Jean van Heijenoort: Kaleidoscope

Leitmotifs in the life of Jean van Heijenoort.     

Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations

This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations; such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [t_n,t_n+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical quadrature. The main purpose of this paper is to present a detailed analysis of the implications of the location of quadrature nodes on the accuracy and stability of the overall method. Comparisons between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau, and uniformly spaced points are presented. Also, for a given set of quadrature nodes, quadrature rules may be formulated that include or exclude function values computed at the left-hand endpoint t_n. Quadrature rules that do not depend on the left-hand endpoint (which are referred to as right-hand quadrature rules) are shown to lead to L(α)-stable implicit methods with α≈π/2. The semi-implicit analog of this property is also discussed. Numerical results suggest that the use of uniform quadrature nodes, as opposed to nodes based on Gaussian quadratures, does not significantly affect the stability or accuracy of these methods for orders less than ten. In contrast, a study of the reduction of order for stiff equations shows that when uniform quadrature nodes are used in conjunction with a right-hand quadrature rule, the form and extent of order-reduction changes considerably. Specifically, a reduction of order to is observed for uniform nodes as opposed to for non-uniform nodes, where Δt denotes the time step and ε a stiffness parameter such that ε→0 corresponds to the problem becoming increasingly stiff. AMS subject classification (2000) 65B05     

14-Noreudesmanes and a phenylpropane heterodimer from sea buckthorn berry inhibit Herpes simplex type 2 virus replication

Two new 14-noreudesmane sesquiterpenes, one new phenylpropane heterodimer, caulilexin C, and uvaol were isolated from the 70% MeOH extract of the fruit peel of Elaeagnus rhamnoides. The structures of the compounds were elucidated by HRESIMS and advanced NMR methods. The absolute configuration of (R)-6,9-dihydroxy-1-oxo-14-noreudesm-5,7,9-triene was determined by the TDDFT-ECD method. The new compounds, together with structurally similar naphthalenes (musizin, musizin-8-O-glucoside, torachrysone-8-O-glucoside) and 1,4-naphthoquinone (2-methylstipandrone), isolated previously from Rumex aquaticus, were investigated for their antiviral activity against Herpes simplex virus type 2 (HSV-2) using two different methods. Applying the traditional virus yield reduction test, (R)-6,9-dihydroxy-1-oxo-14-noreudesm-5,7,9-triene, 1-[3-methoxy-4-(2-methoxy-4-(1E)-propenyl-phenoxy)-phenyl]-propane-1,2-diol, and musizin caused a 2.00 log₁₀, 3.49 log₁₀, and 2.33 log₁₀ reduction of HSV-2 yield, respectively, at a concentration of 12.5?μM. 2-Hydroxy-1-methoxy-6,9-dioxo-14-noreudesm-1,3,5(10),7-tetraene exhibited an antiviral effect at concentration of 50?μM only. Similar results were obtained when the qPCR method was used to test the antiviral activity of the compounds.     

Powder neutron diffraction of SrNbO2N at room temperature and 1.5 K

The structure of strontium niobium dioxygen nitride, SrNbO₂N, has been solved by powder neutron diffraction at room temperature and 1.5 K. SrNbO₂N crystallizes in the tetragonal space group I4/mcm, with a = 5.7056 (4) and c = 8.1002 (9) Å at room temperature, and a = 5.6938 (4) and c = 8.0974 (8) Å at 1.5 K. The crystal structure is derived from the cubic perovskite archetype by a slight rotation of the Nb(O,N)₆ octahedra with respect to the tetragonal axis. A partially ordered distribution of oxygen and nitrogen on the anionic sites was found.     

