Synthesis and photophysical properties of fluorescent 2-aryl-1,3-dialkylbenzimidazolium ions and a l-alkyl-2-arylbenzimidazole with excited state intramolecular proton-transfer

To improve the solubility, photostability and fluorescence quantum yield (Φ) of 2-arylbenzimidazolium ions the N-1 hydrogen was replaced by an alkyl group before N-3 was quatemized; this substitution did not reduce Φ, proving the absence of steric inhibition to attainment of coplanarity in the excited state. A related symmetrical 2,2′-arylenebis(1,3-dimethyldibenzimidazolium ion) had Φ = 0.86. The related 2,5-bis(1-methyl-2-benzimidazolyl)phenol had Φ = 0.38 at 22° as well as a very large Stokes' shift due to proton-transfer. These findings supported a new insight into the electron distribution of the first excited singlet state of oligophenylenes. The compounds are of interest as laser dyes and scintillation fluors.     

Syntheses and photophysical properties of some 5(2)-aryl-2(5)-(4-pyridyl)oxazoles and related oxadiazoles and furans

A number of 5-aryl-2-(4-pyridyl)oxazoles, a 2-aryl-5-(4-pyridyl)oxazole, the related oxadiazole and furan, several 2-(4-pyridyl)cycloalkano[d]oxazoles, and many of their quaternary salts were prepared. No single standard synthesis was effective for preparation of more than a few of the 25 free bases described; methods often unique to a base were employed. Minor variations in structure sometimes produced large differences in absorption and emission wavelengths, as well as in the magnitude of the extinction coefficient. The salts are of interest as laser dyes, scintillation fluors, biological stains, and shifters for luminescent solar concentrators.     

Syntheses of reactive fluorescent stains derived from 5(2)-aryl-2(5)-(4-pyridyl)oxazoles and bifunctionally reactive linkers

Several bifunctionally reactive linkers containing halide or sulfonate ester groups were prepared. The linkers were used to quaternize 5-(4-methoxyphenyl)-2-(4-pyridyl)oxazole and 2-(6-chromanyl)-5-(4-pyridyl)oxazole to produce fluorescent stains that contained a reactive group such as an isothiocyanate, an N-hydroxysuccinimidyl ester, a maleimide, or an oxirane. The stains were derivatized with either 1-propylamine, 1-propanethiol, or piperidine, as appropriate, to help in characterization. The stains may serve as more photostable alternatives to fluoresceins or coumarins.     

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

Completions of GBL-algebras: negative results

We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang’s chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley. Received August 10, 2006; accepted in final form March 8, 2007.     

Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum

We use friction to simultaneously damp and excite a pendulum system. A Froude pendulum attached to a suspension shaft is subjected to a frictional load. We investigate two types of response of the system: regular and chaotic responses, depending on the excitation frequency. A transient chaotic solution was also obtained. We identify the motions using phase portraits, Poincaré maps, and Fourier spectra. Finally, the composite multiscaled entropy was estimated for the specified cases to confirm the preliminary classification.     

Lewis meets Brouwer: Constructive strict implication

C.I. Lewis invented modern modal logic as a theory of “strict implication” $?$. Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than $\square$ and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic $\mathsf{K}$ becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the “strength” axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction has been discovered by the functional programming community in their study of “arrows” as contrasted with “idioms”. Our particular focus is on arithmetical interpretations of intuitionistic $?$ in terms of preservativity in extensions of $\mathsf{HA}$, i.e., Heyting’s Arithmetic.