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Physics/Essays/Fedosin/Velocity circulation quantum

A velocity circulation quantum (VCQ), or quantum vortex, is an auxiliary physical quantity which can be used to calculate fictitious magnetic charge and fictitious torsion mass, as well as the magnetic flux quantum and strong gravitational torsion flux quantum. The value of the quantum vortex depends on the matter level according to Infinite Hierarchical Nesting of Matter.

Definition
The velocity circulation quantum is calculated by the formula:
 * $$ \sigma_x = \omega_x S_x = n \frac{h_x}{2m_x}, \ $$

where $$\omega_x $$ is the angular frequency of oscillation in system, $$S_x $$ is the effective surface area, $$n $$ is the quantum number which can be integer or fractional in the general case, $$h_x $$ is an action constant of the matter level, $$m_x $$ is a mass quantum of the matter level.

There are not very successful attempts to link $$m_x $$ with definite scale (Planck scale, Stoney scale, Natural scale, etc).

History
The first VCQ was proposed in the early 50-th for the quantum superfluids in the general form by R. Feynman and Abrikosov in the form of circulation of velocity $$\mathbf{v} $$ along the closed loop:
 * $$ \sigma = \oint_{L} \mathbf{v}\cdot\,d\mathbf{l} = n\frac{h}{m_e}, \ $$

where $$h $$ is the Planck constant as the action constant at the atomic level of matter, $$m_e $$ is the electron mass.

If $$v=const $$ then circulation of velocity is:
 * $$ \sigma = 2 \pi r v = 2 \pi r^2 \omega = 2S \omega = 2 \sigma_x . $$

The further developments of this approach was made by Yakymakha (1994) for inversion layers in MOSFETs. The velocity circulation quantum is important in gravitational model of strong interaction by Fedosin, in which $$ \sigma$$ is proportional to strong gravitational torsion flux quantum. In particular nucleons equilibrium in nucleus depends on the equilibrium of strong gravitation attraction forces between nucleons and repulsive forces due to repulsion of the nucleons torsion fluxes.

Phase shifts
In the gravitational field with the 4-potential $$ D_\mu $$ and in electromagnetic field with the 4-potential $$ A_\mu $$ the electron acquires phase shifts according to formulas:

 * $$~ \theta_1 - \theta_2 = \frac { m_e }{\hbar } \int_{1}^{2} D_\mu \, dx^\mu, \qquad \theta_1 - \theta_2 = \frac {e}{\hbar } \int_{1}^{2} A_\mu \, dx^\mu , $$

where $$~ dx^\mu = ( cdt \,, \, d \mathbf{r} ) $$ is the displacement 4-vector, $$e $$ is the elementary charge, $$\hbar $$ is the Dirac constant.

The phase shift, obtained due to the electromagnetic 4-potential $$~ A_\mu = ( \varphi/c \,, \, -\mathbf{A} ) $$, is proved by the Aharonov-Bohm effect, when electric scalar potential $$~ \varphi $$ , electric field strength $$~ \mathbf{E}$$ and magnetic field $$~ \mathbf{B}$$ are equal to zero, and there is only vector potential $$~ \mathbf{A}$$ in the system. In the case with vector potentials of gravitational $$~ \mathbf{D}$$ and electromagnetic $$~ \mathbf{A}$$ fields phase shifts are:

 * $$~ \theta_1 - \theta_2 = -\frac { m_e }{\hbar } \int_{1}^{2} \mathbf{D} \cdot \, d \mathbf{r}, \qquad \theta_1 - \theta_2 = -\frac {e}{\hbar } \int_{1}^{2} \mathbf{A} \cdot \, d \mathbf{r}. $$

Since the gravitational torsion field $$ ~\mathbf{\Omega }= \nabla \times \mathbf{D} $$ and the magnetic field $$ ~ \mathbf{B}= \nabla \times \mathbf{A} $$ then using Stokes' theorem we have:

 * $$~ \Phi = \int \mathbf{B} \cdot d\mathbf{S}= \int \nabla \times \mathbf{A} \cdot d\mathbf{S}= \oint_{L} \mathbf{A} \cdot \, d \mathbf{l} = \frac { \hbar }{ e } \Delta \theta. $$

