CPT symmetry is a fundamental principle in theoretical physics that combines three symmetries: Charge conjugation (C), Parity transformation (P), and Time reversal (T). 1. **Charge Conjugation (C)**: This symmetry relates particles to their antiparticles. For example, it transforms an electron into a positron and vice versa. 2. **Parity Transformation (P)**: This symmetry involves flipping the spatial coordinates, effectively reflecting a system through the origin.
Coxeter notation is a way of representing regular polytopes and their higher-dimensional analogs (such as regular polygons, polyhedra, and polychora) using a system based on pairs of numbers. It employs a compact notation that often consists of a string of integers, occasionally including letters or specific symbols to indicate certain geometric properties, relations, or symmetries.
A crystallographic point group is a mathematical classification of the symmetry of a crystal structure. These groups describe the symmetry operations that leave at least one point (typically the origin) invariant, meaning those operations do not alter the position of that point. The main symmetry operations included in crystallographic point groups are: 1. **Rotation**: Turning the crystal around an axis. 2. **Reflection**: Flipping the crystal across a plane.
Cymatics is the study of visible sound and vibration. The term is derived from the Greek word "kyma," meaning "wave." It refers to the phenomenon where sound waves create visible patterns in a medium, usually a viscous substance like water or a powder. In cymatics, sound frequencies are applied to a surface, causing it to resonate.
The FKG inequality, named after its contributors Fortuin, Kasteleyn, and Ginibre, is a result in probability theory that provides a relationship among joint distributions of certain random variables, particularly in the context of lattice structures, such as spins in statistical mechanics. It is most commonly applied in the study of lattice models in statistical physics, including the Ising model.
Inversion transformation typically refers to an operation used in various fields, including mathematics, computer science, statistics, and image processing. The specific meaning can vary based on the context, but here are a few common interpretations: 1. **Mathematics**: In mathematics, an inversion transformation often refers to a transformation that maps points in a space such that points are inverted relative to a particular point (the center of inversion) or a shape (like a circle or sphere).
A **non-Euclidean crystallographic group** refers to a symmetry group that arises in the study of lattices and patterns in geometries that are not based on Euclidean space. Crystallographic groups describe how a pattern can be repeated in space while maintaining certain symmetries, including rotations, translations, and reflections. In Euclidean geometry, the classifications of crystallographic groups are based on the 17 two-dimensional plane groups and the 230 three-dimensional space groups.
In geometry, symmetry refers to a property of a shape or object that remains unchanged under certain transformations, such as reflection, rotation, translation, or scaling. A geometric figure is said to be symmetric if there is a way to map it onto itself while preserving its overall structure and appearance.
Supersymmetry (SUSY) is a theoretical framework in particle physics that proposes a symmetry between two basic classes of particles: fermions (which make up matter, like electrons and quarks) and bosons (which mediate forces, like photons and gluons). In a fully realized supersymmetric model, each particle in the Standard Model of particle physics would have a superpartner with differing spin.
The 20th century saw significant contributions to mathematics from various Mexican mathematicians. Here are some notable figures: 1. **Manuel Sandoval Vallarta (1888–1978)**: A prominent mathematician and physicist, Sandoval Vallarta made contributions in several areas, particularly in physics and applied mathematics. He is known for his work on wave mechanics and for the Vallarta equation.
Mexican women mathematicians have made significant contributions to various fields of mathematics, often overcoming social and institutional challenges. Their work spans pure and applied mathematics, statistics, and mathematical education. Here are a few notable Mexican women mathematicians: 1. **Sor Juana Inés de la Cruz (1648-1695)**: Although primarily known as a writer and philosopher, Sor Juana had a deep interest in mathematics and sciences. She is considered one of the early female intellectual voices in Mexico.
Mexican astrophysicists are scientists from Mexico who specialize in the field of astrophysics, which is the branch of astronomy that deals with the physical properties and behavior of celestial objects and phenomena. These researchers often study topics such as the formation and evolution of stars, galaxies, and the universe as a whole, as well as the fundamental laws of physics that govern cosmic events.
Janez Strnad is not a widely recognized name in common knowledge or popular media. It is possible that he could be a private individual, a professional in a specific field, or a lesser-known public figure.
Radio-frequency microelectromechanical systems (RF MEMS) are a type of technology that combines concepts and techniques from microelectromechanical systems (MEMS) and radio-frequency (RF) engineering. RF MEMS devices leverage mechanical structures that can move and respond to electrical signals, enabling the manipulation of microwave and RF signals for various applications.
Lavo Čermelj is a Slovenian mathematician known for his contributions to various fields within mathematics, particularly in analysis and topology. He is also notable for his work in educational settings, helping to shape mathematical curriculum and fostering research in Slovenia. His research may focus on topics like real analysis, functional analysis, and mathematical education.
Carl Nordling, also known as Carl Johan Nordling, is a Swedish mathematician recognized for his contributions to various fields including nonlinear partial differential equations and mathematical physics. He has worked on topics like fluid dynamics and applied mathematics.
Gunnar Källén is a notable Swedish mathematician known primarily for his work in functional analysis, specifically in the areas of operator theory and quantum mechanics. He has contributed to various mathematical theories and applications, including those related to differential equations and mathematical physics.
As of my last update, Joakim Edsjö does not appear to be a widely recognized public figure, event, or concept in popular culture, history, or academia. It's possible that he may be a private individual, a character from a lesser-known work, or someone who has gained prominence after my latest data in October 2023.
Maria Strømme is a notable physicist and materials scientist, recognized for her work in nanotechnology and material science. She is a professor at Uppsala University in Sweden and has made significant contributions in areas like nanomaterials and their applications, particularly in energy and environmental technologies. Her research often focuses on the development of advanced materials for various applications, including energy storage and conversion.
Charles Enz is a physicist known for his contributions to the field of quantum mechanics and condensed matter physics. He was born in 1935 in Switzerland and has had a significant impact on various areas of physics, including the theoretical underpinnings of magnetic and superconducting materials. He has published extensively and has contributed to the understanding of phenomena such as topological phases and quantum phase transitions.
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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. - Infinitely deep tables of contents:
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





