René Thom (1923–2002) was a French mathematician best known for his contributions to topology and the development of catastrophe theory. Born in Montfavet, France, he made significant advancements in understanding mathematical phenomena that can exhibit sudden changes in behavior, which are modeled using "catastrophes." Catastrophe theory is a branch of mathematics that studies how small changes in the parameters of a system can lead to abrupt changes in its behavior or structure.
The Metabolic Theory of Ecology (MTE) is a theoretical framework that seeks to explain various ecological patterns and processes through the lens of metabolic processes in living organisms. It posits that metabolic rate, which is fundamentally connected to body size and temperature, influences ecological dynamics and patterns across different levels of biological organization, from individuals to populations and communities.
The Vasicek model is a popular mathematical model used in finance and economics to describe the dynamics of interest rates, as well as asset prices. Developed by Oldrich Vasicek in 1977, the model is particularly noted for its ability to capture the mean-reverting behavior of interest rates, which is a common characteristic observed in real-world financial markets. ### Key Features of the Vasicek Model 1.
The Ornstein-Uhlenbeck operator is an important mathematical operator in the context of stochastic processes, particularly in the study of the Ornstein-Uhlenbeck (OU) process, which is a well-known Gaussian process used to model mean-reverting behavior. ### Origin The Ornstein-Uhlenbeck process is named after George Uhlenbeck and Leonard Ornstein, who introduced it in the context of statistical mechanics to describe the velocity of a particle undergoing Brownian motion under the influence of friction.
Palm calculus is a mathematical framework used primarily in the fields of stochastic processes and queueing theory, particularly for analyzing systems involving random points in time or space, such as arrival processes. It is named after the Swedish mathematician Gunnar Palm, who contributed to the development of this theory.
Unified Modeling Language (UML) is a standardized modeling language used in software engineering to visualize, specify, construct, and document the artifacts of a software system. The applications of UML are broad and can be categorized into several areas: 1. **Software Design and Architecture**: - **Object-Oriented Design**: UML helps in designing software systems using object-oriented principles. Class diagrams, component diagrams, and package diagrams are used to represent the structure of a system.
David Harel is a prominent computer scientist known for his contributions to several areas in computer science, particularly in theoretical computer science, software engineering, and the design of programming languages. He is best known for his work on state machines, model checking, and formal methods. One of Harel's key contributions is the development of the Harel State Chart technique, which extends Finite State Machines and is widely used for modeling complex systems.
An inner class in Java is a class that is defined within the body of another class. It has access to the members (fields and methods) of the outer class, even if they are declared private. Inner classes can be used to logically group classes that are only used in one place, increasing the encapsulation and readability of the code. There are four types of inner classes in Java: 1. **Non-static Inner Class**: These are tied to an instance of the outer class.
PlantUML is an open-source tool used to create diagrams from plain text descriptions. It enables users to generate a variety of UML (Unified Modeling Language) diagrams, including class diagrams, sequence diagrams, use case diagrams, activity diagrams, component diagrams, state diagrams, and more. PlantUML's syntax is designed to be simple and intuitive, allowing users to write textual representations of diagrams that can then be rendered into graphical formats, such as PNG, SVG, or PDF.
A use case diagram is a visual representation of the interactions between users (or "actors") and a system to achieve specific goals. It is commonly used in software engineering and system design to help stakeholders understand the functional requirements of a system. Use case diagrams are part of the Unified Modeling Language (UML), which is a standardized modeling language in software engineering.
The Majorana equation is a relativistic wave equation that describes particles known as Majorana fermions. These particles are unique in that they are their own antiparticles, meaning that they possess the same quantum numbers as their antiparticles, unlike traditional fermions (like electrons), which have distinct antiparticles (such as positrons).
C-symmetry, also known as charge conjugation symmetry, refers to a fundamental symmetry in particle physics concerning the transformation of particles into their corresponding antiparticles. Specifically, it involves changing a particle into its antiparticle, which has the opposite electric charge and other quantum numbers. In terms of mathematical representation, charge conjugation transforms a particle state \(| \psi \rangle\) into its charge-conjugated state \(| \psi^C \rangle\).
Per language:
How to decide if an ORM is decent? Just try to replicate every SQL query from nodejs/sequelize/raw/many_to_many.js on PostgreSQL and SQLite.
There is only a very finite number of possible reasonable queries on a two table many to many relationship with a join table. A decent ORM has to be able to do them all.
If it can do all those queries, then the ORM can actually do a good subset of SQL and is decent. If not, it can't, and this will make you suffer. E.g. Sequelize v5 is such an ORM that makes you suffer.
The next thing to check are transactions.
Basically, all of those come up if you try to implement a blog hello world world such as gothinkster/realworld correctly, i.e. without unnecessary inefficiencies due to your ORM on top of underlying SQL, and dealing with concurrency.
github.com/mdawsonuk/LevelDBDumper/tree/e750a27ff58443ecc410b5c16abbdc539d617387#installation worked on Ubuntu 23.10 Annoying installation, but worked: github.com/mdawsonuk/LevelDBDumper/issues/13
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





