Discrete Sturm-Liouville problems with nonlinear parameter in the boundary conditions

This paper deals with discrete second order Sturm-Liouville problems where the parameter that is part of the Sturm-Liouville difference equation appears nonlinearly in the boundary conditions. The operator is extended to a self-adjoint operator and an expansion theorem is proved.     

Discrete versions of continuous isoperimetric problems

Discrete isoperimetric variational problems which model single and double integral isoperimetric problems are formulated and some multiplier rules are derived. For quardratic functionals, the Euler-Lagrange equation is linear and can be analyzed bydeterminant methods. difference equations methods. or numerically bythealgebraic eigenvalue problem. A specific example is given wherethe eigenfuntions and eigenvalue of this discrete problem converge. as the step size goes to zero, to the eigenfunctionsand eigenvalues of the corresponding, continuous problem Recent developments in algebraic geometry offer the hopeof using Groebner (=Gröbner or Grobner) basis methods to numerically solve some systems of equationsgenerated by Lagrange multiplier methods. These methods mayapply to nonlinear systems of equations whenever they can be reduced to systems of polynomial equations. The Groebner basis algorithm of Buchberger is an extension of Gaussian elimination to polynomial systems.     

Study of the cholesterol extraction capacity of β-cyclodextrin and its derivatives, relationships with their effects on endothelial cell viability and on membrane models

Endothelial cells (HUVEC) were treated with β-cyclodextrin and hydroxypropylated or methylated derivatives solutions in order to quantify their cholesterol extraction capacity. Non-toxic concentrations of cyclodextrins (CDs) were determined following methyl thiazol tetrazolium (MTT) assays, total protein measurements, morphological observations and trypan blue assays. The residual cholesterol content of cells was measured and the extraction power of CDs compared to results obtained by phase solubility diagrams. Cholesterol was extracted with a dose-response relationship, the lowest residual cholesterol content being obtained with β-CD at 10 mM. Low substituted derivatives (Crysmeb^® and hydroxypropyl-β-CD) maintained liposomes integrity (as shown before), were the less cytotoxic and presented the lowest affinity for cholesterol contrary to methylated derivatives with degrees of substitution around 2.     

New particle searches and discoveries: A supplement to the 1976 edition of “review of particle properties”

This supplement to the 1976 edition of “Review of particle properties”, Particle Data Group [Rev. Mod. Phys. 48, No. 2, Part II (1976)], contains tabulations of experimental data bearing on the “new particles” and related topics; categories covered include charmed particles, ψ's and their decay products, and heavy leptons. Errata to the previous edition are also given.     

Oscillation theory and numerical solution of fourth-order Sturm--Liouville problems

A shooting method is developed to approximate the eigenvaluesand eigenfunc-tions of a fourth-order Sturm-Liouville problem.The main tool is a miss-distance function M(), which countsthe number of eigenvalues less than A. The method approximatesthe coefficients of the differential equation by piecewise-constantfunctions, which enables an exact solution to be found on eachmesh interval. In order to calculate N() for the approximateproblem, certain oscillation numbers N_L and N_R must be computed.These consist of sums of nullities (or rank deficiencies) of2 x 2 matrices obtained from the solutions of the approximatedifferential equation. Although these solutions can be foundexplicitly, the calculation of N_L and N_R is non-trivial, andis obtained by using certain properties of M().     

4‐[(2‐Hydroxyethyl)iminomethyl]‐5‐hydroxymethyl‐2‐methylpyridin‐3‐ol

The title compound, C₁₀H₁₄N₂O₃, is a Schiff base which is derived from pyridoxal and represents, therefore, a vitamin B₆‐related compound. Molecules are linked into sheets by a combination of O—H...O and O—H...N hydrogen bonds.     

Extraction and chromatography of carotenoids from pumpkin

Vitamin A deficiency is a health problem in Southeast Asia that can be corrected by feeding orange fruits and vegetables such as mango. Pumpkin is a traditional Korean food that is easy to store and is already believed to have health benefits. We extracted carotenoids from pumpkin by liquid-liquid extraction and by supercritical fluid extraction. We measured carotenoids by reversed-phase chromatography with diode array detection. The major carotenoid in pumpkin (> 80%) is beta-carotene, with lesser amounts of lutein, lycopene, alpha-carotene and cis-beta-carotene. Pumpkin is a rich source of beta-carotene and might be useful for preventing Vitamin A deficiency.     

Application of surface science techniques to study a gilded Egyptian funerary mask: A multi-analytical approach

A wide range of analytical techniques has been used to study an Egyptian funerary mask of the Ptolemaic period (305-30 bc ). Secondary electron (SE) and back-scattering (BS) images, recorded by a scanning electron microscope (SEM), provided a detailed representation of the metallurgical techniques used to construct the gilded mask. It is confirmed, that the golden leaf used to cover the mask is the product of an antique refinery practice, so called, cementation process of naturally occurring alloy of gold and silver, namely electrum. Complementary results of SEM-electron dispersion spectroscopy (EDS) and electron probe microanalysis (EPMA)–wavelength dispersion spectroscopy (WDS) provided chemical compositions of the golden leaf as well as in the plaster base of the mask. X-ray photoemission spectroscopy (XPS) revealed the presence of Au, Ag, Si, S, Cl, Ca, and N, in addition to O and C. Relative concentration of Au/Ag at the surface has been measured by XPS to be 70% to 30%. XPS depth profiling verified silver-enrichment at the surface, as ratio of gold to silver is measured to be 80% to 20% at the depth of 15 nm. XPS chemical mapping images of gold and silver confirmed a rather inhomogeneous character of Au/Ag relative concentration at the surface. The main diffraction peaks in the X-ray diffraction (XRD) spectrum coincide with diffraction peaks of pure gold, silver metals, and magnesium calcite Mg_0.03Ca_0.97CO₃. Whereas, Raman spectroscopy results implied the existence of Ag₂S, a tarnishing compound, on the golden area of the mask.     

Biodegradation of poly (vinylalcohol) with enzymatic extracts of phanerochaete chrysosporium

Commercial poly(vinylalcohol) samples (PVOH) of average molecular mass (Mw) 120,000 g/mol, were subjected to biodegradation with enzymatic extracts of the Phanerochaete chrysosporium fungus, in which the lignine peroxidase activity (LiP) was detected. The results of differential refractive index and ultraviolet (UV) absorption Gel Permeation Chromatography (GPC), Fourier Transform Infrared Spectroscopy (FTIR) and Gas Chromatography coupled to a Mass Detector (GC-MS) allow to deduce that in 15 days, under the conditions of this study, the average molar mass of the polymer decreases in 79.3 %. The benzaldehyde was detected as the main degradation product.