Lu Jiaxi (also known as Lu Jiaxi, 1904–1991) was a prominent Chinese mathematician known for his contributions to various fields within mathematics, particularly in complex analysis and algebraic topology. He played a significant role in the development of mathematics in China during the 20th century and was instrumental in the education of many mathematicians. Lu held various academic positions and was involved in research as well as teaching for many years.
Stevo Todorčević is a prominent mathematician, known for his work in set theory and topology. He has made significant contributions to the field, including studies on real-valued functions, cardinal characteristics of the continuum, and the structure of the set of reals. His work often involves the intersection of various areas in mathematics, particularly in relation to large cardinals and forcing. Todorčević has published numerous papers and is recognized in the mathematical community for his research and influence.
A semiperfect magic cube is a three-dimensional generalization of a magic square. Just like a magic square, a semiperfect magic cube is an arrangement of numbers in a cube where the sums of the numbers in each row, each column, and the two main diagonals are all equal.
A ranked poset (partially ordered set) is a specific type of poset that has an additional structure related to its elements' ranks. In a ranked poset, each element can be assigned a rank, which is a non-negative integer that gives a measure of the "level" or "height" of that element within the poset.
The Koszul–Tate resolution is a construction in algebraic geometry and homological algebra used to study certain algebraic structures, particularly those that involve differential forms or algebraic relations. It is named after Jean-Pierre Serre and William Tate, who contributed to the understanding of such resolutions. In simple terms, the Koszul-Tate resolution provides a way to resolve algebraic objects, such as modules or complexes associated with algebraic varieties, using tools from homological algebra.
In mathematics, a Novikov ring is a specific type of algebraic structure that arises in the context of algebraic topology and homological algebra, particularly in the study of loop homology and more generally in the theory of algebraic spaces that involve formal power series.
An optimization problem is a mathematical problem that seeks to find the best solution from a set of feasible solutions. The objective is to maximize or minimize a certain function, called the objective function, while satisfying a set of constraints that define the feasible region.
The longest uncrossed knight's path refers to a path traced by a knight on a chessboard where the knight visits each square without revisiting any square (i.e., without crossing over itself or visiting the same square more than once). This kind of problem is often explored in the context of graph theory and combinatorial optimization.
Persistent homology is a concept from computational topology, a branch of mathematics that studies the shape, structure, and features of data. It provides a way to analyze the topology of data sets, particularly those that vary with a parameter, by examining how the topological features of a shape persist across different scales. ### Key Concepts of Persistent Homology: 1. **Topological Spaces and Chains**: - Topological spaces are sets equipped with a structure that allows for the concept of continuity.
The Museum of Soviet Arcade Machines, located in Moscow, Russia, is a unique attraction that showcases a collection of vintage arcade machines from the Soviet era, primarily from the late 1970s to the early 1990s. The museum aims to preserve and display these nostalgic artifacts, offering visitors a glimpse into Soviet pop culture and entertainment.
Clarisse Iribagiza is a notable entrepreneur and technology advocate from Rwanda. She is best known for her work in the fields of software development and innovation. Iribagiza gained recognition as a co-founder of *HeHe Limited*, a technology company that specializes in mobile solutions and software development for businesses. In addition to her entrepreneurial endeavors, Clarisse has played a significant role in promoting technology and entrepreneurship among women and youth in Rwanda.
.su is a country code top-level domain (ccTLD) that was originally assigned to the Soviet Union (USSR). Although the Soviet Union dissolved in 1991, the .su domain was retained and is still in use today. It is managed by the "Russian Institute for Public Networks" (RIPN). Over the years, .
The Infinite Element Method (IEM) is a numerical analysis technique used to solve problems involving unbounded domains, particularly in engineering and physics. It extends the finite element method (FEM) by allowing for an effective treatment of problems where fields (such as electromagnetic, acoustic, or structural fields) can extend infinitely far from the region of interest. This approach is particularly useful for problems with infinite or semi-infinite domains, such as wave propagation, soil formation, and fluid dynamics.
In the context of physics and engineering, particularly in structural mechanics, **limit load** refers to the maximum load that a structure or component can carry without experiencing failure. This load is associated with the onset of plastic deformation, where the material will no longer return to its original shape upon unloading. The limit load is an important concept in the design and analysis of structures, as it helps engineers determine the safety and reliability of various materials and configurations under expected loads.
Covariance Intersection (CI) is a technique used in the field of Bayesian estimation and data fusion, particularly when it comes to combining estimates and uncertainties from different sources with potentially inconsistent or non-coherent covariance matrices. The basic idea is to merge these estimates in a way that preserves the integrity of the uncertainty information. In traditional Kalman filtering, a common approach is to simply take the average of multiple estimations.
Deadbeat control is a control strategy used in discrete-time control systems that aims to drive the system output to its desired value (setpoint) in the minimum possible time, effectively reaching the target in a finite number of sampling periods without any overshoot. The term "deadbeat" comes from the concept that the response of the system "dies" after the target is achieved, meaning that the control action rapidly stabilizes the system at the desired state without oscillations or lingering transient behavior.
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





