Activation energy asymptotics often refers to the mathematical and physical considerations of how activation energy affects the rates of chemical reactions, particularly in systems where the processes can be analyzed asymptotically. In chemistry and physics, activation energy is the minimum energy that reactants must have for a reaction to take place.
Carbon-13 by Ciro Santilli 37 Updated +Created
Asymptotic homogenization is a mathematical technique used to analyze heterogeneous media – that is, materials with varying properties at different scales. This approach is particularly useful in the study of partial differential equations (PDEs) that describe phenomena in materials with complex microstructures. The primary objective of asymptotic homogenization is to derive effective (or homogenized) equations that can describe the macroscopic behavior of such materials by averaging out the microscopic variations.
Ferranti MRT by Wikipedia Bot 0
Ferranti MRT is a type of digital signal processing system primarily used for the measurement and analysis of electrical signals and parameters. It is particularly popular in the field of power quality assessment, research, and various types of electrical testing. The MRT stands for "Multi-Range Transducer," indicating its capability to handle and analyze a range of electrical measurements, allowing for detailed characterization of power systems.
Big O notation by Wikipedia Bot 0
Big O notation is a mathematical concept used to describe the performance or complexity of an algorithm in terms of time or space requirements as the input size grows. It provides a high-level understanding of how the runtime or space requirements of an algorithm scale with increasing input sizes, allowing for a general comparison between different algorithms. In Big O notation, we express the upper bound of an algorithm's growth rate, ignoring constant factors and lower-order terms.
In large deviations theory, the Contraction Principle is a fundamental result that provides insights into the asymptotic behavior of probability measures associated with stochastic processes. Large deviations theory focuses on understanding the probabilities of rare events and how these probabilities behave in limit scenarios, particularly when considering independent and identically distributed (i.i.d.) random variables or other stochastic systems.
The term "distinguished limit" can refer to different concepts depending on the context, particularly in mathematics or analysis. However, it is not a widely recognized or standard term in mathematical literature. It's possible that you might be referring to one of the following ideas: 1. **Limit in Analysis**: In mathematical analysis, the limit of a function or sequence describes the value that it approaches as the input or index approaches some point.
Divergent series by Wikipedia Bot 0
A divergent series is an infinite series that does not converge to a finite limit. In mathematical terms, a series is expressed as the sum of its terms, such as: \[ S = a_1 + a_2 + a_3 + \ldots + a_n + \ldots \] Where \( a_n \) represents the individual terms of the series. If the partial sums of this series (i.e.
Exponentially equivalent measures are a concept from probability theory and statistics, particularly in the context of exponential families and statistical inference. To understand this term, it is essential to break it down into its components. ### Exponential Families An exponential family is a class of probability distributions that can be expressed in a specific mathematical form.
Hajek projection by Wikipedia Bot 0
The Hajek projection, named after the Czech mathematician Jaroslav Hajek, is a concept from the field of statistics, particularly in the context of nonparametric estimation in statistical inference. It refers to a projection operator that is used in the context of estimating a function, usually with respect to a certain kind of norm.
Crystallographic restriction theorem by Ciro Santilli 37 Updated +Created
"Jewish astronomers" refers to individuals of Jewish heritage or faith who have made significant contributions to the field of astronomy throughout history. Like many other scientific disciplines, astronomy has been influenced by a diverse array of cultures and religions, and Jewish astronomers have played important roles at various times and places.
Astronomy awards are given to individuals or organizations for their contributions to the field of astronomy. These awards can recognize achievements in various areas, including research, education, outreach, and innovation. Some of the most notable astronomy awards include: 1. **Nobel Prize in Physics**: While not exclusively for astronomy, many winners have made significant contributions to the field.
The study of astronomy has a rich history with numerous astronomers who contributed significantly to the field across different periods. Here's a brief overview of some key astronomers categorized by historical periods: ### Ancient Astronomy (Before 500 AD) - **Claudius Ptolemy (c. 100c. 170 AD)**: Proposed the Ptolemaic system, which placed the Earth at the center of the universe. - **Aristarchus of Samos (c.
Astronomers can specialize in various fields of research, each focusing on different aspects of the universe and its phenomena. Here are some common fields of research within astronomy: 1. **Observational Astronomy**: This involves collecting and analyzing data from telescopes and other instruments to study celestial objects and events. Subfields may include radio, optical, and infrared astronomy. 2. **Theoretical Astronomy**: Theoretical astronomers use mathematical models and simulations to explain astronomical phenomena and to make predictions.
Star by Ciro Santilli 37 Updated +Created
Astronomer stubs by Wikipedia Bot 0
"Astronomer stubs" generally refer to short articles or entries about astronomers on platforms like Wikipedia that are not yet fully developed. In the context of Wikipedia, a "stub" is a term used to describe a page that is incomplete and may only contain basic information or a brief overview of a subject, in this case, an astronomer.
Amateur astronomers are individuals who engage in the study and observation of celestial objects and phenomena as a hobby rather than as a profession. They usually do not possess formal training in astronomy but develop their skills and knowledge through personal interest, research, and community involvement. Amateur astronomers often use telescopes, binoculars, or even the naked eye to observe stars, planets, galaxies, and other astronomical features.
Cosmic microwave background anisotropy by Ciro Santilli 37 Updated +Created
There is a slight variation in temperature of CMB across the sky of the order of 200 microKelvin. It is small to the ~2.7 K average temperature, but it can be measured.
If the initial conditions of the Big Bang and the laws of physics were perfectly symmetric, then we could expect the universe to just be one perfectly uniform boring soup.
But instead some asymetry made all the fun weird things we see today happen eventually, like galaxies and life.
And the cosmic microwave background serves as a way for us to look back in time to the early conditions of the universe, as it was set in stone as soon as the universe became transparent to this light during recombination.
Or if you want to get poetic, it is the closest we can ever get to listening to the original word of God when he setup the initial conditions of the universe.
The ansiotropies of CMB is the ultimate astronomical compass we will ever have, as it is the thing with the least proper motion.
Figure 1.
Cosmic microwave background anisotropy measured by the Wilkinson Microwave Anisotropy Probe
. Source.

Pinned article: ourbigbook/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