Convexity Preserving Interpolatory Subdivision Schemes

We construct local subdivision schemes that interpolate functional univariate data and that preserve convexity. The resulting limit function of these schemes is continuous and convex for arbitrary convex data. Moreover this class of schemes is restricted to a subdivision scheme that generates a limit function that is convex and continuously differentiable for strictly convex data. The approximation order of this scheme is four. Some generalizations, such as tension control and piecewise convexity preservation, are briefly discussed. November 29, 1996. Date revised: May 28, 1997.     

On Order-Preserving Properties of Probability Metrics

Stochastic orders and probability metrics are two areas that have received considerable attention in recent literature. A question of interest on its own and for certain applications is the preservation of metrics with respect to orders. This property does not seem to have been examined explicitly so far. Our purpose in this paper is to provide some useful remarks and results related to several orders and metrics which are standard in probability.     

Preservation procedures for arsenic speciation in a stream affected by acid mine drainage in southwestern Spain

A preservation study has been performed for arsenic speciation in surface freshwaters affected by acid mine drainage (AMD), a pollution source characterized by low pH and high metallic content. Two sample preservation procedures described in the literature were attempted using opaque glass containers and refrigeration: i) addition of 0.25 mol L⁻¹ EDTA to the samples, which maintained the stability of the arsenic species for 3 h; and ii) in situ sample clean-up with a cationic exchange resin, in order to reduce the metallic load, which resulted in a partial co-adsorption of arsenic onto Fe precipitates. A new proposed method was also tried: sample acidification with 6 mol L⁻¹ HCl followed by in situ clean-up with a cationic exchange resin, which allowed a longer preservation time of at least 48 h. The proposed method was successfully applied to water samples with high arsenic content, taken from the Aguas Agrias Stream (Odiel River Basin, SW Spain), which is severely affected by AMD that originates at the nearby polymetallic sulfide mine of Tharsis. The speciation results obtained by liquid chromatography–hydride generation–atomic fluorescence spectrometry (HPLC-HG-AFS) indicated that during the summer the main arsenic species was As(V) at the hundred μg L⁻¹ level, followed by DMA (dimethyl arsenic) and As(III) below the ten μg L⁻¹ level. In winter, As(V) and As(III) increased at least fivefold, whereas the DMA was not detected.     

Approximation by local trigonometric splines

For the class of 1-periodic functions, we use the linear noninterpolating method of trigonometric spline approximation possessing extremal and smoothing properties and locally inheriting the monotonicity of the initial data, i.e., the values of a function from at the points of a uniform grid. The approximation error is calculated exactly for this class of functions in the uniform metric. It coincides with the Kolmogorov and Konovalov widths.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 354–363.Original Russian Text Copyright © 2005 by K. V. Kostousov, V. T. Shevaldin.This revised version was published online in April 2005 with a corrected issue number.     

矩形微槽道气体流动的速度分布

矩形微槽道的各个流向截面可以局部近似为平面Poiseuille流动,应用信息保存(IP)方法和直接模拟Monte Carlo(DSMC)方法计算了从连续介质区到自由分子流区的平面Poiseuille流动,利用其结果对Beskok-Karniadadis公式和质量流率动理论因子进行修正和重新拟合,给出在整个稀薄气体流动领域都适用的微槽道气体流动速度分布.     

A Logical Reading of the Nonexistence of Proper Homomorphisms Between Affine Spaces

We provide definitions of and of noncollinearity by positive statements in terms of the ternary predicate of collinearity which are valid in affine n-dimensional geometry. This provides the intrinsic reason for the validity of V. Corbas's theorem stating that surjective maps between affine planes that preserve collinearity are isomorphisms, and of P. Maroscia's higher-dimensional generalization thereof.     

Some Shift-Invariant Integral Operators, Univariate Case, Revisited

In recent articles the first author and H. Gonska [e.g., see G. Anastassiou, C. Cottin, and H. Gonska, Global smoothness of approximating functions, Analysis, 11, 43–57 (1991); G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] studied global smoothness preservation by some univariate and multivariate linear operators over compact domains and ⁿ , n 1. In particular, they studied a very general positive linear integral type operator [e.g., see G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] over ⁿ that was introduced through a convolution-like integration of another general positive linear operator with a scaling-type function. In this article the authors, among others, extend and generalize [G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)]. Also certain new similar but more general integral operators are introduced and studied. These operators arise in a natural way, and for all these sufficient conditions are given for shift invariance, preservation of higher-order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preservation, and preservation of continuous probabilistic distribution functions. Several examples of very general specialized operators, old and new, are given that satisfy all the above properties.     

