Estimating a largest eigenvector by Lanczos and polynomial algorithms with a random start

We study Lanczos and polynomial algorithms with random start for estimating an eigenvector corresponding to the largest eigenvalue of an n × n large symmetric positive definite matrix. We analyze the two error criteria: the randomized error and the randomized residual error. For the randomized error, we prove that it is not possible to get distribution-free bounds, i.e., the bounds must depend on the distribution of eigenvalues of the matrix. We supply such bounds and show that they depend on the ratio of the two largest eigenvalues. For the randomized residual error, distribution-free bounds exist and are provided in the paper. We also provide asymptotic bounds, as well as bounds depending on the ratio of the two largest eigenvalues. The bounds for the Lanczos algorithm may be helpful in a practical implementation and termination of this algorithm. © 1998 John Wiley & Sons, Ltd.     

Peptide Charge Derivatization as a Tool for Early Detection of Preeclampsia by Mass Spectrometry—A Comparison with the ELISA Test

Early detection of any preeclampsia biomarkers may lower the risk of mortality, both for a mother and a child. Our study focuses on techniques for preeclampsia biomarker identification by comparing the results of a method using liquid chromatography mass spectrometry in multiple reaction monitoring mode (LC-MS/MS) with those by the enzyme-linked immunosorbent assay (ELISA) test, as well as by comparing the obtained results with clinical data. In the proposed LC-MS/MS method a tryptic digest peptide charge derivatization strategy was used as a tool for sensitive detection of podocin, i.e., a previously discovered preeclampsia biomarker present in urine samples from pregnant women. Urine samples from pregnant women with diagnosed preeclampsia were collected at different stages of pregnancy and from healthy subjects, and then were analyzed by ELISA test and the proposed method with LC-MS/MS. Charge derivatization of the ε amino group of C-terminal lysine residues in tryptic digests by 2,4,6-triphenylpyrylium salt was performed to increase the ionization efficiency in the LC-MS/MS mode. Podocin was identified at the early stage of pregnancy, while its detection using an ELISA test was not possible. The protocol for urine sample preparation was optimized. Our results show that the proposed method by LC-MS/MS in combination with peptide charge derivatization, provides an ultrasensitive tool for diagnosis of preeclampsia, and provides earlier detection than a clinical diagnosis or ELISA test. The proposed solution may revolutionize medical diagnostics.     

On numerical realizability of thermal convection

Astounded at the regularity of convective structures observed in simulations of mesoscale flow past realistic topography, we investigate the computational aspects of a classical problem of flow over a heated plane. We find that the numerical solutions are sensitive to viscosity, either incorporated a priori or effectively realized in computational models. In particular, anisotropic viscosity can lead to regular convective structures that mimic naturally realizable Rayleigh–Bénard cells, which are unphysical for the specified external parameter range. Details of the viscosity appear to play a secondary role; that is, similar structures can occur for prescribed constant viscosities, explicit subgrid-scale turbulence models, ad-hoc numerical filters, or implicit dissipation of numerical schemes. This implies the need for a careful selection of numerical tools suitable for convection-resolving simulations of atmospheric circulations. The implicit large-eddy-simulation (ILES) approach using non-oscillatory schemes is especially attractive, as for under-resolved calculations it reproduces well the coarsened results of finely-resolved boundary layer convection.     

Studies on the mechanism of decomposition of 1-methyl-1-(1-naphthyl)ethyl hydroperoxides to 2-(1-naphthyloxy)propenes

Abstract  

Thermal decomposition of 1-methyl-1-(4-methyl-1-naphthyl)ethyl hydroperoxide under gas chromatography-mass spectroscopy (GC–MS) conditions gives 2-((4-methyl-1-naphthyl)oxy)propene as the main product (50.5%), without any detectable traces of the isomeric 2-((5-methyl-1-naphthyl)oxy)propene. This finding excludes the rearrangement pathway of 1-methyl-1-(1-naphthyl)ethyl hydroperoxides to the corresponding 2-(1-naphthyloxy)propenes, which involves formation of a naphthofuran derivative as an intermediate and transfer of the isopropenyloxy group to the 8 position. This result, as well as our previous density functional theory (DFT) calculations, points to the rearrangement pathway involving an oxirane-type intermediate as the most plausible pathway to 2-(1-naphthyloxy)propenes. This rearrangement is responsible for the unusual inhibition effects of 1-methyl-1-(1-naphthyl)ethyl hydroperoxide on the liquid-phase oxidation of isopropylarenes with oxygen.     

