Ricci calculus, also known as tensor calculus, is a mathematical framework used primarily in the field of differential geometry and theoretical physics. It provides a systematic way to handle tensors, which are mathematical objects that can be used to represent various physical quantities, including those in general relativity and continuum mechanics. The term "Ricci calculus" is often associated with the work of the Italian mathematician Gregorio Ricci-Curbastro, who developed the formalism in the late 19th century.
The Rizza manifold is a specific example of a 5-dimensional smooth manifold that is characterized by having a nontrivial topology and a certain geometric structure. It was introduced by the mathematician Emil Rizza in a paper exploring exotic differentiable structures. One key feature of the Rizza manifold is that it is a counterexample in the study of differentiable manifolds, particularly in the context of 5-manifolds and their properties related to smooth structures.
Diffraction in time typically refers to the phenomenon where waves spread out and bend around obstacles or through openings, but instead of focusing on spatial dimensions, it considers how these waves behave over time.
"Discoveries" by János Kelemen is likely a reference to a work by the Hungarian author, though specific details about a publication by this name are not widely recognized in mainstream literature as of my last update in October 2023. János Kelemen may have contributed to various fields, including science or literature, but without additional context, it's challenging to pinpoint a specific work titled "Discoveries.
Fraunhofer diffraction describes the diffraction patterns observed when light passes through a small aperture or around an obstacle, and it is analyzed at a far distance from the aperture or object. Under these conditions, the incoming wavefront can be approximated as planar waves. The mathematical formulation of the Fraunhofer diffraction pattern can be expressed in terms of the Fourier transform of the aperture function.
Schaefer–Bergmann diffraction refers to a specific phenomenon related to the diffraction of light or waves when they encounter a periodic structure. This term is often associated with studies in the field of optics or materials science, particularly in the context of understanding how waves interact with different types of materials or surface structures. In general, diffraction occurs when waves, such as light, encounter an obstacle or a slit that is comparable in size to their wavelength.
A codec is a device or software that encodes and decodes digital data. The term "codec" is a combination of "coder" and "decoder." Codecs are commonly used for compressing and decompressing audio and video files, enabling efficient storage and transmission. In the context of audio and video, a codec converts analog signals into digital formats (encoding) and the reverse process (decoding). This is crucial for streaming, editing, and playing multimedia content.
The adjoint filter is a concept commonly used in the context of signal processing, control theory, and particularly in the field of inverse problems and imaging systems. The adjoint filter is often associated with the adjoint operator in linear algebra, which derives from the idea of transposing and taking the complex conjugate of a linear operator.
Märklin Digital refers to the digital control system developed by Märklin, a well-known German manufacturer of model trains and accessories. This system enables model train enthusiasts to control their trains and layouts with more flexibility and precision compared to traditional analog systems.
The cosmological argument is a philosophical argument for the existence of God, which posits that everything that exists has a cause, and since the universe exists, it must also have a cause. This argument is often framed as a way to demonstrate that there must be an ultimate cause or reason for the existence of the universe, which is identified with God.
Publicationes Mathematicae Debrecen is a mathematical journal that publishes research articles in various areas of mathematics. It is associated with the University of Debrecen in Hungary. The journal aims to provide a platform for the dissemination of original research, including both theoretical and applied mathematics. The articles that appear in the journal are usually peer-reviewed to ensure quality and relevance in the field. This journal is one of many academic publications that contribute to the scholarly communication within the mathematical community.
The SIAM Journal on Matrix Analysis and Applications (SIMA) is a scholarly journal published by the Society for Industrial and Applied Mathematics (SIAM). It focuses on research related to matrix theory and its applications in various fields, including numerical analysis, optimization, statistics, and engineering. The journal publishes original research articles that cover a wide range of topics related to matrices, including but not limited to matrix computations, matrix algorithms, and theoretical advancements.
Skewness is a statistical measure that describes the asymmetry of a distribution. It indicates the direction and degree of distortion from the symmetrical bell curve of a normal distribution. In essence, skewness quantifies how much the distribution leans to one side compared to the other. There are three types of skewness: 1. **Positive Skewness (Right Skewness)**: In this case, the tail on the right side of the distribution is longer or fatter than the left side.
"The Analyst, or Mathematical Museum" is a work by the English mathematician and philosopher George Berkeley, published in 1734. In this text, Berkeley critiques the foundational concepts of calculus as developed by his contemporaries, particularly focusing on the notions of infinitesimals and limits. The work is structured in the form of an imaginary museum where mathematical ideas are on display. Berkeley's primary argument is that many of the mathematical practices, particularly those involving infinitesimal quantities, lacked rigor and clarity.
Neo-Riemannian theory is a branch of music theory that focuses on the analysis of harmony and chord progressions through a system of relationships derived from the work of the 19th-century music theorist Hugo Riemann. It is particularly concerned with the transformations between chords and how these transformations can elucidate musical structure, especially in tonal music.
Boids is a simulation model created by computer scientist Craig Reynolds in 1986 to mimic the flocking behavior of birds. The term "Boids" is derived from "birds" and refers to autonomous agents that follow simple rules to simulate realistic flocking behavior. The original Boids algorithm uses three basic rules for each individual "boid": 1. **Separation**: Boids try to maintain a certain distance from each other to avoid crowding and collisions.
The Born–von Karman boundary condition is a mathematical technique used in solid state physics, particularly in the study of periodic systems such as crystals. This condition is employed to simplify the analysis of wave phenomena in materials by imposing periodic boundary conditions on a finite-sized sample, effectively allowing it to be treated as if it were infinite. ### Key Features of Born–von Karman Boundary Condition: 1. **Periodic Boundary Conditions**: The condition assumes that the material is infinitely periodic.
Max Born was a prominent physicist and mathematician who made significant contributions to quantum mechanics and theoretical physics. Various concepts, theorems, and entities in science and mathematics have been named in his honor. Here is a list of notable things named after Max Born: 1. **Born Rule**: A fundamental principle in quantum mechanics that gives the probability of obtaining a particular measurement outcome.
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





