Consistency of decision processes

If a statistical or a voting decision procedure is used by several subpopulations and if each reaches an identical conclusion, then one might expect this conclusion to be the outcome for the full group. It is shown that this property fails to hold for large classes of decision procedures. The geometric reasons why the consistency does not hold are described. A general theorem is given to characterize the procedures that satisfy this property of weak consistency.This research was supported in part by NSF Grant IRI-8803505 and a Guggenheim Fellowship. Also, the author thanks a referee for some comments that stimulated certain revisions.     

Synthesis and reactions of some dihydro and tetrahydro-4H-imidazo[5,4,1-ij]quinoline derivatives

Reaction of phenyl N-(8-quinolinyl)carbamate with sodium borohydride afforded 1,2-dihydro-4H-imidazo-[5,4,1-ij]quinolin-2-one, 2a . The 5,6-double bond of 2a was functionalized by reaction with nitrosyl chloride to give the nitroolefin 4 and by reaction with hypobromous acid to give the trans-bromohydrin 5 . Reaction of 5 with sodium azide led to the rearranged trans-6-azido-5-ol 7 , the structure of which was determined by ¹H nmr studies.     

A comparative study of solvent extraction of total petroleum hydrocarbons in soil

Three non-specific methods for the extraction of total petroleum hydrocarbons (TPH) from soil into organic solvent were compared. The techniques used for sample preparation were Soxhlet extraction, closed-vessel microwave-assisted extraction, and CEN shake extraction. The total concentrations of extracted compounds in the boiling point range of C10–C40 were determined by gas chromatography with flame ionization detection. The best recovery (99%) and repeatability (±3%) from standard oil mixtures were obtained with microwave-assisted extraction. However, the different extraction methods exhibited different behaviour when spiked soil samples were extracted. The best repeatability was obtained with CEN shake extraction (±6%) but the repeatability values for Soxhlet and microwave-assisted methods were quite high (>20%). However, the larger uncertainties of the latter extraction methods does not necessarily limit the applicability of these methods to the determination of petroleum hydrocarbons in soil, as in the assessment of soil contamination the expanded uncertainty of the result is usually not limited by analytical uncertainty, but rather by the uncertainty of the primary sampling stage. However, distinctive variation found in the chromatographic profiles illustrates that discretion should be obeyed when chromatograms obtained after application of different extraction methods on petroleum contaminated samples are to be used in the fingerprinting or age dating studies. Otherwise, misleading conclusions concerning the age of spillage could be drawn.     

Color Bricks: Building Highly Organized and Strongly Absorbing Multicomponent Arrays of Terpyridyl Perylenes on Metal Oxide Surfaces

Terpyridine‐substituted perylenes containing cyclic anhydrides in the peri position were synthesized. The anhydride group served as an anchor for assembly of the terpyridyl‐crowned chromophores as monomolecular layers on metal oxide surfaces. Further coordination with Zn²⁺ ions allowed for layer‐by‐layer formation of supramolecular assemblies of perylene imides on the solid substrates. With properly selected anchor and linker molecules it was possible to build high quality structures of greater than ten successive layers by a simple and straightforward procedure. The prepared films were stable and had a broad spectral coverage and high absorbance. To demonstrate their potential use, the synthesized dyes were employed in solid‐state dye‐sensitized solar cells, and electron injection from the perylene antennas to titanium dioxide was observed.     

Everywhere -repetitive sequences and Sturmian words

Local constraints on an infinite sequence that imply global regularity are of general interest in combinatorics on words. We consider this topic by studying everywhere α-repetitive sequences. Such a sequence is defined by the property that there exists an integer N≥2 such that every length-N factor has a repetition of order α as a prefix. If each repetition is of order strictly larger than α, then the sequence is called everywhere α⁺-repetitive. In both cases, the number of distinct minimal α-repetitions (or α⁺-repetitions) occurring in the sequence is finite.A natural question regarding global regularity is to determine the least number, denoted by M(α), of distinct minimalα-repetitions such that an α-repetitive sequence is not necessarily ultimately periodic. We call the everywhere α-repetitive sequences witnessing this property optimal. In this paper, we study optimal 2-repetitive sequences and optimal 2⁺-repetitive sequences, and show that Sturmian words belong to both classes. We also give a characterization of 2-repetitive sequences and solve the values of M(α) for 1≤α≤15/7.     

The correlation of multiplets in different electronic transitions of 1, 12 benzperylene in solid matrices

Using a selective excitation technique, the correspondence of multiplet structure of spectra in the S₁←S₀, T₁→S₀ and S₂←S₀ electronic transitions of the 1, 12 benzperylene molecule in various matrices at 4.2 K is studied. The occurrence of an ambiguous correspondence of different electronic transition energies is pointed out. The reason for the lack of the sharpening of phosphorescence spectra under the monochromatic S₁←S₀ excitation is discussed.     

The ease of generating chaotic behavior in economics

Supported by the wealth of models demonstrating chaotic behavior in economics, it becomes appropriate to examine whether this phenomenon is restricted to concocted models or is central to economics. After showing why this behavior is prevalent, aspects of economics causing this behavior are identified. Surprisingly, the basic source of problems from choice theory also generate some of the random motion of economics.     

Photochemical time-domain holography of weak picosecond pulses

We show that weak picosecond optical pulse propagation through an absorbing medium with a photochemically burnedin persistent spectral hologram of a picosecond pulse train makes the sample emit coherently a replica of the pulse train applied in the burning-in cycle.