Excess charge for pseudo-relativistic atoms in Hartree-Fock theory

We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge Z and the fine structure constant \alpha as long as Z\alpha is bounded.Comment: 48 Page

Adaptive Bayesian estimation in indirect Gaussian sequence space models

In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data. While this establishes posterior consistency, however, the concentration rate depends on both $\theta^\circ$ and a tuning parameter which enters the prior distribution. We first provide an oracle optimal choice of the tuning parameter, i.e., optimized for each $\theta^\circ$ separately. The optimal choice of the prior distribution allows us to derive an oracle optimal concentration rate of the associated posterior distribution. Moreover, for a given class of parameters and a suitable choice of the tuning parameter, we show that the resulting uniform concentration rate over the given class is optimal in a minimax sense. Finally, we construct a hierarchical prior that is adaptive. This means that, given a parameter $\theta^\circ$ or a class of parameters, respectively, the posterior distribution contracts at the oracle rate or at the minimax rate over the class. Notably, the hierarchical prior does not depend neither on $\theta^\circ$ nor on the given class. Moreover, convergence of the fully data-driven Bayes estimator at the oracle or at the minimax rate is established

Operator Lipschitz functions on Banach spaces

Let $X$, $Y$ be Banach spaces and let $\mathcal{L}(X,Y)$ be the space of bounded linear operators from $X$ to $Y$. We develop the theory of double operator integrals on $\mathcal{L}(X,Y)$ and apply this theory to obtain commutator estimates of the form $\|f(B)S-Sf(A)\|_{\mathcal{L}(X,Y)}\leq \textrm{const} \|BS-SA\|_{\mathcal{L}(X,Y)}$ for a large class of functions $f$, where $A\in\mathcal{L}(X)$, $B\in \mathcal{L}(Y)$ are scalar type operators and $S\in \mathcal{L}(X,Y)$. In particular, we establish this estimate for $f(t):=|t|$ and for diagonalizable operators on $X=\ell_{p}$ and $Y=\ell_{q}$, for $p<q$ and $p=q=1$, and for $X=Y=\mathrm{c}_{0}$. We also obtain results for $p\geq q$. We also study the estimate above in the setting of Banach ideals in $\mathcal{L}(X,Y)$. The commutator estimates we derive hold for diagonalizable matrices with a constant independent of the size of the matrix.Comment: Final version published in Studia Mathematica, with some minor change

High-end fashion manufacturing in the UK - product, process and vision: Recommendations for a Designer and Fashion Manufacturer Alliance and a Designer Innovation and Sampling Centre

The Centre for Fashion Enterprise (CFE) was commissioned by the Department of Culture, Media and Sport (DCMS) to undertake a feasibility study to explore fully the market need for a new high-end production hub. This was in direct response to the need highlighted in the DCMS report, Creative Britain - New Talents For The New Economy, published in 2008. This study has confirmed that there is a need. However the need is for a sampling and innovation facility rather than a production hub. Designers reported a shortage of high quality sampling capacity in the UK, as well as difficulties in getting small quantities produced. Additionally, they do not know where or how to source appropriate manufacturing in the UK, Europe or globally, at the quality the market requires

High-end fashion manufacturing in the UK - product, process and vision. Recommendations for education, training and accreditation

The Centre for Fashion Enterprise (CFE) was commissioned by the Department of Culture, Media and Sport (DCMS) to undertake a feasibility study to explore fully the market need for a new high-end production hub. This was in direct response to the need highlighted in the DCMS report, Creative Britain - New Talents For The New Economy, published in 2008. In addition to finding a need for a sampling and innovation facility1 (outlined in a separate document), the study identified significant problems relating to education and skills training in the sector. Recommendations are given in this report as to how these might be addressed, as well as a recommendation for an accreditation scheme that would aim to raise production quality standards within the sector

Response biases

Response biases comprise a variety of systematic tendencies of responding to questionnaire items. Response biases exert an influence on item responses in addition to any constructs that the questionnaire is designed to measure and can therefore potentially bias the corresponding trait level estimates. This chapter addresses general response biases that are independent of item content, including response styles (e.g., extreme response style, acquiescence) and rater biases (halo effect, leniency/severity bias), as well as response biases that are related to item content and depend strongly on the context (socially desirable responding). The chapter summarizes research on correlates of response biases and research on inter-individual and cross-cultural differences in engaging in response styles and rater biases. It describes different methods that can be applied at the test construction stage to prevent or minimize the occurrence of response biases. Finally, it depicts methods developed for correcting for the effects of response biases.</p