Assessing the nucleophilic character of 2-amino-4-arylthiazoles through coupling with 4,6-dinitrobenzofuroxan: Experimental and theoretical approaches based on structure-reactivity relationships

A kinetic study of the reactions of potentially bioactive 2-amino-4-arylthiazoles with highly reactive 4,6-dinitrobenzofuroxan (DNBF) is reported herein in acetonitrile solution. The complexation reaction was followed by recording the UV–vis spectra with time at λ_max = 482 nm. Electronic effects of substituents influencing the rate of reaction have been studied using structure-reactivity relationships. It is shown that the Hammett plot relative to the reaction of DNBF with 2-amino-4-(4-chlorophenyl)thiazole exhibit positive deviation from the log k₁ versus σ correlation, while it showed excellent linear correlation in terms of Yukawa–Tsuno equation. It has be noticed that the nonlinear Hammett plot observed for 2-amino-4-(4-chlorophenyl) thiazole is not attributed to a change in rate-determining step but is due to nature of electronic effect of substituent caused by the resonance of stabilization of substrates. The second-order rate constant (k₁) relating to the bond C–C and C-N forming step of the complexation processes of DNBF with 4-substituted-aminothiazoles and 2-amino-5-methyl-4-phenylthiazole, respectively, is fit into the linear relationship log k = s_N (N + E), thereby permitting the assessment of the nucleophilicity parameter (N) of the 2-amino-4-arylthiazoles of the range (4.90 < N < 6.85). 2-amino-4-arylthiazoles is subsequently ranked by positioning its reactivity on the general nucleophilicity scale developed recently by Mayr and coworkers (2003) leading an interesting and a direct comparison over a large domain of π-, σ -, and n-nucleophiles. The global electrophilicity/nucleophilicity reactivity indexes of the 2-amino-4-arylthiazoles have been investigated by means of a density functional theory (DFT) method. .     

An exposition of the topological half of the Grothendieck–Hirzebruch–Riemann–Roch theorem in the fancy language of spectra

We give an informal exposition of pushforwards and orientations in generalized cohomology theories in the language of spectra. The whole note can be seen as an attempt at convincing the reader that Todd classes in Grothendieck–Hirzebruch–Riemann–Roch type formulas are not Devil’s appearances but rather that things just go in the most natural possible way.

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Theoretical Investigation of the Reaction Mechanism of the Photoisomerization of 1,2‐Dihydro‐1,2‐azaborine

The photoisomerization of 1,2‐dihydro‐1,2‐azaborine was investigated by high‐level multireference ab initio and density functional theory calculations. The intermediates (IMs) and transition states (TSs) on the S₀ and S₁ states were optimized using the state‐averaged complete active space self‐consistent field method. The multireference configuration interaction method with the Davidson correction was used to obtain accurate energetics. Moreover, the conical intersections (CIs), which play a crucial role in photoisomerization, were also optimized. On the basis of the calculation results, the most favorable proposed reaction pathway is as follows: reactant→Franck‐Condon region→TS₁→CI→IM₀→TS_0P→product. The product was not directly formed through the CI, and the IM₀ existed on the S₀ state. These results show that the isomerization of 1,2‐dihydro‐1,2‐azaborine involves both photoreactions and thermal reactions. The calculated results clarify recent experimental observations.     

Action of generalized symmetric groups on symmetric and exterior powers of their natural representations

We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalized symmetric groups. We adapt the methods of Savitt and Stanley from [4 Savitt, D., Stanley, R. P. (2000). A note on the symmetric powers of the standard representation of S_n. Electron. J. Combin. 7:R6. [Google Scholar]] to obtain bounds both over the complex numbers and in prime characteristic.     

Central Schur rings over the projective special linear groups

In [1 Bannai, E. (1991). Subschemes of some association schemes. J. Algebra 14:167–188.[Crossref], [Web of Science ®] , [Google Scholar]], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these.     

大族长度为pq的伪随机k元序列

Mauduit与Sárkzy在一系列论文中研究了κ元序列的伪随机性.本文通过对模pq剩余类环Z_(pq)进行分割,进而结合离散对数的方法,构造了一大族长度为pq的伪随机κ元序列,并证明其具有很好的伪随机性.     

广义线性多乘积问题的完全多项式时间近似算法

本文针对广义线性多乘积极小化问题,通过一系列的线性规划问题的解提出一种求其全局最优解的完全多项式时间近似算法,并给出该算法的计算复杂性,且数值算例验证该算法是可行的.