Continuous Newton-like Inertial Dynamics for Monotone Inclusions

Set-Valued and Variational Analysis - In a Hilbert framework ℌ, we study the convergence properties of a Newton-like inertial dynamical system governed by a general maximally monotone...     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

The square lattice shuffle

We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Consecutive reactions of diethoxydimethylsilane and triethoxymethylsilane with methoxide ions in methanol solution

The consecutive reactions of (CH₃)₂Si(OC₂H₅)₂ and CH₃Si(OC₂H₅)₃ with methoxide ions were investigated in methanol solutions. The reverse transesterification reactions with ethoxide ions could be neglected in both cases since the concentration of ethoxide in methanol solution was assumed to be low due to the fast equilibrium reaction C₂H₅O^? + CH₃OH ? C₂H₅OH + CH₃O^?. The progress of the reactions was followed by monitoring the formation of ethanol with a Fourier-transform infrared spectrometer. All rate constants were determined at 295 K. The reactions between the dialkoxydimethylsilanes and methoxide ions were assumed to consist of two consecutive steps that can be represented by the net reaction; (CH₃)₂Si(OC₂H₅)₂ + 2CH₃O^? → (CH₃)₂Si(OCH₃)₂ + 2C₂H₅O^?. The two consecutive rate constants were established as 1.93 ± 0.12M^?1s^?1 and 1.00 ± 0.12M^?1s^?1, respectively. The consecutive rate constants for the reactions between the trialkoxymethylsilanes and methoxide ions can be written according to the total reaction; CH₃Si(OC₂H₅)₃ + 3CH₃O^? → CH₃Si(OCH₃)₃ + 3C₂H₅O^?. The three rate constants corresponding to each consecutive step were established as 1.12 ± 0.09 M^?1s^?1, 0.82 ± 0.10 M^?1s^?1, and 0.51 ± 0.06 M^?1s^?1, respectively. © 1995 John Wiley & Sons, Inc.     

Diels-Alder-Reaktionen von Vinylindolen mit Arin und 1,4-Benzochinonen: Neue potentielle DNA-Interkalatoren

Summary Diels-Alder reactions of 2- and 3-vinylindoles with aryne, 1,4-benzo- and 1,4-naphtho-quinone lead to new six-ring annellated carbazoles. Molecular modeling studies predict that the compounds with coplanar framework are able to intercalate with the B-DNA.

     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.