 * $$~ \Phi_g = \int \mathbf{\Omega } \cdot d\mathbf{S}= \int \nabla \times \mathbf{D} \cdot d\mathbf{S}= \oint_{L} \mathbf{D} \cdot \, d \mathbf{l} = \frac { \hbar }{ m_e } \Delta \theta. $$

If circulation of electromagnetic vector potential results in change of phase $$ \Delta \theta = 2\pi $$ then magnetic flux is: $$~ \Phi =\frac { h }{ e }$$. The same for gravitational vector potential and gravitational torsion flux gives: $$~ \Phi_g =\frac { h }{ m_e }$$.

In superconductivity the electrons form pairs with the charge of a pair $$ 2 e $$ so magnetic flux in the superconducting loop or a hole in a bulk superconductor is quantized. The single magnetic flux quantum in the case is $$~ \Phi =\frac { h }{ 2 e }= \Phi_0 $$. Using of gravitational vector potential instead of electromagnetic vector potential in experiments gives single gravitational torsion flux quantum $$~ \Phi_0g =\frac { h }{ 2 m_e } $$ for electron superconductivity.

Bohr atom simple model
The Bohr radius is the averaged electron radius for the first energy level $$(n =1)$$ :
 * $$a_B = \frac{\lambda_0}{2\pi \alpha}, \ $$

where $$\alpha $$ is the fine structure constant, $$\lambda_0 = \frac{h}{m_e c} $$ is the Compton wavelength of electron, and $$c $$ is the speed of light.

The angular frequency of electron rotation in atom is:
 * $$\omega_B = \frac{c \alpha }{ a_B }. \ $$

The flat surface area is:
 * $$S_B = \pi a_B^2. \ $$

Bohr velocity circulation quantum is:
 * $$\sigma_e = \omega_B S_B = \frac {c \lambda_0}{2} = \frac{h}{2m_e}. \ $$

The electron magnetic flux for the first energy level is:
 * $$ \Phi_e = B S_B =\frac { \mu_0 e }{4 \pi a_B }\sigma_e =

\frac {\alpha^2 m_e}{e}\sigma_e = \alpha^2 \Phi_0, \ $$ where $$ B \ $$ is the magnetic field in electron disc, $$\mu_0\ $$ is the vacuum permeability.

The strong gravitational electron torsion flux for the first energy level is:
 * $$ \Phi_{\Omega } = \Omega S_B = \frac { \mu_\Gamma m_e }{4 \pi a_B }\sigma_e = \frac { \Gamma m_e }{c^2 a_B }\sigma_e  = \frac { \Gamma h }{2c^2 a_B }= \frac { \pi  \alpha \Gamma m_e }{c }= \alpha^2 \Phi_\Gamma, \ $$

where $$ \Omega \ $$ is the gravitational torsion field of strong gravitation in electron disc, $$ \mu_\Gamma = \frac {4 \pi \Gamma }{ c^2 } $$ is the gravitomagnetic gravitational constant of selfconsistent gravitational constants in the field of strong gravitation, $$\Gamma = \frac {e^2}{4 \pi \varepsilon_0 m_p m_e}= \frac { \alpha \hbar c}{m_p m_e}$$ is the strong gravitational constant, $$ \varepsilon_0 $$ is the electric constant, $$ \Phi_\Gamma = \frac{h}{2 m_p} $$ is the strong gravitational torsion flux quantum, which is related to proton with its mass $$ m_p $$.

Inversion layer "flat atom"
In experiments with inversion layers in MOSFETs there were found:

Inversion layer surface area is:
 * $$S_0 = 1.4196\cdot 10^{-7}\ $$ m2.

Inversion layer resonance frequency is:
 * $$\omega_0 = 5123.9 \ $$ rad/s.

Resonator electromagnetic reactive parameters are:
 * $$C_0 = \frac{1}{\omega_0 Z_0} = 5.1805\cdot 10^{-7} \ $$ F,
 * $$L_0 = \frac{Z_0}{\omega_0} = 7.3524\cdot 10^{-2} \ $$ H,

where $$ Z_0 = 2\alpha\cdot h/e^2 = \mu_0 c = \frac{1}{\varepsilon_0 c } = \sqrt {\frac{\mu_0 }{\varepsilon_0 }}$$ is the impedance of free space.

