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.     

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.     

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.