Aizik Volpert is a notable mathematician known for his contributions to various areas of mathematics, particularly in the fields of topology, algebra, and mathematical education. He has worked extensively on topics related to mathematical analysis and has published numerous research papers.
A. Edward Nussbaum is a prominent figure known primarily for his work in the field of Jewish studies, particularly in relation to Jewish history and culture. He may also be recognized in the context of specific academic contributions or publications. Without additional context, it's unclear which specific aspects of A. Edward Nussbaum's work you are interested in, such as his academic publications, professional background, or any particular projects he has been involved in. If there's a specific area related to A.
Probability theorists are mathematicians or researchers who specialize in the study of probability theory, which is a branch of mathematics dealing with the analysis of random events and the likelihood of various outcomes. Probability theory provides the mathematical framework to model uncertain situations, helping to quantify the likelihood of events and to make predictions based on observed data. Key areas in the study of probability theory include: 1. **Random Variables**: Understanding the behavior of variables that can take on different values based on chance.
PDE theorists are researchers and mathematicians who specialize in the study of partial differential equations (PDEs). PDEs are equations that involve functions of several variables and their partial derivatives. They are fundamental in various fields of science and engineering because they can describe a wide range of physical phenomena, including heat transfer, fluid dynamics, wave propagation, and electromagnetism.
Measure theory is a branch of mathematics that deals with the study of measures, integration, and the properties of measurable functions. It provides a rigorous framework for understanding concepts such as length, area, volume, and probability. A **measure** is a systematic way to assign a numerical value (non-negative) to subsets of a given space, which can be thought of as a generalized notion of size.
Approximation theorists are mathematicians or researchers who specialize in the field of approximation theory. This area of mathematics deals with how functions can be approximated using simpler or more manageable forms, such as polynomials, trigonometric functions, or other basis functions. The primary focus is on understanding the ways in which functions can be estimated or represented using finite-dimensional subspaces, as well as quantifying the error involved in such approximations.
Zubov's method refers to a mathematical approach used primarily in the field of dynamical systems, particularly for analyzing the stability of solutions to differential equations. This method is named after the Russian mathematician V.I. Zubov, who contributed to the study of stability theory. In essence, Zubov's method deals with determining the stability of equilibrium points by constructing Lyapunov functions and using them to assess the behavior of trajectories in the vicinity of these points.
Zahorski's theorem is a result in the field of mathematical analysis and set theory, particularly dealing with properties of Baire spaces. Specifically, it pertains to the existence of certain types of functions or mappings in the context of continuous functions in Baire spaces.
Young's inequality for integral operators is a fundamental result in functional analysis that provides a way to estimate the \(L^p\) norms of convolutions or the products of functions under certain conditions. It applies to integral operators defined by convolution integrals and plays a crucial role in the theory of \(L^p\) spaces.
The Yang–Mills–Higgs equations arise in theoretical physics, particularly in the context of gauge theories and the Standard Model of particle physics. They describe the dynamics of gauge fields and scalar fields, incorporating both Yang-Mills theory and the Higgs mechanism. Here's a breakdown of the components: 1. **Yang-Mills Theory**: This is a type of gauge theory based on a non-abelian symmetry group.
Wiener amalgam spaces are a type of function space used in harmonic analysis and the study of partial differential equations. They comprehensively blend properties of both local and global function spaces, allowing for the analysis of functions that exhibit both rapidly decaying behavior and certain oscillatory features.
The Whitney covering lemma is a result in differential geometry and manifold theory, named after mathematician Hassler Whitney. It provides a way to cover a subset of a manifold with a countable collection of coordinate charts that have certain nice properties.
A weakly harmonic function is a function that satisfies the properties of harmonicity in a "weak" sense, typically using the framework of distribution theory or Sobolev spaces.
WaveLab is a software package designed for a variety of tasks in applied and computational mathematics, particularly in the areas of wavelet analysis, signal processing, and data compression. It is primarily used by researchers, engineers, and scientists who are involved in signal and image processing applications, as well as in the study of wavelet theory and its applications.
The Volkenborn integral is a type of integral used in the context of p-adic analysis and number theory. It is named after the mathematician Helmut Volkenborn who introduced it. Essentially, it serves as an analogue to the classical Riemann or Lebesgue integrals, but it is defined over the p-adic numbers rather than the real numbers.
The Vivanti–Pringsheim theorem is a result in the field of complex analysis, specifically in the study of analytic functions. It deals with the behavior of a function that is analytic within a disk but may have singularities on the boundary of that disk.
Value distribution theory is a branch of complex analysis that focuses on understanding how holomorphic functions distribute their values in the complex plane. This theory is primarily concerned with the behavior of meromorphic functions (functions that are holomorphic except at a discrete set of poles) and their relationship with their value sets, particularly in terms of how often certain values are attained.
The term "universal differential equation" is not standard in mathematical literature, but it can refer to different concepts depending on the context. In some contexts, it may relate to the notion of a differential equation that can describe a wide range of phenomena across various fields of science and engineering. 1. **Universal Differential Equations in Modeling**: In modeling natural phenomena, scientists may seek equations that can represent multiple systems or processes.
In the context of functional analysis and the theory of operator spaces, a unital map (or unital completely positive map) is a type of linear map between operator spaces or C*-algebras that preserves the identity element.

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 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.
  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