Endoreversible thermodynamics is a branch of thermodynamics that deals with systems that operate under the influence of irreversible processes, yet are evaluated in a way that considers certain idealized, reversible behaviors. The term "endoreversible" typically refers to systems where irreversible phenomena occur internally (within the system itself), while still allowing for some external heat exchanges or processes to be treated as reversible.
The Gaussian function is a specific type of mathematical function that describes a symmetrical, bell-shaped curve. It is often used in statistics, probability, and various fields of science for modeling normal distributions, among other applications.
Ashkan Nikeghbali is not widely recognized in public databases or information up to October 2023. If you are looking for specific information about Ashkan Nikeghbali, please provide more context or specify the field or area you are inquiring about, such as whether they are known for work in academia, technology, art, or another domain. That would help in providing a more accurate response.
Marc Yor (1944–2014) was a prominent French mathematician known for his contributions to the fields of probability theory and stochastic processes. He made significant advancements in various areas, including Brownian motion, stochastic calculus, and financial mathematics. Yor is particularly recognized for his work on the theory of stochastic integrals and the study of processes related to exponential martingales.
Romanas Januškevičius is most likely a reference to an individual, but without specific context or additional information, it is difficult to identify who this person is, as there may be multiple individuals with this name. If you can provide more context or specify the field (such as sports, arts, academia, etc.
Thomas M. Liggett is a prominent mathematician known for his work in probability theory and mathematical biology. He has made significant contributions to the study of stochastic processes, particularly in the areas of interacting particle systems, stochastic models, and their applications to various fields, including statistical physics and evolutionary biology. Liggett has authored several influential papers and books on these topics, and he has been recognized for his contributions to the mathematical community.
Origami paper is a specialized type of paper designed specifically for the art of origami, the Japanese practice of folding paper into intricate shapes and figures. Here are some key characteristics and features of origami paper: 1. **Weight and Thickness**: Origami paper is typically lighter than standard paper, ranging from about 30 to 80 gsm (grams per square meter). This makes it easier to fold and manipulate without tearing.
Rose Rand is a notable figure in the history of philosophy and is best known for her work in the field of feminist philosophy and her contributions to the theory of Objectivism. She was a close associate and collaborator of the philosopher Ayn Rand, but she also had her own philosophical perspectives. However, the name "Rose Rand" may refer to something else in a different context, such as a specific location, event, or another person.
Kripke–Platek set theory (KP) is a foundational system in set theory that serves as a framework for discussing sets and their properties. It is particularly notable for its treatment of sets without the full power of the axioms found in Zermelo-Fraenkel set theory (ZF). KP focuses on sets that can be constructed and defined in a relatively restricted manner, making it suitable for certain areas of mathematical logic and philosophy.
In mathematical set theory, particularly in the context of descriptive set theory, a **coanalytic set** (also known as a **\( \Pi^1_1 \) set**) is a type of set that can be defined as the complement of an analytic set.
Angular resolution refers to the ability of an optical system, such as a telescope or microscope, to distinguish between two closely spaced objects. It is defined as the smallest angular separation between two points that can be resolved or distinguished by the system. In practical terms, a higher angular resolution means that the optical system can discern finer details at a given distance.
In the context of abelian groups, the term "height" can refer to a couple of different concepts depending on the specific area of mathematics being considered, such as group theory or algebraic geometry. 1. **In Group Theory**: The height of an abelian group can refer to a measure of the complexity of the group, particularly when it comes to finitely generated abelian groups.
In the context of algebraic groups and Lie algebras, a **root datum** is a structured way of encoding certain aspects of the symmetries and properties of these mathematical objects. Specifically, a root datum consists of the following components: 1. **A finite set of roots**: These are usually vectors in a Euclidean space, which can be thought of as directions that reflect the symmetries of the system.
In group theory, the concept of normal closure is related to the idea of normal subgroups. Given a group \( G \) and a subset \( H \) of \( G \), the normal closure of \( H \) in \( G \), denoted by \( \langle H \rangle^G \) or sometimes \( \langle H \rangle^n \), is the smallest normal subgroup of \( G \) that contains the set \( H \).
The Picard modular group is an important mathematical concept in the field of number theory and algebraic geometry, specifically in the study of certain types of lattices and modular forms. More precisely, the Picard modular group is associated with the action of the group of isometries of a specific type of quadratic form on a complex vector space.
Chiral homology is a mathematical concept that arises in the field of homotopy theory, particularly in the study of algebraic topology and homological algebra. It is a special type of homology theory that aims to capture certain geometric and algebraic properties of topological spaces or algebraic structures that are sensitive to orientation or chirality (i.e., handedness).
A triangulated category is a particular type of category that arises in the context of homological algebra and derived categories. It provides a framework to study homological properties by relating them to geometric intuition through triangles, similar to how one uses exact sequences in abelian categories.
The Riemann–Hilbert correspondence is a concept in mathematics that establishes a correspondence between certain types of differential equations and analytic data. It primarily concerns the study of systems of linear differential equations with an emphasis on their monodromy and the associated analytic objects, typically in the context of complex analysis and algebraic geometry.
Schur's lemma is a fundamental result in representation theory, particularly in the context of representation of groups and algebras. It applies to representations of a group and its modules over a division ring or field.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . 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. - 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