The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Surface-mediated selective photocatalytic aerobic oxidation reactions on TiO2 nanofibres

N-doped TiO2 nanofibres were observed to possess lower aerobic oxidation activity than undoped TiO2 nanofibres in the selective photocatalytic aerobic oxidation of enzylamine and 4-methoxybenzyl alcohol. This was attributed to the reduction free energy of O2 adsorption in the vicinity of nitrogen dopant sites, as indicated by density functional theory (DFT) calculations when three-coordinated oxygen atoms are substituted by nitrogen atoms. It was found that the activity recovered following a controlled calcination of the N-doped NFs in air. The dependence of the conversion of benzylamine and 4-methoxybenzyl alcohol on the intensity of light irradiation confirmed that these reactions were driven by light. Action spectra showed that the two oxidation reactions are responsive to light from the UV region through to the visible light irradiation range. The extended light absorption wavelength range in these systems compared to pure TiO2 materials was found to result from the formation of surface complex species following adsorption of reactants onto the catalysts' surface, evidenced by the in situ IR experiment. Both catalytic and in situ IR results reveal that benzaldehyde is the intermediate in the aerobic oxidation of benzylamine to N-benzylidenebenzylamine process.

One-pot protection and activation of amino acids using pentafluorophenyl carbonates

Protection of the amino group and activation of the carboxylic acid groups are the most important steps associated with any peptide synthesis protocol; hence, a one-pot process to achieve these is highly desirable. A possible strategy is to use pentafluorophenyl carbonates to simultaneously protect the amino group as a carbamate derivative and activate the carboxylic acid group as a pentafluorophenyl ester. A detailed study is carried out to understand the scope and limitations of this method using five different pentaflurophenyl carbonates. The efficiency of these one-pot reactions depends largely on the nature of the pentafluorophenyl carbonates and also on the nature of the amino acids. Electron deficient and sterically less demanding carbonates reacted faster than the others, whereas amino acids with longeraliphatic side chains gave better yields than more polar amino acids.

New Approaches to the Cannizzaro and Tishchenko Reactions

It is demonstrated that the titled reactions are best carried out at high concentrations, as indicated by mechanistic considerations: the observed high reaction orders and the possibility that the Cannizzaro reaction is driven by the hydrophobic effect, which effects proximity between the two molecules of the aldehyde reactant. The present studies have led to improved conditions, simplified workup, and excellent yields of products. The Tishchenko reaction converted benzaldehyde to benzyl benzoate with catalytic NaOMe/tetrahydrafuran in good yield, which is apparently unprecedented for this product of high commercial value.

Prevalence of foot disease and risk factors in general inpatient populations: A systematic review and meta-analysis

Objective: To systematically review studies reporting the prevalence in general adult inpatient populations of foot disease disorders (foot wounds, foot infections, collective ‘foot disease’) and risk factors (peripheral arterial disease (PAD), peripheral neuropathy (PN), foot deformity). Methods: A systematic review of studies published between 1980 and 2013 was undertaken using electronic databases (MEDLINE, EMBASE and CINAHL). Keywords and synonyms relating to prevalence, inpatients, foot disease disorders and risk factors were used. Studies reporting foot disease or risk factor prevalence data in general inpatient populations were included. Included study's reference lists and citations were searched and experts consulted to identify additional relevant studies. 2 authors, blinded to each other, assessed the methodological quality of included studies. Applicable data were extracted by 1 author and checked by a second author. Prevalence proportions and SEs were calculated for all included studies. Pooled prevalence estimates were calculated using random-effects models where 3 eligible studies were available. Results: Of the 4972 studies initially identified, 78 studies reporting 84 different cohorts (total 60 231 517 participants) were included. Foot disease prevalence included: foot wounds 0.01–13.5% (70 cohorts), foot infections 0.05–6.4% (7 cohorts), collective foot disease 0.2–11.9% (12 cohorts). Risk factor prevalence included: PAD 0.01–36.0% (10 cohorts), PN 0.003–2.8% (6 cohorts), foot deformity was not reported. Pooled prevalence estimates were only able to be calculated for pressure ulcer-related foot wounds 4.6% (95% CI 3.7% to 5.4%)), diabetes-related foot wounds 2.4% (1.5% to 3.4%), diabetes-related foot infections 3.4% (0.2% to 6.5%), diabetes-related foot disease 4.7% (0.3% to 9.2%). Heterogeneity was high in all pooled estimates (I2=94.2–97.8%, p<0.001). Conclusions: This review found high heterogeneity, yet suggests foot disease was present in 1 in every 20 inpatients and a major risk factor in 1 in 3 inpatients. These findings are likely an underestimate and more robust studies are required to provide more precise estimates.

Facile preparation and some applications of an affinity matrix with a cleavable connector arm containing a disulfide bond

A versatile affinity matrix in which the ligand of interest is linked to the matrix through a connector arm containing a disulfide bond is described. It can be synthesized from any amino-substituted matrix by successive reaction with 2-imino-thio-lane, 5, 5'-dithiobis(2-nitrobenzoic acid), and a thiol derivative of the ligand of choice. The repertoire of ligands can be significantly increased by the appropriate use of avidin-biotin bridges. After adsorption of the material to be fractionated, elution can be effected by reducing the disulfide bond in the connector arm with dithiothreitol. Examples of the preparation and use of various affinity matrices based on amino-substituted Sepharose 6MB are given. One involves the immobilization of the Fab' fragment of a monoclonal antibody against Aspergillus oryzae β-galactosidase and the specific binding of that enzyme to the resulting immunoaffinity matrix. Another involves the immobilization of N-biotinyl-2-thioethylamine followed by complex formation with avidin. The resulting avidin-substituted matrix was used for the selective adsorption and subsequent recovery of mouse hybridoma cells producing anti-avidin antibodies. By further complexing the avidin-substituted matrix with appropriate biotinylated antigens, it should be possible to fractionate cells producing antibodies against a variety of antigens.

