Complementarity and Additivity for Covariant Channels

This paper contains several new results concerning covariant quantum channels in d ≥ 2 dimensions. The first part, Sec. 3, based on [4], is devoted to unitarily covariant channels, namely depolarizing and transpose-depolarizing channels. The second part, Sec. 4, based on [10], studies Weyl-covariant channels. These results are preceded by Sec. 2 in which we discuss various representations of general completely positive maps and channels. In the first part of the paper we compute complementary channels for depolarizing and transpose-depolarizing channels. This method easily yields minimal Kraus representations from non-minimal ones. We also study properties of the output purity of the tensor product of a channel and its complementary. In the second part, the formalism of discrete noncommutative Fourier transform is developed and applied to the study of Weyl-covariant maps and channels. We then extend a result in [16] concerning a bound for the maximal output 2-norm of a Weyl-covariant channel. A class of maps which attain the bound is introduced, for which the multiplicativity of the maximal output 2-norm is proven. The complementary channels are described which have the same multiplicativity properties as the Weyl-covariant channels.     

BaO-Al2O3-SiO2微晶玻璃密度的计算

为了评估密度作为BaO-Al2O3-SiO2(BAS)微晶玻璃晶化热处理和质量监控手段的可行性和准确性,提出一种测定微晶玻璃密度的方法.利用x射线衍射和Rietveld结构精修法准确测定烧结制备的BAS微晶玻璃中各晶相的质量分数和密度,研究了加和法则应用于BAS系微晶玻璃的准确性.对比精修得到的晶相的晶胞参数和对应标准卡片上纯晶相的晶胞参数,得到样品中各晶相的密度.结果表明:BAS微晶玻璃中各晶相与对应纯晶相的密度差别极其微小.利用获得的各相的质量分数,根据玻璃工艺学的经验数据计算残余玻璃相的密度.最后,根据加和法则计算得到BAS微晶玻璃样品的密度,所得的密度值与利用Archimedes法测得的密度值的相对偏差小于1.4%.     

三角代数上的Jordan三重初等映射的可加性

主要研究了三角代数上的Jordan三重初等映射的可加性,给出了一个保证Jor-dan三重初等映射满足可加性的充分条件。     

NONSPECIFICITY IN Rn

Open problems posed by Klir and Wierman (1998) for a nonspecificity measure are solved; the measure is proven additive, and its extension to nonconvex sets given. Several different proofs of additivity are given, to suggest certain techniques of wider applicability in system problems and to motivate further research possibihties. A study is initiated to refine nonspecificity separately to each dimension k≤n for the bodies residing in Rⁿ.     

Microkinetic model for the pyrolysis of methyl esters: From model compound to industrial biodiesel

A tool for the generation of decomposition schemes of large molecules has been developed. These decomposition schemes contain radicals which can be eliminated from the model equations if both the μ‐hypothesis and the pseudosteady‐state approximation are valid. The reaction rate coefficients and thermodynamic parameters have been calculated by incorporating a comprehensive group additive framework. A microkinetic model for the pyrolysis of methyl esters with a carbon number of up to 19 has been generated using this tool. It is validated by comparing calculated and experimental yields of the pyrolysis of methyl decanoate and novel rapeseed methyl ester pyrolysis data in the temperature range from 800 to 1100 K and methyl ester partial pressure range from 1 × 10^?3 to 1 × 10^?2 MPa. This modeling frame work allows to not only assess the use of methyl ester mixtures as potential feedstock for olefin production but also their effect as blend‐in or trace impurity. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4309–4322, 2015     

A revised additivity rule for electron scattering from ethylene, propene, butene, ethane, propane and butane

Considering the difference between the bound atom in a molecule and the free atom, the original additivity rule is revised. Using the revised additivity rule, the total cross sections for electron scattering by ethylene (C₂H₄), propene (C₃H₆), butene (C₄H₈), ethane (C₂H₆), propane (C₃H₈) and butane (C₄H₁₀) are calculated over the energy range 10-1000 eV. The results of the revised additivity rule are compared with those obtained by experiments and the revised additivity rule can give better agreement with experimental values than the original additivity rule.     

Parameter design using the Taguchi methodology

This article aims to give an overview of the Taguchi methodology and more specific of its key step: parameter design. The purpose of parameter design is to bring quality into the product/process by determining the relevant parameters and their optimal settings such that the quality characteristics of the product are optimised and have minimal sensitivity to “noise” (i.e., those disturbing factors which are difficult or too expensive to control). The (mainly statistical) tools used in the methodology will be handled and some actual Bell cases will be mentioned as practical examples.     

Relationship between brightness/luminance ratio and additivity‐law failure

The degree of additivity‐law failure of a mixture color consisting of two component chromatic colors has very complex characteristics depending on the used component colors and their mixing conditions. It is significantly affected by the mixture‐color chromaticity and by the brightness/luminance ratio at the chromaticity. A simple relationship was derived between the following quantities: degree of additivity‐law failure, additivity‐law luminance (luminance of the mixture color derived by postulating additivity law), and brightness/luminance ratio at the chromaticity of the mixture color. This relationship can be applied to any additivity‐law failure experiment and any formula on brightness/luminance ratio. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 185–190, 2002; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/col.10045     

Bayesian separation of spectral sources under non-negativity and full additivity constraints

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture model. However, incorporating the full additivity constraint requires further developments. This paper studies a new hierarchical Bayesian model appropriate to the non-negativity and sum-to-one constraints associated to the sources and the mixing coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples obtained with an appropriate Gibbs algorithm. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture data. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.     

The binomial decomposition of OWA functions,the 2‐additive and 3‐additive cases in n dimensions

In the context of the binomial decomposition of ordered weighted averaging (OWA) functions, we investigate the constraints associated with the 2‐additive and 3‐additive cases in n dimensions. The 2‐additive case depends on one coefficient whose feasible region does not depend on the dimension n. On the other hand, the feasible region of the 3‐additive case depends on two coefficients and is explicitly dependent on the dimension n. This feasible region is a convex polygon with n vertices and n edges, which is strictly expanding in the dimension n. The orness of the OWA functions within the feasible region is linear in the two coefficients, and the vertices associated with maximum and minimum orness are identified. Finally, we discuss the 3‐additive binomial decomposition in the asymptotic infinite dimensional limit.