Multi-Dimensional Generalized Integral Transform in the Weighted Spaces of Summable Functions

In this paper, we study a multi-dimensional generalized integral transformation. The functional and compositional properties of the integral transformation in spaces of summable functions are investigated. The scheme of study is similar to the process of constructing the theory of the H-transformation, in which the central place is given to the questions of bounded and one-to-one action of the corresponding integral operator in spaces of integrable functions with weight concentrated at zero and at infinity. Theory of the considered integral transformation in weighted spaces of summable functions is constructed

Intermolecular Photocatalytic Chemo‐, Stereo‐ and Regioselective Thiol–Yne–Ene Coupling Reaction

The first example of an intermolecular thiol–yne–ene coupling reaction is reported for the one-pot construction of C−S and C−C bonds. Thiol–yne–ene coupling opens a new dimension in building molecular complexity to access densely functionalized products. The employment of Eosin Y/DBU/MeOH photocatalytic system suppresses hydrogen atom transfer (HAT) and associative reductant upconversion (via C−S three-electron σ-bond formation). Investigation of the reaction mechanism by combining online ESI-UHRMS, EPR spectroscopy, isotope labeling, determination of quantum yield, cyclic voltammetry, Stern–Volmer measurements and computational modeling revealed a unique photoredox cycle with four radical-involving stages. As a result, previously unavailable products of the thiol–yne–ene reaction were obtained in good yields with high selectivity. They can serve as stable precursors for synthesizing synthetically demanding activated 1,3-dienes

Selectivity control in thiol–yne click reactions via visible light induced associative electron upconversion

An associative electron upconversion is proposed as a key step determining the selectivity of thiol-yne coupling. The developed synthetic approach provided an efficient tool to access a comprehensive range of products - four types of vinyl sulfides were prepared in high yields and selectivity. We report practically important transition-metal-free regioselective thiol-yne addition and formation of the demanding Markovnikov-type product by a radical photoredox process. The photochemical process was directly monitored by mass-spectrometry in a specially designed ESI-MS device with green laser excitation in the spray chamber. The proposed reaction mechanism is supported by experiments and DFT calculations

Solution of One Class of Multi-Dimensional Integral Equations of the First Kind With Hyperbolic Sine Function in Kernels

Рассматривается один класс многомерных интегральных уравнений первого рода с функцией гиперболического синуса в ядрах по ограниченной пирамидальной области специального вида. Следуя методике Я. Тамаркина, выводятся явные формулы решений рассматриваемых многомерных интегральных уравнений. Устанавливаются необходимые и достаточные условия разрешимости таких уравнений в пространствах суммируемых функций.= One class of multidimensional integral equations of the first kind with a hyperbolic sine function in kernels over a bounded pyramidal domain of a special form is considered. Following the technique of Ya. Tamarkin, explicit formulas for the solution of the considered multidimensional integral equations are derived. Necessary and sufficient conditions for the solvability of such equations in spaces of summable functions are established

Reversible Radical Addition Guides Selective Photocatalytic Intermolecular Thiol-Yne-Ene Molecular Assembly

In the realm of modern organic chemistry, harnessing the power of multicomponent radical reactions presents both significant challenges and extraordinary potential. This article delves into this scientific frontier by addressing the critical issue of controlling selectivity in such complex processes. We introduce a novel approach that revolves around the reversible addition of thiyl radicals to multiple bonds, reshaping the landscape of multicomponent radical reactions. The key to selectivity lies in the intricate interplay between reversibility and the energy landscapes governing C-C bond formation in thiol-yne-ene reactions. The developed approach not only allows to prioritize the thiol-yne-ene cascade, dominating over alternative reactions, but also extends the scope of coupling products obtained from alkenes and alkynes of various structures and electron density distributions, regardless of their relative polarity difference, opening doors to more versatile synthetic possibilities. In the present study, we provide a powerful tool for atom-economical C-S and C-C bond formation, paving the way for the efficient synthesis of complex molecules. Carrying out our experimental and computational studies, we elucidated the fundamental mechanisms underlying radical cascades, a knowledge that can be broadly applied in the field of organic chemistry

General cross-coupling reactions with adaptive dynamic homogeneous catalysis

Cross-coupling reactions are among the most important transformations in modern organic synthesis1,2,3. Although the range of reported (het)aryl halides and nucleophile coupling partners is very large considering various protocols, the reaction conditions vary considerably between compound classes, necessitating renewed case-by-case optimization of the reaction conditions4. Here we introduce adaptive dynamic homogeneous catalysis (AD-HoC) with nickel under visible-light-driven redox reaction conditions for general C(sp2)–(hetero)atom coupling reactions. The self-adjustive nature of the catalytic system allowed the simple classification of dozens of various classes of nucleophiles in cross-coupling reactions. This is synthetically demonstrated in nine different bond-forming reactions (in this case, C(sp2)–S, Se, N, P, B, O, C(sp3, sp2, sp), Si, Cl) with hundreds of synthetic examples under predictable reaction conditions. The catalytic reaction centre(s) and conditions differ from one another by the added nucleophile, or if required, a commercially available inexpensive amine base