Nucleoside-boron cluster conjugates - Beyond pyrimidine nucleosides and carboranes

General methods for the synthesis of new purine and pyrimidine nucleosides modified with borane clusters and metallacarborane complexes are presented. They include: (1) attachment of carborane modification at 2′ position of nucleoside via formacetal linkage formation, (2) tethering of the metallacarborane group at nucleobase part of the nucleoside via dioxane ring opening in oxonium metallacarborane, carborane or dodecaborate derivatives, and (3) ‘‘click” chemistry approach based on Huisgen 1,3-dipolar cycloaddition. Proposed methodologies extend the range of nucleoside-boron cluster conjugates available and open new areas for their applications.     

Hamilton cycles in circulant digraphs with prescribed number of distinct jumps

Let G be a digraph that consists of a finite set of vertices V(G). G is called a circulant digraph if its automorphism group contains a |V(G)|-cycle. A circulant digraph G has arcs incident to each vertex i, where integers a_ks satisfy 0<a₁<a₂<a_j≤|V(G)|−1 and are called jumps. It is well known that not every G is Hamiltonian. In this paper we give sufficient conditions for a G to have a Hamilton cycle with prescribed distinct jumps, and prove that such conditions are also necessary for every G with two distinct jumps. Finally, we derive several results for obtaining G^′ with k, k≥2 distinct jumps if the corresponding G contains a Hamilton cycle with two distinct jumps.     

Immersions of spheres and algebraically constructible functions

Let Λ be an algebraic set and let (n is even) be a polynomial mapping such that for each there is r(λ) > 0 such that the mapping g _λ  =  g(· , λ) restricted to the sphere S ⁿ (r) is an immersion for every 0  <  r  <  r (λ), so that the intersection number I(g _λ|S ⁿ (r)) is defined. Then is an algebraically constructible function. I. Karolkiewicz and A. Nowel supported by the grant BW/5100-5-0286-7.     

Experimental verification of heat transfer coefficient for nucleate boiling at sub-atmospheric pressure and small heat fluxes

In this paper we study the influence of sub-atmospheric pressure on nucleate boiling. Sixteen correlations for pool boiling available in literature are gathered and evaluated. Analysis is performed in the pressure range 1–10 kPa and for heat flux densities 10–45 kW/m². Superheats are set between 6.2 and 28.7 K. The results of calculations were compared with experimental values for the same parameters. The experiments were conducted using isolated glass cylinder and water boiling above the copper plate. Results show that low pressure adjust the character of boiling curve—the curve flattened and the natural convection region of boiling is shifted towards higher wall temperature superheats due to the influence of low pressure on the bubble creation and process of its departure. In result, 8 of 16 analyzed correlations were determined as completely invalid in subatmospheric conditions and the remaining set of equations was compared to experimental results. Experimentally obtained values of heat transfer coefficients are between 1 and 2 kW/m²K. With mean absolute deviation (MAD) we have found that the most accurate approximation of heat transfer coefficient is obtained using Mostinski reduced pressure correlation (0.13–0.35 MAD) and Labuntsov correlation (0.12–0.89 MAD).     

Collective diffusion in the presence of substrate inhomogeneities and particle–particle interactions

A novel variational analytic approach to collective diffusion allowing the density dependent collective diffusion coefficient to be calculated in systems of interacting particles adsorbed on a crystalline substrate is presented. The approach, based on a kinetic lattice gas model extracts the diffusion coefficient directly from the master equations which account for the microscopic kinetics of the system in which microscopic processes underlying the diffusion are particle jumps between neighboring adsorption sites. Variational parameters minimizing the evaluated diffusional eigenvalue of the microscopic rate matrix are ‘geometrical’ and ‘correlational’ phases accounting, for the local potential energy landscape experienced by the adsorbed particle and the local correlations, respectively, i.e. an instantaneous occupation pattern of adsorption sites around the particle. Selected results, collective diffusion as a function of particle coverage, for the system of interacting particles adsorbed on a one dimensional non-homogeneous substrate with steps and for a system of non-interacting particles adsorbed on a two dimensional striped–stepped surface are presented and discussed. It is demonstrated in the latter case that the mean field approach which is known in the literature overestimates the diffusion coefficient and corresponds to the variational result in the limit of infinitely fast hopping kinetics in the direction parallel to steps.