A fractal globule is a theoretical model of how certain types of DNA or polymer chains can be organized in a highly compact, yet flexible, manner. The concept was introduced to describe the conformation of long polymers in a way that resembles fractals, which are structures that exhibit self-similarity across different scales. Fractal globules are characterized by: 1. **Compactness**: They are densely packed, minimizing the overall volume of the polymer while maintaining its length.
Jackson's inequality is a result in approximation theory, particularly in the context of polynomial approximation of continuous functions. It provides a way to estimate the best possible approximation of a continuous function using a sequence of polynomial functions.
The term "fractal canopy" can refer to different concepts depending on the context, but it is commonly associated with the study of tree canopies in ecology and environmental science, as well as in art and design. Here are two primary contexts in which "fractal canopy" may be relevant: 1. **Ecological Context**: In ecology, the term can be used to describe the structural complexity and organization of tree canopies in forests, which often exhibit fractal-like patterns.
Glaeser's composition theorem is a result in the field of analysis, specifically dealing with properties of functions and their compositions. The theorem is particularly relevant in the context of continuous functions and measurable sets. While the specific details of Glaeser's composition theorem may vary depending on the context in which it is discussed, the general idea revolves around how certain properties (such as measurability, continuity, or other functional properties) are preserved under composition of functions.
The Lidstone series is a type of series used in the field of mathematics, particularly in the context of numerical analysis and interpolation. It is named after the mathematician who contributed to its development. Specifically, the Lidstone series is often associated with the interpolation of functions, where it serves as a tool for constructing polynomials that approximate functions based on given data points.
Littlewood's \( \frac{4}{3} \) inequality is a result in mathematical analysis, particularly in the area of functional analysis and the theory of Orlicz spaces. It provides a bound for the integral of the product of two functions in terms of the \( L^p \) norms of the functions.
The Measurable Riemann Mapping Theorem is a result in complex analysis that deals with the existence of a conformal (angle-preserving) mapping from a domain in the complex plane onto another domain.
The Modified Morlet wavelet is a commonly used wavelet in time-frequency analysis and signal processing, particularly in the context of analyzing non-stationary signals. A wavelet is a mathematical function that can be used to represent a signal at various scales and positions, allowing for the detection of localized features in time and frequency. ### Key Features of the Modified Morlet Wavelet: 1. **Structure**: The Modified Morlet wavelet is essentially a complex exponential modulated by a Gaussian function.
As of my last update in October 2023, there is no widely known figure or concept named Andrei Bolibrukh in popular media, literature, or significant historical context. It’s possible that he may be a private individual or a lesser-known subject in a specific field.
In the context of computer networking, an autonomous system (AS) is a collection of IP networks and routers under the control of a single organization. It is defined by a unique Autonomous System Number (ASN), which is used for routing purposes on the internet. An AS is typically associated with an internet service provider (ISP), a large enterprise, or a university that manages its own routing policies.
Oka's lemma is a result in complex analysis, particularly in the theory of several complex variables. It deals with the existence of holomorphic (complex-analytic) solutions to certain types of equations on complex manifolds.
The Oka-Weil theorem is a result in complex analysis, specifically concerning the theory of several complex variables and the behavior of holomorphic functions. It is named after the mathematicians Kōsaku Oka and André Weil, who contributed to the field. The theorem addresses the problem of the existence of holomorphic sections of certain line bundles over complex manifolds.
The Ostrowski–Hadamard gap theorem is a result from the field of complex analysis, specifically dealing with the growth of analytic functions. It characterizes the behavior of entire functions (functions that are holomorphic on the entire complex plane) based on their order and type.
The \( p \)-Laplacian is a nonlinear generalization of the classical Laplace operator, typically denoted as \( \Delta_p \). It is used extensively in the study of partial differential equations (PDEs) and variational problems.
A **quadratic quadrilateral element** is a type of finite element used in numerical methods, especially in finite element analysis (FEA) for solving partial differential equations. Quadrilateral elements are two-dimensional elements defined by four vertices, while "quadratic" indicates that the shape functions used to represent the geometry and solution within the element are quadratic functions, as opposed to linear functions used in linear elements.
Regularity theory is a concept that can appear in various fields, including mathematics, physics, economics, and computer science, among others. Its interpretation and application can vary widely depending on the discipline. 1. **Mathematics**: In mathematics, particularly in analysis and differential equations, regularity theory examines the solutions to partial differential equations (PDEs) and seeks to determine the conditions under which solutions possess certain smoothness properties.
The term "singularity spectrum" can refer to a few different concepts in various fields, particularly in mathematics and physics. However, one of the primary contexts in which the term is commonly used is in the study of fractals and dynamical systems, particularly in relation to measures of distributions of singularities in functions or signals.
A **superelement** is a concept used in structural analysis and finite element methods (FEM) in engineering, particularly in the context of large scale problems. It refers to a simplified representation of a set of elements or a subsystem that captures the essential behavior of that system while reducing computational complexity.
Bertram Martin Wilson is not a widely recognized figure in public discourse or popular culture as of my last knowledge update in October 2021. It’s possible that he could be a person of interest in a specific field, such as academia, literature, or another domain that might not have received broad attention.
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 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. - 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





