Cross‐Linked‐Polymer‐Supported N‐{2′‐[(Arylsulfonyl)amino][1,1′‐binaphthalen]‐2‐yl}prolinamide as Organocatalyst for the Direct Aldol Intermolecular Reaction under Solvent‐Free Conditions

A bottom‐up strategy was used for the synthesis of cross‐linked copolymers containing the organocatalyst N‐{(1R)‐2′‐{[(4‐ethylphenyl)sulfonyl]amino}[1,1′‐binaphthalen]‐2‐yl}‐D ‐prolinamide derived from 2 (Scheme 1). The polymer‐bound catalyst 5b containing 1% of divinylbenzene as cross‐linker showed higher catalyst activity in the aldol reaction between cyclohexanone and 4‐nitrobenzaldehyde than 5a and 5c . Remarkably, the reaction in the presence of 5b was carried out under solvent‐free, mild conditions, achieving up to 93% ee (Table 1). The polymer‐bound catalyst 5b was recovered by filtration and re‐used up to seven times without detrimental effects on the achieved diastereo‐ and enantioselectivities (Table 2). The catalytic procedure with polymer 5b was extended to the aldol reaction under solvent‐free conditions of other ketones, including functionalized ones, and different aromatic aldehydes (Table 3). In some cases, the addition of a small amount of H₂O was required to give the best results (up to 95% ee). Under these reaction conditions, the cross‐aldol reaction between aldehydes proceeded in moderate yield and diastereo‐ and enantioselectivity (Scheme 2).     

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An approach to estimate the energy and strength of the intramolecular hydrogen bond in different conformers of 4‐methylamino‐3‐penten‐2‐one

The molecular structure and intramolecular hydrogen bond energy of 32 conformers of 4‐methylamino‐3‐penten‐2‐one were investigated at MP2 and B3LYP levels of theory using the standard 6–31G** basis set and AIM analyses. Furthermore, calculations for all the possible conformations of 4‐methylamino‐3‐penten‐2‐one in water solution were also carried out at B3LYP/6–31G** level of theory. The calculated geometrical parameters and conformational analyses in gas phase and water solution show that the ketoamine conformers of this compound are more stable than the other conformers (i.e., enolimine and ketoimine). This stability is mainly due to the formation of a strong N? H···O intramolecular hydrogen bond, which is assisted by π‐electrons resonance. Hydrogen bond energies for all conformers of 4‐methylamino‐3‐penten‐2‐one were obtained from the related rotamers method. The nature of intramolecular hydrogen bond existing within 4‐methylamino‐3‐penten‐2‐one has been investigated by means of the Bader theory of atoms in molecules, which is based on topological properties of the electron density. The results of these calculations support the results which obtained by related rotamers method. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Automated discovery of noncovalent inhibitors of SARS-CoV-2 main protease by consensus Deep Docking of 40 billion small molecules

Recent explosive growth of ‘make-on-demand’ chemical libraries brought unprecedented opportunities but also significant challenges to the field of computer-aided drug discovery. To address this expansion of the accessible chemical universe, molecular docking needs to accurately rank billions of chemical structures, calling for the development of automated hit-selecting protocols to minimize human intervention and error. Herein, we report the development of an artificial intelligence-driven virtual screening pipeline that utilizes Deep Docking with Autodock GPU, Glide SP, FRED, ICM and QuickVina2 programs to screen 40 billion molecules against SARS-CoV-2 main protease (Mpro). This campaign returned a significant number of experimentally confirmed inhibitors of Mpro enzyme, and also enabled to benchmark the performance of twenty-eight hit-selecting strategies of various degrees of stringency and automation. These findings provide new starting scaffolds for hit-to-lead optimization campaigns against Mpro and encourage the development of fully automated end-to-end drug discovery protocols integrating machine learning and human expertise.

Deep learning-accelerated docking coupled with computational hit selection strategies enable the identification of inhibitors for the SARS-CoV-2 main protease from a chemical library of 40 billion small molecules.     

Growth of single crystals of copper and their thermal profile estimation

Copper crystals have been grown by Czochralski technique in a 6-bar argon gas environment. X-ray analysis shows that these are single crystals and are strain-free. A slight pressure environment that is truly hydrostatic seems to improve the quality of the crystals. Thermal profile estimation results show that the values of temperature which decrease upto the neck region are same in magnitude as those measured during the experiments and that necking improves the thermal profile and, consequently, the crystal quality. No facet formation has been observed in these crystals.     

Exact versus approximate determination of structural reliability

Exact and approximate solutions for the reliability of a circular shaft, simultaneously subjected to a bending moment and a torque, are derived and compared. The closed-form solution is obtained in terms of an equivalent bending moment having a noncentral chi-square distribution, whereas the approximate solution is derived via the Hasofer-Lind reliability index. Comparison shows a remarkably high accuracy of the index.On leave from the Technion, Israel Institute of Technology, Haifa, Israel     

Asymptotics in Bayesian decision theory with applications to global robustness

We provide the rate of convergence of the Bayes action derived from non smooth loss functions involved in Bayesian robustness. Such loss functions are typically not twice differentiable but admit right and left second derivatives. The asymptotic limit of three measures of global robustness is given. These measures are the range of the Bayes actions set associated with a class of loss functions, the maximum regret of using a particular loss when the subjective loss belongs to a given class and the range of the posterior expected loss when the loss ranges over a given class. An application to prior robustness with density ratio classes is provided.     

Rings with Commuting Nilpotents and Zero Divisors

We explore the consequences of certain commutativity hypotheses on a single nilpotent element or the set N of all nilpotent elements. We give several sufficient conditions for N to be an ideal. We present some nontrivial examples, including an example in which N is commutative (in fact, N ² = {0}) and N is not an ideal. Received: April 27, 2006. Revised: July 31, 2006.     

Performance analysis of single stage kanban controlled production systems using parametric decomposition

We present a new approach that permits efficient performance analysis of kanban systems with general demand processes, material arrival processes, and service times. The approach is based on parametric characterization of the traffic processes (arrival and departure) in the network and uses two-moment approximations to estimate performance measures at individual stations. We derive traffic flow constraints that are particular to closed queuing networks with synchronization stations and use these to establish relationships between the parameters characterizing arrival and departure processes at the stations in the network. The resultant set of non-linear equations is solved to estimate network performance measures. Numerical studies show that the approach is not only fast but also reasonably accurate when compared to simulation. These studies also provide insights with respect to the impact of different types of variability on the performance of a kanban system. This work also provides a fundamental building block that can be used in the analysis of multi-stage kanban systems. AMS Subject Classifications 68M20, 60K20, 90B05, 90B30     

Correlated equilibrium and potential games

Any correlated equilibrium of a strategic game with bounded payoffs and convex strategy sets which has a smooth concave potential, is a mixture of pure strategy profiles which maximize the potential. If moreover, the strategy sets are compact and the potential is strictly concave, then the game has a unique correlated equilibrium.