The Bellman equation is a fundamental concept in dynamic programming and reinforcement learning, named after Richard Bellman. It describes the relationship between the value of a decision and the value of future decisions in a given state. The equation provides a recursive way to compute the optimal policy and the value function for a Markov Decision Process (MDP).
"Stephen Hawking's Universe" is a popular television documentary series that aired in the 1990s, originally hosted by the renowned physicist Stephen Hawking. The series explores complex scientific concepts related to cosmology, black holes, the nature of time, and the universe itself, breaking them down into more accessible terms for a general audience. The show is notable for its engaging presentation and use of visual effects to illustrate difficult concepts, making it an influential piece of science communication.
Stephen Kevan is a physicist known for his work in the field of condensed matter physics, particularly in the areas of ultracold atoms and quantum mechanics. He has been involved in research that explores the fundamental properties of matter at very low temperatures and the behaviors of quantum systems.
Stereochemistry is a branch of chemistry that focuses on the spatial arrangement of atoms within molecules and how this arrangement affects their physical and chemical properties. It primarily deals with isomerism, which is the phenomenon where compounds can have the same molecular formula but different structures or arrangements of atoms. There are several key concepts in stereochemistry: 1. **Isomers**: Molecules with the same molecular formula but different structural arrangements.
Steve Mandel can refer to different individuals, but one prominent person associated with that name is the American hedge fund manager and founder of Millennium Management, a global investment management firm. He is known for his work in the finance industry and has been influential in the development of quantitative trading strategies.
Steven E. Koonin is a theoretical physicist and a prominent figure in the fields of science and technology policy, particularly in relation to climate change and energy. He served as the Under Secretary for Science in the U.S. Department of Energy under President Obama and has held various academic and research positions throughout his career. Koonin is known for his work in several areas, including statistical mechanics, complex systems, and computational physics.
Steven T. Bramwell is a physicist known for his work in the field of condensed matter physics, particularly in the areas related to magnetism and spin liquids. He has contributed significantly to the understanding of complex magnetic materials and their properties. Bramwell is associated with various research institutions and has published numerous papers in peer-reviewed journals. His work often involves experimental investigations of magnetic systems and the theoretical implications of their behaviors.
A stochastic game is a generalization of a game that incorporates randomness into the decision-making process. In a stochastic game, the outcomes of players' strategies are influenced not only by their own decisions but also by external random events. These games are characterized by states, actions, transition probabilities, and payoffs. ### Key Components of Stochastic Games: 1. **States**: The game can be in various states, which may represent different conditions or configurations that influence the decisions of the players.
Stokes relations are a set of equations used in the context of fluid mechanics, thermodynamics, and other fields involving the behavior of fluids and gases. They relate the various properties of a fluid in terms of its pressure, temperature, and specific volume, among other variables. In thermodynamics, Stokes relations can also refer to relationships between properties of thermodynamic systems under certain conditions.
Størmer's theorem is a result in number theory that pertains to the distribution of prime numbers. Specifically, it provides conditions under which certain integer sequences can have a density of primes. More precisely, Størmer's theorem can be described in the context of sequences of integers defined by a linear recurrence relation.
Financial correlation refers to a statistical measure that describes the degree to which two financial assets, securities, or variables move in relation to one another. It quantifies the strength and direction of the relationship between the returns, prices, or other financial metrics of those assets. **Key aspects of financial correlation include:** 1. **Types of Correlation:** - **Positive Correlation:** When two assets move in the same direction.
A **String Kernel** is a type of similarity measure used in machine learning, particularly in classification tasks involving string data, such as natural language processing and bioinformatics. It is part of the family of kernel functions, which are mathematical constructs used in Support Vector Machines (SVM) and other algorithms to operate in a high-dimensional space without explicitly transforming the data into that space.
The term "straits" generally refers to narrow bodies of water that connect two larger bodies of water, or it can also refer to a challenging situation or difficult condition. In a geographical context, straits are important for navigation and can often serve as natural boundaries between landmasses. Some well-known examples of straits include: 1. **Strait of Gibraltar**: Connects the Atlantic Ocean to the Mediterranean Sea, separating Spain in Europe from Morocco in Africa.
A strand jack is a mechanical device used for lifting heavy loads, often in construction, engineering, and maintenance applications. It uses a series of high-strength steel cables (strands) to lift and lower objects, providing a controlled and efficient means to handle large structures such as bridges, oil rigs, and heavy machinery. The strand jack operates by employing hydraulic or mechanical tensioning systems to pull the strands through a series of jacks, allowing for precise control over the movement of the load.
A streak camera is a specialized imaging device used to capture fast, transient events by converting the spatial information of a light signal into a time-resolved format. This device is capable of measuring the time evolution of light or other electromagnetic signals with very high temporal resolution, often down to picoseconds or even femtoseconds. **Key Features:** 1.
In fluid dynamics, streamlines, streaklines, and pathlines are three different ways to visualize the flow of a fluid, particularly in a flow field. Each of these concepts provides insight into the behavior of fluid particles in motion. ### 1. Streamlines: - **Definition**: A streamline is an imaginary line in a fluid flow field that is tangent to the velocity vector of the fluid at every point.
Pedro Filipe Soares is a Portuguese politician and a prominent member of the Left Bloc (Bloco de Esquerda), a political party in Portugal. He has served in various capacities within the party and is known for his focus on social justice, progressive policies, and economic reforms. He has been active in Portuguese politics, contributing to debates on issues such as labor rights, public services, and environmental policies.
Strongly Interacting Massive Particles (SIMP) are a proposed type of elementary particle that arise in certain theories of particle physics, specifically in the context of dark matter. SIMPs are characterized by their large mass and strong interactions, similar to those of the particles that make up atomic nuclei (like protons and neutrons) which are governed by the strong nuclear force.
In the context of functional analysis and mathematical optimization, a strongly monotone operator refers to a specific type of mathematical operator that exhibits a strong form of the monotonicity property.
A sun sensor is a device used primarily in aerospace and satellite applications to determine the position of the Sun relative to the sensor's frame of reference. By measuring the direction of sunlight, these sensors help spacecraft and satellites maintain proper orientation and attitude control, enabling efficient solar energy capture and stable communications.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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