized quadrangles are not isomorphic to those of associated flock generalized quadrangles.

Alpha-selenoconotoxins, a new class of potent alpha(7) neuronal nicotinic receptor antagonists

Disulfide bonds are important structural motifs that play an essential role in maintaining the conformational stability of many bioactive peptides. Of particular importance are the conotoxins, which selectively target a wide range of ion channels that are implicated in numerous disease states. Despite the enormous potential of conotoxins as therapeutics, their multiple disulfide bond frameworks are inherently unstable under reducing conditions. Reduction or scrambling by thiol-containing molecules such as glutathione or serum albumin in intracellular or extracellular environments such as blood plasma can decrease their effectiveness as drugs. To address this issue, we describe a new class of selenoconotoxins where cysteine residues are replaced by selenocysteine to form isosteric and non-reducible diselenide bonds. Three isoforms of alpha-conotoxin ImI were synthesized by t-butoxycarbonyl chemistry with systematic replacement of one([ Sec(2,8)] ImI or [Sec(3,12)] ImI), or both([Sec(2,3,8,12)] ImI) disulfide bonds with a diselenide bond. Each analogue demonstrated remarkable stability to reduction or scrambling under a range of chemical and biological reducing conditions. Three-dimensional structural characterization by NMR and CD spectroscopy indicates conformational preferences that are very similar to those of native ImI, suggesting fully isomorphic structures. Additionally, full bioactivity was retained at the alpha(7) nicotinic acetylcholine receptor, with each seleno-analogue exhibiting a dose-response curve that overlaps with wild-type ImI, thus further supporting an isomorphic structure. These results demonstrate that selenoconotoxins can be used as highly stable scaffolds for the design of new drugs.

Computing with elation groups

We have proved that elation groups of a certain infinite family of Roman generalized quadrangles are not isomorphic to those of associated flock generalized quadrangles. The proof is theoretical, but is based upon detailed computations. Here we elaborate on the explicit computer calculations which inspired the proof.

Modernisation in small steps? Comparing the organisational reforms of the British Conservative Party and the German CDU

Research on political parties has long identified “environmental” pressures upon parties to undertake organisational and programmatic reforms – this applies in particular to “catch-all” parties or Volksparteien. Changed social and media structures, the decline of organisations traditionally associated with the parties, and the growth in alternative possibilities of political participation create significant organisational – as well as programmatic – challenges. This paper compares the German CDU and the British Conservatives in two respects: in particular it focuses on their organisational responses to the election defeats they suffered at the end of the 1990s, examining those reforms which took place and consider whether these match the expectations of organisational reforms anticipated by proponents of the “cartel party thesis”. While in both cases there are similarities, but (in particular in the German case) it is important not to understate the extent of internal party resistance to reform, and thus the difficulties with which aspiring party reformers are confronted. This conclusion suggests, more broadly, that in reality the process of party change is more than an almost automatic, isomorphic, and inevitable response to a changing environment. Rather it is punctuated, messy, and often contingent on events and agents.

The nature of international retail divestment:Insights from Ahold

Purpose - This paper aims to explore the nature of divestment within the context of retailer internationalisation. Design/methodology/approach - It focuses on the activities of the Dutch food multinational retailer Royal Ahold (Ahold). Drawing on 37 in-depth interviews with investment banks and executives, this paper provides a number of insights into Ahold's international retail divestment activities within the context of a broadly successful international investment strategy. Findings - It offers some new insights into the multidimensional nature of international retail divestment construct in terms of the operational as well as more subtle and less visible non-operational international retail divestments. It is concluded from this study that, rather than portraying strategic and opportunistic approaches as binary opposites, a retail firm may have varying degrees of approaches to international retail divestment, and these may not necessarily be isomorphic across different countries. Research limitations/implications - The paper explores international retail divestment from a rather broad perspective, although it is hoped that these parameters can be used to raise a new set of more detailed priorities for future research on international retail divestment. Practical implications - This paper raises a number of interesting issues such as whether retailers initially take divestment seriously and the degree to which this is actually possible during market entry. Originality/value - As called for in the literature, this study examines divestment in the broadest possible fashion, thus addressing a major gap in our understanding of the whole internationalisation process. © Emerald Group Publishing Limited.

Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

A structural investigation of the alkali metal site distribution within bioactive glass using neutron diffraction and multinuclear solid state NMR

The atomic-scale structure of Bioglass and the effect of substituting lithium for sodium within these glasses have been investigated using neutron diffraction and solid state magic angle spinning (MAS) NMR. Applying an effective isomorphic substitution difference function to the neutron diffraction data has enabled the Na-O and Li-O nearest-neighbour correlations to be isolated from the overlapping Ca-O, O-(P)-O and O-(Si)-O correlations. These results reveal that Na and Li behave in a similar manner within the glassy matrix and do not disrupt the short range order of the network former. Residual differences are attributed solely to the variation in ionic radius between the two species. Successful simplification of the 2

Towards a web-based progressive handwriting recognition environment for mathematical problem solving

The emergence of pen-based mobile devices such as PDAs and tablet PCs provides a new way to input mathematical expressions to computer by using handwriting which is much more natural and efficient for entering mathematics. This paper proposes a web-based handwriting mathematics system, called WebMath, for supporting mathematical problem solving. The proposed WebMath system is based on client-server architecture. It comprises four major components: a standard web server, handwriting mathematical expression editor, computation engine and web browser with Ajax-based communicator. The handwriting mathematical expression editor adopts a progressive recognition approach for dynamic recognition of handwritten mathematical expressions. The computation engine supports mathematical functions such as algebraic simplification and factorization, and integration and differentiation. The web browser provides a user-friendly interface for accessing the system using advanced Ajax-based communication. In this paper, we describe the different components of the WebMath system and its performance analysis.

Structural characterisation of hypoxia-mimicking bioactive glasses

Nickel and cobalt are both known to stimulate the hypoxia-inducible factor-1 (HIF-1a), thus significantly improving blood vessel formation in tissue engineering applications. We have manufactured nickel and cobalt doped bioactive glasses to act as a controlled delivery mechanism of these ions. The resultant structural consequences have been investigated using the methods of isotopic and isomorphic substitution applied to neutron diffraction. The structural sites present will be intimately related to their release properties in physiological fluids such as plasma and saliva, and hence the bioactivity of the material. Detailed structural knowledge is therefore a prerequisite for optimising material design. Results show that nickel and cobalt adopt a mixed structural role within these bioactive glasses occupying both network-forming (tetrahedral) and network-modifying (5-fold) geometries. Two thirds of the Ni (or Co) occupies a five-fold geometry with the remaining third in a tetrahedral environment. A direct comparison of the primary structural correlations (e.g. Si-O, Ca-O, Na-O and O-Si-O) between the archetypal 45S5 Bioglass® and the Ni and Co glasses studied here reveal no significant differences. This indicates that the addition of Ni (or Co) will have no adverse effects on the existing structure, and thus on in vitro/in vivo dissolution rates and therefore bioactivity of these glasses.

Structure of rare-earth phosphate glasses by neutron diffraction

Neutron diffraction was used to measure the structure of the phosphate glasses RAl0.30P3.05O9.62, where R denotes Dy or Ho, and RAl0.34P3.20O10.04, where R denotes La or Ce. For each glass, isomorphic structures were assumed and difference function methods were employed to separate, essentially, those correlations involving the rare-earth ion, R3+, from the remainder. The ratio of bridging oxygen, OB, to terminal oxygen, OT, atoms in the PO4 tetrahedra was quantified and in both materials R3+ and Al3+ are found to act as network modifying cations which bind to the OT. The R–OT coordination number is 6.7(1) and 7.5(2) for the Dy/Ho and La/Ce glasses respectively.

Identification of the relative distribution of rare-earth ions in phosphate glasses

The relative distribution of rare-earth ions R3+ (Dy3+ or Ho3+) in the phosphate glass RAl0.30P3.05O9.62 was measured by employing the method of isomorphic substitution in neutron diffraction. It is found that 7.9(7) R-R nearest neighbors reside at 5.62(6) Angstrom in a network made from interlinked PO4 tetrahedra. Provided that the role of Al is explicitly considered, a self-consistent account of the local matrix atom correlations can be developed in which there are 1.68(9) bridging and 2.32(9) terminal oxygen atoms per phosphorus.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.