Lichtner Seamount is an underwater volcanic feature located in the Pacific Ocean. Seamounts are essentially submarine mountains formed by volcanic activity. They can vary in height, shape, and size and often serve as important ecological habitats for various marine life. Lichtner Seamount, like other seamounts, may be of scientific interest for studies related to geology, marine biology, and oceanography.
The Louisiade Plateau is a submerged plateau located in the southwestern Pacific Ocean, off the southeastern coast of Papua New Guinea. It is part of the broader geological formation known as the South Pacific Plate and is situated to the southeast of the island of New Guinea, extending towards the ocean. The plateau is characterized by relatively shallow waters and features numerous islands, reefs, and atolls, which are part of the Louisiade Archipelago.
The Makarov Basin is a region located in the Arctic Ocean, specifically within the East Siberian Sea. It is situated north of the Siberian coast and is bordered by the Severnaya Zemlya islands to the west and the New Siberian Islands to the east. The basin is characterized by its relatively deep waters, which are part of the complex underwater topography of the Arctic. The Makarov Basin is named after the Russian explorer and naval officer, Mikhail Makarov.
The Krivine–Stengle Positivstellensatz, often referred to in the context of real algebraic geometry, is a fundamental result that provides a connection between polynomial inequalities and the positivity of polynomials on semi-algebraic sets.
A Mordellic variety refers to a specific type of algebraic variety that has a rational point and whose set of rational points is a finitely generated abelian group. More formally, a variety \( V \) over a number field \( K \) is said to be a Mordellic variety if it satisfies the following conditions: 1. \( V \) has a rational point, which means there exists a point in \( V \) with coordinates in \( K \).
In algebraic geometry, the term "pseudo-canonical variety" often refers to a type of algebraic variety whose canonical class behaves in a particular way. While the term itself may not be universally defined in all texts, it is sometimes used in the context of the study of varieties with singularities, particularly in relation to the minimal model program (MMP) and the study of Fano varieties.
In algebraic geometry, a **quasi-projective variety** is a type of algebraic variety that can be viewed as an open subset of a projective variety.
Present value (PV) is a financial concept that refers to the current worth of a sum of money or stream of cash flows that will be received or paid in the future, discounted back to the present using a specific interest rate. The idea behind present value is that a dollar today is worth more than a dollar in the future due to the potential earning capacity of money, which is often referred to as the time value of money.
Overtone can refer to different concepts depending on the context in which it is used. Here are a few common interpretations: 1. **Music**: In music, an overtone is a frequency that is higher than the fundamental frequency of a sound. When an instrument or voice produces a note, it vibrates at a fundamental frequency, but it also generates additional frequencies that are multiples of the fundamental (harmonics). These overtones contribute to the richness and timbre of the sound.
The term "line complex" can refer to different concepts depending on the context in which it is used. Here are a few interpretations: 1. **Mathematics/Geometry**: In mathematical contexts, especially in geometry, a line complex may refer to a set of lines that share certain properties or configurations. It could involve a study of relationships between these lines, such as concurrency, parallelism, or specific intersections.
Net Positive Suction Head (NPSH) is an important hydrodynamic parameter in pump operation, particularly in ensuring that a pump operates efficiently and does not cavitate. It is a measure of the pressure available at the suction side of the pump compared to the vapor pressure of the liquid being pumped. NPSH is typically expressed in terms of head (usually in meters or feet).
COMOS is a software platform developed by Siemens that is used for integrated engineering, operations, and maintenance of industrial plants. The primary purpose of COMOS is to facilitate the management of data and processes throughout the entire lifecycle of a facility, from planning and design through to operation and decommissioning.
Hyperreal numbers are an extension of the real numbers that include infinitesimal and infinite quantities. They are used in non-standard analysis, a branch of mathematics that reformulates calculus and analysis using these quantities. The hyperreal number system is constructed by taking sequences of real numbers and using an equivalence relation to group them.
The Veronese surface is a well-known example in algebraic geometry, and it is often studied in relation to the projective geometry of higher-dimensional spaces. Specifically, it is defined as a two-dimensional algebraic surface that can be embedded in projective space. The Veronese surface can be constructed by considering the image of the projective plane under the Veronese embedding.
Alexander Anderson is a mathematician known primarily for his work in the field of combinatorial mathematics and is particularly notable for his contributions to the theory of algorithms and computational mathematics. He has published research on topics such as sorting algorithms and the analysis of data structures, and his work often explores the connections between mathematics and computer science.
Alexander Grothendieck (1928–2014) was a highly influential French mathematician, renowned for his groundbreaking work in algebraic geometry, homological algebra, and number theory. He is often considered one of the most important mathematicians of the 20th century. Grothendieck's contributions include the development of a new way of thinking about algebraic geometry through the use of schemes, a concept that generalized classical algebraic varieties.
In algebraic geometry, a **quintic threefold** is a specific type of projective variety. More precisely, it is a three-dimensional algebraic variety defined as a zero set of a homogeneous polynomial of degree 5 in the projective space \(\mathbb{P}^4\).
The Seshadri constant is an important concept in algebraic geometry, particularly in the study of ample line bundles on projective varieties. It measures the "local positivity" of an ample line bundle.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.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. - 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