The Bruss–Duerinckx theorem is a result in the field of probability theory and mathematical finance, specifically related to the pricing and replication of contingent claims in incomplete markets. It presents conditions under which a contingent claim can be obtained as the limit of portfolios in a given financial market. The theorem states that if a financial market is incomplete, then under certain conditions, there exists an equivalent martingale measure (a probability measure that allows for the pricing of contingent claims).
Bulletproof hosting refers to a type of web hosting service that is designed to be resistant to legal action, often providing extremely high levels of privacy and anonymity. These hosting services typically cater to clients who engage in or promote illegal activities, such as cybercrime, malware distribution, phishing, and other illicit online ventures.
Large deviations theory is a branch of probability theory that deals with the study of rare events—specifically, events that deviate significantly from expected behavior. It provides a mathematical framework for quantifying the probabilities of these rare deviations from the average or typical outcome of a stochastic process. The fundamental ideas in large deviations theory include: 1. **Rate Functions**: These are functions that describe the exponential decay rate of the probabilities of rare events.
The mathematics of infinitesimals is an area of calculus and mathematical analysis that involves the study of quantities that are exceedingly small, often approaching zero but not necessarily reaching it. Infinitesimals provide a framework for dealing with concepts such as limits, derivatives, and integrals in a rigorous way. The usage of infinitesimals can be traced back to the work of mathematicians like John Wallis and Isaac Newton in the 17th century.
A crash test dummy, also known as a crash dummy or anthropomorphic test device (ATD), is a life-sized model that simulates the human body during vehicular crash testing. These dummies are used to assess the safety of vehicles and their safety features by providing data on how the human body responds to various types of collisions. Crash test dummies are equipped with various sensors and instruments that measure forces, accelerations, and other data during a crash test.
Quantum pseudo-telepathy refers to a fascinating phenomenon that arises in the context of quantum mechanics and quantum information theory. It describes a situation in which two or more parties can achieve outcomes that seem to suggest some form of instantaneous communication or coordination (akin to telepathy) without any classical means of communication or signaling between them.
David Budescu is a notable figure in the field of psychology, specifically recognized for his work in the area of decision-making and judgment. He has contributed to research on how people interpret and understand probabilistic information and uncertainty. His work often intersects with various fields, including behavioral economics and cognitive psychology.
David Zarefsky is a noted American academic known primarily for his work in the field of rhetoric and communication. He has made significant contributions to the study of argumentation and public discourse. Zarefsky has served as a professor at Northwestern University, where he has focused on the role of rhetoric in political discourse and the historical aspects of communication. His scholarship often explores the intersection of rhetoric with various social and political contexts.
The Diffusing Update Algorithm (DUA) is a method used for computing the shortest paths in a network, particularly in the context of routing protocols. It is an approach that allows for the dissemination of updates regarding path costs throughout a network in a controlled manner and is particularly relevant in scenarios involving dynamic networks where link costs can change over time.
The directional derivative is a concept in multivariable calculus that measures how a function changes as you move in a specific direction from a given point.
George B. Pegram was an American physicist known for his contributions to the fields of nuclear and particle physics. He served as a professor and researcher in several prestigious institutions, including Columbia University. In addition to his research work, he was noted for his leadership roles in various scientific organizations and played a significant part in the development of the field of nuclear science. If you meant something else by "George B.
Cardinality is a mathematical concept that refers to the number of elements in a set or the size of a set. It is used to describe the quantity of items in both finite and infinite sets. 1. **Finite Sets**: For finite sets, cardinality is simply the count of distinct elements.
Chair tiling, also known as chair graph tiling, is a type of mathematical tiling problem that involves covering a region using shapes that are analogous to a chair. Specifically, it typically refers to using small polygons to fill a larger polygonal area without overlaps or gaps, adhering to certain constraints based on the shapes.
The Pyragas method, also known as the Pyragas control or Pyragas feedback control, is a technique used in control theory and dynamical systems to stabilize unstable systems or stabilize periodic orbits. It was introduced by the Lithuanian mathematician and physicist A. Pyragas in the early 1990s. The fundamental idea behind the Pyragas method is based on applying delayed feedback to the system being controlled.
A coincidence circuit is a type of electronic logic circuit that is designed to detect when two or more events occur simultaneously or within a specified time window. The primary use of such a circuit is in digital systems where it is critical to identify when multiple input signals are true at the same time. Coincidence circuits are commonly utilized in various applications, including: 1. **Digital Electronics**: In digital systems, coincidence circuits can help in the implementation of complex logic functions and assist in synchronizing signals.
Wellfoundedness is a concept primarily used in mathematical logic and set theory, particularly in the context of order relations and transfinite induction. A relation \( R \) on a set \( S \) is said to be well-founded if every non-empty subset of \( S \) has a minimal element with respect to the relation \( R \). In simpler terms, this means that there are no infinite descending chains of elements.
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 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