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.     

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.     

Conditional Probabilities and Density Operators in Quantum Modeling

Motivated by a recent proof of free choices in linking equations to the experiments they describe, I clarify some relations among purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. I relate conditional probabilities associated with projection-valued measures to conditional density operators identical, in some cases but not in others, to the usual reduced density operators. While a fatal obstacle precludes associating conditional density operators with general non-projective measures, tensor products of general positive operator-valued measures (POVMs) are associated with conditional density operators. This association together with the free choice of probe particles allows a postulate of state reductions to be replaced by a theorem. An application shows an equivalence between one form of quantum key distribution and another with respect to certain eavesdropping attacks.     

精确计算在π~0重整化链图传播下p→p′微分截面

本文采用中性介子π0与核子N-反核子U-强相互作用的Lorentz不变耦合模型,对质子反质子在中性介子π0重整化链图传播下的散射微分截面,作了严格解析计算后获得了"精确"理论结果;进而,又对该计算结果与π0树图传播下的微分截面作了对比分析,获得了相关辐射修正的重要结果.这对于深入研究质子摊贩质子在高、中、低能区中的弹性碰撞及其描述强相互作用的Lorentz不变耦合模型理论,都将提供某些值得借鉴与参考的理论研究价值.     

Viscosity analysis on the Boltzmann equation

This paper is devoted to investigating the asymptotic properties of the renormalized solution to the viscosity equation tfε + v ·▽xfε = Q (fε,fε ) + εΔvfε as ε→ 0+ . We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L1 ((0 , T ) × RN × RN ). The proof is based on compactness analysis and velocity averaging theory.     

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].