MathJax : demo
https://mathjax.github.io/MathJax-demos-web/
@nasa-pds @cityoflosangeles talk.jekyllrb.com/t/jekyll-and-mathjax-how-to-configure-specific-inline-and-display-math/9551/8 // talk.jekyllrb.com/t/jekyll-and-mathjax/5514/2
When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
The Lorenz Equations
\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}
The Cauchy-Schwarz Inequality
\[
\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq
\left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\]
A Cross Product Formula
\[
\mathbf{V}_1 \times \mathbf{V}_2 =
\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\
\end{vmatrix}
\]
The probability of getting \(k\) heads when flipping \(n\) coins is:
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
An Identity of Ramanujan
\[
\frac{1}{\left(\sqrt{\phi \sqrt{5}}-\phi\right) e^{\frac25 \pi}} =
1 + \dfrac{e^{-2\pi}}{
1 + \dfrac{e^{-4\pi}}{
1 + \dfrac{e^{-6\pi}}{
1 + \dfrac{e^{-8\pi}}{1+\ldots}
}
}
}
\]
A Rogers-Ramanujan Identity
\[
1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q| < 1$}.
\]
Maxwell's Equations
\begin{align}
\nabla \times \vec{\mathbf{B}}\, - \frac{1}{c}\, \frac{\partial\vec{\mathbf{E}}}{\partial t}
& = \frac{4\pi}{c}\vec{\mathbf{j}} \\[3pt]
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\[3pt]
\nabla \times \vec{\mathbf{E}}\, + \frac{1}{c}\, \frac{\partial\vec{\mathbf{B}}}{\partial t}
& = \vec{\mathbf{0}} \\[3pt]
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}
In-line Mathematics
Finally, while display equations look good for a page of samples, the
ability to mix math and text in a paragraph is also important. This
expression $\sqrt{3x-1}+(1+x)^2$ is an example of an inline equation. As
you see, MathJax equations can be used this way as well, without unduly
disturbing the spacing between lines.
Further reading
Mermaid Sequence Diagram: Blogging app service communication
sequenceDiagram
participant web as Web Browser
participant blog as Blog Service
participant account as Account Service
participant mail as Mail Service
participant db as Storage
Note over web,db: The user must be logged in to submit blog posts
web->>+account: Logs in using credentials
account->>db: Query stored accounts
db->>account: Respond with query result
alt Credentials not found
account->>web: Invalid credentials
else Credentials found
account->>-web: Successfully logged in
Note over web,db: When the user is authenticated, they can now submit new posts
web->>+blog: Submit new post
blog->>db: Store post data
par Notifications
blog--)mail: Send mail to blog subscribers
blog--)db: Store in-site notifications
and Response
blog-->>-web: Successfully posted
end
end
Water CoolEr
sequenceDiagram
Alice ->> Bob: Hello Bob, how are you?
Bob-->>John: How about you John?
Bob--x Alice: I am good thanks!
Bob-x John: I am good thanks!
Note right of John: Bob thinks a long
long time, so long
that the text does
not fit on a row.
Bob-->Alice: Checking with John...
Alice->John: Yes... John, how are you?
mindmap
root
(Material)
not sure what hardware requirements to use as a baseline
obsolete hardware specifications
high demand for specific hardware components
(Vendors)
convoluted, slow billing process
limited vendor options
long lead times for hardware delivery
inconsistent communication from vendors
(People)
too many approvals required
unclear when costs for server are passed to client
client is unwilling to procure server
budget unavailable until milestone is met
does not see the need for the server
already has on premises servers
client does not want to use public cloud infrastructure
lack of dedicated procurement personnel
miscommunication between teams
(Systems)
procurement is not automated
outdated procurement software
lack of integration between procurement and project management tools
manual tracking of procurement status
Class Diagram
---
title: Django Watson Class Diagram
---
classDiagram
class SearchAdapter {
fields
exclude
store
__init__(model)
prepare_content(content)
get_title(obj)
get_description(obj)
get_content(obj)
get_url(obj)
get_meta(obj)
serialize_meta(obj)
deserialize_meta(obj)
get_live_queryset()
}
class SearchContextManager {
_stack
__init__()
is_active()
start()
add_to_context(engine, obj)
invalidate()
is_invalid()
end()
update_index()
skip_index_update()
}
class SearchContext {
__init__(context_manager)
__enter__()
__exit__(exc_type, exc_value, traceback)
__call__(func)
}
class SkipSearchContext {
__exit__(exc_type, exc_value, traceback)
}
class SearchEngine {
list _created_engines$
dict _registered_models
str _engine_slug
SearchContextManager _search_context_manager
get_created_engines()$ list
__init__(engine_slug, search_context_manager)
is_registered(model) bool
register(model, adapter_cls, **field_overrides)
unregister(model)
get_registered_models() list
get_adapter(model) SearchAdapter
cleanup_model_index(model)
update_obj_index(obj)
_post_save_receiver(instance, **kwargs)
_pre_delete_receiver(instance, **kwargs)
_create_model_filter(models, backend) list
_get_included_models(models) iter
search(search_text, models, exclude, ranking, backend_name) Queryset
filter(queryset, search_text, ranking, backend_name) Queryset
}
Exception <|-- SearchAdapterError
Exception <|-- SearchEngineError
Exception <|-- SearchContextError
SearchEngineError <|-- RegistrationError
SearchContextManager *-- SearchContext
SearchContext <|-- SkipSearchContext
codepen.io/ricoThaka/pen/GgRdwGd
