OpenLLM-France/wikimedia huggingface dataset:
# Introduction to Astrophysics/Black Dwarfs
## Black Dwarfs

Black dwarfs are thought to be the end stage of stars that initially have between .07 and 10 solar masses. After passing through a red giant phase, a significant proportion of the mass of the star is shed as a planetary nebula. What remains is a white dwarf, which is initially extremely hot, but which does not generate any new energy through nuclear fusion -- and which is supported by electron degeneracy pressure. White dwarfs cool very slowly, eventually becoming dead black dwarfs. This process takes so long that the universe is not thought to be old enough to contain black dwarfs yet, so they are theoretical objects.
A black dwarf is a white dwarf that has cooled down to the temperature of the cosmic microwave background, and so is invisible. Unlike red dwarfs, brown dwarfs, and white dwarfs, black dwarfs are entirely hypothetical.
Once a star has evolved to become a white dwarf, it no longer has an internal source of heat, and is shining only because it is still hot. Like something taken from the oven, left alone a white dwarf will cool down until it is the same temperature as its surroundings. Unlike tonight’s dinner, which cools by convection, conduction, and radiation, a white dwarf cools only by radiation.
Because it’s electron degeneracy pressure that stops it from collapsing to become a black hole, a white dwarf is a fantastic conductor of heat . How fast a white dwarf cools is thus easy to work out … it depends on only its initial temperature, mass, and composition (most are carbon plus oxygen; some maybe predominantly oxygen, neon and magnesium; others helium). At least, part of the core of a white dwarf may crystallize, the cooling curve will have a bit of a bump around then.
The universe is only 13.7 billion years old, so even a white dwarf formed 13 billion years ago (unlikely; the stars which become white dwarfs take a billion years, or so, to do so) it would still have a temperature of a few thousand degrees. The coolest white dwarf observed to date has a temperature of a little less than 3,000 K. A long way to go before it becomes a black dwarf.
Read more: http://www.universetoday.com/41096/black-dwarf/#ixzz26R8gDbl1
# Introduction to Astrophysics/Dark Matter

Observing stars we can calculate their velocity, orbital recession, magnitude and distance using simple physics. The stars rotating in a given galaxy show two different types of motion depending on their distance from the center of the galaxy. The stars closer to the center of the galaxy exhibit the rigid body motion where all the stars have the same period of rotation. However the more distant stars show the differential rotation where each of them have their own separate period of rotation.
As can be seen in the graph above the rotational velocity ‘v’ of the stars do not fall off with the distance from the center of the system, but is rather slowly rising with the radius. According to the data we should have ten times more mass then what we can see to account for the observed velocities. Something must be there and that is what astrophysicists refer to as dark matter. These are the stellar objects that are too dim to be detected directly using current technology. These objects don’t emit, absorb or scatter light at all. Stellar remnants such as white dwarfs, neutron stars, black holes, Weakly Interacting Massive Particles (WIMPs) predicted by the Standard Model of Particle Physics and neutrinos qualify as dark matters.
# Introduction to Astrophysics/Galaxies:Shapes and Evolution/Irregular Galxies

Irregular galaxies have two types, classified by Edwin Hubble: type one are irregulars that have a single bar but did not have enough material to form into a spiral; type two are completely irregular galaxies, which have a lot of star formation.
Irregulars are usually very small and have a lot of star formation (making pink colors), such as the Large and Small Magellanic Cloud, dwarf galaxies that are satellites of the Milky Way and are only a few thousand or more light years across.
# Introduction to Astrophysics

Astrophysics is the study of the physics of the universe. Various objects, such as stars, planets, and galaxies, are studied under the scope of astrophysics. Since astrophysics is a very broad subject, many disciplines of physics are typically applied.

