A well-defined expression is a mathematical or logical expression that is clear and unambiguous in its meaning. This typically means that the expression follows the accepted rules of mathematics or logic and yields a unique, consistent result regardless of how it is interpreted within its given context. For example, the expression \(2 + 3\) is well-defined because it has a clear and universally accepted result: \(5\).

FRACTRAN is a minimalistic programming language invented by mathematician John Conway. It is designed to demonstrate how computation can be implemented using a simple set of rules involving fractions. The primary concept of FRACTRAN is to execute a series of operations on an integer using a list of fractions. The way FRACTRAN works is as follows: 1. You start with a positive integer (usually 1). 2. You have a predefined list of fractions.

DBrn can refer to different things depending on the context. However, without more specific information, it's difficult to provide a precise answer. Here are a couple of possibilities: 1. **DBR in Technology**: In the realm of technology and engineering, "DBrN" could refer to some technical terms like "Designated Block Reference Number" or might be related to a specific programming or hardware terminology.

An air mass is a large body of air that has uniform temperature and humidity characteristics in the horizontal direction. It typically spans thousands of square kilometers and can extend vertically through the atmosphere. The properties of an air mass are influenced by the region over which it forms, known as its source region. Air masses are classified based on their temperature and moisture content: 1. **Temperature:** - **Tropical (T)** - Warm air masses that originate in the tropics.

GLRB can refer to multiple things depending on the context. One of the most common meanings is "Global Risk and Resilience Business," a term often used in business and finance to refer to practices that enhance an organization's ability to manage risks and recover from adverse events.

As of my last knowledge update in October 2021, there is no widely known individual or entity named Timofei Osipovsky. It's possible that he may not be a public figure, or he could have gained prominence after that time.

Polyisocyanurate, often abbreviated as PIR, is a type of thermoset plastic that is derived from the polymerization of isocyanate and polyol. It is a member of the polyurethane family, but with a higher degree of rigidity and thermal stability. Polyisocyanurate is primarily used for its excellent insulating properties, making it a popular choice in the construction and manufacturing sectors.

Ice navigation refers to the techniques, practices, and operations involved in navigating vessels through ice-covered waters. This is a critical area of maritime navigation, especially for ships operating in polar regions or during winter months when waterways become obstructed by ice. Key aspects of ice navigation include: 1. **Types of Ice**: Understanding different types of ice (e.g., pack ice, field ice, brash ice, shorefast ice) and their characteristics is essential.

In economics, an "index" is a statistical measure that reflects changes in a particular variable or group of variables over time. It is commonly used to track economic indicators and trends, making it easier to analyze data and compare performance across different time periods or regions. Here are some common types of economic indices: 1. **Price Indices**: Measure changes in the price level of a basket of goods and services over time.

Xenoy is a brand name for a family of engineering thermoplastic materials produced by SABIC (Saudi Basic Industries Corporation). These materials are primarily a blend of polycarbonate and acrylonitrile-butadiene-styrene (ABS), which gives them a unique combination of properties. Xenoy is known for its high impact resistance, strength, durability, and heat resistance, making it suitable for a variety of applications, including automotive parts, consumer electronics, and industrial components.

Nik Nanos is a prominent Canadian pollster, researcher, and political analyst known for his work in public opinion research and market analysis. He is the founder and CEO of Nanos Research, a company that specializes in polling and survey research across various sectors, including politics, business, and social issues. Nanos is often called upon by media outlets and organizations to provide insights and analyses on public opinion trends in Canada, particularly during elections and significant political events.

Windows 2.0x refers to a series of early versions of Microsoft's Windows operating system that were part of the second major release of Windows. Specifically, Windows 2.0 was released in December 1987, and it was followed by Windows 2.03 in 1988 and Windows 2.1x in 1989. Windows 2.0 introduced several improvements and features over its predecessor, Windows 1.

Shizuo Kakutani is a prominent Japanese mathematician known for his work in functional analysis, game theory, and the Kakutani fixed-point theorem. The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem and is significant in various fields, including economics and game theory, as it provides conditions under which a fixed point exists in a compact, convex set.

As of my last knowledge update in October 2023, Vera Serganova is not a widely recognized figure or concept in popular culture, science, or other well-known contexts. It is possible that Vera Serganova could refer to a private individual or a lesser-known entity that has not gained significant public attention.

A sphenic number is a positive integer that is the product of three distinct prime numbers. In other words, a sphenic number can be expressed in the form \( p_1 \times p_2 \times p_3 \), where \( p_1 \), \( p_2 \), and \( p_3 \) are prime numbers and \( p_1 \), \( p_2 \), and \( p_3 \) are all different from one another.

A skyrmion is a type of topological soliton—a stable, localized configuration of a field—found in certain magnetic materials. It is characterized by a nontrivial topology and can be thought of as a swirling configuration of spins, which are the magnetic moments of atoms. The concept of skyrmions originates from theoretical physics and was first proposed by British physicist Tony Skyrme in the 1960s, primarily in the context of particle physics.

Related: Dirac equation vs quantum electrodynamics.

Described for example in lecture 1.

Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).

Learning it is one of Ciro Santilli's main intellectual fetishes.

While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...

The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!

Experiments: quantum electrodynamics experiments.

Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.

Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?

As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):

That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.

QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.

Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:

Recommended by Ron Maimon at physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics/18643#18643.

Julian Schwinger's selection of academic papers by himself and others.