A direct algorithm for checking equivalence of LL(k) grammars

We deal with the problem of testing equivalence of two LL(k) grammars. The problem had been shown to be decidable for general k by Rosenkrantz and Stearns [2], who solved it by reduction into an equivalence problem for special DPDA's. In a paper by Korenjak and Hopcroft [1] the equivalence problem for LL(1) grammars is solved by a branching algorithm operating directly on the grammars. Our work presents a direct branching algorithm for the general LL(k) grammars equivalence problem.     

Synthesis ofGEM-dibromocyclopropanoid fatty esters using phenyl (tribromomethyl) mercury

Thegem-dibromocyclopropanation of naturally occurring unsaturated hydroxy fatty esters, methyl ricinoleate (I) and methyl isoricinoleate (II), has been undertaken to provide compounds which might have potential utility. Phenyl(tribromomethyl)mercury reacts only with the carbon-carbon double bond of each substrate, leaving the OH group intact. The product, methyl 9,10-dibromomethylene-12-hydroxyoctadecanoate (III) and methyl 12,13-dibromomethylene-9-hydroxyoctadecanoate (IV), obtained from I and II, respectively, were characterized by elemental, infrared (IR) and nuclear magnetic resonance (NMR) analyses.     

β-Ketoester — a Rearranged Product of Epoxidation of α, β-Unsaturated Methyl Ester

Attempted epoxidation of long-chain α,β-unsaturated esters resulted in the formation of the rearranged products of the corresponding epoxyesters. It was observed that reaction of peracids with esters of C₁₆, C₁₈ and C₂₂ trans-2-enoic acids, instead of yielding the expected epoxides, gave the isomerized products characterized as β-ketoesters. The structure of β-ketoester as saturated 3-oxoester was unambiguously established by chemical methods as well as by IR, NMR and Mass spectrometry. The selectivity of this rearrangement provides a useful synthetic pathway for the preparation of β-ketoesters.     

Polarographic behaviour of hansa yellow- like dyes. Reduction mechanism and substituent effects

The electroreduction of a series of 3-phenyl-2,3-dioxopropionanilide 2-arylhydrazones (III) on the dropping mercury electrode (dme) was investigated in ethanolic Britton-Robinson buffers. In each case, the polarographic curves showed two waves, A and B, corresponding to a four- and a two-electron process, respectively. The E_1/2 values for the wave A at pH 8.0 were shown to be a linear function of the Hammett substituent constant σ; -(E_1/2)_A(V) = 0.982 + 0.145 σ (r = 0.989). A mechanism for the polarographic reduction of III is proposed.     

Chromatographic Studies of Cottonseed Oils

Eight varieties of cottonseed cultivated in Pakistan have been studied. These contain 11.6-24.0% oil and their fatty acid composition as determined by G.L.C. is C_14:0 (0.7-2.0%), C_14:1 (0-0.3%), C_16:0(28.3-43.1%), C_16:1 (0.3-2.7%), C_18:0 (0.3-8.5%), C_18:1 (16.2-32.0%), C_18:2 (31.3-41.2%) and C_20:0 (0.2-0.3%).