Kneser's theorem is a result in the theory of differential equations, particularly in the context of linear differential equations with variable coefficients. It addresses the behavior of solutions for higher-order linear ordinary differential equations.
The Knower Paradox is a philosophical problem related to self-reference and knowledge, particularly in the context of epistemology and the philosophy of language. It illustrates difficulties in discussing knowledge and the nature of what it means to "know" something. The paradox can be framed as follows: 1. Consider a proposition "I know that p," where "p" is some statement.
The Korean Mathematical Society (KMS) is an academic organization in South Korea dedicated to the advancement and development of mathematics. Founded in 1946, the society aims to promote mathematical research, education, and collaboration among mathematicians in Korea and internationally. It serves as a platform for the dissemination of mathematical knowledge through publications, conferences, and workshops. KMS also plays a crucial role in fostering communication among mathematicians, supporting young researchers, and enhancing the quality of mathematical education in Korea.
The Kummer–Vandiver conjecture is a statement in number theory concerning the behavior of cyclotomic fields and the behavior of the class groups associated with certain algebraic number fields. More specifically, it deals with the properties of the class number of the field obtained by adjoining a primitive \( n \)-th root of unity to the rationals.
Change of basis is a concept in linear algebra that involves converting coordinates of vectors from one basis to another. In simpler terms, every vector in a vector space can be expressed in terms of different sets of basis vectors. When we change the basis, we are essentially changing the way we describe vectors in that space. A basis for a vector space is a set of linearly independent vectors that span the space.
Mathematical and Statistical Psychology journals are academic publications that focus on the intersection of mathematics, statistics, and psychology. They typically cover a range of topics that deal with the application of mathematical and statistical methods to psychological research, including the development and testing of psychological theories, the analysis of psychological data, and the construction of models to represent psychological phenomena.
Kurt Reidemeister was a German mathematician known for his contributions to knot theory and topology. He lived from 1882 to 1971. Reidemeister is particularly famous for introducing the Reidemeister moves, which are a set of three simple manipulations that can be performed on knot diagrams. These moves are fundamental in the study of equivalence of knots and links, as they provide a way to determine whether two knot diagrams represent the same knot.
The Lamb–Mössbauer factor, often denoted as \( f \), is a key concept in the field of condensed matter physics and spectroscopy, particularly in relation to Mössbauer spectroscopy. It describes the fraction of the total intensity of a Mössbauer spectrum that is related to atoms that are well-ordered and not experiencing significant vibrational displacement or thermal motion.
The laminar sublayer is a thin region in fluid dynamics, specifically within the context of boundary layers that develop along surfaces in flow conditions. In turbulent flow near a solid boundary, the flow can be characterized by various layers: 1. **Viscous Sublayer**: This is the region closest to the wall, where the effects of viscosity are significant. Within this layer, the flow is often considered laminar, meaning that it is orderly and fluid particles move in parallel layers with minimal mixing.
In this malformed Coinbase transaction, the mining pool "nicehash" produced a provably unspendable Bitcoin output script due to a bug, and therefore lost most of the entire block reward of 6.25 BTC then worth about $ 123,000.
The output is unspendable because it ends in a constant 0, the disassembly of the first and main output is this series of constants:
0 017fed86bba5f31f955f8b316c7fb9bd45cb6cbc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
and for the second smaller one:
aa21a9ed62ec16bf1a388c7884e9778ddb0e26c0bf982dada47aaa5952347c0993da 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
the third one being an OP_RETURN message.
Language planning refers to the deliberate efforts to influence the function, structure, or acquisition of a language within a community or country. It is often undertaken by governments, educational institutions, or linguistic organizations to address issues related to language use, development, preservation, or promotion. Language planning can encompass various aspects, including: 1. **Status Planning**: This involves decisions about which languages will have official status, which will be used in government and education, and which may be promoted over others.
The Laplacian vector field typically refers to a vector field that is derived from the Laplacian operator. The Laplacian operator, denoted as \( \nabla^2 \) or \( \Delta \), is a second-order differential operator that acts on scalar or vector fields.
Larry A. Wasserman is a prominent statistician and professor known for his contributions to statistical theory and methodology. He has been involved in various research areas, including statistical learning, Bayesian statistics, and machine learning. Wasserman has authored several influential books and papers in statistics and has been affiliated with institutions such as Carnegie Mellon University. He is also recognized for his work in developing statistical methods in the context of complex data and applications in fields such as genetics and social sciences.
"Laser & Photonics Reviews" is a scientific journal that focuses on research in the fields of lasers and photonics. The journal publishes high-quality reviews, original research articles, and special issues covering various aspects of photonics, including the generation, manipulation, and application of light. Topics often include but are not limited to laser technology, optical materials, photonic devices, and applications in communications, sensing, and imaging.
As of my last knowledge update in October 2023, "Dark Ages Radio Explorer" doesn't refer to a widely recognized product, service, or concept. It could potentially be a niche or emerging project related to radio, history, or perhaps a creative work such as a podcast, music compilation, or an audio exploration of the historical period known as the Dark Ages.
Non-standard cosmology refers to alternative theories and models of the universe that deviate from the widely accepted ΛCDM model (Lambda Cold Dark Matter model). While the ΛCDM model successfully explains many observations in cosmology, such as the cosmic microwave background radiation, large-scale structure, and the expansion of the universe, non-standard cosmological theories propose different mechanisms, components, or interpretations to explain these phenomena.
Physical properties are characteristics of a substance that can be observed or measured without changing the substance's chemical composition. These properties help in identifying and describing materials. Some common physical properties include: 1. **Color**: The color of the material. 2. **Odor**: The smell associated with the substance. 3. **Density**: The mass per unit volume of a substance, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

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 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  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