The electrochemistry of antibody-modified conducting polymer electrodes

The modification of conducting polymer electrodes with antibodies (i.e. proteins) by means of electrochemical polymerization is a simple step that can be used to develop an immunological sensor. However, the electrochemical processes involved leading to the generation of analytical signals by the sensor have not been fully investigated. In this work, we report on the characterization of the interaction between an antigen, human serum albumin (HSA) and an antibody-immobilized polypyrrole electrode (such as anti-HSA) using cyclic voltammetry (CV) and impedance spectroscopy. This interaction was monitored using electrochemical impedance spectroscopy at three different potentials. The potentials correspond to the three redox states of the electroconducting polymer (i.e. reduced, doped and overoxidized states). Evidence from the CV experiments confirmed that there was a shift in the potential, which was found to be proportional to the concentration. Both the CV and the impedance experiments indicated that this potential-dependent shift could be attributed to antibody–antigen (Ab–Ag) binding.     

Byssus Thread: A Novel Support Material for Urease Immobilization

Byssus threads are tough biopolymer produced by mussels (Mytilus viridis) to attach themselves to rocks. These were collected from mussels in their natural habitat (N) and from animals maintained in laboratory condition (L) as a novel support. Byssus thread surfaces were characterized by SEM analysis, chemically modified and used for adsorption of urease. The efficiency of the immobilization was calculated by examining the relative enzyme activity of free and the immobilized urease. The pH stabilities of immobilized urease were higher (0.5 unit) than free enzyme. Immobilized enzymes on byssus (both N and L) when stored at 6 °C retained 50% of its activity after 30 days, but they were more stable in dry condition. The optimum temperature of immobilized enzymes was found to increase (25 °C). A Michaelis-Menten constant (K (m)) value for immobilized urease was also elevated (2.08 mol).     

Milk-Derived Carbon Quantum Dots: Study of Biological and Chemical Properties Provides Evidence of Toxicity

Carbon dots (CDs) are carbon-based zero-dimensional nanomaterials that can be prepared from a number of organic precursors. In this research, they are prepared using fat-free UHT cow milk through the hydrothermal method. FTIR analysis shows C=O and C-H bond presence, as well as nitrogen-based bond like C-N, C=N and –NH₂ presence in CDs, while the absorption spectra show the absorption band at 280 ± 3 nm. Next, the Biuret test was performed, with the results showing no presence of unreacted proteins in CDs. It can be said that all proteins are converted in CDs. Photo luminance spectra shows the emission of CDs is 420 nm and a toxicity study of CDs was performed. The Presto Blue method was used to test the toxicity of CDs for murine hippocampal cells. CDs at a concentration of 4 mg/mL were hazardous independent of synthesis time, while the toxicity was higher for lower synthesis times of 1 and 2 h. When the concentration is reduced in 1 and 2 h synthesized CDs, the cytotoxic effect also decreases significantly, ensuring a survival rate of 60–80%. However, when the synthesis time of CDs is increased, the cytotoxic effect decreases to a lesser extent. The CDs with the highest synthesis time of 8 h do not show a cytotoxic effect above 60%. The cytotoxicity study shows that CDs may have a concentration and time–dependent cytotoxic effect, reducing the number of viable cells by 40%.     

Accurate computation of Stokes flow driven by an open immersed interface

We present numerical methods for computing two-dimensional Stokes flow driven by forces singularly supported along an open, immersed interface. Two second-order accurate methods are developed: one for accurately evaluating boundary integral solutions at a point, and another for computing Stokes solution values on a rectangular mesh. We first describe a method for computing singular or nearly singular integrals, such as a double layer potential due to sources on a curve in the plane, evaluated at a point on or near the curve. To improve accuracy of the numerical quadrature, we add corrections for the errors arising from discretization, which are found by asymptotic analysis. When used to solve the Stokes equations with sources on an open, immersed interface, the method generates second-order approximations, for both the pressure and the velocity, and preserves the jumps in the solutions and their derivatives across the boundary. We then combine the method with a mesh-based solver to yield a hybrid method for computing Stokes solutions at N² grid points on a rectangular grid. Numerical results are presented which exhibit second-order accuracy. To demonstrate the applicability of the method, we use the method to simulate fluid dynamics induced by the beating motion of a cilium. The method preserves the sharp jumps in the Stokes solution and their derivatives across the immersed boundary. Model results illustrate the distinct hydrodynamic effects generated by the effective stroke and by the recovery stroke of the ciliary beat cycle.