OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/2D With Drag Airship Optimal Control
## 2D with Drag and No Wind

{\mathbf Disclaimer}: This is a work in progress... \\
The force due to drag in 2D is given by
$F_{d}={\frac {1}{2}}C_{d}\rho Av^{2}$
Unlike the 1D case, which uses the absolute value, the direction of the drag force in 2D is taken into account by the magnitude of the velocity times the component velocities such that the x and y components of the drag force are
$F_{d}^{x}=-{\frac {1}{2}}C_{d}\rho A{\dot {x}}{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}$ $F_{d}^{y}=-{\frac {1}{2}}C_{d}\rho A{\dot {y}}{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}$
The equations of motion for this problem are
${\dot {x}}={\dot {x}}$ ${\dot {y}}={\dot {y}}$ ${\ddot {x}}=F_{d}^{x}+{\frac {T}{m}}\cos \alpha$ ${\ddot {y}}=F_{d}^{y}+{\frac {T}{m}}\sin \alpha$
where T is the applied Torque in Newtons, $\alpha$ is the angle of applied torque counter clockwise from the negative x-axis and $m$ is the mass of the airship.
The performance measure for the minimum energy problem assuming there is no effort required to change the angle of attack
   $J=\int _{0}^{t_{f}}{\frac {T^{2}}{m^{2}}}dt$
The Hamiltonian for this optimal control problem
   ${\mathcal {H}}={\frac {T^{2}}{m^{2}}}+p_{1}{\dot {x}}+p_{2}{\dot {y}}+p_{3}\left(F_{d}^{x}+{\frac {T}{m}}\cos \alpha \right)+p_{4}\left(F_{d}^{y}+{\frac {T}{m}}\sin \alpha \right)$
The neccessary conditions for the unconstrained control inputs
${\frac {\partial {\mathcal {H}}}{\partial \alpha }}=0$ ${\frac {\partial {\mathcal {H}}}{\partial T}}=0$ \\ ${\frac {\partial {\mathcal {H}}}{\partial \alpha }}=-p_{3}{\frac {T}{m}}\sin \alpha +p_{4}{\frac {T}{m}}\cos \alpha =0$ ${\frac {p_{4}T}{m}}\cos \alpha ={\frac {p_{3}T}{m}}\sin \alpha$ ${\frac {p_{4}}{p_{3}}}={\frac {\sin \alpha }{\cos \alpha }}$
   $\tan \alpha ={\frac {p_{4}}{p_{3}}}$
${\frac {\partial {\mathcal {H}}}{\partial T}}={\frac {2T}{m^{2}}}+{\frac {p_{3}}{m}}\cos {\alpha }+{\frac {p_{4}}{m}}{sin\alpha }=0$ ${\frac {2T}{m}}+p_{3}\cos {\alpha }+p_{4}{sin\alpha }=0$ ${\frac {2T}{m}}=-\left(p_{3}\cos {\alpha }+p_{4}{sin\alpha }\right)$
   $T=-{\frac {m}{2}}\left(p_{3}\cos {\alpha }+p_{4}{sin\alpha }\right)$
The neccessary conditions for the costates are
   ${\dot {p_{1}}}=-{\frac {\partial {\mathcal {H}}}{\partial x}}=0$
   ${\dot {p_{2}}}=-{\frac {\partial {\mathcal {H}}}{\partial y}}=0$
   ${\dot {p_{3}}}=-{\frac {\partial {\mathcal {H}}}{\partial {\dot {x}}}}=-p_{1}+{\frac {1}{2}}p_{3}C_{d}\rho A{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}+{\frac {p_{3}C_{d}\rho A{\dot {x}}^{2}}{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}}+{\frac {p_{4}C_{d}\rho A{\dot {x}}{\dot {y}}}{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}}$
   ${\dot {p_{4}}}=-{\frac {\partial {\mathcal {H}}}{\partial {\dot {y}}}}=-p_{2}+{\frac {1}{2}}p_{4}C_{d}\rho A{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}+{\frac {p_{4}C_{d}\rho A{\dot {y}}^{2}}{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}}+{\frac {p_{3}C_{d}\rho A{\dot {x}}{\dot {y}}}{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}}$
# PlanetPhysics/A Grothendiecks Mathematical Heritage Esquisse Dun Programme
### "Esquisse d'un Programme" ("Sketch of a Program"--the original document was written in French by Alexander Grothendieck)
#### A Concise Summary and Outline of "Esquisse d'un Programme":

