Three-Component,One-Pot Synthesis of 2,4,5-Trisubstituted Imidazoles Catalyzed by TiCl4-SiO2 Under Conventional Heating Conditions or Microwave Irradiation

In this study, silica-supported titanium tetrachloride was prepared and used as a novel catalyst for rapid and efficient synthesis of 2,4,5-trisubstituted imidazoles by a three-component, one-pot condensation of 1,2-diketones and aryl aldehydes in excellent yield under solvent-free conditions using conventional heating or microwave irradiation.

The Nullstellensatz for Systems of PDE

Given an ideal I in , the polynomial ring in n-indeterminates, the affine variety of I is the set of common zeros in ⁿ of all the polynomials that belong to I, and the Hilbert Nullstellensatz states that there is a bijective correspondence between these affine varieties and radical ideals of . If, on the other hand, one thinks of a polynomial as a (constant coefficient) partial differential operator, then instead of its zeros in ⁿ, one can consider its zeros, i.e., its homogeneous solutions, in various function and distribution spaces. An advantage of this point of view is that one can then consider not only the zeros of ideals of , but also the zeros of submodules of free modules over (i.e., of systems of PDEs). The question then arises as to what is the analogue here of the Hilbert Nullstellensatz. The answer clearly depends on the function–distribution space in which solutions of PDEs are being located, and this paper considers the case of the classical spaces. This question is related to the more general question of embedding a partial differential system in a (two-sided) complex with minimal homology. This paper also explains how these questions are related to some questions in control theory.     

Deactivation of Escherichia coli with different volumes in drinking water using cold atmospheric plasma

This experimental study aimed to evaluate the potential of cold atmospheric plasma jet to deactivate Escherichia coli from drinking water. We studied the effect of the volume of water samples on the performance of plasma jet on deactivation of E. coli of 1, 500, 1,000, 1,500, and 2,000 cubic centimetres. The results of deactivation of E. coli in 500 and 1,000 cc water samples were the same as one cc of a water sample and we observed 8-log reduction of E. coli using 50 W. In 1,500 and 2,000 cc water samples at 8 min using a power of 50 W, 4.5 and 2.9 log reduction of E. coli was achieved and while we used 20 W, 2.5 and 1.8 log reduction of E. coli bacteria was performed. This indicated that the increasing volume of water above 1,500 cc caused the reduction of the efficiency of E. coli removal. Also, increasing power caused to increase E. coli removal efficiency. In addition, we monitored changes in pH values and temperature during experiments. Using 20 W, the temperature was increased (natural temperature of the water was 22 °C) 2 °C after 8 min while applying 50 W, the temperatures were raised 5 °C. pH of the water after 8 min in the 1,000 cc water sample, with an input power of 20 W, decreased from 7.1 to 5.5; while the input power was 50 W, pH changed from 7.1 to 4.3. With an increase in plasma irradiation time, the number of E. coli had a significant decrease per min while using in samples of 1 cc. After 8 min, we observed 4-log reductions of E. coli with the input power of 20 W and 8-log reduction of bacteria with the input power of 50 W. In 1,500 and 2,000 cc of water samples using plasma radiation for 8 min, 2.5 log and 1.8 log reduction of E. coli was achieved, respectively. This means that an increasing volume of water above 1,500 cc needs more power and time to deactivate E. coli from the water.     

On the probability of Magnus Carlsen reaching 2900

How likely is it that Magnus Carlsen will achieve his goal of a 2900 Elo rating? At what level of play does Magnus have a reasonable chance of reaching the 2900 goal? These two questions are of great current interest to Magnus and the chess community. The probabilistic properties of Elo's rating system are well known, and together with a Brownian motion model of rating evolution, we use simulation-based methods to address these questions. Our model assesses that Magnus has a 4.5% chance of reaching 2900 if he continues his 2020–2022 level of play. However, this increases dramatically to $80$% chance if he can repeat his hot streak performance of 2019 which is not an easy undertaking. The probabilities are intimately related to Elo's choice $K$-factor used for grandmaster chess play. Finally, we conclude with a discussion of the policy issues involved with the choice of $K$-factor.