## Historical context

* Early Views
* Aristotle
* Nicolas Copernicus
* Galileo
* Johannes Kepler
* Isaac Newton
* Albert Einstein
* Stephen Hawking

## Stars
### Basics

* Stellar Luminosity
* Stellar Classification
* Hertzsprung‐Russell Diagram

### Stellar Types

Real
* Light Stars
* Heavy Stars
* Main Sequence Stars
* Red Giants
* White Dwarfs
* Black holes
* Neutron Stars
Hypothetical
The science of Astronomy relies on universality of Physical laws. "Same in the heavens as on earth". The world of stellar objects presents us with stupendously larger scales of agglomeration of matter and energy, at which to apply the known laws. Thus we are led to new predictions of entities that have never been observed before. Likewise some species of elementary particles and certain states of matter never observed on Earth need to be postulated in order to accord with observations. Some objects and phenomena falling in such categories and awaiting confirmation or further observational details are in this list. Eventually we expect them to be confirmed in all detail. If they contradict our predictions or conflict with phenomena known on Earth, well that would be even more exciting because that would be a new discovery awaiting explanation.
* Black Dwarfs
* Quark Stars
* Protostars
* Dark Matter
* Dark Energy
* Vacuum Energy

### Stellar Formation & Evolution

* Interstellar Medium
* Phases of Stellar Evolution
* Degenerate Stars
* Supernovae
* Compact Stellar & Relativistic Objects
* Close Binary Systems

### Stellar Structure

* Hydrostatic Equilibrium
* Nuclear Reactions
* Energy Transport

### Star clusters and galaxies

* Star Cluster
* Galaxies:Shapes and Evolution

### Quasars and Pulsars

* Quasars
* Pulsars

### Appendices

* A: Laws and Formulae
* B: Astronomical Constants

## See also

* Space Transport and Engineering Methods
# Introduction to Astrophysics/Albert Einstein

Albert Einstein, a rare genius, has something that changes the whole way of looking to the heavens. He developed the theory of relativity, one of the most important discoveries of the 20th century. This deals with very large objects, such as planets and galaxies. The Special Theory pertains to motion without a gravitational field, and the General Theory pertains to motion with a gravitational field.
# HKDSE Geography/Objectives

HKDSE Geography
* Objectives
* Living with our physical environment
** M1: Opportunities and Risks
** M2a: Rivers
** M2b: Coasts
* Facing changes in the human environment
** M3: Industry
** M4: Sustainable City
development mutually exclusive?
* Confronting global challenges
** M5: Famines and Agriculture
** M6: Tropical Rainforests
** M7: Global Warming
* Elective modules
** E1: Dynamic Earth
** E2: Climate
** E3: Transport
** E4: Zhujiang Delta
The objectives of this book are as follows:
* Provide comprehensive notes for the HKDSE syllabus. This includes:
** Concept words. Remember that geography students must not write 'everyday language'. This is a common complaint from the HKEAA's candidate performance reports. In DBQs, if you do not use the exact word provided in the marking scheme, you will not score anything. In essays, your score will be very low. Therefore, it is important to know your keywords. (For instance, you must write 'expressway', not 'highway'.) Keywords are in bold. (Not everything in the curriculum is important, so less important concepts are put instead in italics.)
** Concepts. From waterfall formation to drip irrigation, concepts are very important in geography.
** Examples. Only important and relevant examples are given. (Examples are needed in essays only. They are not required in DBQs.)
* Provide past paper and exam trend information, as well as how to tackle various questions.
When writing this book, we will adhere to these principles:
* Exam-oriented: Not a single word will be wasted on unrelated material. There will be no 'suggested reading', 'further information', 'fun facts', etc.
* Emphasis on both knowledge and application: Reciting everything will not get you a 5**. You need to apply your knowledge to a flexible range of question types.
* Clarity: There will be explanations in plain English. If this book ever gets translated by the Chinese Wikibooks, there will be a translation to which to refer, too. Also, the sequence of the book will not follow strictly HKEAA's, but will instead by altered to facilitate comprehension.
Moreover, note that:
* All photographs are in full colour.
* There will be no maps for map-reading as they require very hefty royalties from the government to be reproduced.
* A lot of annotated diagrams will be in black-and-white. You exam paper will be scanned black-and-white, so it's just as well.

