Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Embeddings of partial Steiner triple systems

Any partial Steiner triple system of order u can be embedded in a Steiner triple system of order v if v equivalent to 1, 3 (mod 6) and v greater than or equal to 3u - 2. (C) 2004 Elsevier Inc. All rights reserved.

Steiner triple systems with two disjoint subsystems

It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.

Configurations in 4-cycle systems

A 4-cycle system of order n, denoted by 4CS(n), exists if and only if nequivalent to1 (mod 8). There are four configurations which can be formed by two 4-cycles in a 4CS(n). Formulas connecting the number of occurrences of each such configuration in a 4CS(n) are given. The number of occurrences of each configuration is determined completely by the number d of occurrences of the configuration D consisting of two 4-cycles sharing a common diagonal. It is shown that for every nequivalent to1 (mod 8) there exists a 4CS(n) which avoids the configuration D, i.e. for which d=0. The exact upper bound for d in a 4CS(n) is also determined.

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.

Some equitably 3-colourable cycle decompositions

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 (i) - n(j) less than or equal to 1 for any i, j is an element of {1, 2,..., k}, then C is 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 C is equitably k-coloured. For m = 4,5 and 6, we completely settle the existence problem for equitably 3-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a 1-factor removed. (C) 2004 Elsevier B.V. All rights reserved.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Implementation of a triple modular redundant FPGA based safety critical system for reliable software execution

This paper describes the implementation of a TMR (Triple Modular Redundant) microprocessor system on a FPGA. The system exhibits true redundancy in that three instances of the same processor system (both software and hardware) are executed in parallel. The described system uses software to control external peripherals and a voter is used to output correct results. An error indication is asserted whenever two of the three outputs match or all three outputs disagree. The software has been implemented to conform to a particular safety critical coding guideline/standard which is popular in industry. The system was verified by injecting various faults into it.

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 Australo-Papuan bird migration system: Another consequence of Wallace's Line

With respect to its avian migrants, Australo-Papua is a largely self-contained region. Only some 30 species of shorebird and 10 species of land bird migrate from Asia to Australo-Papua to winter. Possible factors precluding migration of Asian birds include long over-water distances and lack of suitable habitats in Australia or New Guinea. Whether evolved within the region or descended from Asian relatives, Australasian species all confine their migratory movements east of Wallace's Line. The most likely factors restricting migration to the region are climate and habitat. The open forests and arid habitats of Australasia are absent from south-east Asia, so there is little, if any, selection promoting extra-regional migration. The arid or semi-arid but otherwise mild climates of much of Australia favour partial migration and widely varying movement patterns and pathways, although with an underlying north to south component. Movements also occur between mainland Australia and New Guinea and Tasmania. The restriction of migration within Australo-Papua and the high variability of migratory pathways have important implications for the ecology and evolution of the Australasian avifauna.

The effect of Yb addition in Bi2Sr2Ca1-x,YbxU2Oy partial melted thick films

To study the phase relations in the Bi-2212 and Yb2O3 system, Bi2Sr2Ca1-xYbxCu2Oy thick films are prepared by partial melt processing via an intermediate reaction between Bi-2212 and Yb2O3. When Bi-2212 and Yb2O3 are partially melted and then slowly cooled, solid solutions of Bi2Sr2Ca1-xYbxCu2Oy form by reactions between liquid and solid phases which contain Yb. Following these reactions, Ca is partially replaced in Bi-2212 matrix and participates in the formation of secondary phases, such as Bi-free, (Ca, Sr)O-x and CaO. Variation of the Bi-2212-Yb2O3 ratios and processing parameters changes the balance between the phases and leads to different Yb:Ca ratios in the Bi-2212 matrix of processed thick films. When the partial melting process is optimized for each sample to minimize the growth of secondary phases, x = 0.42-0.46 for the samples prepared at pO(2) = 0.01 atm, x = 0.24-0.29 for the samples prepared at pO(2) = 0.21 atm, x = 0.18-0.23 for the samples prepared at pO(2) = 0.99 atm are obtained regardless to the starting compositions. It is found that superconducting properties of Bi2Sr2Ca1-xYbxCu2Oy thick films strongly depend on the processing conditions, because the conditions result in different Yb content in the Bi-2212 matrix and the volume fraction of the secondary phases. The highest T-c(0) of 77, 90 and 91 K were obtained for the samples processed at 0.01, 0.21 and 0.99 atm of O-2, respectively.

Nitrogen removal from sludge digester liquids by nitrification/denitrification or partial nitritation/anammox: environmental and economical considerations

In wastewater treatment plants with anaerobic sludge digestion, 15-20% of the nitrogen load is recirculated to the main stream with the return liquors from dewatering. Separate treatment of this ammonium-rich digester supernatant significantly reduces the nitrogen load of the activated sludge system. Two biological applications are considered for nitrogen elimination: (i) classical autotrophic nitrification/heterotrophic denitrification and (ii) partial nitritation/autotrophic anaerobic ammonium oxidation (anammox). With both applications 85-90% nitrogen removal can be achieved, but there are considerable differences in terms of sustainability and costs. The final gaseous products for heterotrophic denitrification are generally not measured and are assumed to be nitrogen gas (N-2). However, significant nitrous oxide (N2O) production can occur at elevated nitrite concentrations in the reactor. Denitrification via nitrite instead of nitrate has been promoted in recent years in order to reduce the oxygen and the organic carbon requirements. Obviously this achievement turns out to be rather disadvantageous from an overall environmental point of view. On the other hand no unfavorable intermediates are emitted during anaerobic ammonium oxidation. A cost estimate for both applications demonstrates that partial nitritation/anammox is also more economical than classical nitrification/denitrification. Therefore autotrophic nitrogen elimination should be used in future to treat ammonium-rich sludge liquors.

Treatment of partial-thickness burns: A prospective, randomized trial using Transcyte (TM)

Background: The purpose of the present study was to compare the effectiveness of three burns dressings (TransCyte, a bio-engineered skin substitute; Biobrane; and Silvazine cream (silver sulphadiazine and 0.2% chlorhexidine)), in treating children with partial-thickness burns. The primary objective was to determine the days until greater than or equal to90% re-epithelialization. The secondary objectives were to evaluate the number of wounds requiring autografting and the number of dressing changes/local wound care required. Methods: Study wounds were identified on each patient and the patients were randomized to receive TransCyte or Biobrane or Silvazine. Assessment of study wound closure began at 2 days after treatment and continued at least every other day thereafter until the wounds re-epithelialized or were autografted. A laser Doppler imaging system was used as an adjunct to assessing the depth of the burn. Results: Thirty-three patients with 58 wound sites enrolled in the study (TransCyte, n = 20, Biobrane, n = 17; Silvazine, n = 21). Mean time to re-epithelialization was 7.5 days for TransCyte, 9.5 days for Biobrane, and 11.2 days for Silvazine. The number of wounds requiring autografting were 5/21 (24%) for Silvazine, 3/17 (17%) for Biobrane, and 1/20 (5%) for TransCyte. Conclusions: When used in partial-thickness burns in children, TransCyte promotes fastest re-epithelialization and required less overall dressings then Biobrane or Silvazine. Patients who received Silvazine or Biobrane require more autografting than those treated with TransCyte.