Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.

Dynamic Behavior of the Jahn-Teller distorted Cu(H2O)(6)(2+) ion in Cu2+ doped Cs-2[Zn(H2O)(6)](ZrF6)(2) and the crystal structure of the host lattice

The temperature dependence of the X- and Q-band EPR spectra of Cs-2[Zn(H2O)(6)](ZrF6)(2) containing similar to1% Cu2+ is reported. All three molecular g-values vary with temperature, and their behavior is interpreted using a model in which the potential surface of the Jahn-Teller distorted Cu(H2O)(6)(2+) ion is perturbed by an orthorhombic strain induced by interactions with the surrounding lattice. The strain parameters are significantly smaller than those reported previously for the Cu(H2O)(6)(2+) ion in similar lattices. The temperature dependence of the two higher g-values suggests that in the present compound the lattice interactions change slightly with temperature. The crystal structure of the Cs-2[Zn(H2O)(6)](ZrF6)(2) host is reported, and the geometry of the Zn(H2O)(6)(2+) ion is correlated with lattice strain parameters derived from the EPR spectrum of the guest Cu2+ complex.

Alterations in Plasmodium falciparum genotypes during sequential infections suggest the presence of strain specific immunity

Many of the asexual stage Plasmodium falciparum proteins that are the targets of host protective responses are markedly polymorphic. The full repertoire of diversity is not defined for any antigen. Most studies have focused on the genes encoding merozoite surface proteins 1 and 2 (MSP1, MSP2). We explored the extent of diversity of some of the less studied merozoite surface antigens and analyzed the degree of complexity of malaria field isolates by deriving nucleotide sequences of several antigens. We have determined the genotype of apical membrane antigen 1 (AMA1) in a group of 30 field samples, collected over 29 months, from individuals living in an area of intense malaria transmission in Irian Jaya, identifying 14 different alleles. AMA1 genotyping was combined with previously determined MSP2 typing. AMA1 had the greatest power in distinguishing between isolates but methodological problems, especially when mixed infections are present, suggest it is not an ideal typing target. MSP1, MSP3, and glutamate-rich protein genotypes were also determined from a smaller group of samples, and all results were combined to derive an extended antigenic haplotype. Within this subset of 10 patients, nine different genotypes could be discerned; however, five patients were all infected with the same strain. This strain was present in individuals from two separate villages and was still present 12 months later. This strain was predominant at the first time point but had disappeared at the fourth time point. This significant change in malaria genotypes could be due to strain-specific immunity developing in this population.

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Quality of care of patients hospitalized with acute coronary syndromes

Background: Measurement and improvement of quality of care is a priority issue in health care. Patients hospitalized with acute coronary syndromes (ACS) constitute a high-risk population whose care, if shown to be suboptimal on the basis of available research evidence, may benefit from quality improvement interventions. Aim: To evaluate the quality of in-hospital care for patients with ACS, using explicit quality indicators. Methods: Retrospective case note review was undertaken of 397 patients admitted to three teaching hospitals in Brisbane, Queensland, Australia, between 1 October 2000 and 17 April 2001. The main out-come measures were 12 process-of-care quality indicators, calculated as either: (i) the proportion of all patients who received specific interventions or (ii) the proportion of ideal patients who received -specific interventions (i.e. patients with clear indi-cations and lacking contraindications). Results: Quality indicators with values above 80% included: (i) patient selection for thrombolysis (100%) and discharge prescription of beta-blockers (84%), (ii) antiplatelet agents (94%) and (iii) lipid-lowering agents (82%). Indicators with values between 50% and 80% included: (i) timely per-formance of electrocardiogram (ECG) on admission (61%), (ii) early coronary angiography (75%), (iii) measurement of serum lipids (71%) and (iv) discharge prescription of angiotensin-converting-enzyme (ACE) inhibitors (73%). Indicators with values <50% included: (i) timely administration of thrombolysis (35%), (ii) non-invasive risk assessment (23%) and (ii) formal in-hospital and post-hospital cardiac rehabilitation (47% and 7%, respectively). Conclusion: There were delays in performing ECG and administering thrombolysis to patients who presented to emergency departments with ACS. Improvement is warranted in use of non-invasive procedures for identifying high-risk patients who may benefit from coronary revascularization as well as use of serum lipid measurements, ACE inhibitors and cardiac rehabilitation.

The crystallography and morphology of Mo2C in ferrite

The orientation relationships between hexagonal Mo2C precipitates (H) in ferrite (B) have been determined by electron diffraction to an accuracy of +/-2degrees. With one exception, the 19 results are consistent with the previously reported Pitsch and Schrader (P/S) orientation relationship. However, these more accurate determinations show clearly that there is a systematic deviation of up to 5.5degrees from the exact P/S relationship and that this deviation consists of a small rotation about the parallel close packed directions-[100](B)//[2 (1) over bar(1) over bar0](H). The long direction of the Mo2C needles has been determined unequivocally in terms of the orientation relationship to be [100](B)//[2 (1) over bar(1) over bar0](H). Moire fringes between precipitate and matrix have been used to improve the accuracy of the orientation relationship results and to determine the lattice parameters of the carbide precipitates investigated. The Moire fringe analysis has shown small systematic departures from the exact parallelism between [100](B) and [2 (1) over bar(1) over bar0](H) along the length of Mo2C needles and a lowering of the carbide lattice parameter that is consistent with the replacement of Mo by Fe in the carbide. The orientation relationship results, including the observed systematic deviation from the exact P/S relationship, are shown to be consistent with the edge-to-edge model. (C) 2002 Kluwer Academic Publishers.

Overlarge sets of 2-(11, 5, 2) designs and related configurations

We consider the construction of several configurations, including: • overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs; • an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12 × 12 square with interesting row and column properties; • a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square; • bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

New W-isotope evidence for rapid terrestrial accretion and very early core formation

The short-lived Hf-182-W-182-isotope system is an ideal clock to trace core formation and accretion processes of planets. Planetary accretion and metal/silicate fractionation chronologies are calculated relative to the chondritic Hf-182-W-182-isotope evolution. Here, we report new high-precision W-isotope data for the carbonaceous chondrite Allende that are much less radiogenic than previously reported and are in good agreement with published internal Hf-W chronometry of enstatite chondrites. If the W-isotope composition of terrestrial rocks, representing the bulk silicate Earth, is homogeneous and 2.24 epsilon(182W) units more radiogenic than that of the bulk Earth, metal/silicate differentiation of the Earth occurred very early. The new W-isotope data constrain the mean time of terrestrial core formation to 34 million years after the start of solar system accretion. Early terrestrial core formation implies rapid terrestrial accretion, thus permitting formation of the Moon by giant impact while Hf-182 was still alive. This could explain why lunar W-isotopes are more radiogenic than the terrestrial value. Copyright (C) 2002 Elsevier Science Ltd.