## A Word on Conventions

* Red boxesRed boxes are about common misconceptions in geography. You are frequently tested about them in multiple-choice questions, so make sure you read through these.
* Green boxesGreen boxes provide statistical data and examples that you should cite in essays for higher scores. Only study and remember this if you have time on your hands and want to aim for a 5+ grade.
Let us get started.
# HSC Extension 1 and 2 Mathematics/3-Unit/Preliminary/Polynomials

A polynomial is any curve that can be described by the set of numbers $\{a_{0},a_{1},...,a_{n}\}$ such that $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}$, or alternatively
    $f(x)=\sum _{k=0}^{n}a_{k}x^{k}$
# HKDSE Geography/M7/Temperature

Temperature is measured in degrees Celsius.
# HSC Extension 1 and 2 Mathematics/3-Unit/Preliminary/Harder 2-Unit
## Implicit differentiation

Implicit differentiation is a method of differentiating an expression in $x$ and $y$, where $x$ and $y$ are related in some manner and neither are constant.
For example, one could differentiate $f(x)=y^{2}$ with respect to $x$ as follows:
    Using the chain rule:
       ${\begin{aligned}{\tfrac {df}{dx}}&={\tfrac {df}{dy}}\times {\tfrac {dy}{dx}}\\&=2y\times {\tfrac {dy}{dx}}\end{aligned}}$
It is useful to think of implicit differentiation as normal differentiation with respect to $x$, only whenever you come across a term with $y$, you multiply the differentiated term by $dy/dx$.
Another example: find the derivative $dy/dx$ of $x^{2}+y^{2}=r^{2}$
Working:
    ${\begin{aligned}2x+2y.{\frac {dy}{dx}}&=0\\2x&=-2y.{\frac {dy}{dx}}\\{\frac {dy}{dx}}&=-{\frac {x}{y}}\end{aligned}}$
# HSC Extension 1 and 2 Mathematics/3-Unit/Preliminary/Other inequalities

In Mathematics Extension 1, higher-order inequalities are introduced. I have written down the steps that need to be taken in order to solve these challenging problems.
When you have a rational function as an inequality (e.g. f(x)/g(x)>a), g(x) might be negative, so you cannot simply multiply g(x) by both sides and cancel out.
There are serveral methods for this kind of problems.
The first method to use is to subtract 'a' to both sides so that you get (f(x)/g(x))-a>0
Rearrange the expression so that there is a common denominator and a single rational function.
After you rearrange the expression, multiply the denominator by the numerator. This would be your 'sign graph'. Using your polynomial skills learnt from Year 10 Advanced Mathematics, perform a rough sketch of the function. Be sure to write down the 'regions' in which the polynomial is greater than 0 (or less than 0, depending on the question). These would be the solutions to your inequality.
You would also have to be careful with the original rational function's denominator and see when the function is undefined. For example if the denominator is x+1, -1 should not be in the solution set of the inequality, because the function will be undefined (i.e. it would be a vertical asymptote if you sketch the function).
The second method is to multiply both sides with the square of the denominator [g(x)]2. By this way, you do not need to worry whether g(x) is negative or not since the square of anything is positive. I found this way more effective.
Hope this helps!
# HSC Extension 1 and 2 Mathematics/4-Unit/Conics
## Ellipses
### Tangent to an ellipse: Cartesian approach

The Cartesian equation of the ellipse is ${\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1$. Differentiating (using the technique of Implicit differentiation to simplify the process) to find the gradient:

## Hyperbolae
### Tangent to a hyperbola: Cartesian approach

The Cartesian equation of the hyperbola is ${\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1$. Differentiating (using the technique of Implicit differentiation to simplify the process) to find the gradient:
    ${\begin{aligned}0&={\frac {2x}{a^{2}}}-{\frac {2y}{b^{2}}}{\frac {dy}{dx}}\\{\frac {dy}{dx}}{\frac {y}{b^{2}}}&={\frac {x}{a^{2}}}\\{\frac {dy}{dx}}&={\frac {b^{2}}{a^{2}}}\times {\frac {x}{y}}\end{aligned}}$
We can then substitute this into our point-gradient form, $y-y_{1}=m(x-x_{1})$, using the point $P(x_{1},y_{1})$:
    at $P$, $m={\frac {b^{2}}{a^{2}}}{\frac {x_{1}}{y_{1}}}$.
    ${\begin{aligned}y-y_{1}&={\frac {b^{2}}{a^{2}}}{\frac {x_{1}}{y_{1}}}(x-x_{1})\\yy_{1}-y_{1}^{2}&={\frac {b^{2}}{a^{2}}}x_{1}(x-x_{1})\\{\frac {yy_{1}}{b^{2}}}-{\frac {y_{1}^{2}}{b^{2}}}&={\frac {x_{1}}{a^{2}}}(x-x_{1})\\{\frac {yy_{1}}{b^{2}}}-{\frac {y_{1}^{2}}{b^{2}}}&={\frac {xx_{1}}{a^{2}}}-{\frac {x_{1}^{2}}{a^{2}}}\\{\frac {x_{1}^{2}}{a^{2}}}-{\frac {y_{1}^{2}}{b^{2}}}&={\frac {xx_{1}}{a^{2}}}-{\frac {yy_{1}}{b^{2}}}\\\end{aligned}}$
    But we know that ${\frac {x_{1}^{2}}{a^{2}}}-{\frac {y_{1}^{2}}{b^{2}}}=1$ from the definition of the hyperbola, so
    ${\frac {xx_{1}}{a^{2}}}-{\frac {yy_{1}}{b^{2}}}=1$

