Chemical constituents of the lichen Usnea baileyi (Stirt.) Zahlbr

Investigation of the chemical constituents of the lichen Usnea baileyi (Stirt.) Zahlbr led to the isolation of a new dimeric xanthone, bailexanthone (1), and a novel depsidone, bailesidone (2), along with twenty-five known metabolites (3–27). Their structures were established by means of extensive spectroscopic analysis and comparison with data reported in the literatures. Compound 1 derives from secalonic acid scaffold with C-8/8′ reduction and compound 2 represents the first example of menegazziaic acid derivative with an unprecedented B-ring moiety. Two new compounds 1–2 were evaluated for their cytotoxic activities against A549 (human lung carcinoma) and HT29 (human colorectal adenocarcinoma) cell lines. All of them showed weak or no activity against two cell lines.     

Extension of Donnan theory to predict calcium ion exchange on phenolic hydroxyl sites of unbleached kraft fibers

The Donnan theory is extended to formulate a model for determination of the distribution coefficient of calcium in slurries of fully bleached and unbleached kraft fibers at different pH, taking into account the presence of both carboxylic and phenolic groups in the fibers. The intrinsic dissociation constants of the carboxylic acid groups and phenolic hydroxyl, which are the key inputs of the extended model, were determined by potentiometric titration. The extension improves the model prediction significantly, particularly when the presence of phenolic lignin in fibers becomes significant. However, when the pH exceeds 10, the model underestimates the distribution coefficient, suggesting that other factors may influence the fiber charge. The structural changes of the fiber wall at high pH and the presence of hydroxyl groups on the cellulose, which ionize at high pH, may be major factors.     

Use of CdSe/ZnS luminescent quantum dots incorporated within sol-gel matrix for urea detection

In this work, urea detection techniques based on the pH sensitivity of CdSe/ZnS QDs were developed using three types of sol-gel membranes: a QD-entrapped membrane, urease-immobilized membrane and double layer consisting of a QD-entrapped membrane and urease-immobilized membrane. The surface morphology of the sol-gel membranes deposited on the wells in a 24-well microtiter plate was investigated. The linear detection range of urea was in the range of 0-10 mM with the three types of sol-gel membranes. The urea detection technique based on the double layer consisting of the QD-entrapped membrane and urease-immobilized membrane resulted in the highest sensitivity to urea due to the Michaelis-Menten kinetic parameters. That is, the Michaelis-Menten constant (K_m =2.0745 mM) of the free urease in the QD-entrapped membrane was about 4-fold higher than that (K_m =0.549 mM) of the immobilized urease in the urease-immobilized membrane and about 12-fold higher than that (K_m =0.1698 mM) of the immobilized urease in the double layer. The good stability of the three sol-gel membranes for urea sensing over 2 months showed that the use of sol-gel membranes immobilized with QDs or an enzyme is suitable for biomedical and environmental applications.     

Mechanical properties of metallic thin films: theoretical approach

The statistical moment method in statistical mechanics was developed to investigate themechanical properties of free-standing metallic thin films at ambient conditions includingthe anharmonicity effects of thermal lattice vibrations. Analytical expressions ofisothermal areal modulus B_T, Young’s modulusE and shearmodulus Gwere derived in terms of the power moments of the atomic displacements. Numericalcalculations have been performed for metallic Ni, Au and Al thin films, and compared withthose of bulk metals. This method is physically transparent and it successfully describedthe temperature effects on mechanical properties of metallic thin films.     

CR singular images of generic submanifolds under holomorphic maps

The purpose of this paper is to organize some results on the local geometry of CR singular real-analytic manifolds that are images of CR manifolds via a CR map that is a diffeomorphism onto its image. We find a necessary (sufficient in dimension 2) condition for the diffeomorphism to extend to a finite holomorphic map. The multiplicity of this map is a biholomorphic invariant that is precisely the Moser invariant of the image, when it is a Bishop surface with vanishing Bishop invariant. In higher dimensions, we study Levi-flat CR singular images and we prove that the set of CR singular points must be large, and in the case of codimension 2, necessarily Levi-flat or complex. We also show that there exist real-analytic CR functions on such images that satisfy the tangential CR conditions at the singular points, yet fail to extend to holomorphic functions in a neighborhood. We provide many examples to illustrate the phenomena that arise.     

An overlapping additive Schwarz preconditioner for the Laplace-Beltrami equation using spherical splines

We present an overlapping domain decomposition technique for solving the Laplace?CBeltrami equation on the sphere with spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by $O\left(H^2/h^2\right)$ , where H and h are the sizes of the coarse and fine meshes, respectively. In the case that the degree of the splines is even, a better bound $O\left(\max_{1\leq k \leq J}\left(1+H_k/\delta_k\right)\right)$ is proved. Here J is the number of subdomains, H _k is the size of the kth subdomain, and ?? _k is the size of the overlap of the kth subdomain. The method is illustrated by numerical experiments on large point sets taken from magsat satellite data.     

Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces

Mathematical Notes - In this paper, we prove the boundedness of matrix Hausdorff operators and rough Hausdorff operators in the two weighted Herz-type Hardy spaces associated with both power...