Product analysis of the reaction of OH with benzene,toluene, and 1,3,5-trimethylbenzene at 300 K

Products of the reaction of OH with benzene, toluene, and 1,3,5-trimethylbenzene have been identified in crossed molecular beam experiments conducted at 300 K. Ionization potentials of the most intense products were also measured.     

The nonexistence of a certain Steiner system S(3, 12, 112)

Although the automorphism group of a projective plane of order 10, if one exists, must be very small, such a plane could be the derived design of a Steiner system S(3, 12, 112) with a larger group. There are several reasons why the Frobenius group of order 56 is a promising candidate for the latter group. However, in this paper it is shown that there is no S(3, 12, 112) which is fixed by this Frobenius group.     

On asymmetric coverings and covering numbers

An asymmetric covering is a collection of special subsets S of an n‐set such that every subset T of the n‐set is contained in at least one special S with . In this paper we compute the smallest size of any for We also investigate “continuous” and “banded” versions of the problem. The latter involves the classical covering numbers , and we determine the following new values: , , , , and . We also find the number of non‐isomorphic minimal covering designs in several cases. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 218–228, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10022     

A Note on Projecting the Cubic Lattice

It is shown that, given any (n−1)-dimensional lattice Λ, there is a vector v∈ℤ ⁿ such that the orthogonal projection of ℤ ⁿ onto v ^⊥ is, up to a similarity, arbitrarily close to Λ. The problem arises in attempting to find the largest cylinder anchored at two points of ℤ ⁿ and containing no other points of ℤ ⁿ .     

Four icosahedra can meet at a point

What is the maximal number of nonoverlapping copies of a regular polyhedron ∏ that can share a common vertex? The answer is shown to be 4 if ∏ is an icosahedron or dodecahedron, and is conjectured to be 7 for an octahedron and 20 for a tetrahedron. (For a cube the answer is trivially 8.)     

Self-dual codes over GF(5)

It is shown that a self-orthogonal code over GF(5) which is generated by words of weight 4 has a decomposition into components belonging to three infinite families: d_n (n = 4, 5, 6, 7, 8, 10, 12,…), e_n (n = 6, 8, 10,…) and F_n (n = 6, 8, 10,…). All maximal self-orthogonal (and self-dual) codes of length ? 12 are classified, and a number of interesting codes of greater length are constructed.     

On the classification and enumeration of self-dual codes

A complete classification is given of all [22, 11] and [24, 12] binary self-dual codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 6] self-dual code. Several theorems on the enumeration of self-dual codes are used, including formulas for the number of such codes with minimum distance ? 4, and for the sum of the weight enumerators of all such codes of length n. Selforthogonal codes which are generated by code words of weight 4 are completely characterized.     

Can Coordination‐Driven Supramolecular Self‐Assembly Reactions Be Conducted from Fully Aliphatic Linkers?

The reaction between a preassembled Cu^I bimetallic molecular clip with a short intermetallic distance and a series of fully aliphatic cyano‐capped ditopic linkers with increasing lengths was investigated. It is shown that, depending on the length of the ditopic linkers, the rational design of unprecedented supramolecular compact metallacycles containing fully aliphatic walls is possible. The specific preorganized molecular arrangement of the molecular clip used favors stabilizing interlinker London dispersion interactions, which allow, as the length of the linkers increases, the selective formation of discrete compact metallacycles at the expense of 1D coordination polymers. The generalizability of this approach was demonstrated by the reaction of fully aliphatic cyano‐capped linkers with two other types of preassembled Cu^I bimetallic molecular clips that also had short intermetallic distances.     

Double Circulant Codes over \mathbb{Z}_4 and Even Unimodular Lattices

With the help of some new results about weight enumerators of self-dual codes over we investigate a class of double circulant codes over , one of which leads to an extremal even unimodular 40–dimensional lattice. It is conjectured that there should be Nine more constructions of the Leech lattice     

Oxygen isotope analysis of carbonates in the calcite-dolomite-magnesite solid-solution by high-temperature pyrolysis: initial results

Accurate and efficient measurement of the oxygen isotope composition of carbonates (delta(C) (18)O) based on the mass spectrometric analysis of CO(2) produced by reacting carbonate samples with H(3)PO(4) is compromised by: (1) uncertainties associated with fractionation factors (alpha(CO)(2)C) used to correct measured oxygen isotope values of CO(2)(delta(CO(2)(18)O) to delta(C) (18)O; and (2) the slow reaction rates of many carbonates of geological and environmental interest with H(3)PO(4). In contrast, determination of delta(C) (18)O from analysis of CO produced by high-temperature (>1400 degrees C) pyrolytic reduction, using an elemental analyser coupled to continuous-flow isotope-ratio mass spectrometry (TC/EA CF-IRMS), offers a potentially efficient alternative that measures the isotopic composition of total carbonate oxygen and should, therefore, theoretically be free of fractionation effects. The utility of the TC/EA CF-IRMS technique was tested by analysis of carbonates in the calcite-dolomite-magnesite solid-solution and comparing the results with delta(C) (18)O measured by conventional thermal decomposition/fluorination (TDF) on the same materials. Initial results show that CO yields are dependent on both the chemical composition of the carbonate and the specific pyrolysis conditions. Low gas yields (<100% of predicted yield) are associated with positive (>+0.2 per thousand) deviations in delta(C(TC/EA) (18)O compared with delta(C(TDF) (18)O. At a pyrolysis temperature of 1420 degrees C the difference between delta(C) (18)O measured by TC/EA CF-IRMS and TDF (Delta(C(TC/EA,TDF) (18)O) was found to be negatively correlated with gas yield (r = -0.785) and this suggests that delta(C) (18)O values (with an estimated combined standard uncertainty of +/-0.38 per thousand) could be derived by applying a yield-dependent correction. Increasing the pyrolysis temperature to 1500 degrees C also resulted in a statistically significant correlation with gas yield (r = -0.601), indicating that delta(C) (18)O values (with an estimated uncertainty of +/-0.43 per thousand) could again be corrected using a yield-dependent procedure. Despite significant uncertainty associated with TC/EA CF-IRMS analysis, the magnitude of the uncertainty is similar to that associated with the application of poorly defined values of alpha(CO)(2), (C) used to derive delta(C) (18)O from delta(CO(2) (18)O measured by the H(3)PO(4) method for most common carbonate phases. Consequently, TC/EA CF-IRMS could provide a rapid alternative for the analysis of these phases without any effective deterioration in relative accuracy, while analytical precision could be improved by increasing the number of replicate analyses for both calibration standards and samples. Although automated gas preparation techniques based on the H(3)PO(4) method (ISOCARB, Kiel device, Gas-Bench systems) have the potential to measure delta(CO)(2) (18)O efficiently for specific, slowly reacting phases (e.g. dolomite), problems associated with poorly defined alpha(CO)(2), (C) remain. The application of the Principle of Identical Treatment is not a solution to the analysis of these phases because it assumes that a single fractionation factor may be defined for each phase within a solid-solution regardless of its precise chemical composition. This assumption has yet to be tested adequately.