Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone

We give some criteria for a-minimally thin sets and a-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or ∞ with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside an a-rarefied set. Finally we illustrate the relation between the a-minimally thin set and the a-rarefied set in a cone

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Entangled Systems:Gravitationally mediated entanglement, coherence and knots

Since 2017, there has been a quest to measure gravity-induced quantum entanglement. Quantum entanglement is a phenomenon where two quantum particles cannot be described separately. It is used in, for example, quantum computers and quantum communication. Measuring quantum entanglement generated by gravity should determine whether gravity is a quantum or classical interaction, one of the most debated questions in modern physics. Moreover, the technological advancements needed to conduct this experiment could benefit various quantum technologies, including enhanced quantum earthquake detectors.However, significant challenges remain before this experiment can be realised. In my thesis, I propose several ways to improve the experiment's design, making the technology more feasible. Additionally, I examine potential environmental factors that could sabotage the experiment. Quantum experiments are highly sensitive to environmental effects—such as collisions between air particles and the quantum particle—which can render the measurement of quantum phenomena impossible. By analysing these environmental influences, we can better understand how to protect the experiment, ensuring that the desired quantum phenomena can be measured

Library buildings around the world

"Library Buildings around the World" is a survey based on researches of several years. The objective was to gather library buildings on an international level starting with 1990