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We report the Pd-catalyzed α-arylation of α,α-difluoroketones with aryl and heteroaryl bromides and chlorides catalyzed by an air- and moisture-stable palladacyclic complex containing P(t-Bu)Cy2 as ligand. The combination of this Pd-catalyzed arylation and base-induced cleavage of the acyl-aryl C-C bond within the α-aryl-α,α-difluoroketone constitutes a one-pot, two-step procedure to synthesize difluoromethylarenes from aryl halides. A broad range of electronically varied aryl and heteroaryl bromides and chlorides underwent these two transformations, providing α-aryl-α,α-difluoroketones, difluoromethylarenes, and difluoromethylheteroarenes in high yields.
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In this tutorial paper, we consider an infinite-dimensional extension of Chua's circuit, as shown in Fig. 1, where the transmission line is lossless. As we shall see, if the capacitance C 1 is set to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced, without any approximation, to that of a continuous scalar nonlinear difference equation. This type of equation can lead to space-time chaos which, due to the absence of viscosity in our system, will be termed "dry turbulence". Another interesting property of this system occurs under certain conditions, when the corresponding 1-D map has two segments and is piecewise-linear. The extreme simplicity of this map will allow us to derive, without any approximation, the exact analytical solution of the stability boundaries of stable cycles of every period n. Since the stability region is non-empty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.
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Abstract Background The memory support intervention (MSI) was developed to improve patient memory for treatment as poor memory for treatment is associated with poorer adherence and outcomes. This study aimed to (1) validate the Cognitive Behavior Change interview, which was developed for and used as a measure in this study, (2) assess differences in specific factors impacting behavior change (domains) described in the Theoretical Domains Framework (TDF) among participants who received the MSI alongside cognitive therapy (CT) compared to those who received CT-as-usual, and (3) assess whether memory for treatment facilitates behavior change. Methods Participants ( N = 64) from a trial of adults with Major Depressive Disorder were randomly allocated to CT + Memory Support (MS) or CT-as-usual. To ascertain whether CT + MS better improves knowledge of domains of behavior change, the Cognitive Behavior Change Interview was administered at the 12-month follow-up (12FU) assessment. This qualitative and quantitative interview is grounded in the TDF and includes ratings of potential facilitators of behavior change. Regression was used to examine relations between memory support, these facilitators, and behavior change. Results Internal consistency for the Cognitive Behavioral Change interview fell in the acceptable range, whereas interrater reliability ranged from unreliable to excellent. Participants who received CT + MS demonstrated better overall engagement with domains compared to participants who received CT-as-usual. Improved memory for treatment was positively associated with overall engagement and the number of domains engaged. Overall engagement and the number of domains engaged were associated with utilization of skills learned in CT and improved impairment and depression at 12FU. Conclusions This study enhances our understanding of the potential role of memory for treatment improving long-term behavior change. Exploratory analyses highlight specific domains that may be factors driving changes in behavior due to CT resulting in improvements in depression.
Substituted pyrroles were prepared by a gold(I)-catalyzed acetylenic Schmidt reaction of homopropargyl azides. The reaction allows for regiospecific substitution at each position of the pyrrole ring under mild conditions. A mechanism in which azides serve as nucleophiles toward gold(I)-activated alkynes with subsequent gold(I)-aided expulsion of dinitrogen is proposed.