Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.     

Synthesis and characterisation of a silicon oxide film solid-phase extraction system for lead traces determination: an all the way green analytical method

In this work, an all the way green analytical procedure based on a silicon oxide film-solid phase extraction system is proposed for lead traces determination. From the synthesis of a solid phase extraction (SPE) system and throughout the metal preconcentration and determination only aqueous media were employed. Characterisation of the film was carried out by Scanning Electron Microscopy and Attenuated Total Reflectance-Fourier Transform Infrared Spectroscopy. Preconcentration conditions, prior to Pb(II) Electrothermal Atomic Absorption Spectrometry (ETAAS) determination, such as adsorption and desorption time, pH and temperature, were optimised. Langmuir, Freundlich and Dubinin-Radushkevich isotherm models were analysed along with the evaluation of adsorption energy and standard free energy (ΔG ⁰). The greatest adsorption was obtained with incubation at pH 7 and 37°C. By using a small volume of 0.5?mol?L^?1 HNO₃ (0.5?mL) lead was desorbed from the silicon oxide film after 2?h incubation, generating low amount of waste. The films showed better adjustment for the Langmuir model (R^{2 ?}=?0.989). The detection limit (3.29σ) for Pb(II) was 0.228?µg?L^?1. The developed procedure is 10-fold more sensitive in comparison to direct ETAAS determination. Recovery values from soft tap-water and soft well-water were above 95%. When hard water was analysed, Pb(II) adsorption was found to be interfered by Mg²⁺ and Ca²⁺. After five preconcentration cycles relative recovery was found not to decay below 90%, indicating that the silicon oxide film could be used for multiple lead determinations.     

The Index of Cusp Operators on Manifolds with Corners

We recall a Fredholm criterion for fully elliptic cusp(pseudo)differential operators on a compact manifold with corners ofarbitrary codimension, acting on suitable Sobolev spaces. Then we give aformula for the index in terms of regularized `trace' functionalssimilar to the residue trace of Wodzicki and Guillemin.     

Stationary phases for gas chromatography; chemical stability of polysiloxanes

A number of polysiloxanes have been shown to be sensitive to acids when dissolved in chloroform. At 26O°C polysiloxanes were found to degrade under the influence of several compounds used or produced during the preparation of glass capillary columns.     

The Dichotomy Between Traces on d-sets F in R^n and the Density of D（R^n／Г） in Function Spaces

A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are introduced and calculated.     

Dixmier traces are weak dense in the set of all fully symmetric traces

We extend Dixmier's construction of singular traces (see [2]) to arbitrary fully symmetric operator ideals. In fact, we show that the set of Dixmier traces is weak^? dense in the set of all fully symmetric traces (that is, those traces which respect Hardy–Littlewood submajorization). Our results complement and extend earlier work of Wodzicki [22].     

Radicmetric and Spectrophotometric Determination of Trace Amounts of Selenium Using 3,3′-Diamino-Benzidine as the Initial Reagent

Abstract

Radiometric and spectrophotometric procedures for selenium analysis have been developed which are based on the formation and separation of the mono-and di-piazseLenols of 3,3′-diaminobenzidine. Analysis of samples, reaction conditions, and sensitivity of the procedures are discussed.     

关于“Several Inequalities of Matrix Traces一文的几点意见

本文指出了《数学季刊》第十卷第二期中发表的一篇文章“Several Inequalities of Matrix Traces”中的几点失误。