Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space

In this paper, we derive necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a Gram matrix defined in an indefinite inner product space using indefinite matrix multiplication. These conditions include the acuteness of a pair of closed convex cones.     

Synthesis of secondary amines by titanium-mediated transfer of alkenyl groups from alcohols

Reaction of Ti(NMe2)4 with allyl alcohols and primary amines leads to the selective formation of secondary allylic amines. The allyl transfer from the alcohol to the amine occurs with selective allylic transposition. Due to substituent effects in the reactions, we postulate that the reaction occurs through a [2 + 2]/retro-[2 + 2]-cycloaddition mechanism. It was also found that a similar reaction could be accomplished with homoallylic alcohol. In this case, the more complex mechanism leads to the formation of 1-aza-spiro[5.5]undecane. Possible pathways for the homoallylic transfer and cyclization are discussed.     

A short enantioselective synthesis of the antiepileptic agent, levetiracetam based on proline-catalyzed asymmetric α-aminooxylation

An efficient enantioselective synthesis of a new antiepileptic drug, levetiracetam is described, in high optical purity (>99.5% ee), using proline-catalyzed α-aminooxylation of n-butyraldehyde as the key step.     

On the Rogers-Ramanujan continued fraction

In the “Lost” note book, Ramanujan had stated a large number of results regarding evaluation of his continued fraction for certain values of τ. It is shown that all these results and many more have their source in the Kronecker limit formula.     

Immuno-arrays for multianalyte analysis of chlorotriazines

In this paper, a novel strategy for multicomponent analysis of two classes of pesticides such as triazines (atrazine and simazine) and phenoxyalkanoic acids (2,4-dichlorophenoxy acetic acid (2,4-D), 2,4,5-trichlorophenoxyacetic acid (2,4,5-T), 4-chlorophenoxyacetic acid (CPOAc), phenoxyacetic acid (POAc)) employing immuno-arrays is demonstrated. The approach is based on cross-reactive arrays of specific antibody pairs coupled to chemometric pattern recognition. The monoclonal antibody pairs employed in this work (atrazine-simazine and 2,4-D) are specific towards a set of analytes and preclude a particular set of others present in the sample matrix. Antibody pairs of atrazine, simazine, and 2,4-D are used to discriminate and quantify analyte of interest. Atrazine was quantified in presence of trace concentration of simazine and that of 2,4-D. The combinatorial cross-reactivity of antibody pairs towards simazine, atrazine and 2,4-D is used to distinguish among different classes of analytes and their influence on the signal suppression in immuno-techniques. These sensors exclude recognition by carbamates such as carbaryl and carbofuran.     

Ion cyclotron resonance mass spectrometric study of ion—molecule reactions in toluene—pyridine mixtures

Ion—molecule reactions in toluene, toluene-d₈, pyridine, 4-methyl-, 4-ethyl- and 4-terr-butylpyridine and quinoline and their mixtures were studied by ICR mass spectrometry at 10^-7 Torr (1 Torr = 133.3 Pa). The reactions of benzyl (m/z 91), benzyl-d₇ (m/z 98), methylbenzyl (m/z 105), and azabenzyl (m/z 92) ions with pyridines and quinoline were observed. The reactions of protonated pyridines with unprotonated molecules leading to homoconjugated ions (BHB)⁺ were detected.