A strange pigeon-hole principle

Using Ramsey theory, we establish the following pigeon-hole type principle: From a large number of random variables (functions, vectors, etc.) one can always select two, X and Y, such that P(X < Y) 1/2. We apply the principle for a poset problem.     

Variations on the theme of repeated distances

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ^{d, d}4. We also give asymptotically tight upper bounds on the total number of occurrences of the favourite distances fromn points in ^{d, d}4. Related results are proved for distances determined byn disjoint compact convex sets in ².At the time this paper was written, both authors were visiting the Technion — Israel Institute of Technology.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

Characterization of reaction products formed during thin-layer chromatographic detection of thiocarbamate herbicides

The reaction between thiocarbamate herbicides and 2,6-dichlorobenzoquinone-N-chloroimine or 2,6-dibromobenzoquinone-N-chloroimine is suitable for the detection of these herbicides on thin-layer plates with high sensitivity. The reactions were followed by infrared, nuclear magnetic resonance and mass spectrometry. We have established the formation of 2,6-dichlorobenzoquinone-S-alkyl sulphenylimines. In the case of the bromo-derivative, halogen exchange and substitution on the quinone ring took place simultaneously leading to the formation of mixed halogenated 2,6-dihalo- and, in addition, 2,3,6-trihalobenzoquinone-S-alkyl sulphenylimines. The final product of the detection reaction, i.e. 2,6-dichlorobenzoquinone-S-alkyl sulphenylimine was reacted with 2,6-dibromobenzoquinone-N-chloroimine where 2,6-dichloro-3-bromobenzoquinone-S-alkyl sulphenylimine formed as a consequence of the looser bromine-carbon linkage on the 2 and 6 positions of the quinone ring.     

Inductively coupled plasma compared with direct current arc spectrometry for analysis of minor elements in aluminium baths

A validation study was carried out in order to evaluate the efficiency of inductively coupled plasma-optical emission spectrometry (ICP-OES) for the analysis of minor elements (manganese, chromium, copper, iron, and titanium) in aluminium alloys. Aluminium casting samples were obtained by adding compressed powder compacts of each alloying element and aluminium (minitablets) to aluminum baths in a laboratory crucible furnace. Digestion of solid samples was performed using concentrated HCI and H202 35% (v/v) previous to analysis by ICP-OES without any matrix separation. This solution-based method was validated considering direct current arc spectrometry as the reference method based on direct analysis without any pretreatment of the solid samples considered. Univariate statistical procedures were carried out, for which precision <3% and trueness of the analytical results were taken into account.     

Polarization Fourier transform infrared spectroscopy on ionic single crystal surfaces: Davydov splittings, adsorbated structures and 2D-phase transitions on NaCl(100) and MgO(100)

Polarized infrared spectra of adsorbates on NaCl(100) and MgO(100) single crystal cleavage planes reveal Davydov splittings, structures with adsorbate orientations and/or 2D-phase transitions, in concert with diffraction studies. CO₂ on NaCl shows the sharpest adsorbate spectra known ( ).     

Study of migration of active components of phosphorescent oxygen sensors for food packaging applications

A study of migration of the active components of oxygen sensors into food is presented. Six types of sensors, based on different oxygen sensitive dyes (two metalloporphyrins and one ruthenium dye), polymers (polystyrene and polysulfone) and support materials, were exposed to a number of standard ‘food simulants’ recommended by FDA/EU guidelines and then assayed for migration or sensor components and changes in oxygen calibration. Both metalloporphyrin sensor dyes leached only in olive oil and in 95% ethanol (used as a positive control), at maximum levels of 19.22 μg/dm² for PtOEPK and 113.96 μg/dm² for PtTFPP. The RuDPP dye showed maximum leaching in 95% ethanol (25.19 μg/dm²) while also migrating in an acidic aqueous simulant. Planar supports such as polyester tended to enhance the stability of the sensor. Migration of the styrene monomer from the polystyrene encapsulation medium was concluded to be low enough to be insignificant. Migration of sensor components was shown to correlate with the changes in sensor response to oxygen. Based on these results, sensor combinations were ranked on the basis of their resistance to leaching and their general stability, safety and suitability for use on a large scale in packaged foods and related food applications was proven.