Borodin–Okounkov formula,string equation and topological solutions of Drinfeld–Sokolov hierarchies

Letters in Mathematical Physics - We give a general method to compute the expansion of topological tau functions for Drinfeld–Sokolov hierarchies associated with an arbitrary untwisted affine...     

Visible-Light-Driven Strain-Increase Ring Contraction Allows the Synthesis of Cyclobutyl Boronic Esters

There are a limited number of ring-contraction methodologies which convert readily available five-membered rings into strained four-membered rings. Here we report a photo-induced radical-mediated ring contraction of five-membered-ring alkenyl boronate complexes into cyclobutanes. The process involves the addition of an electrophilic radical to the electron-rich alkenyl boronate complex, leading to an α-boryl radical. Upon one-electron oxidation, ring-contractive 1,2-metalate rearrangement occurs to give a cyclobutyl boronic ester. A range of radical precursors and vinyl boronates can be employed, and chiral cyclobutanes can be accessed with high levels of stereocontrol. The process was extended to the preparation of benzofused cyclobutenes and the versatility of the boronic ester was demonstrated by conversion to other functional groups.     

Implementation of chaotic circuits with a digital time-delay block

In this paper, the implementation of time-delay chaotic circuits is investigated. To implement the time-delay block, a solution based on a digital circuitry has been adopted. This solution leads to a programmable hardware which can be realized by using available field programmable gate arrays. In this paper, issues raised from this implementation such as the behavior of the system with respect to the precision and the sampling rate of the conversion process have been investigated. The synchronization error is proposed as an indicator of the accuracy of the whole implementation.     

Asymmetric organocatalytic α-amination of 2-oxindoles with bis(2,2,2-trichloroethyl)azo-dicarboxylate

An enantioselective electrophilic amination of 3-substituted-2-oxindoles is reported, using bis(2,2,2-trichloroethyl)azo-dicarboxylate and commercially available Cinchona alkaloid organocatalysts. The best results were obtained in the reaction of 3-aryl substrates, with high to excellent yields (75% to quantitative) and good stereoselectivity (64–77% ee). Facile reductive conversion of the protected 3-hydrazino fragment into the corresponding primary amine was also demonstrated, to expand the synthetic flexibility of asymmetric electrophilic amination with azo-dicarboxylic esters en route to enantioenriched 3-amino-2-oxindoles. The absolute configuration of 3-amino-3-phenyl-2-oxindole was independently established by electronic circular dichroism (ECD), combined with time-dependent density functional theory (TDDFT).     

Logarithmic Picard groups,chip firing,and the combinatorial rank

Mathematische Zeitschrift - Illusie has suggested that one should think of the classifying group of $$M_X^{gp}$$ -torsors on a logarithmically smooth curve X over a standard logarithmic point as a...     

Control of the Intermolecular Coupling of Dibromotetracene on Cu(110) by the Sequential Activation of CBr and CH Bonds

Dibromotetracene molecules are deposited on the Cu(110) surface at room temperature. The complex evolution of this system has been monitored at different temperatures (i.e., 298, 523, 673, and 723 K) by means of a variety of complementary techniques that range from STM and temperature‐programmed desorption (TPD) to high‐resolution X‐ray spectroscopy (XPS) and near‐edge X‐ray absorption fine structure spectroscopy (NEXAFS). State‐of‐the‐art density‐functional calculations were used to determine the chemical processes that take place on the surface. After deposition at room temperature, the organic molecules are transformed into organometallic monomers through debromination and carbon‐radical binding to copper adatoms. Organometallic dimers, trimers, or small oligomers, which present copper‐bridged molecules, are formed by increasing the temperature. Surprisingly, further heating to 673 K causes the formation of elongated chains along the Cu(110) close‐packed rows as a consequence of radical‐site migration to the thermodynamically more stable molecule heads. Finally, massive dehydrogenation occurs at the highest temperature followed by ring condensation to nanographenic patches. This study is a paradigmatic example of how intermolecular coupling can be modulated by the stepwise control of a simple parameter, such as temperature, through a sequence of domino reactions.