The effect of closed boundary conditions on a stationary dynamo

One of two boundary conditions generally assumed in solutions of the dynamo equation is related to the disappearance of the azimuthal field at the boundary. Parker (1984) points out that for the realization of this condition the field must escape freely through the surface. Escape requires that the field be detached from the gas in which it is embedded. In the case of the sun, this can be accomplished only through reconnection in the tenuous gas above the visible surface. Parker concludes that the observed magnetic activity on the solar surface permits at most three percent of the emerging flux to escape. He arrives at the conclusion that, instead of B(phi) = 0, the partial derivative of B(phi) to r is equal to zero. The present investigation is concerned with the effect of changing the boundary condition according to Parker's conclusion. Implications for the solar convection zone are discussed.

Asymmetric total synthesis of erythromycin. 2. Synthesis of an erythronolide A lactone system

In reporting a total synthesis of erythromycin (la) we described in the preceding paper1 the synthesis of the erythronolide A seco acid derivative 2 in optically active form. In this paper we wish to report a successful transformation of 2 to 12 (synthetically equivalent to erythronolide A) via lactonization and also demonstrate that the proper functionalization of a substrate is critical for the successful lactonization.

Asymmetric total synthesis of erythromycin. 3. Total synthesis of erythromycin

In the preceding paper' we described the preparation of the key lactone intermediate la in optically active form. In this paper we report the synthesis of erythromycin (2) from la. In essence,this transformation involves the glycosidation of a suitable derivative of la with L-cladinose and D-desosamine and the generation of the C-9 ketone functionality.

Human alveolar T lymphocyte responses to Mycobacterium tuberculosis antigens: role for CD4+ and CD8+ cytotoxic T cells and relative resistance of alveolar macrophages to lysis.

T cell-mediated cytotoxicity against Mycobacterium tuberculosis (MTB)-infected macrophages may be a major mechanism of specific host defense, but little is known about such activities in the lung. Thus, the capacity of alveolar lymphocyte MTB-specific cell lines (AL) and alveolar macrophages (AM) from tuberculin skin test-positive healthy subjects to serve as CTL and target cells, respectively, in response to MTB (H37Ra) or purified protein derivative (PPD) was investigated. Mycobacterial Ag-pulsed AM were targets of blood CTL activity at E:T ratios of > or = 30:1 (51Cr release assay), but were significantly more resistant to cytotoxicity than autologous blood monocytes. PPD- plus IL-2-expanded AL and blood lymphocytes were cytotoxic for autologous mycobacterium-stimulated monocytes at E:T ratios of > or = 10:1. The CTL activity of lymphocytes expanded with PPD was predominantly class II MHC restricted, whereas the CTL activity of lymphocytes expanded with PPD plus IL-2 was both class I and class II MHC restricted. Both CD4+ and CD8+ T cells were enriched in BL and AL expanded with PPD and IL-2, and both subsets had mycobacterium-specific CTL activity. Such novel cytotoxic responses by CD4+ and CD8+ T cells may be a major mechanism of defense against MTB at the site of disease activity.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

A kinetic analysis of the tumor-associated galactopyranosyl-(1→3)-2-acetamido-2-deoxy-α-d-galactopyranoside antigen—lectin interaction

A kinetic study of the tumor-associated galactopyranosyl-(1→3)-2-acetamido-2-deoxy-α-d-galactopyranoside (T-antigen) with lectin peanut agglutinin is described. The disaccharide antigen was synthesized by chemical methods and was functionalized suitably for immobilization onto a carboxy-methylated sensor chip. The ligand immobilized surface was allowed interaction with the lectin peanut agglutinin, which acted as the analyte and the interaction was studied by the surface plasmon resonance method. The ligand—lectin interaction was characterized by the kinetic on-off rates and a bivalent analyte binding model was found to describe the observed kinetic constants. It was identified that the antigen-lectin interaction had a faster association rate constant (k a1) and a slower dissociation rate constant (k d1) in the initial binding step. The subsequent binding step showed much reduced kinetic rates. The antigen-lectin interaction was compared with the kinetic rates of the interaction of a galactopyranosyl-(1→4)-β-d-galactopyranoside derivative and a mannopyranoside derivative with the lectin.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

Conformationally locked thiosugars alpha-mannosidase inhibitors: Synthesis, and docking studies as potent biochemical

series of thiosugar derivatives (thiolevomannosans) derived from mannose were synthesized and their inhibitory activity was tested against alpha-mannosidase (jack bean). These inhibitors were found to be more potent than the well-known inhibitors like kifunensine and deoxymannojirimycin based on docking and biochemical studies. The sulfone derivative 10 was shown to be the best inhibitor of alpha-mannosidase with the K-i value of 350 nM. (c) 2007 Elsevier Ltd. All rights reserved.