Polar Foliations on Positively Curved Manifolds

We investigate the geometric and topological restrictions imposed by a polar foliation of codimension no less than two on a positively curved, simply con- nected, compact riemannian manifold. Inspired by a result of Fang, Grove and Thorbergsson on polar actions on such manifolds we associate to the foliation a chamber complex and show that in absence of point leaves this is covered by a spherical building, which under certain technical assumptions is isomorphic to the building at infinity of a non-compact symmetric space. This implies that the given manifold has the homeomorphism type of a com- pact symmetric space of rank one. We crucially employ results on the local homogeneity of singular riemannian foliations. In the case of point leaves we apply more direct methods to determine the diffeomorphism type or the cohomology ring of the manifold, respectively

Fisher Information in Noisy Intermediate-Scale Quantum Applications

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning

THE PROVISION OF SUPPORT MATERIAL TO ASSIST FET PHASE ACCOUNTING EDUCATORS IN THE FREE STATE PROVINCE

Thesis (Ph. D.) - Central University of Technology, Free State, 2008This study primarily focuses on the factors that should be taken into account when developing Learning and Teaching Support Material (LTSM) to be used by FET Accounting educators to improve the results of their learners. In order to accomplish this aim, literature from published books, textbooks, guidelines and syllabi from the Department of Education, speeches and articles on the internet, interviews and questionnaires were used in capturing data to establish the essence of Accounting and Accounting principles, to determine the educational changes regarding the curriculum that were made and the influence of these changes on the Accounting syllabi for the FET phase, to identify the factors that hamper the improvement of FET Accounting results in schools and to identify, describe and analyse a curriculum and LTSM. A triangulation methodology was employed in this study where qualitative data (interviews) and quantitative data (questionnaires) were captured. Through the interviews with the Learning Facilitators of Accounting and questionnaires completed by Accounting educators, it became clear that a lack of LTSM exist in Accounting. Accounting educators indicated that they are in dire need of LTSM for the FET phase to be able to improve the results of their Accounting learners in tests and examinations

Анализ средств разработки информационной технологии по профориентации школьников

In this article the main approaches to career guidance of school students are described. The choice of information approach for the solution of an objective is reasonable. The analysis of development tools of information technology on career guidance of school students is carried out

Tetra-μ-acetato-bis­[(1,3-benzothia­zole)copper(II)](Cu—Cu)

The title compound, [Cu2(CH3CO2)4(C7H5NS)2] or [(C7H5NS)Cu]2(μ-O2CCH3)4, crystallizes with one mol­ecule per unit cell. The coordination number of copper is six with four basal O atoms, one axial N atom and one axial Cu atom. Four acetate ligands act as bidentate linker and connect two Cu atoms, with a crystallographic inversion center located at the mid-point of the Cu—Cu bond. The acetate ligands form slightly distorted square planes around each metal ion, while the copper ions are displaced by 0.2089 (4) Å from these planes towards the N atoms. Thus, the Cu—Cu distance is elongated to 2.6378 (7) Å, compared with the 2.2180 (7) Å distance between the two basal planes. The angle between the basal plane and the Cu—N bond is 4.84 (6)°