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"Projectors"
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Moving images : nineteenth-century reading and screen practices
This text examines how the interplay between nineteenth-century literary and visual media paralleled the emergence of a modern psychological understanding of the ways in which reading, viewing and dreaming generate moving images in the mind.
Robert Paul and the origins of British cinema
\"Time Traveler, tells the story of the white-hot years of filmmaking in the 1890s and seeks nothing less than to restore Robert Paul to his rightful place in that scene. Paul improved upon the Kinetoscope (which Edison had neglected to patent in the UK). He also created the first movie camera in the UK and went on to unveil a highly effective projector called the Theatograph in 1896. Paul patented numerous devices, including a wireless telegraphy kit and submarine navigation devices that were instrumental in WWI. This book covers Paul's life, the race among inventors (including Edison, the Lumieres, and many more) to develop lucrative technologies, the jumbled culture of patent-snatching, tinkering, showmanship, music halls and movie palaces that then prevailed\"-- Provided by publisher.
FACTORIZATION OF THE MATRIX OF ORTHOGONAL PROJECTOR ON A.sub.PACE
2023
A deep factorization of the orthogonal projection matrix onto a suhspace is obtained. The LQ decomposition is used. For construction of an orthogonal matrix Q the method of successive rank reduction is applied. Bibliography: 4 titles.
Journal Article
NONASYMPTOTIC UPPER BOUNDS FOR THE RECONSTRUCTION ERROR OF PCA
2020
We analyse the reconstruction error of principal component analysis (PCA) and prove nonasymptotic upper bounds for the corresponding excess risk. These bounds unify and improve existing upper bounds from the literature. In particular, they give oracle inequalities under mild eigenvalue conditions. The bounds reveal that the excess risk differs significantly from usually considered subspace distances based on canonical angles. Our approach relies on the analysis of empirical spectral projectors combined with concentration inequalities for weighted empirical covariance operators and empirical eigenvalues.
Journal Article
Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps
2021
Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost.
Journal Article