An influential research proposal submitted by Alexander Grothendieck in 1984 that continues to inspire even today several related areas of mathematics. Of considerable interest to many mathematicians are the recent Galois groupoid and categorical generalizations of Galois theory initiated by Alexander Grothendieck, now developed towards maturity by several other seasoned mathematicians.
In the second section of the Esquisse Grothendieck sketched what he called the "Galois-Teichm\"uller theory"--a study of the abstract Galois group $Gal({\overline {Q}}/Q)$ via the action of this group on the mapping class (Teichm\"uller) groups; the latter are the fundamental groups of the moduli spaces of Riemann surfaces with marked points. Then, in the third section he focuses on the `simple' but non-trivial case of the smallest moduli space of spheres with four ordered marked points. The Galois action on the fundamental group of this space--which is the profinite completion of the free group on two generators leads to the "dessin d' enfants". The generalization of this theme to all moduli spaces discussed in the second section was the subject of a 1995 mathematics conference published as the "Geometric Galois Actions: The inverse Galois." (London Mathematical Series No. 243, Cambridge University Press., Leila Schneps and Pierre Lochak, Eds. )
Abstract of the paper (In French: "Sommaire")
* The Proposal and enterprise (Envoi).
* Teichm\"uller's Lego-game and the Galois group of Q over Q ("Un jeu de "Lego-Teichm\"uller et le groupe de Galois de Q sur Q).
* Number fields associated with "dessin d'enfants".
(or in orig. : Corps de nombres associ\'es \`a un dessin d' enfant).
* regular polyhedra over finite fields ("Poly\'edres r\'eguliers sur les corps finis").
* General topology or a `Moderated topology' ("Haro sur la topologie dite 'g\'en\'erale', et r\'eflexions heuristiques vers une topologie dite ``mod\'er\'ee").
* Differentiable theories and moderated theories ("Th\'eories diff\'erentiables" (\`{a} la Nash) et "th\'eories mod\'er\'ees").
* Pursuing Stacks ("\`A la Poursuite des Champs").
* Digression on two-dimensional geometry ("Digressions de g\'eom\'etrie bidimensionnelle";
now called "Higher Dimensional Algebra" that Alexander Grothendieck anticipated by several years).
* A Synthesis of the proposed Research Activity (Bilan d'une activit\'e enseignante).
* Epilogue.
* Notes
\mathbf Reference
Alexander Grothendieck, 1984. "Esquisse d'un Programme", (1984 manuscript), finally published in "Geometric Galois Actions", L. Schneps, P. Lochak, eds., London Math. Soc. Lecture Notes 242,Cambridge University Press, 1997, pp.5-48; English transl., ibid., pp. 243-283. MR 99c:14034.
# PlanetPhysics

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## About

* See also Wikipedia: PlanetPhysics
PlanetPhysics was a free, collaborative, online physics, mathematical physics, computational physics and physical mathematics project, including original articles, lectures, books and encyclopedia entries. It was hosted at [https://planetphysics.org https://planetphysics.org].
The original website is no longer available, but an archive from late 2011 has been restored here to continue the effort. It should be noted that the Talk pages contain the original restored PlanetPhysics content in TeX format. The TeX content was converted to Wikitext using a Latex2wiki.py script. Any discrepancies in content should refer to the original TeX for verification and authorship.
# PlanetPhysics/2C Category

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }
A $2-C^{*}$ -category , ${{\mathcal {C}}^{*}}_{2}$, is defined as a (small) 2-category for which the following conditions hold:
* for each pair of $1$-arrows $(\rho ,\sigma )$ the space $Hom(\rho ,\sigma )$ is a complex Banach space.
* there is an anti-linear involution `$*$' acting on $2$-arrows, that is,
$*:Hom(\rho ,\sigma )\to Hom(\rho ,\sigma )$, $S\mapsto S^{*}$ , with $\rho$ and $\sigma$ being $2$-arrows;
$\left\|T\circ S\right\|\leq \left\|S\right\|\left\|T\right\|$, when the composition is defined, and satisfies the $C^{*}$ -condition: $\left\|S^{*}\circ S\right\|=\left\|S^{2}\right\|;$
$Hom(\rho ,\rho )$, (denoted also as $End(\rho )$).
Note: The set of $2$-arrows $End(\iota A)$ is a commutative monoid, with the identity map $\iota :{\mathcal {C}}_{0}^{2*}\to {\mathcal {C}}_{1}^{2*}$ assigning to each object $A\in {\mathcal {C}}_{0}^{2*}$ a $1$-arrow $\iota A$ such that $s(\iota A)=t(\iota A)=A.$
# Professional Development for Teachers of Health Professionals/Connect and communicate

