We study the development of nonlinear conjugate gradient methods, Fletcher Reeves (FR) and Polak Ribiere (PR). FR extends the linear conjugate gradient method to nonlinear functions by incorporating two changes, for the step length αk a line search is performed and replacing the residual, rk (rk=b-Axk) by the gradient of the nonlinear objective function. The PR method is equivalent to FR method for exact line searches and when the underlying quadratic function is strongly convex. The PR method is basically a variant of FR and primarily differs from it in the choice of the parameter βk. On applying the nonlinear Rosenbrock function to the MATLAB code for the FR and the PR algorithms we observe that the performance of PR method (k=29) is far better than the FR method (k=42). But, we observe that when the MATLAB codes are applied to general nonlinear functions, specifically functions whose minimum is a large negative number not close to zero and the iterates too are large values far off from zero the PR algorithm does not perform well. This problem with the PR method persists even if we run the PR algorithm for more iterations or with an initial guess closer to the actual minimum. To improve the PR algorithm we suggest finding a better weighing parameter βk, using better line search method and/or using specific line search for certain functions and identifying specific restart criteria based on the function to be optimized.

No description available.

Enantioselective conjugate addition (ECA) reactions between organometallic reagents and cyclohexadienone 165 are being investigated. Previous studies have shown that ECAs, of organometallic reagents to á,â-unsaturated cyclohexadienones, are useful in many natural product syntheses. The substrates used in earlier studies were simple 2,5-cyclohexadienones, with a proton at the C-3 position, resulting in the synthesis of a trisubstituted C-3 atom. ECAs that afford all-carbon quaternary stereogenic centers are a much more challenging problem and few examples have been reported. Some natural products contain a ã-hydroxy group, however, no ECA substrates have incorporated this motif. ECAs have been accomplished with substrates having a g-ether substituent. The cyclohexadienone 165 system presents three challenging problems to overcome for an ECA reaction: the tertiary methyl substituents at the 3 and 5 positions, facial selectivity and enantioselectivity. An ECA to 165 using an organoaluminum reagent and an external chiral ligand 26 was successful in producing a product that showed the reaction was moderately stereoselective. A diastereoselective conjugate addition reaction (DCA) to 165 using a chiral auxiliary 68 was also successful in producing a product that showed the reaction was moderately enantioenriched. Lastly, a variable temperature NMR study was performed to establish the presence of dynamic motions of the C=N bond present in sulfinyl imines 229 and 230. As a result, the sulfinyl imines 229 and 230 were found to be interconverting at -78°C.

In order to extend the scope of asymmetric conjugate alkenylation catalyzed by 3,3′-disubstituted binaphthols, two classes of compounds were examined. Asymmetric 1,4-addition of alkenylboronates onto N-acylimines was investigated. Chiral allylic amides were obtained in good yields and high enantioselectivities. This represents one of the very few methods for synthesizing chiral allylic amides without the use of transition metal catalysts. Chiral binaphthol-catalyzed conjugate addition of alkenylboronates to -silyl--unsaturated ketones afforded highly enantioenriched chiral -silylcarbonyls. Asymmetric addition onto -silyl-enones is still a largely unexplored area, with only a handful of transition metal-catalyzed reactions reported. The first asymmetric reaction using these silicon-containing enones without using transition metal were described.

In order to extend the scope of asymmetric conjugate alkenylation catalyzed by 3,3′-disubstituted binaphthols, two classes of compounds were examined. Asymmetric 1,4-addition of alkenylboronates onto N-acylimines was investigated. Chiral allylic amides were obtained in good yields and high enantioselectivities. This represents one of the very few methods for synthesizing chiral allylic amides without the use of transition metal catalysts. Chiral binaphthol-catalyzed conjugate addition of alkenylboronates to -silyl--unsaturated ketones afforded highly enantioenriched chiral -silylcarbonyls. Asymmetric addition onto -silyl-enones is still a largely unexplored area, with only a handful of transition metal-catalyzed reactions reported. The first asymmetric reaction using these silicon-containing enones without using transition metal were described.

Enantioselective conjugate addition (ECA) reactions between organometallic reagents and cyclohexadienone 165 are being investigated. Previous studies have shown that ECAs, of organometallic reagents to á,â-unsaturated cyclohexadienones, are useful in many natural product syntheses. The substrates used in earlier studies were simple 2,5-cyclohexadienones, with a proton at the C-3 position, resulting in the synthesis of a trisubstituted C-3 atom. ECAs that afford all-carbon quaternary stereogenic centers are a much more challenging problem and few examples have been reported. Some natural products contain a ã-hydroxy group, however, no ECA substrates have incorporated this motif. ECAs have been accomplished with substrates having a g-ether substituent. The cyclohexadienone 165 system presents three challenging problems to overcome for an ECA reaction: the tertiary methyl substituents at the 3 and 5 positions, facial selectivity and enantioselectivity. An ECA to 165 using an organoaluminum reagent and an external chiral ligand 26 was successful in producing a product that showed the reaction was moderately stereoselective. A diastereoselective conjugate addition reaction (DCA) to 165 using a chiral auxiliary 68 was also successful in producing a product that showed the reaction was moderately enantioenriched. Lastly, a variable temperature NMR study was performed to establish the presence of dynamic motions of the C=N bond present in sulfinyl imines 229 and 230. As a result, the sulfinyl imines 229 and 230 were found to be interconverting at -78°C.