Yakymakha velocity circulation quantum is:
 * $$\omega_0 S_0 = \frac{h}{m_e}= 2 \sigma_e . \ $$

Electromagnetic quantum resonator
For the electromagnetic wave which runs in a circle with the Bohr radius in the electron matter the lowest resonance frequency is:
 * $$ \omega_e = \frac { 2 \pi }{T }= \frac {c}{a_B} = \frac {\omega_B}{\alpha }= \frac {1}{\sqrt {LC}}, \ $$

where $$ ~T $$ is the wave period, $$ ~L $$ is the Bohr atom electric quantum inductance, $$ ~C $$ is the Bohr atom electric quantum capacitance.

We can suppose that the wave impedance equals to impedance of free space:
 * $$ Z = \sqrt { \frac {L} {C}}= Z_0 . \ $$

With regard to these two equations the inductance and capacitance are as follows:
 * $$ L = \frac { Z_0} {\omega_e }= \mu_0  a_B. \ $$
 * $$ C = \frac { 1} {\omega_e Z_0}= \varepsilon_0  a_B. \ $$

On the other hand in Bohr atom the electron in the form of a flat disc has density of states, the inductance and capacitance according to definition:
 * $$ D_B= \frac {m_e}{\pi \hbar^2}. \ $$
 * $$ L = \phi^2_R  D_B S_B.  \ $$
 * $$ C = q^2_R  D_B S_B.  \ $$

From these equations the induced magnetic flux $$ \phi_R $$ and the induced charge $$q_R  $$ can be found:
 * $$ \phi_R = \frac {\alpha h}{\sqrt \pi e}= \frac {2 \alpha m_e}{\sqrt \pi e} \sigma_e = \frac {2\alpha}{\sqrt \pi } \Phi_0 =\frac {2 }{\sqrt \pi \alpha } \Phi_e,  $$

 * $$ q_R = \frac {e}{2\sqrt \pi }.$$

As it can be seen the induced magnetic flux $$ \phi_R $$ related to the velocity circulation quantum $$ \sigma_e $$ of the electron disc and exceed the electron magnetic flux $$ \Phi_e $$ of Bohr atom.

For the quantum electromagnetic resonator approach we can derive the following maximal values for the energies stored on capacitance and inductance:
 * $$W_C = \frac{q_R^2}{2C} = \frac{\hbar \omega_B }{2} = \frac{\alpha \hbar \omega_e }{2}, \ $$

 * $$W_L = \frac{\phi_R^2}{2L} = W_C . \ $$

The energy looks like the energy of quantum oscillator in zero state with the frequency $$\omega_B\ $$. But the real wave frequency is $$\omega_e\ $$. So the action constant for the matter inside the electron with such wave is $$ \alpha \hbar << \hbar $$. The same follows from the Infinite Hierarchical Nesting of Matter where different action constants connected to different matter levels.

Gravitational quantum resonator
The gravitational quantum capacitance for Bohr atom is:
 * $$C_\Gamma = m^2_R  D_B S_B = \varepsilon _\Gamma a_B, \  $$

where $$ ~ m_R = \frac { \sqrt {m_p m_e}}{2 \sqrt \pi } $$ is the induced mass, $$ \varepsilon _\Gamma = \frac {1 }{4 \pi \Gamma } $$ is the gravitoelectric gravitational constant of selfconsistent gravitational constants in the field of strong gravitation.

