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.

Combined chemical separation of Lu, Hf, Sm, Nd, and REEs from a single rock digest: Precise and accurate isotope Determinations of Lu-Hf and Sm-Nd using multicollector-ICPMS

A combined procedure for separating Lu, Hf, Sm, Nd, and rare earth elements (REEs) from a single sample digest is presented. The procedure consists of the following five steps: (1) sample dissolution via sodium peroxide sintering; (2) separation of the high field strength elements from the REEs and other matrix elements by a HF-free anion-exchange column procedure; (3) purification of Hf on a cation-exchange resin; (4) separation of REEs from other matrix elements by cation exchange; (5) Lu, Sm, and Nd separation from the other REEs by reversed-phase ion chromatography. Analytical reproducibilities of Sm-Nd and Lu-Hf isotope systematics are demonstrated for standard solutions and international rock reference materials. Results show overall good reproducibilities for Sm-Nd systematics independent of the rock type analyzed. For the Lu-Hf systematics, the reproducibility of the parent/daughter ratio is much better for JB-1 (basalt) than for two analyzed felsic crustal rocks (DR-N and an Archaean granitoid). It is demonstrated that this poorer reproducibility of the Lu/Hf ratio is truly caused by sample heterogeneity; thus, results are geologically reasonable.

Comparison of an ELISA and an LC/MS/MS method for measuring tacrolimus concentrations and making dosage decisions in transplant recipients

This study compared an enzyme-linked immunosorbent assay (ELISA) to a liquid chromatography-tandem mass spectrometry (LC/MS/MS) technique for measurement of tacrolimus concentrations in adult kidney and liver transplant recipients, and investigated how assay choice influenced pharmacokinetic parameter estimates and drug dosage decisions. Tacrolimus concentrations measured by both ELISA and LC/MS/MS from 29 kidney (n = 98 samples) and 27 liver (n = 97 samples) transplant recipients were used to evaluate the performance of these methods in the clinical setting. Tacrolimus concentrations measured by the two techniques were compared via regression analysis. Population pharmacokinetic models were developed independently using ELISA and LC/MS/MS data from 76 kidney recipients. Derived kinetic parameters were used to formulate typical dosing regimens for concentration targeting. Dosage recommendations for the two assays were compared. The relation between LC/MS/MS and ELISA measurements was best described by the regression equation ELISA = 1.02 . (LC/MS/MS) + 0.14 in kidney recipients, and ELISA = 1.12 . (LC/MS/MS) - 0.87 in liver recipients. ELISA displayed less accuracy than LC/MS/MS at lower tacrolimus concentrations. Population pharmacokinetic models based on ELISA and LC/MS/MS data were similar with residual random errors of 4.1 ng/mL and 3.7 ng/mL, respectively. Assay choice gave rise to dosage prediction differences ranging from 0% to 30%. ELISA measurements of tacrolimus are not automatically interchangeable with LC/MS/MS values. Assay differences were greatest in adult liver recipients, probably reflecting periods of liver dysfunction and impaired biliary secretion of metabolites. While the majority of data collected in this study suggested assay differences in adult kidney recipients were minimal, findings of ELISA dosage underpredictions of up to 25% in the long term must be investigated further.

Breadth-first search and the Andrews-Curtis conjecture

Andrews and Curtis conjectured in 1965 that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. Recent computational work by Miasnikov and Myasnikov on this problem has been based on genetic algorithms. We show that a computational attack based on a breadth-first search of the tree of equivalent presentations is also viable, and seems to outperform that based on genetic algorithms. It allows us to extract shorter proofs (in some cases, provably shortest) and to consider the length thirteen case for two generators. We prove that, up to equivalence, there is a unique minimum potential counterexample.

Enhancing the ratio of molecular ions to non-covalent compounds in the electrospray interface of LC-MS in quantitative analysis

A common problem encountered during the development of MS methods for the quantitation of small organic molecules by LGMS is the formation of non-covalently bound species or adducts in the electrospray interface. Often the population of the molecular ion is insignificant compared to those of all other forms of the analyte produced in the electrospray, making it difficult to obtain the sensitivity required for accurate quantitation. We have investigated the effects of the following variables: orifice potential, nebulizer gas flow, temperature, solvent composition and the sample pH on the relative distributions of ions of the types MH+, MNa+, MNH+, and 2MNa(+), where M represents a 4 small organic molecule: BAY 11-7082 ((E)-3-[4-methylphenylsulfonyl]-2-propenenitrile). Orifice potential, solvent composition and the sample pH had the greatest influence on the relative distributions of these ions, making these parameters the most useful for optimizing methods for the quantitation of small molecules.

The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.