Topics (292k) Articles (302k) Users (381) Discussions (237) Comments (383) Files (8k) New article
Eady instability arises when counterpropagating Rossby waves localized on the upper and lower boundaries phase-lock and amplify one another.
A dark-matter core is an inner halo region whose density approaches a finite value rather than continuing as a steep cusp. Repeated rapid potential fluctuations driven by bursty stellar feedback can transfer orbital energy to dark matter and create such a core.
A plane distribution on a three-manifold is a rank-two distribution. Locally it is the kernel of a nowhere-zero differential 1-form .
A distribution is integrable when every point lies on an immersed submanifold whose tangent spaces equal the distribution. Such submanifolds are its integral manifolds.
At steady state, the displacement-ventilation interface lies where the total plume volume flux equals the imposed ventilation flux. For one triangular-profile wall line plume with kinematic buoyancy flux , entrainment coefficient , and ventilation flux per unit span,
The Kronecker symbol extends the Jacobi symbol to all integer denominators. For a fundamental discriminant , the function is the primitive quadratic Dirichlet character associated with .
A cycle cover of a finite directed graph is a collection of vertex-disjoint directed cycles containing every vertex exactly once. Cycle covers of the weighted directed graph with adjacency matrix are the terms in the permanent of a matrix .
This is a vertex cycle cover with the additional requirements of directed cycles and vertex disjointness.
For on-shell Dirac spinors in standard relativistic normalization,These completeness identities turn spin-summed squared amplitudes into gamma-matrix traces.
The Dirac adjoint of a spinor is . It transforms contragrediently, making a Lorentz scalar and a Lorentz vector.
A distribution is homogeneous of degree when for every . With the unnormalized angular-frequency convention, its Fourier transform is homogeneous of degree .
The elementary diagram of is the set of all first-order sentences true in the expansion of by a constant symbol for each element. A model of the elementary diagram contains an elementary copy of .
An inner model is projectively well-ordered when there is a projective relation that well-orders the real numbers belonging to .
The set consists of the reals coding well-orders of . For , the norm is the order type of the well-order coded by .
A subset of a Polish space has the perfect set property when it is countable or contains a nonempty perfect subset. Every uncountable analytic set contains a perfect subset and consequently has cardinality .
A pointclass is a collection of subsets of topological spaces, usually specified by a common definability or closure condition.
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