A **smooth projective plane** is a specific type of geometric object in algebraic geometry. In simple terms, it is a two-dimensional projective variety that is smooth, meaning it has no singular points, and it is defined over a projective space.
Japaridze's polymodal logic is a type of non-classical logic that extends modal logic by allowing for multiple modalities that can interact in various ways. It was developed by the logician Georgi Japaridze, who aimed to create a framework for reasoning that captures more complex relationships than standard modal logics. In traditional modal logic, the most common modalities include necessity (typically represented as □) and possibility (◊), which deal with notions of truth across possible worlds.
The Coulomb operator is a mathematical operator that describes the interaction between charged particles due to electrostatic forces. In the context of quantum mechanics and quantum chemistry, it is most commonly used to represent the potential energy arising from the Coulomb attraction or repulsion between charged particles, such as electrons and nuclei.
The Society for Psychophysiological Research (SPR) is an organization dedicated to advancing the understanding of the relationship between psychological processes and physiological responses. Founded in 1961, the SPR promotes research and education in the field of psychophysiology, which examines how psychological factors such as thoughts, emotions, and behaviors can affect physiological functions and vice versa. The society serves as a platform for researchers, clinicians, and educators to share findings, enhance collaboration, and disseminate knowledge in the field.
A **branching quantifier** is a type of quantifier used in logic and formal languages, specifically in the context of predicate logic and more complex logical systems. It is often represented in formulas involving multiple variables, separating different instances of quantification that can branch off from a certain point in the formula. In standard quantifiers, like the universal quantifier \(\forall\) and the existential quantifier \(\exists\), there is a linear, hierarchical structure to the quantified variables.
The Bohr model is primarily a model of the atom rather than specifically a model of chemical bonding. Proposed by Niels Bohr in 1913, it describes the structure of the hydrogen atom and explains how electrons inhabit quantized energy levels around the nucleus. In the Bohr model, electrons orbit the nucleus in fixed paths or orbits, and each orbit corresponds to a specific energy level. Electrons can jump from one orbit to another by absorbing or emitting energy in the form of photons.
Electronic structure refers to the arrangement and behavior of electrons in an atom or molecule. It encompasses the distribution of electrons among various energy levels, subshells, and orbitals, as well as their interactions with one another. The electronic structure is fundamental to understanding the chemical properties and reactivity of elements and compounds.
In quantum mechanics, various types of potentials are used to describe the interactions of particles. These potentials are critical in solving the Schrödinger equation, which governs the behavior of quantum systems. Here is a list of some common quantum-mechanical potentials: 1. **Infinite Square Well Potential**: A potential that is zero inside a finite region and infinite outside, leading to quantized energy levels.
The Kuzyk quantum gap refers to a concept in quantum optics and condensed matter physics that arises in the context of bound states in quantum systems. It is named after the physicist Robert Kuzyk, who has contributed to the understanding of quantum mechanical systems and their energy states. The term typically describes the energy difference between two quantized states, particularly in systems where quantum mechanical interactions lead to unique binding characteristics.
A proportional counter is a type of gas-filled radiation detector used to measure ionizing radiation. It operates by counting the number of ion pairs produced when radiation interacts with the gas inside the counter. Proportional counters are particularly effective for detecting alpha, beta, and gamma radiation.
An ionization chamber is a type of radiation detector that measures ionizing radiation by collecting and measuring the charge created when radiation interacts with a gas within the chamber. It consists of a gas-filled chamber with two electrodes: an anode (positive electrode) and a cathode (negative electrode). When ionizing radiation, such as alpha particles, beta particles, or gamma rays, passes through the gas, it ionizes the gas molecules, creating positive ions and free electrons.
Cargo scanning refers to the use of various technologies and methods to inspect and analyze cargo containers, vehicles, or shipments for security, safety, and compliance purposes. This process is critical in ports, customs, and logistics to prevent illegal activities such as smuggling, trafficking, and the transport of hazardous materials. Key aspects of cargo scanning include: 1. **Technologies Used**: - **X-ray Scanning**: A common method that uses X-ray imaging to see inside containers.
Numerical linear algebra is a branch of mathematics that focuses on the development and analysis of algorithms for solving problems in linear algebra using numerical methods. It deals with the theory and practical application of techniques for the manipulation of matrices and vectors, which are fundamental structures in many scientific computing and engineering problems.
In philosophy, "mechanism" refers to a worldview or theoretical framework that explains phenomena, particularly in the natural world, in terms of mechanical processes and interactions. It asserts that all natural phenomena can be understood as results of the movements and interactions of physical particles and forces, much like the workings of a machine. This view contrasts with teleological perspectives, which emphasize purpose or design in explaining natural events.
Pete Waterman is a British music producer, songwriter, and radio DJ, best known for his work in the 1980s and 1990s. He is a key figure in the pop music scene, particularly associated with the Stock Aitken Waterman (SAW) production team, which produced numerous hits for various artists. The team was known for its catchy pop songs and played a significant role in shaping the sound of pop music in the UK during that era.
Resonance fluorescence is a process in which a photon with energy matching the energy difference between two quantum states of a system (such as an atom or molecule) is absorbed, promoting the system to an excited state. After a brief period in the excited state, the system returns to its lower energy state, emitting a photon in the process.
**New York v. United States** is a significant Supreme Court case decided in 1992, which addressed the balance of power between the federal government and the states under the Tenth Amendment. The case centered around a provision in the Low-Level Radioactive Waste Policy Amendments Act of 1985. This law required states to take responsibility for disposing of low-level radioactive waste generated within their borders.
"Ilium" is a science fiction novel written by Dan Simmons, published in 1995. The novel is notable for its imaginative blend of classical literature, particularly Homer's "Iliad," with futuristic technology and themes.
Novels about parallel universes often explore themes of alternate realities, the nature of existence, and the consequences of choices. Here are some notable examples: 1. **"The Man in the High Castle" by Philip K. Dick** - This novel depicts an alternative history where the Axis powers won World War II and explores the lives of characters in a divided America, along with the concept of alternate realities.
"Atom" is a book by physicist Lawrence Krauss, published in 2012. In this work, Krauss explores the fundamental nature of atoms and their significance in understanding the universe. The book delves into various topics related to atomic theory, quantum mechanics, and the broader implications of atomic science in fields such as chemistry and cosmology. Krauss presents complex scientific concepts in an accessible manner, aiming to engage a general audience with the wonders of science.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact