The Einstein tensor is a fundamental concept in the field of general relativity, named after the physicist Albert Einstein. It is used to describe the curvature of spacetime in relation to the distribution of matter and energy within that spacetime. Mathematically, the Einstein tensor \( G_{\mu\nu} \) is defined in terms of the metric tensor \( g_{\mu\nu} \) and its derivatives.
Einstein–Cartan theory is an extension of general relativity that incorporates an intrinsic connection between geometry and matter, specifically by allowing for the presence of torsion alongside curvature in the spacetime.
Einstein's thought experiments are hypothetical scenarios conceived by Albert Einstein to illustrate and explore complex ideas in physics, particularly in the realms of relativity and quantum mechanics. These mental exercises allowed him to visualize and analyze problems that could not be easily tested in a laboratory setting. Here are some of the most notable thought experiments associated with Einstein: 1. **The Train and the Lightning Strikes**: In this thought experiment, Einstein imagines a train moving at a significant fraction of the speed of light.
Burt Totaro is a mathematician known for his work in algebraic geometry and algebraic topology. His contributions include research on issues related to algebraic cycles, K-theory, and motives, as well as the study of specific mathematical structures and their implications in various areas of mathematics. He has also been involved in the education and mentoring of students and has published numerous papers in mathematical journals.
The Einstein-Rosen metric refers to a solution to the Einstein field equations of general relativity that describes a specific type of spacetime geometry. It is typically associated with the Einstein-Rosen bridge, also known as a wormhole. Here's an overview of its key aspects: ### Origin The Einstein-Rosen bridge concept was introduced in 1935 by Albert Einstein and Nathan Rosen in their paper titled "The Particle Problem in the General Theory of Relativity.
Many things have been named in honor of Albert Einstein, reflecting his immense contributions to science, particularly in the fields of physics and mathematics. Here’s a list of notable items, concepts, and places named after him: 1. **Einstein's Theory of Relativity** - This includes both the Special Theory of Relativity (1905) and the General Theory of Relativity (1915), fundamentally altering our understanding of space, time, and gravity.
Mass-energy equivalence is a principle in physics that suggests that mass and energy are interchangeable, and they are two forms of the same entity. This concept is famously encapsulated in Albert Einstein's equation: \[ E = mc^2 \] In this equation: - \( E \) is the energy, - \( m \) is the mass, - \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) meters per second).
As of my last knowledge update in October 2023, Olympia Academy could refer to various educational institutions or programs under that name, but there isn't a widely recognized organization known specifically as "Olympia Academy." The name might be used by different schools, tutoring centers, or online educational programs in various locations or contexts.
Harbi al-Himyari is a fictional character or name that appears in Arabic literature and folklore, but it is most commonly associated with a historical figure, Al-Himyari, from pre-Islamic Arabia. The term "Harbi" can mean "war" or "warrior," and al-Himyari is often related to Yemenite lineage. In some contexts, the name could symbolize themes of conflict, tribal identity, or honor in traditional narratives.
Robert M. Place is a well-known artist, author, and expert in the field of tarot and cartomancy. He is recognized for his work in creating tarot decks, particularly the "Tarot of the Sevenfold Mystery," which reflects a unique artistic interpretation of tarot symbolism and mythology. Place is also noted for his writings on the history, philosophy, and practical applications of tarot, including how it intersects with various spiritual and psychological practices.
As of my last knowledge update in October 2021, I don't have specific information on an individual named Aaron Pixton. It's possible that he may not be widely recognized in mainstream media or public records, or he may be a private individual.
Alexander Beilinson is a prominent mathematician known for his significant contributions to several areas of mathematics, particularly algebraic geometry, mathematical physics, and representation theory. Born in Russia in 1955, he has worked extensively on topics such as sheaf theory, derived categories, and the study of motives.
Bernard Dwork (1923–2019) was an influential American mathematician known for his contributions to number theory and algebraic geometry. He made significant strides in the study of p-adic analysis and the theory of Diophantine equations, particularly through his work on p-adic cohomology and the Dwork hypothesis. Dwork is perhaps best recognized for the Dwork hypersurface, a concept in algebraic geometry that connects the fields of number theory and algebraic geometry.
Kai Behrend might refer to a person, but there isn’t any widely recognized figure or concept by that name based on my training data, which only goes up until October 2023. It could be a name relevant in specific contexts, such as a local figure, an emerging public personality, or someone from a specific field like science, art, or academia.
Lê Thị Thanh Nhàn is a Vietnamese entrepreneur and public figure known for her involvement in the business sector, particularly in the fields of healthcare and pharmaceuticals. She is often recognized for her leadership in various companies and organizations within Vietnam.
Montserrat Teixidor i Bigas is a prominent Spanish figure, known for her work in various fields, potentially including literature, academia, or activism, but there may not be extensive publicly available information about her.
Pasquale del Pezzo (born in 1938) is an Italian mathematician known for his contributions to the fields of algebraic geometry and topology. He is particularly recognized for his work on the theory of algebraic varieties and has made significant contributions to the understanding of geometric properties of solutions to polynomial equations. Del Pezzo surfaces, which are a class of algebraic surfaces in algebraic geometry, are named after him.
The Gorenstein–Walter theorem is a result in the area of algebra, particularly in the study of Gorenstein rings and commutative algebra. It essentially characterizes certain types of Gorenstein rings. The theorem states that a finitely generated algebra over a field which has a Gorenstein ring structure is Cohen-Macaulay and that such rings have certain properties related to their module categories.
The Generalized Jacobian is a mathematical concept that extends the idea of the Jacobian matrix, which is primarily used in calculus to describe how a function's output changes in response to small changes in its input. While the traditional Jacobian is applicable to smooth functions, the Generalized Jacobian is particularly useful in the context of nonsmooth analysis and optimization.
Seligmann Kantor is likely a reference to a specific individual or family name, but without additional information, it is difficult to determine its context. If you are referring to a scholar, artist, or historical figure by that name, please provide more details. Alternatively, Seligmann Kantor may also relate to a specific organization, event, or concept in various fields such as literature, science, or history. More context would be helpful to give a more accurate answer.
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





