Pathwise rate- stability for input-output processes

An input-output processZ = {Z(t), t 0} is said to be-rate stable ifZ(t) = o((t)) for some non-negative function(t). We prove that the processZ is -rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for-rate-stability can be verified from input data. For example, using input information, we establish-rate stability of the workload for multiserver queues, an ATM multiplexer, and-rate stability of queue-length processes for infinite server queues.     

The facile and efficient Michael addition of indoles and pyrrole to alpha,beta-unsaturated electron-deficient compounds catalyzed by aluminium dodecyl sulfate trihydrate [Al(DS)3].3H2O in water

Aluminium dodecyl sulfate trihydrate [Al(DS)3].3H2O is easily prepared and can be used as a Lewis acid surfactant catalyst in water to conduct the highly efficient Michael addition of indoles and pyrrole to alpha,beta-unsaturated electron-deficient compounds at room temperature.     

An efficient and chemoselective method for protection of thiols catalyzed by aluminumdodecatungstophosphate (AlPW12O40), as a highly water tolerant Lewis acid catalyst

Protection of various thiols with diphenylmethanol was achieved in high yields at room temperature using catalytic amounts of AlPW₁₂O₄₀ in CH₂Cl₂. In the presence of this catalyst, protection of SH versus OH was achieved with high chemoselectivity and yields. The catalyst can be easily recovered and reused. Deprotection of DPM thioethers was also achieved using molecular iodine at reflux in CH₂Cl₂ in high yields.     

Isolation, characterization, and theoretical study of La2@C78

A new metallofullerene, La2@C78, has been synthesized by DC arc discharge method, isolated by high-performance liquid chromatography, and characterized by laser desorption time-of-flight mass spectrometry, UV-vis-NIR absorption, differential pulse voltammetry, 13C NMR spectroscopy, and theoretical calculations. The La2@C78/CS2 solution is dark violet and presents several characteristic absorption features at 647, 561, 533, and 386 nm, with an onset around 1000 nm. With respect to empty D3-C78, the capability of La2@C78 as an electron acceptor or donor is stronger. Addition of 1,1,2,2-tetrakis(2,4,6-trimethylphenyl)-1,2-disirane to La2@C78 photochemically, as well as thermally, affords bis- and mono-adducts. Theoretical studies and 13C NMR spectroscopic analysis of La2@C78 indicate that it possesses a D3h-C78 cage (78:5).