Informatics Publishing Limited

Abstract

Opening of the five-member ring of dihydrofuran-2,5-dione with amines was used to synthesize a series of amides of4-oxo-4-(substituted) butanoic acid.4-oxo-4-(substituted) butanoic acidamine coupling using 1,1'-carbonyldiimidazole (CDI) was designed to synthesize newbis-acid amide derivatives and pharmacological activities of the compounds were evaluated. Good functional group transformations were observed upon conventional synthesis. Infrared spectroscopy (IR), ¹H and ¹³C nuclear magnetic resonance (NMR) and liquid chromatography-mass spectrometry (LC-MS) analysis were used to establish the structures of the newly synthesized compounds. All the compounds were tested for in-vitro antibacterial and anti-inflammatory activity, some of the compounds were proven to be potent antibacterial and anti-inflammatory agents.

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Abstract

Suppose {X_n, n ∈ Z₊) - see below for the notations used - is a sequence of random variables (rv's) such that, for every t > 0 and for ψ given by (1.1) below,

ψ(X_(nt);α_n;β_n)->Y(t),

where Y\l) (in particular) is (assumed) nondegenerate. Then it is shown that, for some positive functions α and β on (0,∞) and for every t > 0,

Y(t)=ψ(Y(1);α(t),β(t))

Explicit expressions for a and p are derived. As an application, the (Pancheva) class of all possible limit laws for power normalized partial maxima of i.i.d rv's ("the p-max stable laws") is re-derived.

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