Applications of electron paramagnetic resonance spectroscopy to study interactions of iron proteins in cells with nitric oxide

Nitric oxide and species derived from it have a wide range of biological functions. Some applications of electron paramagnetic resonance (EPR) spectroscopy are reviewed, for observing nitrosyl species in biological systems. Nitrite has long been used as a food preservative owing to its bacteriostatic effect on spoilage bacteria. Nitrosyl complexes such as sodium nitroprusside, which are added experimentally as NO-generators, themselves produce paramagnetic nitrosyl species, which may be seen by EPR. We have used this to observe the effects of nitroprusside on clostridial cells. After growth in the presence of sublethal concentrations of nitroprusside, the cells show they have been converted into other, presumably less toxic, nitrosyl complexes such as (RS)₂Fe(NO)₂. Nitric oxide is cytotoxic, partly due to its effects on mitochondria. This is exploited in the destruction of cancer cells by the immune system. The targets include iron–sulfur proteins. It appears that species derived from nitric oxide such as peroxynitrite may be responsible. Addition of peroxynitrite to mitochondria led to depletion of the EPR-detectable iron–sulfur clusters. Paramagnetic complexes are formed in vivo from hemoglobin, in conditions such as experimental endotoxic shock. This has been used to follow the course of production of NO by macrophages. We have examined the effects of suppression of NO synthase using biopterin antagonists. Another method is to use an injected NO-trapping agent, Fe–diethyldithiocarbamate (Fe–DETC) to detect accumulated NO by EPR. In this way we have observed the effects of depletion of serum arginine by arginase. In brains from victims of Parkinson's disease, a nitrosyl species, identified as nitrosyl hemoglobin, has been observed in substantia nigra. This is an indication for the involvement of nitric oxide or a derived species in the damage to this organ.     

Method development for the determination of wood preservatives in commercially treated wood using gas chromatography-mass spectrometry

Fungicides and insecticides are commonly used preservatives to protect wood products against microbiological degradations. Currently, there is a lack of analytical methods addressing the quantitative determination of a wide range of wood preserving species in wood matrices. In this study, a reliable method was developed for the determination of a mixture of wood preserving agents with differing chemical structures (i.e., properties), including tebuconazole (TAZ), propiconazole (PAZ), 3-iodo-2-propynyl butylcarbamate (IPBC), and permethrin (PER), in pine wood. The analyte recoveries obtained by Soxhlet and multiple-stage sonication extractions were compared. While both extraction methods yielded similar results (80–100%), Soxhlet extraction was found to be less labor-intensive and thus preferred providing also lower RSDs of 1–6%. In comparison to methanol, commonly used as an extraction solvent for triazoles, acetone yielded similar extraction efficiencies for all analytes while reducing the time of sample concentration. The solid phase extraction method for triazoles was adapted to allow for a separation of IPBC and PER from the wood matrix. As opposed to previous studies, three recovery standards were employed, which enabled the correction of individual analyte losses during the sample preparation. The matrix-affected limits of detection (LODs) using gas chromatography with mass spectrometric detection were nearly the same for triazoles 0.07 and 0.21 ng g⁻¹ for PAZ and TAZ in sapwood and 0.18 and 0.21 ng g⁻¹ in heartwood, respectively. Higher LODs were observed for IPBC and PER: 3.9 and 1.7 ng g⁻¹ in sapwood, and 2.0 and 6.0 ng g⁻¹ in heartwood, respectively. The recoveries in the wood submitted to commercial sample treatment showed gradient distribution of analytes depending on the penetration of the treatment.     

Bernstein-type operators in Chebyshev spaces

We prove that it is possible to construct Bernstein-type operators in any given Extended Chebyshev space and we show how they are connected with blossoms. This generalises and explains a recent result by Aldas/Kounchev/Render on exponential spaces. We also indicate why such operators automatically possess interesting shape preserving properties and why similar operators exist in still more general frameworks, e.g., in Extended Chebyshev Piecewise spaces. We address the problem of convergence of infinite sequences of such operators, and we do prove convergence for special instances of Müntz spaces.