Specific energy is a term used to describe the amount of energy stored or released per unit mass of a substance or system. It is typically expressed in units such as joules per kilogram (J/kg) or calories per gram (cal/g). Specific energy provides a way to compare the energy content of different materials or fuels regardless of their mass, making it a useful metric in fields such as engineering, chemistry, and physics.
The speed of sound varies depending on the medium through which it is traveling. For elements in their solid, liquid, or gaseous states, the speed of sound can differ significantly. Below are some approximate speeds of sound for various elements at room temperature and standard atmospheric pressure. Keep in mind that these values can vary based on temperature, pressure, and specific material properties.
The Wirtinger sextic refers to a particular type of polynomial that arises in the context of algebraic geometry and is related to the study of algebraic curves. Specifically, the term "Wirtinger sextic" often refers to a degree-six (or sextic) polynomial associated with the geometric properties of certain curves, particularly in relation to their moduli.
Equanimity refers to a mental state of calmness, stability, and composure, especially in difficult circumstances. It is the ability to maintain emotional balance and respond to situations with a sense of inner peace, regardless of external pressures or challenges. Equanimity is often associated with practices in mindfulness, meditation, and various philosophical traditions, particularly in Buddhism, where it is seen as an essential quality for achieving a deeper understanding of the mind and reducing suffering.
A ternary operation is a type of operation that takes three operands or arguments. It is often used in programming and mathematics to perform a specific function or return a value based on the input provided. The most common example of a ternary operation in programming is the conditional (or ternary) operator, which is typically represented as `? :`. In programming languages like C, C++, and Java, the syntax for the ternary operator is as follows: ```plaintext condition ?
Knowledge is a multifaceted concept that encompasses information, understanding, skills, and awareness gained through experience, education, or practice. It can be categorized in various ways, including: 1. **Types of Knowledge**: - **Explicit Knowledge**: This is documented information that can be easily articulated, shared, and stored, such as books, manuals, and databases.
The term "isospectral" typically refers to a condition in mathematics and physics where two or more objects (such as shapes, operators, or systems) share the same spectrum. The most common applications of the term can be found in the context of: 1. **Mathematics (particularly in geometry and algebra)**: Isospectral spaces can refer to geometric objects that have the same spectral properties, such as having the same eigenvalues of their Laplace operator.
Avrim Blum is a prominent computer scientist known for his contributions to algorithm design, machine learning, and computational learning theory. He has been involved in research related to topics such as approximation algorithms, game theory, and online algorithms. Blum has published numerous papers and has played a significant role in advancing theoretical computer science. He is affiliated with institutions such as Carnegie Mellon University, where he has taught and conducted research over the years.
Environment variables are dynamic values that can affect the way running processes on a computer behave. They are part of the operating system's environment in which a process runs and can be used by applications to retrieve configuration information. Here are some key points about environment variables: 1. **Key-Value Pairs**: Environment variables are typically stored as key-value pairs (e.g., `PATH=/usr/local/bin`), where the key is the name of the variable and the value is its corresponding data.
In programming, an **uninitialized variable** refers to a variable that has been declared but not assigned a value before it is used in the program. The contents of an uninitialized variable can be unpredictable—meaning they may contain garbage values (random data from memory) or default values, depending on the programming language and its rules. Using an uninitialized variable can lead to undefined behavior, bugs, or unexpected results in a program.
A unary function is a function that takes a single argument or input value. In mathematical notation, a unary function can be represented as \( f(x) \), where \( f \) is the function and \( x \) is the single input. The key characteristic of a unary function is that it operates on just one variable. For example, common unary functions include: 1. **Square function**: \( f(x) = x^2 \) 2.
A time trial is a racing event in which competitors race against the clock to achieve the best time over a specific distance or course. Unlike traditional races where competitors start together and compete in a pack, a time trial typically features individual riders or teams starting at intervals, allowing each participant to focus on their own performance without direct competition from others during the race.
The concept of a functional derivative is a generalization of the ordinary derivative to functionals, which are mappings from a space of functions to the real numbers (or complex numbers). In essence, while a regular derivative gives the rate of change of a function with respect to its variables, a functional derivative captures the rate of change of a functional with respect to changes in the function it depends on.
SimRank is a similarity measurement framework used primarily for comparing the similarity between objects in a graph or network structure. Introduced by Jeh and Widom in 2002, SimRank defines the similarity between two objects based on the idea that "two objects are similar if they are related to similar objects." It is particularly useful in recommendation systems, social network analysis, and various applications involving relational data.
Barbara McClintock (1902–1992) was an American scientist and geneticist who is best known for her groundbreaking work in the field of genetics, particularly in maize (corn). She was awarded the Nobel Prize in Physiology or Medicine in 1983 for her discovery of "jumping genes," or transposable elements. McClintock's research demonstrated that genes could change positions on chromosomes and that this could affect the expression of traits in organisms.
The Drift-barrier hypothesis is a concept in evolutionary biology that seeks to explain the maintenance of genetic diversity within populations. Proposed by Theodosius Dobzhansky and others, it suggests that genetic drift can play a significant role in shaping the genetic structure of populations, particularly in small, fragmented populations.
In the context of mathematics and theoretical physics, particularly in the fields of twistor theory and geometric analysis, a **local twistor** refers to an object or concept that is derived from the broader framework of twistor theory, as developed by Roger Penrose in the 1960s. Twistors provide a different way to analyze spacetime events and geometric structures, focusing on complex geometries rather than traditional real-number representations of space and time.
A palindrome is a word, phrase, number, or any other sequence of characters that reads the same forwards and backwards (ignoring spaces, punctuation, and capitalization). Examples of palindromic words include "racecar" and "level." Palindromic phrases could include "A man, a plan, a canal, Panama!" or "Madam, in Eden, I'm Adam." In numbers, an example of a palindrome is 12321.
The symmetry of second derivatives refers to a result in multivariable calculus often associated with functions of several variables. Specifically, if a function \( f \) has continuous second partial derivatives, then the mixed second derivatives are equal.

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