I. Enantioselective Rhodium-Catalysed Arylation of Electron-Deficient Alkenylarenes β-substituted alkenyl-para-nitroarenes, an unexplored substrate class for catalytic asymmetric addition reactions, undergo highly enantioselective rhodium-catalysed arylations with arylboronic acids in the presence of a dibenzylamide-containing chiral diene ligand. One example of the asymmetric arylation of an alkenyl-p-cyano-m-( trifluoromethyl)benzene is also reported. The scope of this process is broad with variation in the β-position of the alkene, additional substituents on the electrondeficient arene, and sterically and electronically unique arylboronic acids all tolerated. The synthetic utility of the developed methodology is demonstrated by smoothly converting one arylated product into its corresponding indole via the Bartoli reaction. II. Enantioselective Copper-Catalysed Reductive Coupling of Alkenylazaarenes with Ketones Catalytic enantioselective methods for the preparation of chiral azarene-containing compounds are of high value. By combining the utility of copper hydride catalysis with the ability of C=N-containing azaarenes to activate adjacent alkenes toward nucleophilic additions, the enantioselective reductive coupling of alkenylazaarenes with ketones has been developed. The process is tolerant of a wide variety of azaarenes and ketones, and provides aromatic heterocycles bearing tertiary-alcoholcontaining sidechains with high levels of diastereo- and enantioselection.

A Research report submitted to the Faculty of Health Sciences, University of Witwatersrand, Johannesburg, in partial fulfillment of the requirements for the degree of Master of Medicine in Paediatrics Johannesburg 2015 / Children hospitalized with culture-confirmed pulmonary tuberculosis (PTB) frequently present with acute symptoms, possibly because underlying PTB may predispose to superimposed bacterial pneumonia. Immunization of children with pneumococcal conjugate vaccine (PCV) could protect against such superimposed bacterial pneumonia and reduce the incidence of PTB hospitalization. OBJECTIVE We studied the temporal association of childhood immunization with pneumococcal conjugate vaccine on the incidence of hospitalization for culture-confirmed PTB in children. METHODS A retrospective study on the incidence of hospitalization for culture-confirmed childhood PTB at Chris Hani Baragwanath Academic Hospital was undertaken from 2005 to 2012. This included a pre-PCV era (2005-2008) and a PCV era (2011-2012). RESULTS Overall, there was a 69.2% (95% CI: 62.8-74.6%) decline in the incidence of hospitalization for culture-confirmed PTB when comparing the PCV and pre-PCV-eras, with the decline in HIV-uninfected children only significant in the 3-11 month age category and the decline in HIV-infected significant across all age categories. There was a trend for reduced pneumococcal bacteraemia in the PCV era compared to the pre-PCV era, with the odds of having a blood culture positive for pneumococcus being 1.91-fold (95% CI, 0.26-84.56) greater in the Pre-PCV era. CONCLUSION There has been a significant decline in culture-confirmed PTB hospitalization in children comparing the pre-PCV to the PCV-era. However, the incidence of culture-confirmed PTB prior to the introduction of PCV had been reduced to low levels due to antiretroviral therapy. This confounder together with the retrospective ecological study design and other several possible confounders limited any robust estimate as to whether there was a temporal association between PCV immunization and incidence of culture-confirmed PTB hospitalization in our study setting.

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographic references (p.50-52).

The upper atmosphere, a region above ~85 km called the ionosphere and thermosphere, has been studied extensively for over one hundred years. Measurements were often considered in isolation, but today, advances in technology and ground-based distributed arrays have allowed concurrent multi-instruments measurements. In this dissertation, I combine measurements from all-sky imagers (ASIs), coherent scatter radars, incoherent scatter radars (ISRs), and Fabry-Perot interferometers (FPIs). I focus on two phenomena, the midnight temperature maximum (MTM) and equatorial spread F (ESF), using observations from equatorial to mid-latitudes. The spatial characteristics of these phenomena are not fully understood. I combine observations at various latitudes and longitudes to extend MTM detection to mid-latitudes. I present the first simultaneous detections of the MTM at multiple altitudes and latitudes over North America and the first observations below the F-region peak using the Millstone Hill Observatory ISR in a south pointing, low-elevation mode. The MTM can also be observed with an ASI and I present concurrent measurements of the MTM with an ASI and ISR. The Whole Atmosphere Model, a global circulation model, was found to be consistent with these observations. This further verifies that the MTM is partially created by lower atmospheric tides, demonstrating coupling between the lower and upper atmosphere. In addition to the MTM, I investigate different aspects of ESF using ASIs concurrently with other instruments. I compare various scale sizes (sub-meter to kilometers) using coherent scatter radar and an ASI and conclude that the lower hybrid drift instability causes radar echoes to occur preferentially on the western wall of large-scale depletions. The source of day-to-day variability in ESF is not fully known but I show that one driver may be large-scale wave structures (~400 km) that modulate the development of ESF. Finally, I compare concurrent observations of ESF plasma depletions with ASIs at magnetically-conjugate foot points and show how the magnitude and structure of the Earth’s magnetic field is responsible for differences in the morphology and velocity of these depletions. In summary, I have used multi-instrument observations of ESF and the MTM to provide a deeper understanding of the dynamics of the upper atmosphere.