### Normal to a hyperbola: Cartesian approach

The gradient of the normal is given by $-{\frac {dx}{dy}}$, i.e., $-{\frac {a^{2}}{b^{2}}}\times {\frac {y}{x}}$. Finding the equation,
    ${\begin{aligned}y-y_{1}&=-{\frac {a^{2}}{b^{2}}}{\frac {y_{1}}{x_{1}}}(x-x_{1})\\yb^{2}-y_{1}b^{2}&=-a^{2}{\frac {y_{1}}{x_{1}}}(x-x_{1})\\{\frac {b^{2}y}{y_{1}}}-b^{2}&=-{\frac {a^{2}}{x_{1}}}(x-x_{1})\\{\frac {b^{2}y}{y_{1}}}-b^{2}&=-{\frac {a^{2}x}{x_{1}}}+a^{2}\\{\frac {a^{2}x}{x_{1}}}+{\frac {b^{2}y}{y_{1}}}&=a^{2}+b^{2}\end{aligned}}$
# Handbook for Doctoral Students in Education/EndNote Tips?

This is still in develop,ment, so please contribute. There are two versions of EndNote: one on-line, and one as a resident application. The latter is more expensive, but allows for more flexibility.
# Handbook for Doctoral Students in Education/Guiding questions
## Guiding questions

Once you can answer all questions, you should be ready to defend your dissertation. However, you need to start somewhere!
* What is your area of interest? Why do you care about THAT? Why do YOU care about that?
* What is the practical problem you want to address?
* What is the theoretical problem you want to address? In other words, what knowledge we are lacking?
* What is you hunch about a possible theoretical solution?
* What are the two-three key concepts you are planning to use to think about this problem?
* Why do you need each of them? What is each concept’s purpose? How all of them fit with each other, and why do you need all three?
* What do you think is already known about your topic?
* Which fields or subfields, which “schools” or research traditions crated this knowledge? Do you know any big shots?
* What can you add to what people have already found?
* What is your impression of the state of the field(s) with which you’re working?
* What is the title of your dissertation?
* What are your empirical methods? What’s the project?
* What is the hypothesis?
* What is your conceptual framework? Please use narrative, not a picture.
* What is the foundational literature for your topic?
* How do you evaluate the state of foundational literature?
* What are the core research findings you will be using?
* What is new in your project?
* Divide literature in groups in a logical way; explain how these different groups of lit have a job to do in your dissertation.
* Tell a short narrative about the research literature you will be using.
# Handbook for Doctoral Students in Education/How important is APA or another reference format?

In undergraduate and Masters programs, much emphasis is given to reference formatting, and for a good reason. It is a part of professional socialization. However, in doctoral programs, these concerns should fade into background, and become what they are supposed to be - a tool fo scholarshipn, not a measure of its quality.
Most fields in Educational research use APA, although some publications will use Chicago or MLA. No publication have ever been rejected because it author used a comma instead of semi-colon. Therefore, it does not pay off to invest much time in investigating every little detail of APA reference style. Just use any brief reference guide, for example, the OWL at Purdue This should be just enough.
We are trying to investigate whether software such as EndNote are worth the effort. See the on-line version of EndNote.
# Handbook for Doctoral Students in Education/Capturing and organizing your research notes

