text:
User talk:Remi89~enwikiversity

 Hello Remi89, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 15:18, 11 February 2011 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Remi89. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Remi89~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:49, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:19, 19 April 2015 (UTC)

title: User talk:Remi89~enwikiversity


text:
User talk:CBennett

 Hello CBennett, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 15:18, 11 February 2011 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:CBennett


text:
Nonstandard physics

The purpose and intent of this field of study
The field of physics is a broad and sometimes controversial topic. Through the course of diligent research and the scientific method, new ideas have come and gone, leading to the acceptance of certain fields of study and cosmological frameworks. It also has led to the rejection of many more.

This is not to say that there are no new or diverging opinions or theories. Many of these theories have but few supporters or do not possess an accepted means to receive peer review and undergo the scientific process. In this category are a list of hypothesis, papers, research projects, and controversial observations which in some way go against the orthodox understanding of the physical world.

As such, students and scientists are encouraged to read these ideas with a discerning mind and an eye towards the key terms of observation, reason, falsifiable claims, and evidence. Do these claims follow the scientific method?

In the talk pages of these articles, the reader is encouraged to add substantive discussions, rebuttals, or even flat out debunking of the ideas presented. This is the best means to ensure the upholding of scientific principles.

Some of these articles claim to be full blown theories, yet it is suggested that the reader view them as hypotheses that are still under the purview of serious scrutiny by the discerning reader to find logical inconsistencies or opposition to established research. Then where it is appropriate, for the reader to add into the talk pages serious reasoned comments about the subject matter being discussed.

A good rule of thumb to observe is: "Only by keeping an open mind can the truth be reached, but don't keep such an open mind as to where your brains fall out."

Essays
All these pages have now been moved to Physics/Essays subspace.

Fedosin
Some pages had previously been moved to Physics/Essays/Fedosin as Fedosin had been involved in them. He has now consented to all pages being moved into that essay subspace, where he may verify them, and discuss eventual return, of some of them at least, to mainspace, probably as subpages of other more general resources, either as ordinary subpages or as essays.

In the future, alleged or possible "nonstandard physics" pages should be created or moved to resource subpages as attributed essays, as resources subject to editing for neutrality, or to user space. Nonstandard science pages may otherwise be subject to deletion.

Wherever a page is located, discussion of the content is possible and encouraged. Generally, in user space, the user will have wide discretion over what discussion is allowed. In mainspace essay subpages, any user may comment (as on ordinary mainspace pages), subject only to general Wikiversity policy on civility, etc. As the essay is attributed to a responsible user, that user may object to changes.

A user dissenting from this is free to create a parallel essay, which would generally be neutrally linked from the page supra.

title: Nonstandard physics


text:
User talk:Beanbag1

Hello, My friend. Have us learned the history,

This was from Draubb

title: User talk:Beanbag1


text:
Dignity/You are worthy simply because you exist

You are worthy simply because you exist
These words, from the poem Desiderata help to make the point:

You are a child of the universe, no less than the trees and the stars; you have a right to be here.

Consider each of the natural, living organisms show below: Which of these is the most beautiful?, Fascinating?, Precious?, Worthy? Why?

Welcome, accept, and enjoy the dignity of yourself.

Contemplate the essence of your being.

Enjoy this Faces of Dignity photo gallery.


title: File:Fe1.s11.tm7.HW3.fig3.1.jpg


title: File:Fe1.s11.tm7.HW3.fig3.2.jpg


text:
User:Eml5526.s11.team7.jin/HW3

=Problem 3.3=

Given
Consider the truss structure given in the figure. Nodes A and B are fixed. A 10N force acts in the positive x-direction at node C. Coordinates of joints are given in meters. Young ‘ s modulus is $$ E = {10^{11}}{\text{Pa}} $$ and the cross-sectional area for all bars are $$ A = 2 \cdot {10^{ - 2}}{{\text{m}}^2} $$

Find

 * 1) Number the elements and nodes.
 * 2) Assemble the global stiffness and force matrix.
 * 3) Partition the system and solve for the nodal displacements.
 * 4) Compute the stresses and reactions.

Solution
1. The elements and nodes numbers are shown in the figure below:

2. Dividing the structure into 4 elements and 4 nodes, and deals with each element starting with element 1: Element 1 is numbered with global nodes 1 and 4. It is positioned at an angle $$ {\phi ^{\left( 1 \right)}} = {90^ \circ } $$with respect to positive x-axis. Then,
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\cos {90^ \circ } = 0

$$     (Eq 3.1)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\sin {90^ \circ } = 1

$$     (Eq 3.2)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{l^{\left( 1 \right)}} = 1{\text{m}}

$$     (Eq 3.3)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{k^{\left( 1 \right)}} = \frac = 2 \times {10^9}{\text{N/m}}

$$     (Eq 3.4)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\mathbf{K}}^{\left( 1 \right)}} = 2 \times {10^9}\left[ {\begin{array}{ccccccccccccccc} 0&0&0&0 \\  0&1&0&{ - 1} \\   0&0&0&0 \\   0&{ - 1}&0&1 \end{array}} \right]

$$     (Eq 3.5) Element 2 is numbered with global nodes 2 and 4. It is positioned at an angle $${\phi ^{\left( 2 \right)}} = {135^ \circ }  $$with respect to positive x-axis.
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\cos {135^ \circ } = - \frac{1}

$$     (Eq 3.6)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\sin {135^ \circ } = \frac{1}

$$     (Eq 3.7)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{l^{\left( 2 \right)}} = \sqrt 2 {\text{m}}

$$     (Eq 3.8)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{k^{\left( 2 \right)}} = \frac = \frac{2} \times {10^9}{\text{N/m}}

$$     (Eq 3.9)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\mathbf{K}}^{\left( 2 \right)}} = \frac{2} \times {10^9}\left[ {\begin{array}{ccccccccccccccc} {\frac{1}{2}}&{ - \frac{1}{2}}&{ - \frac{1}{2}}&{\frac{1}{2}} \\ { - \frac{1}{2}}&{\frac{1}{2}}&{\frac{1}{2}}&{ - \frac{1}{2}} \\ { - \frac{1}{2}}&{\frac{1}{2}}&{\frac{1}{2}}&{ - \frac{1}{2}} \\ {\frac{1}{2}}&{ - \frac{1}{2}}&{ - \frac{1}{2}}&{\frac{1}{2}} \end{array}} \right]

$$     (Eq 3.10) Element 3 is numbered with global nodes 3 and 4. It is positioned at an angle $$ {\phi ^{\left( 3 \right)}} = {180^ \circ } $$with respect to positive x-axis.
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\cos {180^ \circ } = - 1

$$     (Eq 3.11)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\sin {180^ \circ } = 0

$$     (Eq 3.12)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{l^{\left( 3 \right)}} = 1{\text{m}}

$$     (Eq 3.13)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{k^{\left( 3 \right)}} = \frac = 2 \times {10^9}{\text{N/m}}

$$     (Eq 3.14)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\mathbf{K}}^{\left( 2 \right)}} = 2 \times {10^9}\left[ {\begin{array}{ccccccccccccccc} 1&0&{ - 1}&0 \\  0&0&0&0 \\   { - 1}&0&1&0 \\   0&0&0&0 \end{array}} \right]

$$     (Eq 3.15) Element 4 is numbered with global nodes 2 and 3. It is positioned at an angle $$ {\phi ^{\left( 4 \right)}} = {90^ \circ } $$with respect to positive x-axis.
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\cos {90^ \circ } = 0

$$     (Eq 3.16)
 *
 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\sin {90^ \circ } = 1

$$     (Eq 3.17)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{l^{\left( 4 \right)}} = 1{\text{m}}

$$     (Eq 3.18)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{k^{\left( 4 \right)}} = \frac = 2 \times {10^9}{\text{N/m}}

$$     (Eq 3.19)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{{\mathbf{K}}^{\left( 4 \right)}} = 2 \times {10^9}\left[ {\begin{array}{ccccccccccccccc} 0&0&0&0 \\  0&1&0&{ - 1} \\   0&0&0&0 \\   0&{ - 1}&0&1 \end{array}} \right]

$$     (Eq 3.20) Assemble the global stiffness matrix
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\mathbf{K}} = 2 \times {10^9}\left[ {\begin{array}{ccccccccccccccc} 0&0&0&0&0&0&0&0 \\  0&1&0&0&0&0&0&{ - 1} \\   0&0&{\frac{1}}&{ - \frac{1}}&0&0&{ - \frac{1}}&{\frac{1}} \\ 0&0&{ - \frac{1}}&{1 + \frac{1}}&0&{ - 1}&{\frac{1}}&{ - \frac{1}} \\ 0&0&0&0&1&0&{ - 1}&0 \\  0&0&0&{ - 1}&0&1&0&0 \\   0&0&{ - \frac{1}}&{\frac{1}}&{ - 1}&0&{1 + \frac{1}}&{ - \frac{1}} \\ 0&{ - 1}&{\frac{1}}&{ - \frac{1}}&0&0&{ - \frac{1}}&{1 + \frac{1}} \end{array}} \right]

$$     (Eq 3.21) The external force and reaction matrix
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\mathbf{f}} = \left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   0 \\   0 \\   {10} \\   0 \\   0 \\   0 \end{array}} \right]

$$     (Eq 3.22)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\mathbf{r}} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\    \\   0 \\   0 \\   0 \\   0 \end{array}} \right]

$$     (Eq 3.23) And the displacement matrix
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\mathbf{d}} = \left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   0 \\   0 \\    \\    \\    \\ \end{array}} \right]

$$     (Eq 3.24) 3. Global system of equation
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

2 \times {10^9}\left[ {\begin{array}{ccccccccccccccc} 0&0&0&0&0&0&0&0 \\  0&1&0&0&0&0&0&{ - 1} \\   0&0&{\frac{1}}&{ - \frac{1}}&0&0&{ - \frac{1}}&{\frac{1}} \\ 0&0&{ - \frac{1}}&{1 + \frac{1}}&0&{ - 1}&{\frac{1}}&{ - \frac{1}} \\ 0&0&0&0&1&0&{ - 1}&0 \\  0&0&0&{ - 1}&0&1&0&0 \\   0&0&{ - \frac{1}}&{\frac{1}}&{ - 1}&0&{1 + \frac{1}}&{ - \frac{1}} \\ 0&{ - 1}&{\frac{1}}&{ - \frac{1}}&0&0&{ - \frac{1}}&{1 + \frac{1}} \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   0 \\   0 \\    \\    \\    \\ \end{array}} \right] = {\mathbf{r}} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\    \\   {10} \\   0 \\   0 \\   0 \end{array}} \right]

$$     (Eq 3.25) Partition the system
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{\overline {\mathbf{d}} _E} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   0 \\   0 \end{array}} \right],{{\mathbf{d}}_F} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right],{{\mathbf{f}}_F} = \left[ {\begin{array}{ccccccccccccccc} {10} \\  0 \\   0 \\   0 \end{array}} \right],{{\mathbf{K}}_F} = \left[ {\begin{array}{ccccccccccccccc} 1&0&{ - 1}&0 \\  0&1&0&0 \\   { - 1}&0&{1 + \frac{1}}&{ - \frac{1}} \\ 0&0&{ - \frac{1}}&{1 + \frac{1}} \end{array}} \right]

$$
 *

 * }

$$ \displaystyle

{{\mathbf{r}}_E} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right],{{\mathbf{K}}_{EF}} = \left[ {\begin{array}{ccccccccccccccc} 0&0&0&0 \\  0&0&0&{ - 1} \\   0&0&{ - \frac{2}}&{\frac{2}} \\ 0&{ - 1}&{\frac{2}}&{ - \frac{2}} \end{array}} \right]

$$
 Solve for the nodal displacements
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

2 \times {10^9}\left[ {\begin{array}{ccccccccccccccc} 1&0&{ - 1}&0 \\  0&1&0&0 \\   { - 1}&0&{1 + \frac{1}}&{ - \frac{1}} \\ 0&0&{ - \frac{1}}&{1 + \frac{1}} \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \left[ {\begin{array}{ccccccccccccccc} {10} \\  0 \\   0 \\   0 \end{array}} \right]

$$     (Eq 3.26)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

\left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \frac{1}{2} \times {10^{ - 9}}\left[ {\begin{array}{ccccccccccccccc} {48.2843} \\  0 \\   {38.2843} \\   {10} \end{array}} \right]

$$     (Eq 3.27) 4. The reaction matrix is
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\mathbf{r}}_E} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = {{\mathbf{K}}_E}{{\mathbf{\bar d}}_E} + {{\mathbf{K}}_{EF}}{{\mathbf{d}}_F} = \left[ {\begin{array}{ccccccccccccccc} 0&0&0&0 \\  0&0&0&{ - 1} \\   0&0&{ - \frac{1}}&{\frac{1}} \\ 0&{ - 1}&{\frac{1}}&{ - \frac{1}} \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} {48.2843} \\  0 \\   {38.2843} \\   {10} \end{array}} \right] = \left[ {\begin{array}{ccccccccccccccc} 0 \\  { - 10} \\   { - 10} \\   {10} \end{array}} \right]

$$     (Eq 3.28) The stresses in the two elements are
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:95%" |
 * style="width:95%" |

{\sigma ^e} = \frac\left[ {\begin{array}{ccccccccccccccc} { - \cos {\phi ^e}}&{ - \sin {\phi ^e}}&{\cos {\phi ^e}}&{\sin {\phi ^e}} \end{array}} \right]{{\mathbf{d}}^e}

$$     (Eq 3.29) For element 1:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\mathbf{d}}^{\left( 1 \right)}} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \frac{1}{2} \times {10^{ - 9}}\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   {38.2843} \\   {10} \end{array}} \right]

$$     (Eq 3.30)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\sigma ^{\left( 1 \right)}} = \left[ {\begin{array}{ccccccccccccccc} 0&{ - 1}&0&1 \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   {38.2843} \\   {10} \end{array}} \right]\frac{1} = 500{\text{Pa}}

$$     (Eq 3.31) For element 2:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\mathbf{d}}^{\left( 2 \right)}} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \frac{1}{2} \times {10^{ - 9}}\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   {38.2843} \\   {10} \end{array}} \right]

$$     (Eq 3.32)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\sigma ^{\left( 2 \right)}} = \left[ {\begin{array}{ccccccccccccccc} {\frac{1}}&{ - \frac{1}}&{ - \frac{1}}&{\frac{1}} \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   {38.2843} \\   {10} \end{array}} \right]\frac{1} =  - 1000{\text{Pa}}

$$     (Eq 3.33) For element 3:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\mathbf{d}}^{\left( 3 \right)}} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \frac{1}{2} \times {10^{ - 9}}\left[ {\begin{array}{ccccccccccccccc} {48.2843} \\  0 \\   {38.2843} \\   {10} \end{array}} \right]

$$     (Eq 3.34)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\sigma ^{\left( 3 \right)}} = \left[ {\begin{array}{ccccccccccccccc} 1&0&{ - 1}&0 \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} {48.2843} \\  0 \\   {38.2843} \\   {10} \end{array}} \right]\frac{1} = 500{\text{Pa}}

$$     (Eq 3.35) For element 4:
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{{\mathbf{d}}^{\left( 4 \right)}} = \left[ {\begin{array}{ccccccccccccccc} \\   \\    \\ \end{array}} \right] = \frac{1}{2} \times {10^{ - 9}}\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   {48.2843} \\   0 \end{array}} \right]

$$     (Eq 3.36)
 *

 * }
 * {| style="width:100%" border="0"

$$ \displaystyle
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |

{\sigma ^{\left( 3 \right)}} = \left[ {\begin{array}{ccccccccccccccc} 0&{ - 1}&0&1 \end{array}} \right]\left[ {\begin{array}{ccccccccccccccc} 0 \\  0 \\   {48.2843} \\   0 \end{array}} \right]\frac{1} = 0

$$     (Eq 3.37)
 *

 * }

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User:Atcovi/Protect/Aaqib user expanding property connection

This have bin poly for this page chapter

 * 1) REDIRECT User:Draubb/Aaqib user expanding property connection


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Physics/Essays/Fedosin/Gravitational induction

Gravitational induction is a property of gravitational field to drive matter as a result of changing of torsion field flux.

Theory of phenomenon
One of the four equations of Lorentz-invariant theory of gravitation (see also ../Gravitoelectromagnetism/ and Maxwell-like gravitational equations) has the following form:
 * $$~ \nabla \times \mathbf{\Gamma } = - \frac{\partial \mathbf{\Omega} } {\partial t}, \qquad\qquad (1) $$

where:
 * $$~ \mathbf{\Gamma } $$ is gravitational field strength or gravitational acceleration,
 * $$~\mathbf{\Omega}$$ is gravitational torsion field or simply torsion.

According to $$(1)$$, after a change in time of $$~\mathbf{\Omega}$$ there appear circular field (rotor) of $$~\mathbf{\Gamma }$$, having the opportunity to lead matter in rotation.

If the vector of torsion $$~\mathbf{\Omega}$$ crosses a certain surface $$~S$$, then we can calculate the flux of this field through this surface:
 * $$~\Phi = \int   \mathbf{\Omega}\cdot \mathbf{n }ds,  \qquad\qquad (2)  $$

where $$~\mathbf{n}$$ – the vector normal to the element of surface $$~dS$$.

Let’s take the partial derivative in equation $$(2)$$ with respect to time with the minus sign and integrate over the surface, taking into account the equation $$(1)$$:
 * $$~ -\int \frac{\partial \mathbf{\Omega} }{\partial t} \cdot \mathbf{n }ds = -\frac{\partial \Phi }{\partial t}= \int  [\nabla \times \mathbf{\Gamma }] \cdot \mathbf{n }ds = \int \mathbf{\Gamma }\vec d\ell.  \qquad\qquad (3)  $$

In the integration was used Stokes' theorem, replacing the integration over a surface of the curl of vector on the integration of this vector over the boundary of the surface. In the right side of $$(3)$$ is a term, equal to the work on transfer of a unit mass of matter on closed path $$~\ell$$, bounding the surface $$~S$$. By analogy with electromagnetism, this work could be called gravitomotive force. In the middle of $$(3)$$ is time derivative of the flux $$~\Phi $$. According to $$(3)$$, gravitational induction occurs when the flux of field through a certain surface changes and is expressed in occurrence of rotational forces acting on particles of matter.

Gravitational induction can be regarded as gravitational analogue of the law of electromagnetic induction.

Typical cases
Just as in electromagnetism, there are two different cases of gravitational induction. In the first case the flux $$~\Phi $$ is changed due to variable $$~\mathbf{\Omega}$$ with a constant flow surface, bounded by a loop.

In the second case, the torsion $$~\mathbf{\Omega}$$ remains constant, but the flux $$~ \Phi $$ changes due to changes in the area occupied by the matter of the loop. For example, consider rubber hose filled with liquid and arranged in a closed rectangular loop in the torsion field $$~\mathbf{\Omega}$$. Let the three sides of the loop are fixed, while the fourth side extends with speed $$~\mathbf{V}$$, increasing the area of the loop. Since the flux $$~ \Phi $$ through the loop changes, the liquid in the hose begins to circulate. The direction of motion of the fluid will be such that torsion field $$~\mathbf{\Omega^\prime }$$ of the fluid will be sent in the same direction as initial torsion field created the circulation of fluid (this is contrary to the Lenz's_law in electromagnetism).

The second case, with expanding of the loop, can also be considered using the expression for full gravitational force:
 * $$~\mathbf{F}_{m} = m \left( \mathbf{\Gamma } + \mathbf{V} \times  \mathbf{\Omega} \right), \qquad\qquad (4)  $$

where:
 * $$~ m$$ – the mass of the fluid particles on which the force is acting,
 * $$~ \mathbf{V} $$ – the particle velocity as the velocity of stretching of the loop.

From $$(4)$$ for the unit mass, located only in torsion field $$~\mathbf{\Omega}$$, should:
 * $$~\mathbf{\Gamma_{S }} =\mathbf{V} \times  \mathbf{\Omega}. \qquad\qquad (5)  $$

The integral of field strength $$(5)$$ around the contour of the loop gives gravitomotive force, as the work of gravitational force on the displacement of unit mass. This integral will be:

 * $$~ \int \mathbf{\Gamma_{S }} \vec d\ell  =  \int \left( \mathbf{V}  \times  \mathbf{\Omega}\right) \vec d\ell  =\int \left( \vec d\ell \times  \mathbf{V}\right)  \mathbf{\Omega}=-\int \frac {d\vec S}{dt}\cdot \mathbf{\Omega}=-\frac {d\Phi_S}{dt}, \qquad (6)  $$

where $$~d\vec S$$ is the vector describing change in the area of the loop during time $$~dt $$, arises due to the movement of one side of the loop $$~ d\ell$$ in the direction of velocity $$~ \mathbf{V} $$.

Expression (6) is the rate of change of the flux of torsion field when the contour of the area changes. Comparing $$(3)$$, $$(5)$$ and $$(6)$$ we find for the induced field strength: $$~ \mathbf{\Gamma_{S }}= \mathbf{V}\times \mathbf{\Omega}$$. Thus, during of changing the flux $$~\Phi $$ liquid inside the hose comes in motion and begins to circulate in the direction specified by the vector of induced field strength $$~ \mathbf{ \Gamma_{S }} $$. Gravitational induction regards to the matter of the hose too, so that if the hose is not attached, it will rotate synchronously together with its contents.

The differential approach
The theory of phenomena of gravitational induction can be explained also by means of differential quantities. If we assume that the flux of torsion field instead of (2) is determined by the expression $$~\Phi = \mathbf{\Omega}\cdot \mathbf{S} $$, where $$~ \mathbf{S}=\mathbf{n} S $$ is the vector of a certain small area, and torsion $$ ~ \mathbf {\Omega} $$ is homogeneous in this area, then the rate of change of the flux of torsion field can be written:

 * $$~ - \frac{\partial \Phi }{\partial t} = - \frac{\partial \mathbf{\Omega} }{\partial t} \cdot \mathbf{S}- \mathbf{\Omega} \frac{\partial \mathbf{S} }{\partial t}. $$

Substituting (1) and (6):

 * $$~ - \frac{\partial \Phi }{\partial t} = [\nabla \times \mathbf{\Gamma }] \cdot \mathbf{S} + [\mathbf{V} \times  \mathbf{\Omega}] \cdot \vec \ell =- \frac{\partial \Phi_{\Omega}}{\partial t} - \frac{\partial \Phi_{S}}{\partial t}.$$

From this, taking into account (3) in the general case follows:

 * $$~ - \frac{\partial \Phi_{\Omega}}{\partial t} = - \frac{\partial \mathbf{\Omega} }{\partial t} \cdot \mathbf{S} = \int \mathbf{\Gamma_{\Omega}}\vec d\ell, $$

 * $$~ - \frac{\partial \Phi_{S}}{\partial t} = - \mathbf{\Omega}\cdot \frac{\partial \mathbf{S} }{\partial t} = \int \mathbf{\Gamma_{S}}\vec d\ell,  $$

so in the case of changing of field torsion $$~\mathbf{\Omega}$$, or in the case of changing of vector of area $$~\mathbf{S} $$ when contour is intersecting the torsion field, the flux of torsion field is changing and gravitomotive force is creating. When the vector of area is changing gravitomotive force arises in the sides of the loop, which move at the speed $$~ \mathbf{V} $$ crossing lines of torsion field. The direction of the force acting on matter of the loop is determined by vector product $$~ \mathbf{V}  \times  \mathbf{\Omega}$$.

Application in physics
In covariant theory of gravitation (CTG) gravitational stress-energy tensor has the form:
 * $$~ U^{ik} = \frac{c^2_{g}} {4 \pi G }\left( -g^{im}\Phi_{mr}\Phi^{rk}+ \frac{1} {4} g^{ik}\Phi_{rm}\Phi^{mr}\right) $$,

where $$~c_g $$ – speed of gravity, $$~G $$ – gravitational constant, $$~ g^{ik} $$ – metric tensor, and gravitational tensor is calculated through gravitational four-potential $$~D_i = \left( \frac {\psi }{ c_{g}}, -\mathbf{D}\right) $$ as follows:
 * $$ ~\Phi_{ik}= \nabla _{i} D_{k}- \nabla_{k} D_{i} = \partial_{i} D_{k}-\partial_{k} D_{i} $$.

In weak field approximation, when the curvature of spacetime can be set almost equal to zero, the equations of CTG become close to equations of Lorentz-invariant theory of gravitation. This causes the wave equations for potentials of gravitational field ($$~\psi $$ – scalar potential, $$~ \mathbf{D} $$ – vector potential), and for field strength $$~ \mathbf{\Gamma } $$ and torsion (gravitomagnetic) field $$~ \mathbf{\Omega}$$. In stationary case, the wave equations of gravitational field become Poisson's equations of classical physics. In this approximation components of gravitational stress-energy tensor can be written explicitly:

 * $$~ U^{00} = -\frac {1}{8 \pi G} (\Gamma^2 + c^2_g \Omega^2)$$ – energy density of gravitational field,

 * $$~ U^{0k} = \frac {1}{c_g} H^k $$, where index $$~ k = 1 {,}2 {,} 3 $$ and  $$~ H^k  = \mathbf{H} = -\frac { c^2_g }{4 \pi G} [\mathbf{\Gamma } \times \mathbf{\Omega }  ]$$ is the vector of energy flux density of gravitational field or Heaviside vector.

Negative energy density and energy flux lead to unique property inherent to gravitational field. This property lies in the fact that the gravitational effect of induction between two masses under certain conditions is not damped, and may increase in amplitude, as in systems with positive feedback. For example, if two bodies are attracted by gravitation and rotate in the same direction, then the change of potential energy of gravitational field will transform into rotational energy of the bodies through gravitational induction. Thus, the bodies will rotate each other, increasing torsion field $$~\mathbf{\Omega }$$ around them.

Described mechanism is proposed to explain the nuclear forces between nucleons in atomic nuclei. With proper arrangement of nucleons in nucleus due to the gravitational induction nucleons spin up to a maximum angular velocity. The result is a repulsive force of nucleons spins (in gravitoelectromagnetism these forces are called gravitomagnetic forces) of such magnitude that are enough to compensate the force of attraction of the nucleons from the field of strong gravitation. In such evaluating of the forces acting in atomic nuclei, is used strong gravitational constant.


text:
Talk:Physics/Essays/Fedosin/Gravitational induction

New authors
As a result of search of new references were found two papers about gravitational induction, of Myron W. Evans, and C.J. de Matos, M. Tajmar. They are welcom to edit the article.

At the end of the article are references to Russian version, which was the first, and to Wikipedia article Gravitational induction as it's translation in to English. Fedosin 05:19, 26 April 2011 (UTC)


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User:Egm6341.spring-11.5.D/HW3

= Problem 1 - Find n st. $$Er^{T}\left(f_n^T\left(\frac{7 \pi }{8}\right)\right) < Er^{L}\left(f_5^L\left(\frac{7 \pi }{8}\right)\right)$$ = From (meeting 14 page 1)

Given
Taylor Series Expansion (meeting 3 page 2)

$$f_n^T(x)=f(x0)+\frac{(x-x0)^n}{n!} f^n(x0)$$

Lagringain Expansion (meeting 11 page 3)

$$f_n^L\left(x\right)=\sum _{i=0}^n f\left(x_i\right) l_{i,n}(x)$$

Where

$$l_{i,n}(x)= \prod _i^n \frac{x-xli}{xlj-xli}$$

$$ i\neq j$$ and $$xl\left(1,n\right)$$ is a set of n given points

Find
A value of n such that the error of the nth Taylor expansion is equal or less than the 5th Lagringain Expansion of the same funciton

$$\left|f\left(\frac{7 \pi }{8}\right)-f_n^T\left(\frac{7 \pi }{8}\right)\right|=\left|e_n^T\left(\frac{7 \pi }{8}\right)\right|\leq \left|f\left(\frac{7 \pi }{8}\right)-f_4^L\left(\frac{7 \pi }{8}\right)\right|=\left|e_4^L\left(\frac{7 \pi }{8}\right)\right|$$

$$f\left(x\right)=Sin\left(x\right)$$

Solution
 We solved this problem on our own

The 5th Lagringain Interpolation Functions of $$Sin\left(x\right) $$  was calculated using 5 evenly divided data points from  $$\displaystyle 0  $$ to  $$\displaystyle 2\pi $$

$$xl=\left( \begin{array}{ccccc} 0 & \frac{\pi }{4} & \frac{\pi }{2} & \frac{3 \pi }{4} & \pi \end{array} \right)$$

Resulting in

$$f\left(x_i\right)=\left( \begin{array}{ccccc} 0 & \frac{1}{\sqrt{2}} & 1 & \frac{1}{\sqrt{2}} & 0 \end{array} \right)$$

$$l_{i,5}(x)=\left( \begin{array}{c} \frac{32 (x-\pi ) \left(x-\frac{3 \pi }{4}\right) \left(x-\frac{\pi }{2}\right) \left(x-\frac{\pi }{4}\right)}{3 \pi ^4} \\ -\frac{128 x (x-\pi ) \left(x-\frac{3 \pi }{4}\right) \left(x-\frac{\pi }{2}\right)}{3 \pi ^4} \\ \frac{64 x (x-\pi ) \left(x-\frac{3 \pi }{4}\right) \left(x-\frac{\pi }{4}\right)}{\pi ^4} \\ -\frac{128 x (x-\pi ) \left(x-\frac{\pi }{2}\right) \left(x-\frac{\pi }{4}\right)}{3 \pi ^4} \\ \frac{32 x \left(x-\frac{3 \pi }{4}\right) \left(x-\frac{\pi }{2}\right) \left(x-\frac{\pi }{4}\right)}{3 \pi ^4} \end{array} \right)$$

Error from the Lagringain Interpolation evaluated at $$ x = \frac{7 \pi }{8}$$ is

$$Er^{L}=sin\left( \frac{7 \pi }{8}\right)-f_5^L\left(x\right)$$

Where $$f_5^L\left(x\right)$$ simplifies to be $$\frac{4 (\pi -x) x \left(16 \left(2 \sqrt{2}-3\right) x^2+16 \left(3-2 \sqrt{2}\right) \pi x+\left(8 \sqrt{2}-9\right) \pi ^2\right)}{3 \pi ^4}$$

Resulting in

$$\displaystyle Er^L= 0.00148078$$

To determine the nth order of Taylor series expansion necessary to be at least as accurate as the Lagringain expansion the Taylor series was calculated one order at a time and the resulting error term comprared. The generated series is presented here:

$$f_n^T\left(\frac{7 \pi }{8}\right)=$$

$$\left( \begin{array}{l} \cos \left(\frac{\pi }{8}\right) \\ \left(x-\frac{3 \pi }{8}\right) \sin \left(\frac{\pi }{8}\right)+\cos \left(\frac{\pi }{8}\right) \\ \left(x-\frac{3 \pi }{8}\right) \sin \left(\frac{\pi }{8}\right)-\frac{1}{2} \left(x-\frac{3 \pi }{8}\right)^2 \cos \left(\frac{\pi }{8}\right)+\cos \left(\frac{\pi }{8}\right) \\ -\frac{1}{6} \left(x-\frac{3 \pi }{8}\right)^3 \sin \left(\frac{\pi }{8}\right)+\left(x-\frac{3 \pi }{8}\right) \sin \left(\frac{\pi }{8}\right)-\frac{1}{2} \left(x-\frac{3 \pi }{8}\right)^2 \cos \left(\frac{\pi }{8}\right)+\cos \left(\frac{\pi }{8}\right) \\ -\frac{1}{6} \left(x-\frac{3 \pi }{8}\right)^3 \sin \left(\frac{\pi }{8}\right)+\left(x-\frac{3 \pi }{8}\right) \sin \left(\frac{\pi }{8}\right)+\frac{1}{24} \left(x-\frac{3 \pi }{8}\right)^4 \cos \left(\frac{\pi }{8}\right)-\frac{1}{2} \left(x-\frac{3 \pi }{8}\right)^2 \cos \left(\frac{\pi }{8}\right)+\cos \left(\frac{\pi }{8}\right) \\ \frac{1}{120} \left(x-\frac{3 \pi }{8}\right)^5 \sin \left(\frac{\pi }{8}\right)-\frac{1}{6} \left(x-\frac{3 \pi }{8}\right)^3 \sin \left(\frac{\pi }{8}\right)+\left(x-\frac{3 \pi }{8}\right) \sin \left(\frac{\pi }{8}\right)+\frac{1}{24} \left(x-\frac{3 \pi }{8}\right)^4 \cos \left(\frac{\pi }{8}\right)-\frac{1}{2} \left(x-\frac{3 \pi }{8}\right)^2 \cos \left(\frac{\pi }{8}\right)+\cos \left(\frac{\pi }{8}\right) \\ \frac{1}{120} \left(x-\frac{3 \pi }{8}\right)^5 \sin \left(\frac{\pi }{8}\right)-\frac{1}{6} \left(x-\frac{3 \pi }{8}\right)^3 \sin \left(\frac{\pi }{8}\right)+\left(x-\frac{3 \pi }{8}\right) \sin \left(\frac{\pi }{8}\right)-\frac{1}{720} \left(x-\frac{3 \pi }{8}\right)^6 \cos \left(\frac{\pi }{8}\right)+\frac{1}{24} \left(x-\frac{3 \pi }{8}\right)^4 \cos \left(\frac{\pi }{8}\right)-\frac{1}{2} \left(x-\frac{3 \pi }{8}\right)^2 \cos \left(\frac{\pi }{8}\right)+\cos \left(\frac{\pi }{8}\right) \end{array} \right)$$

The resulting errors from the above Taylor series expansions evaluated at $$ x = \frac{7 \pi }{8}$$ is

$$Er^{T}=sin\left( \frac{7 \pi }{8}\right)-f_n^T\left(x\right)= \left( \begin{array}{c} 0.541196 \\ 1.14231 \\ 0.00252314 \\ 0.244677 \\ 0.0103165 \\ 0.0201805 \\ 0.000905156 \end{array} \right)$$

$$\therefore Er^{T}\left(f_7^T\left(\frac{7 \pi }{8}\right)\right) < Er^{L}\left(f_5^L\left(\frac{7 \pi }{8}\right)\right)$$

n=7

Author and proof-reader
[Author]J Davis 19:15, 11 February 2011 (UTC)

[Proof-reader]

= Problem 3 = From (meeting 15 page 1)

Given
= Problem 4 - Area of a Bifolium = From (meeting 15 page 2)

Given
The bifolium: $$\displaystyle r(t)=2sin(t)cos^{2}(t)$$, where $$\displaystyle t=[0,\pi]$$.

Find
1. Do literature search to find history and application, if any, of this classic curve. 2. Find the area of one folium,with an accuracy of $$10^{-6}$$ by:
 * 2.1 Composite trapezoidal
 * 2.2 Composite Simpson
 * 2.3 Area of triangles

Solution
''' We solved this problem on our own. '''

1. Lit research 2. Area of one folium:

 * 2.1 Composite Trapezoidal
 * 2.2 Composite Simpson
 * 2.3 Area of triangles

Author and proof-reader
[Author]

[Proof-reader]

title: User:Egm6341.spring-11.5.D/HW3


text:
Sociolinguistics/Introduction

Language and Society
In our everyday lives, we are engage in spontaneous social acts that are interconnected with the activities of those around us without taking notice. These well-established practices are considered aspects of the social norm derived from the culture in which one habituates. The subtleness and intricacy of these spontaneous joint activities is strongly reflected not only in our social acts but also in the way language is used within social groups. Compared to cognitive research, which largely sees language as an individual process, and to social science research, which sees language as a social process, it has been argued that language use embodies both individual and social processes (Clark, 1996, p. 1) When considering what people are talking about in a conversation and what they are tying to achieve by conversing, language can be seen as being used as a form of joint action (Clark, 1996, p.1) Language is more than the sum of the speaker and the listener, but the joint action that emerges when they perform their individual actions in coordination (Clark, 1996, p. 1). It can be said that everything we do and say as humans is rooted in the information we have about our perceptions, emotions, interests, activities, and surroundings (Clark, 1996, p. 92). In a given culture or subgroup, common ground, such as mutual knowledge, mutual beliefs, and mutual expectations, shift to accommodate the circumstances and the parties with whom we are conversing. Language comes to exist in conversational layers that can shift and enable the establishment of new common grounds (Clark, 1996, p. 92). In this chapter, the ways in which language functions within society is going to be thoroughly examined. This chapter will highlight the relationships between the way different subgroups think and how this determines the words used in their languages. To further understand how speech shifts as a function of one’s social situation, this chapter will look at the use of slang, sexual talk, and taboo words in different contexts.

What is Slang?
Slang is an informal set of words and phrases that are used to reinforce or establish one’s identity within a social group or with a trend in society (Eble, 1996, p. 11). Slang is an important aspect of language to touch on in this chapter because it is vocabulary that embodies the social functions of language. Slang seems to be as old as language itself given that it is part of ordinary interactions in all languages in which communities are large and diverse enough to have identifiable subgroups (Eble, 1996, p.11). Because of slang’s social and psychologically complex vocabulary, four identifying criteria have been proposed (Eble, 1996, p. 11):
 * 1) The presence of slang will, at least momentarily, lower the formality of serious         speech.
 * 2) The use of slang implies the user’s special familiarity with a class of people who also have special familiarity and use the term.
 * 3) The slang term is a taboo term in discourse with people of higher social status or greater responsibility.
 * 4) Slang is used as a replacement for a well-known conventional synonym to either protect the user from the discomfort caused by the conventional term or to protect the used from the bother of elaboration.

According to authors Bethany Dumas and Jonathan Lighter, when at least two of these defining criteria are met, a linguistically sensitive audience will react to the word or phrase in some way (Eble, 1996, p.12). This immeasurable reaction is the fundamental identifying characteristic of slang (Eble, 1996, p.12). For instance, take the phrase, “that guy was a jerk for cutting me off before the intersection!” According to the criteria, jerk would qualify as slang because it satisfies criteria 1, 2, and 4.

Why Do People Use Slang?
The existence of certain slang words and phrases may in fact seem to be part of a short-lived pattern of overused terms being reinvented with new meanings when mainstream culture deems appropriate. The vocabulary of particular subgroups such as, college students, can actually illustrate this innovative characteristic of slang. For example, Dead Soldier, a military slang term that has been around since the eighteenth century when it meant ‘empty bottle’, re-emerged in 1987 at University of North Carolina with a more modern definition of ‘empty beer can’ (Eble, 1996, p. 15).

Another important identifying characteristic of slang is its group-identifying function. Slang is often used when the user wants to be accepted by a select social group (Eble, 1996, p. 119). A strong sense of belonging can stem from the sharing and maintaining of an ever-changing vocabulary that undoubtedly serves to include and exclude members from social groups (Eble, 1996, p. 119). Like keeping up with fashion trends, slang must be new and appealing, and must be effective enough to gain group acceptance (Eble, 1996, p. 120). Slang’s function within subgroups is to enhance the feeling of internal solidarity and the shared vocabulary helps specific groups such as sports teams to work together in a stressful environment (Eble, 1996, p. 123). In the fall of 1990, members of the cross-country track team at UNC were using terms like rigging, which stood for the tightening of muscles at the end of a tough race, and doing carbo-loading, which stood for drinking beer after a race (Eble, 1996, p. 122).

Intergenerational Differences in Language and Slang Use
In prior linguistic research, age has been considered the principal correlate of language change among speakers (Barbieri, 2008). An important factor to consider when studying slang is intergenerational differences in language use for instance, how language varies across the life span. Taking into account the fundamentally different nature of linguistic variation in syntactic and lexical levels amongst individuals, a linguistic analytical technique suited to the exploration of major lexico-grammatical differences is key word analysis (Barbieri, 2008). This technique is a powerful statistical approach that allows the unveiling of important lexical differences within a collection of spoken material, thus neglecting potential syntactic  differences (Barbieri, 2008). To explore age-based linguistic variation in spontaneous conversation, the following study employed key word analysis on a large variety of casual conversation in American English (Barbieri, 2008).

The subjects in this study were of two age groups: youths aged 15-25 and adults aged 35-60. In terms of the key word analysis, “key word” is defined as a word that occurs with unusual or outstanding frequency (Barbieri, 2008). For example, the word like is a very frequent key word among young speakers because the rate of occurrence of its use in young speakers is significantly higher than in older speakers (approximately 1,749 to 1,736 occurrences per 100,000 words respectively) (Barbieri, 2008). One of the most significant patterns that emerged from the key word analysis is younger speakers’ frequent use of slang words, ranging from taboo or swear words to non-derogatory slang words (Barbieri, 2008). Key words such as man, dude, cool, guy, pissed, bucks, screwed, sucks, dope, booze, and bummer indicated that non-derogatory slang is common in American youth’s casual interaction (Barbieri, 2008). Key words man, dude, and cool were the three most commonly used non-derogatory slang words in younger speakers occurring among the top twenty key words (see table 1). Within the analysis of the use of key words, for the most part, older speakers’ patterns of speech were characterized as a departure from younger speakers’ norms in the fact that they had much lower use of attitudinal adjectives and lower use of slang and swear words (Barbieri, 2008). This research also indicated that the main cutoff in age-based differentiation is between the mid-twenties and that differences between the age groups above 35 years tend to become smaller (Barbieri, 2008). This study suggests that, in terms of slang use, slang is a more prominent feature of the language of the youth than of adults.

Table 1: Sample key slang words output (3 of the first 25 key words from the younger corpus (Barbieri, 2008).

In terms of slang use in social contexts, the current study found that cool was the most frequent slang term used amongst the youth and coincidentally, the most pervasive term of approval used by speakers born in the 1980's (Barbieri, 2008). Barbieri (2008) goes on to argue that cool is a prime example of basic slang which differs from most slang terms by two unique traits: it is pervasive, being used to express approval and to align the speaker with an attitude or set of values characterizing their generation and it endures over long periods of time.

Sexual Terminology
Sexual terminology is learned at a young age through interactions with our peers (Jay, 2000, p. 85). Parental inhibition and punishment of the use of sexual references teaches children that sexual words are powerful (Jay, 2000, p. 85). In a study done on the topic of how children learn to talk about sex, parents discussed their difficulties and solutions with their children’s use of sexual slang (Jay, 2000, p. 124). The findings of this study revealed that learning about sexual terminology is a process of socialization (Jay, 2000, p. 125). From this study, we learn that a double standard in sex talk is obvious; parents will speak to their friends differently than to their children and fathers will speak differently with female friends than male friends (Jay, 2000, p. 125). Due to differences in socialization, daughters and sons of the same household will even acquire different sexual vocabularies (Jay, 2000, p.125).

As we develop linguistically and sexually, sex talk becomes more dependent on who is listening rather than the fear of parental negation and omission that comes with sex talk (Jay, 2000, p. 86). Sexual talk is an interesting topic because it is one that holds strong personal relevance yet maintains a socially unaccepted stigma in formal contexts. The following research on sexual talk will illustrate the differences in the use of sexual language in interpersonal and social contexts.

The Four Systems of Sexual Language
As we develop psychologically and as our social contexts shift, the sexual lexicon modifies accordingly (Jay, 2000, p.127). There are four different systems for sexual talk:

 * 1) child language – taught to children by parents, allowing them to describe body parts and functions without using slang or medical terms (e.g., wienie, tushy, poo-poo, bum)
 * 2) street language – used by peers, to indicate in-group identification and often to impress other (e.g., screw, make out)
 * 3) euphemisms – used to avoid using explicit terms for sex in any conversation by adults (e.g. making love, sleeping together)
 * 4) medical-scientific language – a technical and concrete language of sexual terms learned in school and from books (e.g., penis, vagina, defecate, coitus) (Jay, 2000, p. 127)

According to this set of systems, childhood terms eventually evolve into more offensive terms or euphemisms. The medical-scientific language system is used in more formal exchanges and settings.

Sexual Talk in Different Interpersonal Contexts
Given that sexual talk is highly dependent on one’s surroundings, it is not surprising that other factors play a role on how one uses sexual lexicon. Many studies have been done that look at the relationship between context and sexual terms, which highlight how the overt expression of sexual identity highly depends on social contexts. Much research has focused on the different use of sexual vocabulary amongst genders, showing that males make greater use of sexual slang than females (Wells, 1989). Given the fact that different cultures and sub-groups tend to maintain their own in-group slang, it is appropriate to consider the impact of sexual orientation on the use of sexual vocabulary. In a study investigating the use of sexual language amongst genders in different interpersonal contexts based on sexual orientation, results indicated that differences in sexual vocabulary are significant (Wells, 1989). This study used a sample of 440 heterosexual and homosexual undergraduate male and female students from the University of Northern Iowa with a mean age of 22 (Wells, 1989). A questionnaire was given to the participants asking them to write the word or phrase they would use for male genitalia, female genitalia, and sexual intercourse when with a spouse or lover, mixed-company, in a same-sex conversation, and a conversation with parents (Wells, 1989). The results shown in the following table demonstrate that lesbians used more female-oriented terms for male genitalia, love making, and oral sexual contact than did heterosexual males, homosexual males, or heterosexual females (Wells, 1989). Homosexual males used slang more often with a spouse or lover than any other group of participants (Wells, 1989). Further, heterosexual males made the largest change in language use when shifting from the primary use of slang in a same-sex context to more formal terms or euphemisms when with a spouse or lover in all sexual concepts (Wells, 1989). This study demonstrates that sexual orientation is yet another dimension that affects the use of sexual language.

Table 2. Total Language Use for Social Context by Gender and Sexual Orientation in Percentages (Wells, 1989).

Table 3. Total Language Use for Sexual Context by Gender and Sexual Orientation in Percentages (Wells, 1989).

A Relevant Aspect of Language
It is important to note that when scholars disregard swearing as an irrelevant aspect of language, we are left with a false understanding of verbal communication (Jay, 2009). In the past, psycholinguists strongly held Noam Chomsky’s structuralist theory of language, which did not touch on the idea of emotional language at all (Jay, 2009). For a more complete understanding of language, conventional interpretations of language must expand to include the communication of emotional information, which is spoken and understood through word choice, emphasis, and speech volume (Jay, 2009). It has been argued that the emotional aspects of words are stored in the brain along with the word’s semantic and syntactic properties (Jay, 2009). Once a semantic network with lexical emotional information develops, emotion can be used as a basis for lexical access when swearing (Jay, 2009). This means that once emotional words are processed with information regarding their level of arousal, offensiveness, and appropriateness, the use can choose to use an offensive or inoffensive word (Jay, 2009). Given some background information on how taboo words are processed and expelled, the next section will discuss the origin of taboo words, why they exit, and what motivates people to use them.

What Are Taboo Words and Why Do They Exist?
According to the American Heritage Dictionary of the English Language, a taboo is a “ban or inhibition resulting from social custom or aversion” (Jay, 2009). Taboo words, or swear words, are deemed offensive at an institutional and social level (Jay, 2009). Taboo words acquire this offensive status and arousing effects by aversive classical conditioning (Jay, 2009). As children, we are taught that swear words are bad and when they are used, punishment is often the result. Hence, swear words are leaned through the socialization of speech.

History of Taboo Words
The use of taboo words in language goes back to ancient history. Religious authorities have prohibited profanity and blasphemy since biblical times (Jay, 2009). More recently, in 1966, ethnic slurs such as Redskin were being used; a term coined by the first British settlers to describe the Native American Indians (Allen, 1990, p. 3). As other ethnic groups arrived and the country became more diverse, the name-calling increased exponentially (Allen, 1990, p.3). Many taboo terms originated from great events in American history such as waves of immigration, urbanization, wars, and depressions (Allen, 1990, p.4). Today, taboos in English tend to be primarily based on sexual, profane, and blasphemous references and new terms are constantly emerging, especially in slang (Jay, 2009).

Taboo Words and Social Context
As with the use of slang and sexual talk, the use and interpretation of taboo words depends on contextual variables. For instance, in the previously discussed college study where students were asked to list which sexual terms they would use in different contexts (i.e. with a partner, lover, parent, or mixed company), technical terms were said to be more likely used with mixed crowd and with parents whereas sexual obscenities were used with same-sex crowds and with a partner or lover (Wells, 1989). Ultimately, the offensiveness and appropriateness of swear words are determined by the relationship between those conversing as well as the social setting (Jay, 2009). This sense of offensiveness is also determined by age and level of maturity (Jay, 2009). For instance, a young boy would find terms such as baby and wimp to be more offensive than adults (Jay, 2009). The task at hand for the social speaker is to determine what words are appropriate in a given social setting.

Conclusion
This chapter identified the ways in which language functions within society through examining the means by which different subgroups’ unique thought processes determine the words used in their language. To understand speech as a function of one’s social situation, this chapter discussed how the use of slang, sexual talk, and taboo words are dependent on social cues in their immediate or enduring social state. It was noted that slang term use is somewhat dependent on mainstream culture (Eble 1996), its means of enabling the identification and acceptance by social groups (Eble 1996), and its function of aligning the speaker with a set of values characterized by their generation (Barbieri 2008). This chapter also revealed that sexual talk is dependent on who is listening (Jay, 2000) and on one's gender, sexual orientation and interpersonal context (Well, 1989). Lastly, this chapter explained that offensiveness and appropriateness of taboo words are determined by the relationship of those who are conversing and on the social setting of the speaker (Jay, 2009).

Learning Exercise Part 1
The following link is of a video depicting two instances in which people speak differently depending on their interpersonal context. In the first scene, a mother and daughter are engaging in a conversation about sexual activity. The second scenario is of the daughter and a friend engaging in a conversation about sexual activity while using slang terms. Please watch the video from this link and then answer the following questions.Learning Exercise Video

Questions
1. Based on information from this chapter, does it seem fitting that the mother used the formal term "sexual intercourse" when discussing the subject of sexual activity with her daughter as opposed to a more casual term like, "sex"? Why or why not?

2. How many slang terms were used in the second scenario? What were they and how would you define them?

3. Based on information from this chapter, does it seem fitting that the friends were using many slang terms when conversing? Why?

4. When using the slang term, "cool", which of Eble's (1996) identifying criteria are met, if any?

Learning Exercise Part 2- Essay Question
Please watch the following link depicting the use of taboo words in different scenarios and then answer the following essay question. Learning Exercise Part 2- Taboo Words

As discussed in the chapter, words acquire offensive status and arousing effects by aversive classical conditioning (Jay, 2009). From a young age, children are taught that swear words are "bad" and are often punished as a consequence of their use. Through the socialization of speech, children recognize the negative connotation of swear words, enabling less than favourable associations to the use of taboo words. As we grow into adolescence and adulthood however, as you can see from the video, using taboo words is highly dependent on one's social context. While swearing is forbidden amongst parent and child in the video's fictional household, taboo word use is not deemed offensive when used casually between a couple having a conversation about a hard day at work. Why is it considered wrong to use vulgarity in different social contexts? While taboo words seem to lose their intrinsically unethical status somewhere between childhood to adulthood, they are still often deemed offensive at an institutional and social level (Jay, 2009). Yet, one must consider why it is that it can be far more hurtful to speak a sentence composed of a handful of every day words than it can with any one curse word, or even a combination of cruse words, yet taboo words maintain this offensive status? Through social pressures such as shame, shunning, and encouragement, some behaviors are deemed acceptable while others are not; among these are using highly informal and inappropriate language in many settings. Upon reading this chapter and watching the video for learning exercise (part 2), please discuss your opinion on the topic of taboo word use. In your response, consider ethics as well as the important aspect of language use as a function of one's social context.

Learning Exercise Part 3
Test your knowledge on slang, jargon, and taboo word use from this chapter by filling out the crossword puzzle below!

Across 1. Taboo words are, in fact, a _______ aspect of language. 4. According to Clark (1996), what kind of action emerges from the social coordination of speakers during a conversation? 7. Aside from Eble’s (1996) list of criteria, another important identifying characteristic of slang is its _______-________ function. 11. Sexual ________ has an effect on language use amongst genders in different interpersonal contexts. 13. According to Well 1989, heterosexual _______ make the largest shift in language use when changing from the primary use of slang in a same-sex context to more formal terms when with a spouse or lover. 15. Ultimately, the offensiveness and appropriateness of taboo words are determined by the relationship between those conversing as well as the social ________. 16. How many slang identifying criteria are set out by Eble (1996)? 17. As we develop, sex talk becomes more dependent on who is ______ rather than the fear of parental negation and omission that comes with sex talk. 18. The third system of sexual language described by Jay (2000). 19. Taboo words acquire an offensive status and arousing effects by aversive ________ conditioning.

Down 2. This technique is a powerful statistical approach that allows the unveiling of important lexical differences within a collection of spoken material, thus neglecting potential syntactic differences. 3. The word, _____, is a prime example of basic slang which differs from most slang terms. 5. According to Barbeiri, what has been considered the principal correlate of language change among speakers? 6. Slang is the _______ that embodies the social functions of language. 8. Among the identifying criteria for slang set out by Eble (1996), one implies the need for a speaker’s special _____ with a class of people who also use the term. 9. It has been argued that language use embodies both individual and ______ processes. 10. ‘Dead Soldier’, a military slang term that has been around since the eighteenth century when it meant ‘empty bottle’, re-emerged in 1987 at University of North Carolina with a more modern definition of ‘empty _____ can’. 12. Much like _______, one must keep up with slang to ensure the use of new and appealing terms that are effective enough to gain group acceptance. 14. Parental inhibition and _______ of the use of sexual references teaches children that sexual words are powerful.

Part 1 Answers
Question 1: Yes because the college student experiment in Wells (1989) explains that technical terms are more likely to be used with parents whereas sexual obscenities are more likely to be used among same-sex crowds and with a partner or lover (Wells, 1989).

Question 2: Three ("vibing"= enjoying each other's company, "cool"= acting in a relaxed, fun, aspiring manner, "it"= used in this case to mean "sexual intercourse")

Question 3: Yes. The group-identifying function of slang makes its an important characteristic of communication that enables and encourages acceptance among members of select social groups (Eble, 1996). The girls in the video were likely using many slang terms when conversing due to the strong sense of belonging that stems from keeping up with the latest trends in language.

Question 4: All four of Eble's (1996) identifying criteria are met: The presence of slang will, at least momentarily, lower the formality of serious speech; The use of slang implies the user’s special familiarity with a class of people who also have special familiarity and use the term; The slang term is a taboo term in discourse with people of higher social status or greater responsibility; Slang is used is used as a replacement for a well-known conventional synonym to either protect the user from the discomfort caused by the conventional term or to protect the used from the bother of elaboration.

Part 3 Answers

 * 1) social
 * 2) joint action
 * 3) vocabulary
 * 4) four
 * 5) familiarity
 * 6) beer
 * 7) group-identifying
 * 8) fashion
 * 9) age
 * 10) linguistic analytical
 * 11) cool
 * 12) punishment
 * 13) listening
 * 14) euphemisms
 * 15) orientation
 * 16) males
 * 17) relevant
 * 18) classical
 * 19) setting

title: Sociolinguistics/Introduction