S. Ramanujan introduced a technique, known as Ramanujan's Master Theorem, which provides an analytic expression for the Mellin transform of a function. The main identity of this theorem involves the extrapolation of the sequence of coefficients of the integrand, defined originally as a function on N to C. The history and proof of this result are reviewed. Applications to the evaluation of a variety of definite integrals is presented.

Objectives: We describe the antimicrobial activity against Pseudomonas aeruginosa of the de novoderived antimicrobial peptide WLBU2 in an animal model of infection.Methods: For this study, an intravenous (iv) model of P. aeruginosa infection was established. The minimum lethal murine dose of P. aeruginosa strain PA01 was determined to be 3 3 10 7 cfu when bacteria were administered iv. Increasing concentrations of WLBU2 were instilled either prior to or following PA01 septic exposure.Results: For the mice given peptide post-bacterial infection, in the 1 mg/kg group, nine of nine animals died because of Pseudomonas sepsis; in the 3 mg/kg group, only one of nine succumbed to infection and in the 4 mg/kg group, all mice were protected (P < 0.0001). Similar results were obtained when WLBU2 was given 1 h prior to Pseudomonas infection. Conclusions:Although the therapeutic window in this model is narrow, the results nonetheless provide encouraging evidence for WLBU2 as a potential prophylactic or treatment of bacterial infection.

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We present an improved form of the integration technique known as NDIM (Negative Dimensional Integration Method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a φ 3 ⊕ φ 4 theory in D = 4 − 2ǫ dimensions, considering generic topologies of L loops and E independent external momenta, and where the propagator powers are arbitrary. The method transforms the Schwinger parametric integral associated to the diagram into a multiple series expansion, whose main characteristic is that the argument contains several Kronecker deltas which appear naturally in the application of the method, and which we call diagram presolution. The optimization we present here consists in a procedure that minimizes the series multiplicity, through appropriate factorizations in the multinomials that appear in the parametric integral, and which maximizes the number of Kronecker deltas that are generated in the process. The solutions are presented in terms of generalized hypergeometric functions, obtained once the Kronecker deltas have been used in the series. Although the technique is general, we apply it to cases in which there are 2 or 3 different energy scales (masses or kinematic variables associated to the external momenta), obtaining solutions in terms of a finite sum of generalized hypergeometric series de 1 and 2 variables respectively, each of them expressible as ratios between the different energy scales that characterize the topology. The main result is a method capable of solving Feynman integrals, expressing the solutions as hypergeometric series of multiplicity (n − 1), where n is the number of energy scales present in the diagram.

[reaction: see text] Nitrogen-containing 15-membered triacetylenic macrocycles known as 1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3,8,13-triynes (1) and enediynic macrocycles called 1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3-ene-8,13-diynes (4 and 5) were satisfactorily prepared. [2+2+2] cycloisomerization processes catalyzed by transition metals were tested in the above-mentioned macrocycles. Readily available and familiar cyclotrimerization precatalysts were examined for efficiency. Among them, the RhCl(CO)(PPh(3))(2) complex was found to catalyze the cycloisomerization reaction giving the desired cycloadducts in high yields.