The Stratonovich integral is a type of stochastic integral used in the theory of stochastic calculus, particularly in the context of stochastic differential equations (SDEs). It is named after the Russian mathematician Rostislav Stratonovich. The Stratonovich integral is specifically designed to handle the integration of stochastic processes where the integrators are often modeled as continuous-time martingales or Wiener processes (Brownian motion).
Tanaka's formula is a result in stochastic calculus that provides a way to express the solution of a stochastic differential equation (SDE) in terms of the Itô integral and the quadratic variation of a continuous local martingale. The formula is particularly significant because it allows for the computation of expectations involving the stochastic processes that satisfy certain SDEs.
Topological entropy is a concept from dynamical systems, particularly in the study of chaotic systems, that measures the complexity or rate of growth of information about the system over time. It was introduced by the mathematician Jakob (Jacques) Y. R. D. W. Topologists in the context of topological dynamical systems, and it has applications in various fields, including physics.
Tsallis entropy is a generalization of the classical Boltzmann-Gibbs entropy, introduced by Brazilian physicist Constantino Tsallis in 1988. It is used in the context of non-extensive statistical mechanics, a framework that describes systems with long-range interactions, fractal structures, and other complex behaviors that are not adequately captured by traditional statistical mechanics.
The Virial coefficients are a set of coefficients in the virial equation of state, which describes the relationship between pressure, volume, and temperature for a real gas. The virial equation is often expressed as an expansion in terms of the density of the gas: \[ \frac{P}{kT} = \rho + B(T)\rho^2 + C(T)\rho^3 + \ldots \] Here: - \( P \) is the pressure of the gas.
Wick rotation is a mathematical technique used primarily in quantum field theory and statistical mechanics to relate problems in particle physics to problems in statistical physics. Named after the physicist Giovanni Wick, this technique involves a transformation of the time coordinate in a Minkowski spacetime formulation from real to imaginary values.
The Wien approximation, often referred to in the context of blackbody radiation, is related to Wien's law, which describes the shift of the peak of the emission spectrum of a blackbody as a function of its temperature.
"Die Reihe" was a significant avant-garde publication that emerged in the mid-20th century, particularly focused on contemporary music and its theoretical aspects. Founded in 1955 by composers and theorists, including Herbert Eimert and Karlheinz Stockhausen in Germany, the journal played a critical role in the development and dissemination of new music concepts and techniques, particularly related to serialism and electronic music.
Cristina Bazgan is a notable figure in the field of computer science, particularly recognized for her contributions to algorithms, computational complexity, and related areas. She is also known for her work in optimization and game theory. Bazgan has published numerous research papers and has been involved in various academic and professional activities.
The weather of 2011 was notable for a variety of extreme weather events across the globe. Some significant highlights include: 1. **Tornadoes in the United States**: One of the most devastating tornado seasons occurred in 2011, with an outbreak in April that included the Joplin tornado, which killed over 150 people and caused extensive damage.
A crore is a unit in the Indian numbering system that denotes ten million (10,000,000). It is commonly used in India, Bangladesh, Nepal, and other South Asian countries to express large numbers, particularly in financial and population contexts. The term is often abbreviated as "Cr" or represented by the numeral "1 crore" to signify the value of ten million. For instance, 5 crore would mean 50 million.
"Crush" is a puzzle-platform video game developed by Zoe Mode and published by Sega. It was first released for the PlayStation Portable (PSP) in 2007. The game features a unique gameplay mechanic that revolves around the concept of perspective and the manipulation of 3D environments. In "Crush," players control a character named Danny who navigates through a series of surreal, dream-like levels.
The Cube Root Law, often referred to in the context of acoustics and other fields, states that the intensity of sound (or another phenomenon) emanating from a point source is inversely proportional to the cube of the distance from the source.
Wavelet packet decomposition is a technique used in signal processing and data analysis that extends the principles of traditional wavelet decomposition. Here’s a breakdown of the concept: ### Basics of Wavelet Decomposition 1. **Wavelets**: A wavelet is a mathematical function that can be used to represent signals at different scales or resolutions. Unlike traditional Fourier transform methods, wavelets can localize signals both in time (or space) and frequency.
Curiosity is a fundamental human drive characterized by a desire to learn, explore, and understand new things. It motivates individuals to seek out new experiences, ask questions, and pursue knowledge. Curiosity can manifest in numerous forms, including intellectual curiosity, which drives people to explore academic subjects, and personal curiosity, which promotes exploration of one's surroundings, relationships, and experiences. In psychology, curiosity is often viewed as an essential component of cognition and learning.
Cyclone Kyarr was a powerful tropical cyclone that formed in the Arabian Sea during late October 2019. It was one of the most intense storms in that region for several years. Kyarr rapidly intensified into a very severe cyclonic storm, reaching its peak strength with sustained winds of approximately 140 mph (220 km/h) and a minimum central pressure of about 950 hPa.
"Dali's Mustache" is a reference to the iconic mustache of the surrealist artist Salvador Dalí. Known for his eccentric personality and distinctive style, Dalí's mustache became almost as famous as his artwork. It is often characterized by its elaborate, twisted points and was part of his theatrical persona.
The Darwin–Fowler method is a statistical approach used primarily in the analysis of time-to-event data, particularly in the context of survival analysis. It is named after the British mathematicians Charles Darwin and William Fowler. This method is particularly influential in the field of biostatistics and epidemiology, where researchers often need to understand the time until certain events occur, such as death, disease progression, or failure of an experiment.
David Bernard is a meteorologist known for his work as a broadcast meteorologist in the United States. He has been involved in weather reporting and forecasting, primarily in the southeastern region. Bernard is recognized for his expertise in meteorology, particularly in relation to tropical weather systems and hurricanes, given the prominence of such events in that area. He has worked for various television stations and has been involved in community outreach and education related to weather safety and preparedness.
David Chilton Phillips is an American biophysicist best known for his work in the field of cryobiology, which studies the effects of low temperatures on living organisms. He has contributed significantly to understanding how cells respond to freezing and thawing, which has implications for areas such as organ preservation, fertility treatments, and food preservation.

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