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.

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.

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.

Embedding partial G-designs where G is a 4-cycle with a pendant edge

Let D denote the graph consisting of a cycle of length 4 with a pendant edge. In this paper, two very different small embeddings of partial D-designs are presented. (c) 2005 Elsevier B.V. All rights reserved.

Embedding a restricted class of partial K-4-designs

Given a partial K-4-design (X, P), if x is an element of X is a vertex which occurs in exactly one block of P, then call x a free vertex. In this paper, a technique is described for obtaining a cubic embedding of any partial K-4-design with the property that every block in the partial design contains at least two free vertices.

Reflexive OKN with partial and full field stimulation: Effects of age and light level

We recorded reflexive OKN in ten younger (32.3±5.98 years) and older (65.6±6.53) visually normal subjects under viewing conditions designed to differentiate M-pathway functioning from other pathways. Subjects were required to gaze straight ahead while viewing vertical gratings of either 0.43 or 1.08 cpd, drifting at either 5 or 20°/sec and presented at either 8 or 80% contrast. Gratings were presented as full field stimulation, central stimulation or peripheral (>15°) stimulation. The order of presentation of conditions was pseudo-randomised at two blocked light levels: ‘mesopic’ or twilight conditions (1.8 cdm-2) and ‘photopic’ or full light conditions (71.5 cdm-2). For the partial fields, central stimulation, mesopic light level, lower temporal frequencies (i.e. number of stripes passing per second) each contributed to greater OKN strength as measured by slow-phase velocity (SPV). For full field stimulation, and especially for higher temporal frequencies and low contrast, there was a significant interaction between age group × light level (p = 0.017): SPV diminished much more among the older than the younger group for the twilight condition compared to full light. Such a clear diminution in M-pathway sensitivity revealed by OKN response has important implications for everyday situations like crash avoidance under twilight driving conditions.