On Existence of Common Fixed Points Under Lipschitz-Type Mapping Pairs with Applications

In this paper, we propose some su?cient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs, J. Math. Anal. Appl. 240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space.     

Response Factor Correction for Estimation of Ester Content in Biodiesel

EN 14103 is generally used for quantification of ester content in biodiesel free of heptadecanoate ester (C17:0) or methyl nonadecanoate (C19:0), which are employed as internal standards. It was observed that ester content obtained by EN 14103 method did not match with theoretical value of biodiesel, as the method did not take care of response factors of each component to compensate for changes in detector sensitivities. In this study, the whole range of fatty acid (C₆–C_24:1) methyl esters have been taken into consideration for the calculation of the ester content. Methyl nonadecanoate (C19:0) was used as an internal standard. The response factors of both the saturated and unsaturated methyl esters in the range C₆–C_24:1 were estimated and found in the range 0.97–1.16. The ester content was calculated after applying the response factors of each methyl ester. The results obtained by this method agreed well with the theoretical value as compared to estimated value using EN14103 method. The results obtained from this method also show good correlation (R ² = 0.98) with ¹H-NMR method. Further, this method does not depend on nature of biodiesel feed stock and is applicable to all methyl biodiesel samples obtained from different raw materials.     

A Facile Route for the Synthesis of Novel Heterocyclic Prostaglandin F2α Analogs

A general synthetic approach has been developed for heterocyclic prostaglandins (PGF_2α type) starting from the key intermediate ( 6 ). (±) 6 was obtained from (±) ‐Corey lactone. The key intermediate (±) 6 was, in turn, converted in to several new heterocyclic prostaglandins consisting of furan and thiophene moieties in ω‐side chain in two to three steps. Horner–Wadsworth–Emmons reaction and Grignard reaction as the key reactions in these transformations.     

Oxidative fragmentation of oxiranes to nitriles with hypervalent iodine(V) reagents in aqueous ammonia

Oxiranes undergo oxidative fragmentation when treated with hypervalent iodine(V) reagents particularly o-iodoxybenzoic acid in aqueous ammonia to give nitriles. The reaction goes via the formation of 1, 2-amino alcohols as intermediates followed by C-C bond cleavage.     

Production, Purification, and Biochemical Characterization of a Fibrinolytic Enzyme from Thermophilic Streptomyces sp. MCMB-379

Production of the fibrinolytic enzyme was carried out using 2.5-L glass fermentor, culture of thermophilic Streptomyces sp., and glucose yeast extract peptone medium of pH 8.0. Five successive batches were carried out under controlled fermentation conditions viz., agitation 140 rpm, aeration 0.5 vvm, 55 °C, and 18 h. The total protein extracellularly produced in the cell-free broth was ~300-500 mg/L. The enzyme belongs to serine endopeptidase type. Studies on the fibrin degradation indicate that the enzyme degrades the fibrin into small molecular weight products as seen from HPLC profile. Phase-contrast microscopic structure of fibrin showed that enzyme cleaves the fibrin filaments. The ex vivo activity of the actinokinase was compared with 500 IU of urokinase and 350 IU of streptokinase. The ex vivo clot lysis was found to be faster as compared to the commercial available enzymes.     

Evidence for a near-resonant charge transfer mechanism for double-stranded peptide nucleic acid

We present evidence for a near-resonant mechanism of charge transfer in short peptide nucleic acid (PNA) duplexes obtained through electrochemical, STM break junction (STM-BJ), and computational studies. A seven base pair (7-bp) PNA duplex with the sequence (TA)(3)-(XY)-(TA)(3) was studied, in which XY is a complementary nucleobase pair. The experiments showed that the heterogeneous charge transfer rate constant (k(0)) and the single-molecule conductance (σ) correlate with the oxidation potential of the purine base in the XY base pair. The electrochemical measurements showed that the enhancement of k(0) is independent, within experimental error, of which of the two PNA strands contains the purine base of the XY base pair. 7-bp PNA duplexes with one or two GC base pairs had similar measured k(0) and conductance values. While a simple superexchange model, previously used to rationalize charge transfer in single stranded PNA (Paul et al. J. Am. Chem. Soc. 2009, 131, 6498-6507), describes some of the experimental observations, the model does not explain the absence of an enhancement in the experimental k(0) and σ upon increasing the G content in the duplexes from one to two. Moreover, the superexchange model is not consistent with other studies (Paul et al. J. Phys. Chem. B 2010, 114, 14140), that showed a hopping charge transport mechanism is likely important for PNA duplexes longer than seven base pairs. A quantitative computational analysis shows that a near-resonant charge transfer regime, wherein a mix of superexchange and hopping mechanisms are expected to coexist, can rationalize all of the experimental results.     

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, β(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D=I(2ω,X,X)/I(2ω,Z,X) and D(')=I(2ω,X,C)/I(2ω,Z,C) in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, β(HRS), and the value of macroscopic depolarization ratios, D and D('), are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical β(HRS), D and D(') values as a function of the geometry of the complex. The calculated β(HRS), D, and D(') values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30° is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution.     

Synthesis, spectroscopic, and in vitro photosensitizing efficacy of ketobacteriochlorins derived from ring-B and ring-D reduced chlorins via pinacol-pinacolone rearrangement

In this report, we present a regioselective oxidation of a series bacteriochlorins, which on reacting with either ferric chloride (FeCl(3)) or 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ) yielded the corresponding ring-B or ring-D reduced chlorins. The effect of the number of electron-withdrawing groups present at the peripheral position, with or without a fused isocyclic ring (ring-E), did not make any significant difference in regioselective oxidation of the pyrrole rings. However, depending on the nature of substituents, the intermediate bis-dihydroxy bacteriochlorins on subjecting to pinacol-pinacolone reaction conditions gave various ketochlorins. The introduction of the keto-group at a particular position in the molecule possibly depends on the stability of the intermediate carbocation species. The newly synthesized bacteriochlorins show strong long-wavelength absorption and produced significant in vitro (Colon26 cells) photosensitizing ability. Among the compounds tested, the bacteriochlorins containing a keto-group at position 7 of ring-B with cleaved five-member isocyclic ring showed the best efficacy.     

SYNTHESIS AND PHOTOSENSITIZING ACTIVITY OF A DI-PORPHYRIN ETHER

Abstract A simple, well characterized porphyrin dimer with ether linkage was synthesized from 2- (1-hydroxyethyl)deuteroporphyrin dimethyl ester and found to be an effective in vivo photosensitizer in the murine SMT-F tumor system. The structure of the pure dimer was confirmed by NMR and mass spectroscopy.