A One-Pot Divergent Sequence to Pyrazole and Quinoline Derivatives

The hydroxy-pyrazole and 3-hydroxy-oxindole motifs have been utilised in several pharma and agrochemical leads but are distinctly underrepresented in the scientific literature due to the limited routes of preparation. We have developed a one-pot procedure for their synthesis starting from simple isatins. The method employs cheap and easy-to-handle building blocks and allows easy isolation.

A modular and divergent approach to spirocyclic pyrrolidines

A three-step, modular and divergent sequence accessing challenging spirocyclic pyrrolidines has been developed, featuring a novel reductive spirocyclization cascade.

Summability of subsequences of a divergent sequence by regular matrices II

C. Stuart proved in [27, Proposition 7] that the Ces?ro matrix C1 cannot sum almost every subsequence of a bounded divergent sequence. At the end of the paper he remarked ?It seems likely that this proposition could be generalized for any regular matrix, but we do not have a proof of this?. In [4, Theorem 3.1] Stuart?s conjecture is confirmed, and it is even extended to the more general case of divergent sequences. In this note we show that [4, Theorem 3.1] is a special case of Theorem 3.5.5 in [24] by proving that the set of all index sequences with positive density is of the second category. For the proof of that a decisive hint was given to the author by Harry I. Miller a few months before he passed away on 17 December 2018.

RH-regular transformations which sums a given double sequence

In 1946 P. Erdos and P. C Rosenbloom presented the following theorem that arose out of discussions they had with R. P. Agnew. Let {xn} be a bounded divergent sequence. Suppose that {xn} is summable by every regular Toeplitz method which sums {xn}. Then {yn} is of the form {cxn + an} where {an} is convergent. The goals of the paper includes the presentation of a multidimensional analog of Erdos and Rosenbloom results in [1].

STOCHASTIC PROPERTIES OF DEGENERATED QUANTUM SYSTEMS

We study Schrödinger equation with degenerated symmetric but not self-adjoint Hamiltonian. The above properties of the quantum Hamiltonian arise in the description of the asymptotic behavior of the regularizing self-adjoint Hamiltonians sequence. A quantum dynamical semigroup corresponding to degenerated Hamiltonian is defined by means of the passage to the limit for the sequence of the regularizing dynamical semigroups. These semigroups are generated by the regularizing self-adjoint Hamiltonians. The necessary and sufficient conditions are obtained for the convergence of the regularizing semigroups sequence. The description of the divergent sequence of semigroups requires the extension of the stochastic process concept. We extend the stochastic process concept onto the family of measurable functions defined on the space endowed with finite additive measure. The above extension makes it possible to describe the structure of the partial limits set of the regularizing semigroups sequence.