Discrete symmetry refers to a type of symmetry that involves distinct, separate transformations rather than continuous transformations. In physics and other scientific disciplines, symmetry is often related to invariance under specific transformations, and discrete symmetry encompasses situations where certain operations map a system onto itself in a non-continuous way. There are several types of discrete symmetries, including: 1. **Parity (P)**: This is the symmetry of spatial inversion, where the coordinates of a system are inverted (e.g.
In syntax, dislocation refers to a construction where a constituent, such as a noun phrase or a clause, is moved away from its canonical position in a sentence, often to the periphery, while still maintaining a clear link to the rest of the sentence. Dislocation is commonly used to highlight, emphasize, or provide additional information about the dislocated element.
Order summability is a concept in the field of summability theory, which deals with the summation of sequences and series, particularly when the usual methods fail to produce a finite limit. It is a generalization of the notion of convergence for series and sequences. In essence, a sequence is said to be **order summable** if it can be summed in a particular way that accounts for the arrangement of its terms, often by weighting or structuring them.
A dogcart is a type of lightweight vehicle or cart that is specifically designed to be pulled by dogs, typically one or more. This mode of transportation was historically used for purposes such as carrying goods or passengers, particularly in rural areas. The design of a dogcart generally includes a platform or a simple cart structure with wheels, which is hitched to the dog or dogs.
The Erdős–Turán inequality is a result in combinatorial number theory that deals with the distribution of sums in sequences of integers.
An ergodic process is a type of stochastic (random) process in which the long-term average of a function of the process can be approximated by the average over time for a single realization of the process. In simpler terms, ergodicity implies that time averages and ensemble averages are equivalent. ### Key Characteristics of Ergodic Processes: 1. **Time Average vs. Ensemble Average**: - **Time Average**: Calculated from a single sample path of the process over time.
Eric Allender is a prominent computer scientist known for his work in the field of theoretical computer science. He is particularly noted for his research in computational complexity theory, particularly on topics such as the complexity classes within the context of Boolean circuits, algorithms, and the relationships between different complexity classes. Allender has contributed to understanding the power and limitations of various computational models, including the analysis of problems that can be solved efficiently versus those that are believed to be intractable.
The Zimm–Bragg model is a statistical mechanical model used to describe the conformational behavior of polymer chains, particularly in the context of helix-coil transitions. It provides a framework for understanding how polypeptides can exist in different structural forms—typically as alpha-helices or random coils—under varying conditions, such as temperature and solvent environment. Developed by William H. Zimm and David R.
Autonomy generally refers to the capacity to make informed, independent choices and to have the freedom to act according to one's own values and interests. The concept of autonomy can be applied in various contexts, including: 1. **Philosophy and Ethics**: In ethical discussions, autonomy is often associated with the idea of self-determination and the moral right of individuals to make their own choices. It is a fundamental principle in discussions about consent, especially in medicine and research.
Fofão is a popular Brazilian character, initially created for children's television in the 1980s. The character was portrayed by actor and puppeteer Orival Pessini and became known for its distinctive fluffy appearance, large eyes, and a cheerful personality. Fofão gained fame as part of the children's programming on the show "Balão Mágico," which combined music, puppetry, and interactive segments aimed at young audiences.
Donemus is a Dutch music publishing company that specializes in the promotion and licensing of contemporary classical music. It serves as a platform for composers to share their works, providing access to a catalog of scores and facilitating performances. Donemus plays a crucial role in supporting composers, helping them with the distribution of their music, and connecting them with performers and ensembles. The organization often collaborates with various artists and institutions to promote new music and encourage innovative projects in the field of classical music.
The Dose-Fractionation Theorem is a principle used primarily in the field of radiotherapy, particularly in the treatment of cancer. The theorem pertains to how radiation dosage can be fractionated, meaning that the total dose of radiation is divided into smaller, more manageable doses (fractions) administered over a period of time. This approach is based on the understanding that cancer cells and normal cells respond differently to radiation.
"Drawing Hands" is a famous illustration by the Dutch artist M.C. Escher, created in 1948. The artwork features two hands that appear to be drawing each other. Each hand holds a pencil and is engaged in the act of sketching the other hand, creating a paradoxical situation where the drawing seems to generate the drawers. The image plays with concepts of recursion and self-reference, challenging the viewer's perception of reality and the relationship between two-dimensional and three-dimensional space.
Dr. Kawashima's Brain Training for Nintendo Switch is a video game developed by Nintendo, part of the popular Brain Training series created by Dr. Ryuta Kawashima. Released in July 2020, the game is designed to challenge players' cognitive abilities through various brain exercises and mini-games. The game features a diverse range of activities that test memory, attention, calculation, reading, and other mental skills.
The Dubna 48K, also known as the Дубна-48К, is a vintage home computer that was developed in the early 1980s in the Soviet Union, specifically in the city of Dubna. It was aimed at educational institutions and enthusiasts, offering a variety of features that were competitive with other home computers of the time.
The Widom insertion method is a technique used in statistical mechanics and computational chemistry to calculate the chemical potential of a system, particularly in the context of molecular simulations. The method is named after B. Widom, who introduced it in the early 1970s.
Earthquake clusters, swarms, and sequences are terms used to describe specific patterns of seismic activity that occur in close temporal and spatial proximity. Here's a brief overview of each term: 1. **Earthquake Clusters**: - These are groups of earthquakes that occur in a specific region over a relatively short time period. The earthquakes within a cluster are usually closely spaced in both time and location, but they may not have a direct causal relationship with one another.
Ecological theories are frameworks used to understand the relationships between individuals and their environments, emphasizing how these interactions shape behavior, development, and social structures. These theories originate from ecology, the study of organisms and their interactions with one another and their environment, and are often applied in fields such as psychology, sociology, and education. **Key Aspects of Ecological Theories:** 1.
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