It is often said that the majority of learning happens informally, especially professional learning. To support this, we have established Teachers of Health Professionals, an online community of practitioners. You can use this community to network and socialise generally, or find peer support for your efforts in this program.

## Instructions

* Create an account with Google (you might want to click the link saying "..keep my current email address")
* Setup your Google+ profile
* Join the Teachers of Health Professionals community, and consider turning notifications on - so announcements there will forward to your email address.
* When you have joined the community, please consider introducing yourself by giving a brief intro in the "Share what's new" box on the community page.
* Do the same for sharing links, asking questions or simply sharing an account of your work

## Assessment and recognition

If you can demonstrate proficient use of Google+ and the Teachers of Health Professionals Google+ Community, you are eligible to receive the digital badge Online community of practice. This badge is a visual signal that you are a skilled and valued member of the Teachers of Health Professionals community. It may be used for recognition purposes such as teaching awards, performance review or assessment of prior learning for other courses.

## Other modules in this program

* Connect and communicate
* Write a subject outline
* Produce educational content
* Activities, assignments and assessment
* Evaluate teaching practice
# Professional Development for Teachers of Health Professionals/Activities, assignments and assessment

The design of efficient and effective learning activities, assignments and assessment methods is probably where the art in teaching is. We are continually collecting up and documenting interesting examples of these, and will list them in the Activity, assignments and assessment. If you have an interesting example or method, please feel free to add it to that page.

## Instructions

Your goal is to devise an appropriate range of activities, assignments and assessments that effectively teach your subject's learning objectives and assesses a student's learning outcomes. Describe your plans and methods on your subject outline.
* Review your subject's learning objectives and devise activities that teach and ultimately assess a student's learning outcomes. Consider how formative assessment can be used to teach, and how 3 different types of assessment activities can triangulate assessment.
* Review the recorded examples on the Activity, assignments and assessment page, note any that strike you as interesting and possibly useful. Consider adding your own.
* Account for the workload of your subject and adjust accordingly

## Assessment and recognition

Outline your attempt at the above assignment in the discussion page of this Wikiversity module. Upon successful evaluation of your efforts you will be awarded the ... badge (TBA)

## Other modules in this program

* Connect and communicate
* Write a subject outline
* Produce educational content
* Activities, assignments and assessment
* Evaluate teaching practice
# Professional Development for Teachers of Health Professionals/Albury Wodonga - ways to connect

This is the possible start of regular, open gatherings for teachers seeking professional development in developing independent, teaching practices - contemporary practices that engage with informal and networked learning.
Some examples include using Youtube, Wikipedia and Google in more sophisticated ways for teaching, learning and research. Others include consideration of the Melbourne Free University and open education generally.
The meeting is open to all faculties as well as anyone from outside La Trobe who is interested, including online. The first meeting will be next Wednesday, the 11th September from 1pm in room 6104 Albury Wodonga Campus La Trobe University, and via Hangouts Live. This will be a more hands on session with discussion time included. Please bring a laptop or similar.
The organising page that has been used to try and plan, promote and document this work is the Wikiversity page Professional Development for Teachers of Health Professionals - while this does suggest a focus on health, we think people outside this scope will gain and offer things as well.
Professional Development for Teachers of Health Professionals
On that page is a link to a few communication channels, with more options to follow.
Please forward on to anyone in your networks who might be interested.
Looking forward to seeing you there!

## See Also

* Activities, assignments and assessment
* Open Conference on Open Education
* Creating Accessible Courses
* Professional Development for Teachers of Health Professionals
* Blended learning and online teaching
# Professional Development for Teachers of Health Professionals/Template:Nav

* Connect and communicate
* Write a subject outline
* Produce educational content
* Activities, assignments and assessment
* Evaluate teaching practice
# Professional Development for Teachers of Health Professionals/Write a subject outline

It is likely the case that, despite the value of learning informally through connection to a social network, that your own teaching work will remain focused on the development and delivery of a formal course. Here you will investigate the requirements of a formal education regulator and design and develop a formal course to the standards of that regulator.

