Stephen Semmes is a mathematician known primarily for his work in differential geometry, analysis, and mathematical physics. He has contributed significantly to the study of geometric analysis and has been involved in various areas of research, including the theory of minimal surfaces, differential equations, and the geometry of manifolds. Semmes has authored numerous papers and is recognized in the mathematical community for his contributions to these fields.
Spectral purity refers to the quality and fidelity of a signal's frequency components, particularly in the context of audio, telecommunications, and radio frequency technologies. It expresses how closely the spectral content of a signal resembles that of an ideal or pure signal, often associated with the desired frequency being transmitted or processed.
René Maurice Fréchet (1879–1973) was a French mathematician best known for his contributions to various fields of mathematics, particularly in topology and functional analysis. He is renowned for his work on the concept of a metric space, the introduction of the Fréchet space (a type of topological vector space), and for developing the Fréchet derivative, which extends the concept of differentiation to more general settings beyond traditional calculus.
Thomas Wolff could refer to different individuals depending on the context, but one notable figure is Thomas S. Wolff, an American physicist known for his contributions to the field of condensed matter physics and materials science.
Walter Rudin (1921–2010) was a prominent mathematician known for his contributions to pure mathematics, particularly in the fields of real and complex analysis, topology, and functional analysis. He is perhaps best known for his textbooks, which are widely used in graduate-level mathematics courses. His most famous works include "Principles of Mathematical Analysis" (often referred to as "Baby Rudin"), "Real and Complex Analysis," and "Functional Analysis.
William Mann was a mathematician known for his contributions to functional analysis and numerical methods. He is particularly noted for the Mann iteration method, which is a technique used in the study of fixed-point theory and has applications in various areas of mathematics, including optimization and differential equations. Mann's work primarily focused on the convergence properties of iterative processes. While information about Mann is less prevalent compared to more prominent figures in mathematics, his contributions remain significant in certain mathematical fields.
Zoia Ceaușescu was a Romanian mathematician and a prominent figure in the country's academic community. Born on November 28, 1929, she was the daughter of Nicolae Ceaușescu, the former General Secretary of the Romanian Communist Party, and Elena Ceaușescu. Zoia was known for her contributions to mathematics, particularly in the areas of functional analysis and topology. She also became a notable public figure, often involved in cultural and scientific endeavors throughout her life.
Adaptive sampling is a technique used in various fields such as statistics, environmental monitoring, machine learning, and computer graphics, among others. The core idea behind adaptive sampling is to dynamically adjust the sampling strategy based on previously gathered information or observations. This approach helps to optimize the data collection process, improve efficiency, and enhance the quality of results.
Moiety conservation is a concept primarily found in the field of chemistry, particularly in the study of chemical systems and reactions. It refers to the principle that certain properties or quantities associated with specific parts or components (moieties) of a molecule remain constant during a chemical reaction or process. In a broader context, moiety conservation may relate to the idea that certain molecular features, such as functional groups or parts of a molecule, are preserved or transformed in a way that can be tracked throughout a chemical transformation.
Breath analysis is a diagnostic technique that involves measuring various components of exhaled breath to assess health conditions, metabolic processes, or the presence of specific substances. It is a non-invasive method that can provide insights into physiological and biochemical changes in the body. Breath analysis can be used to detect: 1. **Metabolic Disorders**: Changes in the concentration of volatile organic compounds (VOCs) in the breath can indicate metabolic disorders like diabetes, where acetone levels can be elevated.
In biochemistry, the control coefficient is a quantitative measure of how much a particular enzyme or step in a metabolic pathway influences the overall flux (rate of reaction) through that pathway. Control coefficients are essential for understanding metabolic regulation and how changes in the activity of specific enzymes can affect the overall metabolism of a cell or organism. The concept is rooted in the field of metabolic control analysis (MCA), which aims to quantify the control that different reactions have on the metabolic flux.
The Crank-Nicolson method is a numerical technique used for solving partial differential equations, particularly parabolic types (like the heat equation). It is widely utilized in computational physics and finance due to its efficacy in handling time-dependent problems. ### Key Features of the Crank-Nicolson Method: 1. **Implicit Method**: The Crank-Nicolson method is an implicit scheme, meaning that it involves solutions to equations that require solving a system of equations at each time step.
The elasticity coefficient is a measure used in economics to quantify the responsiveness of one variable to changes in another variable. It indicates how much one variable will change when a corresponding change occurs in another variable. There are several types of elasticity coefficients, but they are often used in the context of price elasticity of demand and supply. Here are some common forms: 1. **Price Elasticity of Demand (PED)**: This measures how much the quantity demanded of a good responds to a change in its price.
The Fixation Index, commonly referred to as FST, is a measure used in population genetics to quantify the degree of genetic differentiation between populations. Specifically, it reflects the proportion of genetic variance that can be attributed to differences between populations compared to the total genetic variance within and among those populations. FST values range from 0 to 1: - An FST of 0 indicates that there is no genetic differentiation between populations, suggesting that they are genetically identical or very similar.
Circuit topology refers to the arrangement and interconnection of components in an electrical or electronic circuit. It describes how the various elements of a circuit—such as resistors, capacitors, inductors, and active devices like transistors and operational amplifiers—are connected to each other and to the power supply.
Integrodifference equations are a type of mathematical equation used to model discrete-time processes where dynamics are influenced by both local and non-local (or distant) interactions. These equations are particularly useful in various fields such as population dynamics, ecology, and spatial modeling where the future state of a system depends not only on its current state but also on the states of neighboring systems or regions.
The Journal of Biological Dynamics is a scientific journal that focuses on the mathematical and computational modeling of biological phenomena. It publishes research articles that explore theoretical and applied aspects of dynamics in biological systems, including but not limited to population dynamics, ecological interactions, disease dynamics, and the modeling of biological processes. The journal serves as a platform for researchers to share their findings and methodologies, often emphasizing interdisciplinary approaches that combine biology, mathematics, and computational techniques.
The Population Balance Equation (PBE) is a mathematical formulation used to describe the dynamics of a population of particles or entities as they undergo various processes such as growth, aggregation, breakage, and interactions. It is widely used in fields like chemical engineering, materials science, pharmacology, and environmental engineering to model systems involving dispersed phases, such as aerosols, emulsions, or biological cells.
"Crucifixion (Corpus Hypercubus)" is a notable painting created by the Spanish artist Salvador Dalí in 1954. The work is considered one of Dalí's masterpieces and is emblematic of his surrealist style, which combines dream-like imagery with complex symbolism. In this painting, Christ is depicted on a cross that resembles a hypercube, or tesseract, which is a four-dimensional geometric shape.
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





