Rice's Formula is a result in probability theory and statistics that provides a way to compute the expected number of zeros of a random function or, more generally, the expected number of level crossings of a stochastic process. Specifically, it is often used in the context of Gaussian processes. The formula is particularly relevant in fields like signal processing, communications, and statistical mechanics.
Gloria Ford Gilmer is a prominent African American mathematician, educator, and author known for her contributions to mathematics education and her efforts to promote diversity in the field. She was born on November 24, 1934, in Pittsburgh, Pennsylvania. Gilmer is particularly recognized for her work in developing curricula and teaching strategies aimed at improving math education for African American students and other underrepresented groups.
The Sinai–Ruelle–Bowen (SRB) measure is a key concept in the study of dynamical systems, particularly in the context of chaotic systems and statistical mechanics. Named after Ya. G. Sinaï, David Ruelle, and Rufus Bowen, the SRB measure provides a way to describe the long-term statistical behavior of a system that exhibits chaotic dynamics.
A stationary ergodic process is a concept from the field of probability theory and stochastic processes. It combines two important properties: **stationarity** and **ergodicity**. ### Stationarity A stochastic process is said to be stationary if its statistical properties do not change over time. There are two main types of stationarity: 1. **Strict Stationarity**: A process is strictly stationary if the joint distribution of any set of random variables in the process is invariant to shifts in time.
The Buckley–Leverett equation is a fundamental equation in petroleum engineering and reservoir engineering that describes the movement of two-phase fluids (typically oil and water) in porous media. It models the flow behavior of immiscible fluids in a reservoir when one fluid displaces another, commonly used to analyze waterflooding operations during oil recovery. The equation is derived from the conservation of mass principle and reflects the dynamics of the interfaces between the two fluids.
The Boussinesq approximation is a mathematical simplification used in fluid dynamics, particularly in the study of weakly non-linear and dispersive wave phenomena, such as water waves. Named after the French physicist Joseph Boussinesq, this approximation is particularly useful for analyzing the behavior of surface waves in fluids where the amplitude of the waves is small compared to the wavelength.
The Borda-Carnot equation describes the relationship between the temperature, pressure, and specific properties of a fluid in a thermodynamic context, particularly for a fluid undergoing adiabatic (no heat transfer) expansion or compression. It is commonly associated with the performance of turbines and compressors. The equation itself typically relates how the enthalpy, pressure, and temperature of the fluid change during these processes.
The term "black oil equations" refers to a set of mathematical relations used in reservoir engineering and petroleum production to model the behavior of black oil, a type of crude oil characterized by its relatively high viscosity and the presence of dissolved gases and lighter hydrocarbon components. Black oil models help in understanding and predicting the behavior of oil reservoirs during production.
Just add GDB Dashboard, and you're good to go.
The Fuss–Catalan numbers are a generalization of the Catalan numbers. They count certain combinatorial structures that can be generalized to several parameters.
Pierre Sikivie is a physicist known for his work in theoretical physics, particularly in the fields of astrophysics and particle physics. He is best known for his research on axions, hypothetical particles proposed as a solution to the strong CP problem in quantum chromodynamics and as candidates for dark matter. Sikivie's work has contributed to the understanding of axions and their potential implications for both fundamental physics and cosmology.
Graph enumeration is the field of study in combinatorial mathematics and computer science focused on counting, listing, and studying the properties of different types of graphs. A graph is a mathematical structure consisting of vertices (or nodes) connected by edges. Graph enumeration involves exploring how many distinct graphs can be formed under various conditions and constraints.
The Inclusion-Exclusion Principle is a fundamental concept in combinatorics and probability theory that is used to calculate the size of the union of multiple sets when there is overlap between the sets. It provides a systematic way to count the number of elements in the union of several sets by including the sizes of the individual sets and then systematically excluding the sizes of their intersections to avoid over-counting.
Open source development model in which developers develop in private, and only release code to the public during releases.
Notable example project: Android Open Source Project.
The term "list of partition topics" could refer to several different contexts, so I will provide an overview of a few possibilities: 1. **Partitioning in Databases**: In database management systems, partitioning refers to the process of dividing a database into smaller, more manageable pieces, known as partitions. Each partition can be considered a separate topic if they represent different types of data or if they are used for different purposes.
The Möbius inversion formula is a result in number theory and combinatorics that provides a way to invert certain types of relationships expressed in terms of sums over divisors. It is named after the German mathematician August Ferdinand Möbius.
Pinned article: ourbigbook/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