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An entanglement witness is a Hermitian operator such that for every separable quantum state , but for at least one entangled state .
A partially linear model combines a linear coefficient with an unrestricted nuisance function, for example .
A semiparametric estimator targets a finite-dimensional parameter while estimating or otherwise accommodating an infinite-dimensional nuisance component.
Let and . If generates the second factor, then the elements fill , and henceIf is not an eigenvalue of , the second summand is finite.
The restricted wreath product of groups and iswhere acts on the finitely supported functions by translation.
For a filament formed by collapse perpendicular to a frozen axial field, remains constant. The axial magnetic pressure can then be combined with a quadratic equation of state into an effective polytropic constant.
If counts the -step self-avoiding walks from a fixed vertex of a transitive lattice, the connective constant is the exponential growth rateSubmultiplicativity of and the Fekete lemma applied to prove existence of this limit.
The Schwarzschild--anti-de Sitter heat capacity has the sign of . It is positive precisely for , so these large black holes are locally stable in a fixed-temperature reservoir.
For a non-Archimedean local field , the Schwartz-Bruhat space consists of the locally constant, compactly supported complex-valued functions on .
The Rushbrooke scaling relation isIt follows from the homogeneous scaling form of the singular free energy.
The Widom scaling relation isIt follows by differentiating the homogeneous critical equation of state with respect to the external field.
A scalar-field shift symmetry acts by for constant . Its Noether charge is the spatial integral of the canonical momentum, up to the normalization of , and interactions invariant under the symmetry contain derivatives of the scalar field.
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