Wolfgang Krull is a prominent mathematician, particularly known for his contributions to the field of algebraic geometry and commutative algebra. His work has focused on the theory of rings, ideals, and algebraic structures. Among his notable contributions is the development of Krull dimension, a concept used to define the "size" of a ring in terms of the length of chains of prime ideals.

Non-linearity is needed otherwise the input energy would just make the state go to higher and higher energy levels, e.g. from 1 to 2. But we only want to use levels 0 and 1.

The way this is modelled in by starting from a pure LC circuit, which is an harmonic oscillator, see also quantum LC circuit, and then replacing the linear inductor with a SQUID device, e.g. mentioned at: youtu.be/eZJjQGu85Ps?t=1655 Video "Superconducting Qubits I Part 1 by Zlatko Minev (2020)".

This is unlike atomic systems like trapped ion quantum computers, where each atom is necessarily exactly the same as the other.

Abstract algebra is a branch of mathematics that studies algebraic structures, which are sets equipped with operations that satisfy certain axioms. The main algebraic structures studied in abstract algebra include: 1. **Groups**: A group is a set equipped with a single binary operation that satisfies four properties: closure, associativity, the existence of an identity element, and the existence of inverses. Groups can be finite or infinite and are foundational in many areas of mathematics.

The history of the electric vehicle (EV) is a fascinating journey that spans more than a century, reflecting changes in technology, societal needs, and environmental awareness. Here’s an overview of key milestones in the development of electric vehicles: ### 19th Century Beginnings - **1830s**: The first known electric vehicles were developed in the early 1830s. Scottish inventor Robert Anderson created a crude electric carriage powered by non-rechargeable batteries.

Why. Why. Why is there no limit to how much I can help, but there is a limit to how many thanks I can get?

At most, limit it to a single answer to avoid highly publicized events, e.g. an answer being shared on Reddit. But across answers? It makes no sense.

The two ways main ways to overcome this limit are the 15 point answer accept reputation and bounties.

200 reputation per day works out 73k a year BTW.

The link will break, and the answer will lose. Or the person who summarizes inline will get more upvotes because people are lazy to click the link. Also, web archiving exists.

This is especially idiotic when it is a link to another post in Stack Overflow itself.

The Switching Kalman Filter (SKF) is an extension of the classical Kalman filter used to handle systems that exhibit switching behavior among multiple models or modes. It is particularly useful in situations where the system dynamics or measurements can switch between different states or regimes, leading to changes in the parameters governing the state estimation. ### Key Characteristics: 1. **Multiple Models**: The SKF operates under the assumption that the system can be described by multiple linear or nonlinear models.

Scenario optimization is a mathematical and computational approach used to make decisions under uncertainty by evaluating multiple possible future scenarios. This method is particularly relevant in fields such as finance, supply chain management, operations research, and energy systems, where outcomes can significantly vary based on uncertain factors. Here are the key elements of scenario optimization: 1. **Scenarios**: These are distinct representations of future states based on different assumptions regarding uncertain parameters.

Waste of time sub-sites that should instead be merged into Stack Overflow as different tags.

Nowhere is this waste more visible than at: cs50.stackexchange.com/. A website just for some specific course that is completely covered by other sites of the network? What a humongous waste!!!

A sampled data system is a type of system that processes continuous signals by taking discrete samples at specific intervals. This process involves converting a continuous-time signal into a discrete-time signal, which can then be analyzed and processed using digital methods. Key characteristics of sampled data systems include: 1. **Sampling**: This is the process of measuring the value of a continuous signal at regular intervals. The points at which the signal is measured are called samples.

Robust control is a branch of control theory that deals with the design and analysis of controllers for dynamic systems that are subject to uncertainties and variations. The primary goal of robust control is to ensure that the system behaves reliably under a range of conditions, despite potential disturbances, parameter variations, or model inaccuracies.

The term "Wheeler Jump" typically refers to a specific technical drill or maneuver within the context of various sports or physical training, particularly in disciplines like track and field, gymnastics, or martial arts. However, it could also refer to a jump or leap associated with an athlete named Wheeler or in a specific context like an event or competition.

Rise time is a term used in various fields, particularly in electronics and signal processing, to describe the time it takes for a signal to change from a specified low level to a specified high level. It is often measured from 10% to 90% of the maximum amplitude of the waveform.

In music, an accent refers to a specific way of emphasizing a note or chord, making it stand out from the surrounding notes. This can be achieved through various means, such as increasing the volume (loudness), altering the duration (length), or changing the articulation (the manner in which the note is played or sung).

Each transaction isolation level specifies what can or cannot happen when two queries are being run in parallel, i.e.: the memory semantics of the system.

Remember that queries can affects thousands of rows, and database systems like PostgreSQL can run multiple such queries at the same time.

Good summary on the PostgreSQL page: www.postgresql.org/docs/14/transaction-iso.html

Implementation specifics: