OpenLLM-France/wikimedia huggingface dataset:
# Elasticity/Rayleigh-Ritz method
## The Rayleigh-Ritz method

The potential energy functional has the form
    $\Pi [\mathbf {u} ]={\frac {1}{2}}\int _{\mathcal {B}}{\boldsymbol {\nabla }}\mathbf {u} :({\text{C}}:{\boldsymbol {\nabla }}\mathbf {u} )~dV-\int _{\mathcal {B}}\mathbf {f} \bullet \mathbf {u} ~dV-\int _{\partial {\mathcal {B}}}{\widehat {\mathbf {t} }}\bullet \mathbf {u} ~dV$
The standard method of finding an approximate solution to the mixed boundary value problem is to minimize $\Pi$ over a restricted class of functions (the Rayleigh-Ritz method), by assuming that
    $\mathbf {u} _{\text{approx}}=\mathbf {w} _{0}+\sum _{n=1}^{N}a_{n}\mathbf {w} _{n}$
where $\mathbf {w} _{n}$ are functions that are chosen so that they vanish on $\partial {\mathcal {B}}^{u}$ and $\mathbf {w} _{0}$ is a function that approximates the boundary displacements on $\partial {\mathcal {B}}^{u}$. The constants $a_{n}$ are then chosen so that they make $\Pi [\mathbf {u} _{\text{approx}}]$ a minimum.
Suppose,
    $\Pi [\mathbf {u} _{\text{approx}}]=\Pi _{\text{approx}}=\Pi [a_{1},a_{2},,a_{n}]$
Then,
    $\Pi _{\text{approx}}=A+{\frac {1}{2}}\sum _{m,n=1}^{N}B_{mn}~a_{m}~a_{n}+\sum _{n=1}^{N}D_{n}~a_{n}$
where,
    ${\begin{aligned}A&=\int _{\mathcal {B}}U(\mathbf {w} _{0})~dV-\int _{\mathcal {B}}\mathbf {f} \bullet \mathbf {w} _{0}~dV-\int _{\partial {\mathcal {B}}^{t}}{\widehat {\mathbf {t} }}\bullet \mathbf {w} _{0}~dA\\B_{mn}&=\int _{\mathcal {B}}{\boldsymbol {\nabla }}{\mathbf {w} _{m}}:({\text{C}}:{\boldsymbol {\nabla }}{\mathbf {w} _{n}})~dV\\D_{n}&=\int _{\mathcal {B}}{\boldsymbol {\nabla }}{\mathbf {w} _{0}}:({\text{C}}:{\boldsymbol {\nabla }}{\mathbf {w} _{n}})~dV-\int _{\mathcal {B}}\mathbf {f} \bullet \mathbf {w} _{n}~dV-\int _{\partial {\mathcal {B}}^{t}}{\widehat {\mathbf {t} }}\bullet \mathbf {w} _{n}~dA\end{aligned}}$
To minimize $\Pi _{\text{approx}}$ we use the relations
    ${\frac {\partial \Pi }{\partial a_{i}}}=0~~~(i=1,2,,n)$
to get a set of $N$ equations which provide us with the values of $a_{i}$.
This is the approach taken for the displacement-based finite element method. If, instead, we choose to start with the complementary energy functional, we arrive at the stress-based finite element method.
# Elasticity/Sample final6
## Sample Final Exam Problem 6

Two long cylinders are in contact as shown in the figure below. Both cylinders are made of the same material which has a Young's modulus of 10 GPa and a Poisson's ratio 0.20. The smaller cylinder has a radius of 4 cm while the outer one has a radius of 10 cm. What is the width of the region of contact of the two cylinders under the action of a force of 1 kN per unit length of the cylinders.
* Contact between two cylinders

## Solution

The area of contact per unit length is given by
    $a={\sqrt {{\frac {Pr_{1}r_{2}}{\pi (r_{1}+r_{2})}}\left({\frac {\kappa +1}{\mu }}\right)}}$
For plane strain
    $\kappa =3-4\nu$
Therefore, for the material of the cylinders
    $\kappa =3-(4)(0.20)=2.2~~;~~\mu ={\frac {E}{2(1+\nu )}}={\frac {10}{2(1+0.20)}}=4.2~{\text{GPa}}$
Since the outer cylinder contains the inner one, the radius of curvature can be considered to be negative.
Therefore,
    $r_{1}=4~{\text{cm}}=0.04~{\text{m}}~~;~~r_{2}=-10~{\text{cm}}=-0.1~{\text{m}}~~;~~$
The area of contact per unit length of the cylinders is
    $a={\sqrt {{\frac {(1)(10^{3})(0.04)(-0.1)}{\pi (0.04-0.1)}}\left({\frac {2.2+1}{(4.2)(10^{9})}}\right)}}=0.13~{\text{mm}}$
The width of the region of contact is
    ${a=0.13~{\text{mm}}}$
# Literature/1965

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Subpages

* Bernal, J. D. (1965). "Review of the Science Citation Index." Science Progress 53 (211): 455-459. $^{[^]}$
* Literature/1965/Davis $^{[^]}$
* Easton, David (1965). Systems Analysis of Political Life. New York: Wiley. $^{[^]}$
* Kochen, Manfred (1965). Some Problems in Information Science. Scarecrow Press. (Jan 1, 1965) $^{[^]}$
* Licklider, J. C. R. (1965). Libraries of the Future. MIT Press. $^{[^]}$
* Price, Derek J. de Solla (1965). "Networks of Scientific Papers." Science 149 (3683): 510-515. $^{[^]}$
* Literature/1965/Zadeh $^{[^]}$
# Human vision and function/Part 2: Understanding vision: visual acuity, colour vision and 3D perception
## Part 2: Understanding vision: visual acuity, colour vision and 3D perception

"Understanding vision" explains what vision is, not just the recognition of shape and form but also the human visual system's ability to recognise colour and depth.
This topic addresses Learning Outcome 2 (Describe and document measurement of visual function).
Each topic contains: (i) a short written introduction to the topic (ii) a Youtube lecture playlist (iii) supplementary reading and (iv) revision questions.
You should work through all the topics in Part 2 in weeks 4-7 of semester, taking approximately 12-14 hours to complete this section.
Watch the short introductory lectorial on this topic.
2.1 What is vision and how is it measured?
2.2 Colour vision
2.3 Depth perception
# Human vision and function/Part 2: Understanding vision: visual acuity, colour vision and 3D perception/2.1 What is vision and how is it measured?
## 2.1 What is vision and how is it measured?

This topic will enable you to describe simply, the steps that occur when light travels from an object being viewed, through the eye, to the brain for perception to occur. You will also be able to define vision and visual acuity and describe how visual acuity is tested in an eye clinic.

### Task 1

Begin by watching the What is vision? playlist.

### Task 2

The Centre for Eye Research Australia has compiled an excellent resource called Low Vision Online. Please access this resource and complete the reading. The aim of the resource is to enable you to:
* Understand how distance and near visual acuity is tested,
* Understand the purpose of testing vision with a pinhole
* To identify people with low vision as distinct from those who have normal vision and those who are blind
* To test near and distance visual acuity
After you have completed the reading, there is a quiz to check if you have understood the material. Good luck!

### Supplementary reading

1. Kalloniatis M & Luu C (2014) Visual Acuity.
2. Visual Acuity of the Human Eye (NDT Resource centre) see link below.
The eye has a visual acuity threshold below which an object will go undetected. This threshold varies from person to person, but as an example, the case of a person with normal 20/20 vision can be considered. As light enters the eye through the pupil, it passes through the lens and is projected on the retina at the back of the eye. Muscles called extraocular muscles, move the eyeball in the orbits and allow the image to be focused on the central retinal or fovea.
The excerpt above is from the NDT Resource Centre. To read the whole section please view this supplementary reading link.

### Revision questions

Discuss the answers to these questions on your group LMS forum.
* Name the two photoreceptor cells of the retina and describe their distribution.
* Briefly describe the process of “vision”.
* Define the term “visual acuity”.
* What is the most common chart used to test visual acuity?
* How can you adapt a clinic testing room so that the distance the patient sits from the chart is 6 meters when the room is not 6 meters long?
* Write down the formula we use to record visual acuity.
* What value is considered normal vision?
* What does visual acuity of 6/18 mean?
* List 2 things that could be the problem if a patient is not able to read the line on a visual acuity chart for normal vision.
* What should you do if a patient is not able to see the top letter on the vision chart?
Answers
# Human vision and function/Part 2: Understanding vision: visual acuity, colour vision and 3D perception/2.1 What is vision and how is it measured?/Answers

1. Name the two photoreceptor cells of the retina and describe their distribution.
Rods and cones. Rods are distributed in the periphery, cones are distributed most densely around the macula and decrease in density in the periphery.
2. Briefly describe the process of “vision”.
Light strikes the photoreceptors, this is converted into an electrochemical signal and it travels down the visual pathway to the visual cortex of the brain for interpretation.
3. Define the term “visual acuity”.
Visual acuity (VA) is determined by the smallest retinal image which can be clearly distinguished at a certain distance (usually 6 meters).
4. What is the most common chart used to test visual acuity?
Snellen Chart (Or Tumbling E chart for someone who is illiterate or doesn’t recognise letters).
5. How can you adapt a clinic testing room so that the distance the patient sits from the chart is 6 meters when the room is not 6 meters long?
Sit patient 3 meters from a mirror with a backwards facing Snellen chart behind them reflected in it. Or use a specially adapted chart made for 3 meters.
6. Write down the formula we use to record visual acuity.
    Distance from the chart
    Number next to lowest line read
7. What value is considered normal vision?
6/6
8. What does visual acuity of 6/18 mean?
It means that the patient can see at 6 meters what a normal eye can see at 18 meters.
9. List 2 things that could be the problem if a patient is not able to read the line on a visual acuity chart for normal vision.
Refractive error (need to wear glasses) or pathology in the eye.
10. What should you do if a patient is not able to see the top letter on the vision chart?
Move the patient closer to the chart, progressively until they can see a letter, or if the still cannot see it you check if they can Count Fingers, Hand Movements or Light Perception.
# Human vision and function/Part 2: Understanding vision: visual acuity, colour vision and 3D perception/2.2 Colour vision/Answers

1. Why does staring at a red background cause you to see a green afterimage?
Because the centre-surround arrangement of retinal receptive fields is opponent for colour.
2. List the primary colours of pigments.
Yellow, blue and red
3. List the primary colours of light.
Green, red and blue
4. If you mix all the primary pigment colours, what colour will you get?
Black
5. If you mix all the primary colours of light you, what colour will you get?
White
6. How did John Dalton explain his colour vision deficit and what was discovered in the 1990s about his colour vision defect?
He thought that the fluids inside his eye were tinted blue. It was discovered that the green cone pigment in his eyes was missing
7. How common is colour blindness in men compared with women?
1 in 8 men or 1 in 50 women
8. What is the effect if you have colour deficiency whereby one cone type is missing and what is this called?
It results in you having only 2 cones with which to distinguish colour. This is termed dicrhomacy (or dichromat)
9. On which chromosome are the red and green photopigment genes located and what is the impact of this?
On the x-chromasome, this means they are x-linked and can exchange parts (recombine).
10. What is the name of a commonly used test to check for colour vision problems?
Ishihara test for colour blindness.
# Human vision and function/Part 1: Perception of objects/Sensitivity of the sensory cells within the eye

For this activity, we are going to consider the concepts of light sense and vision.

## Light sense and vision

The concept of vision involves a process that begins with a stimulus. Generally speaking, that stimulus is light. Light enters the eye and undergoes optical refraction (bending) as it passes through the structures of the eyeball that are transparent. It is transmitted to photoreceptor cells within the retina and evokes a chemical reaction. This then evokes an electrical stimulus which travels along the optic nerve and the visual pathways: optic chiasm (crossing), optic tract, lateral geniculate nucleus (LGN), optic radiations to the primary visual cortex in the brain. The light rays form an image on the retina and the amount of electrical impulses transmitted to the brain are interpreted, and we 'see'. We 'see' with our brain. Different parts of the brain, for example memory, are then involved in the process of perception.
Visual awareness of the environment can be studied in separate categories, although all functions are simultaneous.
* Light sense - differentiating between light and dark
* Colour sense - discrimination of different wavelengths of light
* Form sense - discrimination of the parts of an image of the retina

## Activity

Let's observe how the sensory cells within the eye perceive vision and how sensitive they are.
What you need:
* 3 different coloured pens or texta lids (eg: red, blue, green)
* A volunteer (friend, family member, neighbour etc)
With your volunteer, sit opposite each other (examiner & observer) about 0.5 m apart. Use palm of hand to cover one eye. Observer stares at the examiner’s nose, without moving their eye. Examiner slowly brings a vertically held coloured pen lid (colour unknown to subject) towards the centre: along the horizontal midline, then the vertical midline (holding horizontally), first from one side & then the other. This video about Confrontation Visual Field testing will show you the technique.

## Questions

* What conclusions can you draw from your observations?
* Is your observer sensitive to changes for different coloured pen lids? Do they see one particular colour better in a different position or are they all the same?
* What could this mean about the eye receptors?

## Handy hint

The questions related to the bovine eye dissection and sensitivity of the cells within the eye will help you with test 1. Start thinking about the visual system and how it works. This will help you with your preparation for your poster assignment.
# Human vision and function/Part 2: Understanding vision: visual acuity, colour vision and 3D perception/2.3 Depth perception
## 2.3 Depth perception

At the end of this topic you will gain an introductory understanding of how binocular vision and stereopsis (3D vision) work and be able to describe the physiological basis for design of stereoscopic (3 D) vision tests.

### Task 1

The sensation of depth occurs when the two eyes look at two slightly different objects, each object falling on either retina, and blend them into one. The perception of depth or 3D is termed "stereopsis" and is a binocular phenomenon, meaning that both eye must be working perfectly together.
Start by watching the YouTube playlist to understand stereopsis.

### Task 2

Watch this very short video and complete the activity it asks you to do which demonstrates the principle of binocular vision and stereopsis.

### Supplementary reading

1. Wikipedia has a great overview of Stereopsis.
2. For more detailed reading, see the chapters on Space Perception and Depth Perception by Kalloniatis M & Luu C (2014).

### Revision Questions

Discuss the answers to these questions on your group LMS forum.
1. Why must both eyes work together in order to perceive stereopsis?
2. What was the purpose of the visual cliff experiments?
3. There are two ways to determine depth. What are these?
4. What type of patterns does the Randot stereotest use to assess stereopsis?
5. What type of depth cue us interposition? Describe how it works.
Answers
# Human vision and function/Part 2: Understanding vision: visual acuity, colour vision and 3D perception/2.3 Depth perception/Answers

1. Why must both eyes work together in order to perceive stereopsis?
Because when the two eyes look at an object they see a slightly different image and each image falls on the retina and it is then blended into one.
2. What was the purpose of the visual cliff experiments?
To determine whether a baby would crawl over the edge of an artificial cliff, to work out whether stereopsis was developed by the time a baby could crawl.
3. There are two ways to determine depth. What are these?
Binocular cues and monocular cues.
4. What type of patterns does the Randot stereotest use to assess stereopsis?
A series of radom dots.
5. What type of depth cue us interposition? Describe how it works.
This is a monocular depth cue. When one object is placed in front of another, and is partially blocking the object behind it, we perceive that the first object is closer.
# Bible/King James/Documentary Hypothesis/Priestly source/Midianite spoils list

<Bible, English, King James, According to the documentary hypothesis | Priestly source
According to the documentary hypothesis, the torah was redacted together from a number of earlier source texts. The largest of these is referred to as the "Priestly source", due to its concentration on details which would be of interest to the Aaronid priesthood.
The reconstructed text of this source contains several elements which are separable from the narrative, including several laws, and descriptions of how rituals should be carried out. It is sometimes believed that these were originally separate documents held as priestly records. One of these separable elements is the spoils from the battle against the midianites (expressed somewhat repetatively at Numbers 31:25-54):
The text is based on numbers 31:25-54, but does not reproduce it, instead presenting a simplified version containing the same information

## The Midianite spoils list

1 Take the sum of the prey that was taken,
2 And divide the prey into two parts; between them that took the war upon them, who went out to battle, and between all the congregation:
3 And levy a tribute unto the LORD of the men of war which went out to battle, take it of their half:
4 One soul of five hundred, for an heave offering of the LORD.
5 And of the children of Israel's half, thou shalt take one portion of fifty,
6 And give them unto the Levites, which keep the charge of the tabernacle of the LORD.
| The booty | The full number | The half portion that went out to war | The LORD's tribute | The half pertaining to the congregation |
| Sheep | 675,000 | 337,500 | 675 | 337,500 |
| Beeves | 72,000 | 36,000 | 72 | 36,000 |
| Asses | 61,000 | 30,500 | 61 | 30,500 |
| Women that had not known man by lying with him | 32,000 | 16,000 | 32 | 16,000 |
7 And the officers which were over thousands of the host, the captains of thousands, and captains of hundreds,
8 Brought an oblation for the LORD, what every man hath gotten,
9 Of jewels of gold, chains, and bracelets, rings, earrings, and tablets, to make an atonement for our souls before the LORD.
10 And all the gold of the offering that they offered up to the LORD, was 16,750 shekels.
# Literature/1976/Fillmore

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Author
### w: Charles J. Fillmore

* University of California, Berkely

## Wikimedia
### w: Frame semantics (linguistics)

| w: FrameNet w: Construction Grammar | w: Encyclopedism |

## Chronology

* Trigg, Randall Hagner (1983). A Network-based Approach to Text Handling for the On-line Scientific Community. Doctoral Dissertation, University of Maryland, College Park, MD. $^{[^]}$
* Shneiderman, Ben (1983). "Direct Manipulation: A Step Beyond Programming Languages," Computer, Vol. 16, No. 8 (August 1983) pp. 57-69. $^{[^]}$
* Literature/1982/Brown $^{[^]}$
* Fillmore, Charles J. (1982). "Frame Semantics," in: Linguistics in the Morning Calm. Hanshin Publishing Co., Seoul. pp. 111-137. $^{[^]}$
* Literature/1980/Berners-Lee $^{[^]}$
* Judge, Anthony (1977). "Knowledge-representation in a Computer-supported Ennvironment," International Classification, 4(2): 76-81. $^{[^]}$
* Soergel, Dagobert (1977). "An Automated Encyclopedia: A Solution of the Information Problem?" International Classification, 4(1): 4-10; 4(2): 81-89. $^{[^]}$
* Belkin, Nicholas J. & Stephen E. Robertson (1976). "Information Science and the Phenomenon of Information," Journal of the American Society for Information Science (Jul-Aug 1976) 27 (4): 197-204. $^{[^]}$
* Fillmore, Charles J. (1976). "Frame Semantics and the Nature of Language," in: Annals of the New York Academy of Sciences: Conference on the Origin and Development of Language and Speech. Volume 280: 20-32. $^{[^]}$
* Kochen, Manfred, ed. (1975). Information for Action: from Knowledge to Wisdom. New York: Academic Press. $^{[^]}$
* Kochen, Manfred (1974). Principles of Information Retrieval. New York: Wiley. $^{[^]}$
* Nelson, Ted (1974). Computer Lib/Dream Machines. $^{[^]}$
* Kochen, Manfred (1972). "WISE: A World Information Synthesis and Encyclopaedia." Journal of Documentation, 28: 322-341. $^{[^]}$
* Kochen, Manfred (1969). "Stability in the Growth of Knowledge." American Documentation, 20 (3): 186-197. $^{[^]}$
* Literature/1968/Engelbart $^{[^]}$
* Kochen, Manfred & R. Tagliacozzo (1968) "A Study of Cross-referencing." Journal of Documentation. 24: 173-191. $^{[^]}$
* Kochen, Manfred, ed. (1967). The Growth of Knowledge: Readings on Organization and Retrieval of Information. New York: Wiley. $^{[^]}$
* Kochen, Manfred (1965). Some Problems in Information Science. Scarecrow Press. (Jan 1, 1965) $^{[^]}$
* Licklider, J. C. R. (1965). Libraries of the Future. MIT Press. $^{[^]}$
* Literature/1965/Nelson $^{[^]}$
* Bohnert, Herbert G. & Manfred Kochen (1963). "The automated multilevel encyclopedia as a new mode of scientific communication." In: Proceedings of the American Documentation Institute, Oct. 1963, pp. 269-270. $^{[^]}$
* Literature/1962/Engelbart $^{[^]}$
* Licklider, J. C. R. (1960). "Man-Computer Symbiosis." In: IRE Transactions on Human Factors in Electronics, vol. HFE-1, pp. 4–11. $^{[^]}$
* Wells, H. G. (1938). World Brain. Garden City, NY: Doubleday, Doran & Co. $^{[^]}$
# Literature/1976/Gadamer

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Excerpts

* It is not so much our judgments as it is our prejudices that constitute our being.... The historicity of our existence entails that prejudices, in the literal sense of the word, constitute the initial directedness of our whole ability to experience. Prejudices are biases our our openness to the world. They are simply conditions whereby we experience something -- whereby what we encounter says something to us. (p. 9)

## Wikimedia

| w: Truth and Method w: Hermeneutics w: Universal pragmatics | w: Jürgen Habermas |

## Chronology

* Gadamer, Hans-Georg (1976). Philosophical Hermeneutics. (trans. and ed. by David Linge). University of California Press, 1976. $^{[^]}$
* Ogden, C. K. & I. A. Richards (1923). The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism. London: Routledge & Kegan Paul Ltd. $^{[^]}$
# Literature/1976/Fish

Authors :
* A B C D E F G H I J K L M N O P Q R S T U V W X Y Z &

## Wikimedia

| w: Interpretive communities | w: Reader-response criticism |

## Chronology

* Fish, Stanley (1980). Is There A Text in This Class?: The Authority of Interpretive Communities. Harvard University Press. $^{[^]}$
* Lakoff, George & Mark Johnson (1980). Metaphors We Live By. University of Chicago Press. $^{[^]}$
* Ortony, Andrew, ed. (1979). Metaphor and Thought, Cambridge University Press. 2nd. ed. 1993. $^{[^]}$
* Sacks, Sheldon, ed. (1978). Critical Inquiry, vol. 5, no. 1 (Special Issue: On Metaphor), University of Chicago. $^{[^]}$
* Literature/1977/Rogers $^{[^]}$
* Fish, Stanley (1976). "Interpreting the 'Variorum'." Critical Inquiry, Vol. 2, No. 3, (Spring 1976), pp. 465-485. $^{[^]}$
* Literature/1976/Ricoeur $^{[^]}$
* Ricoeur, Paul (1975). The Rule of Metaphor: Multi-Disciplinary Studies in the Creation of Meaning in Language. Robert Czerny, Kathleen McLaughlin & John Costello, trans., London: Routledge and Kegan Paul, 1978. $^{[^]}$
* Eco, Umberto (1975). A Theory of Semiotics. London: Macmillan, 1976. $^{[^]}$