One of the fundamental tasks for Doctoral students is to figure out to take and keep notes about the reading and research he/she is conducting. Somehow, middle school note cards seem a bit dated. Surely there are better ways of doing this. The purpose of this chapter is for people to write down how they keep their notes and find them later. The skill of capturing information and storing it for later use is something that every scholar must figure out for a successful life of research.
Some people are visual. They want to see and touch everything at the right time. You’ve heard of “just in time inventory?” Well these folks like "just in time data!" Now, some have been known to have strings hung from wall to wall in their homes with their notes taped to the strings. That certainly is visual!
Some people make copies of entire articles then highlight the relevant sections. Next they cut and paste on pages with citation numbers that match the source of that information. Organizing the pages in order is easy and can be easily changed. Whew! Sounds like a lot of work.
Another solution is to use Excel software. This simple spreadsheet software is usually used to work with numbers but it can be useful for words and sentences as well. Opening up a blank spread sheet, one creates enough columns for the project. The first column might be a cue about the citation or the whole citation but I prefer to link it to the Endnotes citation with either a number or author name/year. Next is a column for key words that describe what that data is about. You can also put a column in for where the data might go in your paper (introduction, argument for/against, methodology, etc.). Finally, the last column is where the actual information is typed. By turning on the wrap around feature, you can type as much as you like.
After collecting your data, you can use your computer to move text around or highlight it in different colors. Each color may be assigned a meaning such as a location in your paper or all information about a particular strand in one color. This makes it easy for scholars who are visual to find “just in time” data from their notes! For those of us whose handwriting is not the most readable, using Excel is a good way to ensure that notes are legible.
There are other techniques for those who aren’t visual or who learn by feeling (kinetics), hearing, etc. How do you keep track of your notes so that you can find the right information when needed?
# Handbook for Doctoral Students in Education/Defending Dissertation Proposal

Faculty and students preparing for a dissertation proposal may want to consider the following questions:
* Between the comprehensive exams and proposal hearing, how have the research interests and questions changed, and how have they remained consistent? How aware are committee members of these shifts in substance?
* How can each of us express our confidence in the professional choice of this study as the beginning of a research agenda?
* How confident are participants (including committee members and the doctoral candidate) that the candidate is working with researchable questions?
* How confident are participants that the candidate is ready to collect the right kind of data that will help answer the research questions?
* How can we help the candidate move smoothly toward data collection and analysis?
* How do committee members see their roles in consulting with the candidate when the proposal is accepted?
* How would committee members like to push on the candidate at the hearing to make revisions in chapters 1-3 between an accepted proposal and the dissertation defense, revisions that would increase the quality and professional significance of the study?
# Handbook for Doctoral Students in Education/EndNote Tips

This page is under development. Quaylan will fill it up after he defens his dissertation.
# Handbook for Doctoral Students in Education/How do you track down the foundational research?

For any research project, one can identify "foundational" literature. Who first introduced the key concepts you are using? Who first drew attention to the set of problems and issues you are dealing with? Who contributed significantly to the development of your sub-field(s)?
You do not need to go all the way back to Plato. All intellectual history is related, all is built on top of previous knowledge. So, it does not make sense to invest a lot of time in tracing the intellectual roots of your research inspiration. However, almost any problem or issue is associated with just a few most important names.
For example, if you are writing about learning motivation, there is no need to cover a whole gamut of motivational theories from Freud to Skinner (unless your research directly looks at different approaches to learning motivation). However, you would not want to miss, for example, the pioneering work of Edward Deci (1971) or Mark Lepper (1973). How do you find those two? Use all of these ways:
* Ask your adviser or other more experienced researchers. If they work in exactly the same sub-field as you, those names might be just at the top of their heads, or in their bibliography files.
* Take a look at relevant textbooks and handbooks, and see who the authors cite in the appropriate section. Those are the names you need to look up.
* Read any contemporary research on the subject; in most cases, the foundational names will be referred to at the beginning of each paper.

#### References

* Deci,Edward L. (1971) “Effects of Externally Mediated Rewards on Intrinsic Motivation,” Journal of Personality and Social Psychology 18/1: 105-115.
* Lepper, Mark R., David Greene and Richard Nisbet,(1973) “Undermining Children’s Intrinsic Interest with Extrinsic Reward; A Test of ‘Overjustification’ Hypothesis,” Journal of Personality and Social Psychology 28: 129-37.