Potential of CE for the determination of inorganic and acidic anions in cyanoacrylate adhesives

In this work, a CZE method with indirect UV detection was developed for the simultaneous determination of the inorganic and acidic anions, chloride, sulfate, nitrate, fluoride, formate, phosphate, diethylphosphate, methyl sulfonate, cyanoacetate, and methacrylate present in cyanoacrylate adhesives. Chromate was employed as the probe ion, and the EOF was reversed by incorporating CTAB into BGE. Detection limits of 0.7-4.6 microg/mL were obtained for all the anions studied. The CE method developed is a significant improvement on traditionally used chromatographic methods such as ion chromatography, as it resulted in shorter analysis times with enhanced separation efficiencies. This method was successfully employed for the analysis of inorganic and acidic anions in cyanoacrylate adhesive samples.     

Asymmetric platinum group metal-catalyzed carbonyl-ene reactions: carbon-carbon bond formation versus isomerization

A comparative study of the carbonyl-ene reaction between a range of 1,1'-disubstituted or trisubstituted alkenes and ethyl trifluoropyruvate catalyzed by Lewis acid-platinum group metal complexes of the type [M{(R)-BINAP}]2+ (M = Pt, Pd, Ni; BINAP is 2,2'-bis(diphenylphosphino)-1,1'-binaphthyl) revealed subtle but significant differences in their reactivity. For instance, the palladium-based Lewis acid [Pd{(R)-BINAP}]2+ catalyzes the ene reaction between methylene cycloalkane to afford the expected alpha-hydroxy ester in good yield and excellent diastereo- and enantioselectivity. In contrast, under the same conditions, the corresponding [M{(R)-BINAP}]2+ (M = Pt, Ni) catalyzes isomerization of methylene cycloalkane and the ene reaction of the resulting mixture of methylene cycloalkane and 1-methylcycloalkene at similar rates to afford a range of -hydroxy esters in high regioselectivity, good diastereoselectivity, and good to excellent enantioselectivity. In addition, [Pt{(R)-BINAP}]2+ also catalyzes postreaction isomerization of the ene product as well as consecutive ene reactions to afford a double carbonyl-ene product. The sense of asymmetric induction has been established by single-crystal X-ray crystallography, and a stereochemical model consistent with the formation of (S)-configured -hydroxy ester has been proposed; the same model also accounts for the observed exo-diastereoselectivity as well as the level of diastereoselectivity.     

A study of the analytical behaviour of selected synthetic and naturally occurring quinolines using electrospray ionisation ion trap mass spectrometry, liquid chromatography and gas chromatography and the construction of an appropriate database for quinoline characterisation

Mass spectral fragmentation of quinoline alkaloids of significance in plants has been investigated using electrospray ionisation ion trap mass spectrometry (ESI-MSⁿ) with a view to characterisation of molecules of unknown structure isolated from these natural sources. This investigation has led to the generation of an appropriate database incorporating data from ESI-MSⁿ and also from gas liquid chromatography (GLC) and liquid chromatography (HPLC) for these low molecular mass quinolines. This has been put to practical application in the identification of quinoline alkaloids in a plant extract. Thus, an acid extraction of the leaves of Choisya ternata containing such tertiary alkaloids was analysed by liquid chromatography-electrospray ionisation mass spectrometry (HPLC-ESI-MS) and the resulting behaviour of the quinolines was compared with that of the quinoline alkaloids in the database.     

The monic integer transfinite diameter

We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval . The monic integer transfinite diameter is defined as the infimum of all such supremums. We show that if has length , then .

We make three general conjectures relating to the value of for intervals of length less than . We also conjecture a value for where . We give some partial results, as well as computational evidence, to support these conjectures.

We define functions and , which measure properties of the lengths of intervals with on either side of . Upper and lower bounds are given for these functions.

We also consider the problem of determining when is a Farey interval. We prove that a conjecture of Borwein, Pinner and Pritsker concerning this value is true for an infinite family of Farey intervals.

     

Topological graph dimension

In the invited chapter Discrete Spatial Models of the book Handbook of Spatial Logics, we have introduced the concept of dimension for graphs, which is inspired by Evako’s idea of dimension of graphs [A.V. Evako, R. Kopperman, Y.V. Mukhin, Dimensional properties of graphs and digital spaces, J. Math. Imaging Vision 6 (1996) 109-119]. Our definition is analogous to that of (small inductive) dimension in topology. Besides the expected properties of isomorphism-invariance and monotonicity with respect to subgraph inclusion, it has the following distinctive features:

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Local aspect. That is, dimension at a vertex is basic, and the dimension of a graph is obtained as the sup over its vertices.

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Dimension of a strong product G×H is dim(G)+dim(H) (for non-empty graphs G,H).

In this paper we present a short account of the basic theory, with several new applications and results.     

A Probabilistic Characterization of the Dominance Order on Partitions

We present a probabilistic characterization of the dominance order on partitions. Let ν be a partition and Y _ν its Ferrers diagram, i.e. a stack of rows of cells with row i containing ν _i cells. Let the cells of Y _ν be filled with independent and identically distributed draws from the random variable X = B i n(r, p) with r ≥ 1 and p ∈ (0, 1). Given j, t ≥ 0, let P(ν, j, t) be the probability that the sum of all the entries in Y _ν is j while the sum of the entries in each row of Y _ν is no more than t. It is shown that if ν and μ are two partitions of n, ν dominates μ if and only if P(ν, j, t) ≤ P(μ, j, t) for all j, t ≥ 0. It is shown that the same result holds if X is any log-concave integer valued random variable with {i : P(X = i) > 0} = {0, 1,…,r} for some r ≥ 1.     

Zur Bestimmung des Rauchgehaltes der Luft

Ohne Zusammenfassung     

There are Only Eleven Special Pisot Numbers

A special Pisot number is a Pisot number such that /(–1)is also a Pisot number. Lagarias, Porta and Stolarsky found11 special Pisot numbers. Here it is proved that there are nomore. Also, the one known Salem number with the property that/(–1) is a Pisot number is shown to be the only such number.1991 Mathematics Subject Classification 11R06.