Microwave-mediated synthesis and manipulation of a 2-substituted-5-aminooxazole-4-carbonitrile library

A 2-substituted-5-aminooxazole-4-carbonitrile library has been synthesised and modified via microwave-mediated and flow chemistries. One synthesised compound, 5-(1H-pyrrol-1-yl)-4-(1H-tetrazol-5-yl)-2-(thien-2-yl)oxazole, contains three distinct heterocycles attached to the central oxazole core, highlighting the structural diversity of this approach. Three oxazoles had micromolar k_i values against cannabinoid (CB1/CB2) receptors.     

Crystal Structures of Two Palladacycles from the C–H Activation of 2-(Thiophen-2-yl)pyridine

Abstract  

A C,N-bound palladacycle dimer has been synthesised by reaction of 2-(thiophen-2-yl)pyridine, LH, with palladium acetate in acetic acid. Characterisation by single crystal X-ray diffraction showed the palladacycle dimer, [(L)Pd(OAc)]₂, to crystallise in the monoclinic space group P2₁/n with cell parameters a = 9.5853(1) ?, b = 19.1332(3) ?, c = 12.3889(2) ?, β = 103.732(1)°. Reaction of [(L)Pd(OAc)]₂ with triphenylphosphine afforded a trans-substituted monomeric complex, [(L)PdPPh₃(OAc)] which was also analysed using single crystal X-ray diffraction. [(L)PdPPh₃(OAc)] crystallises in the monoclinic space group P2₁/c with cell parameters a = 9.4839(1) ?, b = 11.0427(2) ?, c = 26.0770(4) ?, β = 95.022(1)°.     

The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology

One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this study, we consider a row of n plants in which m are infected. We then develop a rigorous mathematical approach to investigate the total number of ways to obtain k isolated individuals among m infected plants. We give a recurrence relation in three parameters that describes the problem, then we find a closed-form solution, and give two different approaches to tackle the proof. Finally, we find interesting formulae for the expectation and variance of the random variable that represents the number of infected and isolated plants.     

Bi2223带材临界电流沿长度方向的统计分布

本文采用四引线法测量了Bi2223带材临界电流沿长度方向的分布,采用正态分布、对数正态分布、威布尔分布和最小极值分布对临界电流分布进行了拟合检验,确定了临界电流的最优统计分布模型.