## Instructions

You will develop a basic draft subject outline that describes the subject concisely, lists learning objectives, and describes assessments of learning outcomes.
* Study the Australian Qualifications Framework, or other equivalent qualifications-standardising body. Health professions often have over arching accrediting bodies as well, get to know their expectations of a qualified practitioner relevant to what you're teaching.
* Use the subject outline template on Wikiversity to guide your drafting of a subject outline.
* When finished, provide a link to your subject on the Participant examples page.
Many people continue on from this first draft to develop a comprehensive study guide, but remember, your goal is to develop a basic first draft subject outline.

## Assessment and recognition

By listing a suitably completed project from the Creating Accessible Courses below in the Participant examples section, you will receive a digital badge to recognise your effort and progress in the Teachers of Health Professionals program.

## Other modules in this program

* Connect and communicate
* Write a subject outline
* Produce educational content
* Activities, assignments and assessment
* Evaluate teaching practice
# Professional Development for Teachers of Health Professionals/Produce educational content

Teaching often requires the sourcing and possibly the production of content. From instructional videos through to deliberative forums, the scope and range of options here are enormous. In this part of the Professional Development for Teachers of Health Professionals program, we will look at some contemporary methods for sourcing and reusing content, and some simple techniques for producing content.

## Instructions

Your goal is to develop a range of links and resources on your subject's Wikiversity page (or equivalent accessible webpage), and an introductory video to your subject. You should spend between 10-20 hours on this task.
* Read through the guideline on Sourcing and producing educational content.
* Update your subject outline with links to external resources and embedded media. Produce a video that introduces your subject and explains how it can be studied. Remember to ask the Teachers of Health Professionals online community if you have a question or need some assistance.
* When your subject outline is complete with educational content and a range of activities, assignments and assessments, copy it into an accessible website for your subject. You can use Wikiversity, Google Sites, your organisation's website or learning management system

## Assessment and Recognition

Include content and/or links to content in your Wikiversity subject or course page, as evidence that you can legitimately source and create content. Once your efforts can be reviewed on your subject page you will be awarded the Educational content production and management badge.

## Other modules in this program

* Connect and communicate
* Write a subject outline
* Produce educational content
* Activities, assignments and assessment
* Evaluate teaching practice
# Professional Development for Teachers of Health Professionals/Write a subject outline/Participant examples

Edit this section and add the following code excluding the quotation marks
"# '''[[Your page name]]''' - ~~~~"
Do it once for each of your subjects or courses.
* Professional Development for Teachers of Health Professionals - Leighblackall (discuss • contribs) 05:00, 9 July 2014 (UTC)
* Indigenous and Intercultural Health - Nick8june (discuss • contribs) 05:33, 9 July 2014 (UTC)
* Multicultural Perspectives on Health and Wellbeing - SabrinaGupta (discuss • contribs) 05:56, 9 July 2014 (UTC), --SusanCSChong (discuss • contribs) 00:28, 10 July 2014 (UTC)
* Health Education and Development - SusanCSChong (discuss • contribs) 00:32, 10 July 2014 (UTC)
* Principles of Public Health Practice - SusanCSChong (discuss • contribs) 00:32, 10 July 2014 (UTC)
* Zombie Response - SusanCSChong (discuss • contribs) 00:32, 10 July 2014 (UTC)
* Evidence based practice in speech pathology - Shane Erickson (discuss • contribs) 05:19, 10 July 2014 (UTC)
* Incomitant Strabismus - Kkoklanis (discuss • contribs) 02:31, 7 August 2014 (UTC)
* Orthoptic clinical practice - Kkoklanis (discuss • contribs) 02:31, 7 August 2014 (UTC)
* Public Health Policy - Evelyne de Leeuw (discuss • contribs) 02:50, 7 August 2014 (UTC)
* International Health Policy - Evelyne de Leeuw (discuss • contribs) 02:50, 7 August 2014 (UTC)
* Macro strategies to enable occupation - Tracy Fortune (discuss • contribs) 04:09, 8 August 2014 (UTC)
* Listen and learn - Tracy Fortune (discuss • contribs) 04:09, 8 August 2014 (UTC)
* Human vision and function - Merivuki (discuss • contribs) 04:50, 17 September 2014 (UTC)
* Low Vision Rehabilitation - Merivuki (discuss • contribs) 04:50, 17 September 2014 (UTC)
# Professional Development for Teachers of Health Professionals/Activities, assignments and assessment/Subject workload

Below are some basic guides for working out student and teacher workload in a subject.

