Foundations of continuous-time recursive utility: differentiability and normalization of certainty equivalents

This paper relates recursive utility in continuous time to its discrete-time origins and provides an alternative to the approach presented in Duffie and Epstein (Econometrica 60:353–394, 1992), who define recursive utility in continuous time via backward stochastic differential equations (stochastic differential utility). We show that the notion of Gâteaux differentiability of certainty equivalents used in their paper has to be replaced by a different concept. Our approach allows us to address the important issue of normalization of aggregators in non-Brownian settings. We show that normalization is always feasible if the certainty equivalent of the aggregator is of the expected utility type. Conversely, we prove that in general Lévy frameworks this is essentially also necessary, i.e. aggregators that are not of the expected utility type cannot be normalized in general. Besides, for these settings we clarify the relationship of our approach to stochastic differential utility and, finally, establish dynamic programming results.     

An Aggregating Amphiphilic Squaraine: A Light-up Probe That Discriminates Parallel G-Quadruplexes

G-quadruplexes (G4s) are peculiar DNA or RNA tertiary structures that are involved in the regulation of many biological events within mammalian cells, bacteria, and viruses. Although their role as versatile therapeutic targets has been emphasized for 35 years, G4 selectivity over ubiquitous double-stranded DNA/RNA, as well as G4 differentiation by small molecules, still remains challenging. Here, a new amphiphilic dicyanovinyl-substituted squaraine, SQgl , is reported to act as an NIR fluorescent light-up probe discriminating an extensive panel of parallel G4s while it is non-fluorescent in the aggregated state. The squaraine can form an unconventional sandwich π-complex binding two quadruplexes, which leads to a strongly fluorescent (Φ_F=0.61) supramolecular architecture. SQgl is highly selective against non-quadruplex and non-parallel G4 sequences without altering their topology, as desired for applications in selective in vivo high-resolution imaging and theranostics.     

Dependence of collision‐induced dissociation energy on molecular degrees of freedom as a means to assess relative binding affinity in multivalent complexes

In collision‐induced dissociation mass spectrometry experiments, the collision energy required for dissociation linearly depends on the degrees of freedom in the precursor ion. The magnitude of the slope of this relationship previously has been shown to qualitatively correlate to the relative binding strength of a noncovalently bound, monovalent complex. The goal of the work presented here is to determine if a similar methodology can be applied for assessing relative binding strengths in multivalent species. We have tested the method on complexes formed from 18‐crown‐6 and a variety of protonated, primary alkylamines, [C_nH_2n+1NH₃]⁺ (n = 9, 12, 14, 16 and 18) and alkyldiamines, [H₃NC_nH_2nNH₃]²⁺ (n = 3, 5, 6, 9 and 12), and compared our results with dissociation energies calculated using density functional theory at the B3LYP/6‐31G* level. We found that the method correctly assessed the stronger crown ether/headgroup interaction in the two divalent species (1:1 and 2:1 complexes formed from the diaminoalkanes) compared with the weaker interaction in the monovalent species (1:1 complexes formed from mono‐aminoalkanes). However, the experimental method could not distinguish between the binding strengths of the two divalent complexes, perhaps because their calculated dissociation energies were quite similar. Our preliminary results suggest that this method could potentially be used for a quick and simple analysis of binding strengths in multivalent species if the binding strengths of the species are significantly different from one another. Copyright © 2011 John Wiley & Sons, Ltd.     

Annihilators for Harmonic Differential Forms Via Clifford Analysis

In this paper we describe completely the annihilators of harmonic differential forms into the Clifford analysis approach.     

Huxley��s Model of Muscle Contraction with Compliance

Huxley??s cross-bridge dynamics of muscle contraction is widely used in understanding, in particular, laboratory experiments on muscles and subunits of muscle. The hard-connection version of the model has several defects. In this paper I present a detailed and precise method of solution of the problem with a compliant element in series with the muscle.     

Environmentally friendly sonocatalysis promoted preparation of 1-thiocarbamoyl-3,5-diaryl-4,5-dihydro-1H-pyrazoles

An efficient and green synthesis of thiocarbamoyl-3,5-diaryl-4,5-dihydro-1H-pyrazoles via the condensation of chalcones with thiosemicarbazide in ethanol and KOH under ultrasound irradiation is reported. The products were isolated in good yields after short reaction times.     

Exciton‐Vibrational Couplings in Homo‐ and Heterodimer Stacks of Perylene Bisimide Dyes within Cyclophanes: Studies on Absorption Properties and Theoretical Analysis

The optical properties of a series of three cyclophanes comprising either identical or different perylene bisimide (PBI) chromophores were studied by UV/Vis absorption spectroscopy and their distinctive spectral features were analyzed. All the investigated cyclophanes show significantly different absorption features with respect to the corresponding constituent PBI monomers indicating strong coupling interactions between the PBI units within the cyclophanes. DFT calculations suggest a π‐stacked arrangement of the PBI units at close van der Waals distance in the cyclophanes with rotational displacement. Simulations of the absorption spectra based on time‐dependent quantum mechanics properly reproduced the experimental spectra, revealing exciton‐vibrational coupling between the chromophores both in homo‐ and heterodimer stacks. The PBI cyclophane comprising two different PBI chromophores represents the first example of a PBI heterodimer stack for which the exciton coupling has been investigated. The quantum dynamics analysis reveals that exciton coupling in heteroaggregates is indeed of similar strength as for homoaggregates.