## Estimate student workload

* Determine how many hours per week someone is expected to commit to studying your subject. This is usually determined by the qualifications standard, such as the Australian Qualifications Framework.
* Determine the actual workload for your subject. You might like to calculate this based on 'readings' + activities + assignments and assessment. As a guide, a 1000 word reading might take 1 hour to study; a 2 hour tutorial might take 4 hours to prepare for and study afterwards; how many hours per week would you expect someone to commit if they were to complete an assignment in your subject?
* To anticipate the levels of engagement you can expect from people studying your subject, estimate how many hours per week they must work to meet their costs of living. You might consider the likely minimum wage

## Estimate teacher and assessor workload

* Workout how many hours your organisation has budgeted for you to coordinate, teach and assess your subject. This is usually calculated by the income generated from fees and/or subsidy after the organisation takes a levy. Here's an example
* Estimate how many hours you will spend coordinating the subject, teaching it and assessing each student's learning outcomes.
* Budgeted hours - coordination/teaching and assessing hours = hours you have to prepare and update your subject outline and educational resources.
# Professional Development for Teachers of Health Professionals/Evaluate teaching practice

In this module you will evaluate your teaching practice. You will seek observations and comments from your peers, survey and collect feedback from your students, and write an evaluative report of your practice.

## Instructions

* Contact a peer who will observe the range of your teaching practice. They are to look at your subject website, observe your teaching and assessment methods, and give constructive feedback. Document that feedback online, preferably publicly accessible as a link from the subject website.
* Prepare an online survey for students, both formative and summative. The formative survey consists of 2 or 3 questions asked at key stages in your subject's schedule. They are used to check progress and make necessary adjustments to the program so as to aid student progress. The summative survey is taken at the conclusion of the subject, and asks for overall feedback. If you're teaching in an educational organisation, consider using or adapting the questions they would ask in their surveys.
* Write an evaluation of your work that includes:
** a statement of your objectives and/or the issues you are trying to address in the development of your subject;
** descriptions of the range of methods you used, key insights gained from the peer observations and student feedback surveys, and what you did to respond to this feedback as the subject progressed;
** and finally, a statement of what you will do next in your developments.
* Publish the evaluation online and link it to your subject website. Take care to de-identify data cited from the surveys and observations, unless you have approval to publish their identities. Once published, you can be awarded the Evaluate teaching practice badge.
# Very Small Information Systems/Research

This page is a start for an open discussion about a real-time API for Java. A summary of the result should be published at a relevant workshop (e.g. at JTRES2006).

## Comments

Rup.inf(Rasmus): One thing to mention/discuss is the potential to use the embedded controllers for soft-real time tasks along the hard-real time tasks. Systems like JOP or JStamp represent fairly powerful processors and in the simplest case they run one control thread with WCET<<T (worst-case-execution-time much less than the period). In traditional real-time systems the designer would select the cheapest processor possible, but even so (and particularly for powerful 32 bit Java processors) there will be a large unused capacity. But the processor might be useful for other things in its vicinity such as measuring a number of temperature inputs and communicating these values across a UDP network or other non-mission-critical issues. Such soft-real-time tasks can occasionally return false from the waitForNextPeriod as they take longer than the allotted slot, but it would not matter. The Ravenscar profile on JStamp does not return true/false if the period is exceeded so that could not be used in this regard. In smart sensors, which might use some learning algorithm, it can be an advantage to get access to excess CPU power to continuously enhance the underlying model. The model might be use in the control loop. This could be achieved by assigning the lowest priority to this utility-thread (soft-real-time) such that the rest of the threads can preempt it and the hard-real time part of the system remains schedulable. Perhaps it could be an idea to discuss these things along the other issues. Perhaps the constructor of a thread can state if the thread is hard-real time or soft-real time. In the latter case the system would not see itself as failed if deadlines were broken. The real time garbage collection also needs to accommodate missed deadlines as a legal construct.

## Available APIs

* RTSJ
* Ravenscar Java
* JOP real-time profile