The gravitational quantum inductance is:
 * $$ L_\Gamma = \phi_\Gamma ^2 D_B S_B = \mu _\Gamma a_B, \  $$

where the induced gravitational torsion flux is:
 * $$ \phi_\Gamma = \frac {\alpha h }{\sqrt {\pi m_p m_e } }= \frac {2 \alpha \sqrt{m_e} }{ \sqrt {\pi m_p } } \sigma_e = \frac {2 \alpha \sqrt{m_p} }{ \sqrt {\pi m_e } } \Phi_\Gamma = \frac {2 \sqrt{m_p} }{ \alpha \sqrt {\pi m_e } } \Phi_\Omega .$$

The gravitational wave impedance is:
 * $$ \rho_\Gamma = \sqrt {\frac{ L_\Gamma }{ C_\Gamma }}= \sqrt{\frac {\mu _\Gamma }{\varepsilon _\Gamma }} = \frac{4\pi \Gamma }{c} = 6.346\cdot 10^{21} \mathrm {m^2/(s\cdot kg)}. \ $$

The resonance frequency of gravitational oscillation is:
 * $$\omega_\Gamma = \frac{1}{\sqrt{L_\Gamma C_\Gamma }} = \frac{ c}{a_B} = \omega_e = \frac {\omega_B}{\alpha }. \ $$

For the quantum gravitational resonator approach we can derive the following maximal values for the energies stored on capacitance and inductance:
 * $$W_C = \frac{m_R^2}{2 C_\Gamma } = \frac{\hbar \omega_B }{2} = \frac{\alpha \hbar \omega_e }{2}= W_B, \ $$
 * $$W_L = \frac{ \phi_\Gamma ^2}{2 L_\Gamma } = W_B .\ $$

The energy $$ W_B \ $$ of the wave of strong gravitation in the electron matter has the same value as in case of rotating electromagnetic wave, and can be associated with the mass:
 * $$m_{Bmin} = \frac{W_B}{c^2} = \frac{\hbar \omega_B}{2 c^2} = \frac{\alpha^2}{2}m_e << m_e, \ $$

which could be named as the minimal mass-energy of the quantum resonator.

One way to explain the minimal mass-energy $$m_{Bmin}$$ is the supposition that Planck constant can be used at all matter levels including the level of star. As a result of the approach one should introduce different scales such as Planck scale, Stoney scale, Natural scale, with the proper masses and lengths. But such proper masses do not relate with the real particles.

Another way recognizes the similarity of matter levels and SPФ symmetry as the principles of matter structure where the action constants depend on the matter levels. For example there is the stellar Planck constant at the star level that describes star systems without any auxiliary mass and scales.

Neutron star
The stellar Planck constant $$h_s = 3.5 \cdot 10^{42}$$ J• s can be found with the help of Planck constant and coefficients of similarity on mass, speed and size :
 * $$h_s = h \Phi S P .$$

For the star with mass $$ M_s = 1.35$$ of Solar mass the stellar gravitational torsion flux quantum is:
 * $$ \Phi_s = \frac{h_s}{2M_s} = 6.4 \cdot 10^{11}$$ m2/s.

As in the case with the proton we should expect that the angular momentum of typical neutron star of mass $$ M_s $$ and radius $$ R_s $$ equals to:
 * $$ L= \frac {2}{5} M_s R^2_s \omega_s = \frac { h_s }{4 \pi } = \frac { \hbar_s }{2 },$$

where $$ \omega_s $$ is the typical angular frequency of star rotation, and $$ \hbar_s $$ is the stellar Dirac constant.

We find that the stellar velocity circulation quantum equals to the stellar gravitational torsion flux quantum of the neutron star:
 * $$ \sigma_s = \omega_s S_s = \frac{h_s}{2M_s}= \frac{2 \pi L}{M_s}= \frac {4}{5}\pi R^2_s \omega_s = \frac {4}{5}\pi R_s V_s = \Phi_s, \ $$

where $$ V_s $$ is the equatorial rotation speed, and effective area of the star is close to the star section: $$ S_s = \frac {4}{5}\pi R^2_s .$$

The gravitational torsion field in the center of star is:
 * $$ \Omega_c = \frac {G M_s \omega_s }{R_s c^2}= \frac {5G L}{2R^3_s c^2} = \frac {5G h_s }{8 \pi R^3_s c^2}. $$

The product of $$ \Omega_c $$ and the effective area of the star gives the stellar gravitational torsion flux of the star which is less then $$ \Phi_s$$ :
 * $$ \Omega_c S_s = \frac {G h_s }{2 R_s c^2} = \frac {\Phi_s \psi}{ c^2} = 0.17 \Phi_s, $$

where $$ \psi = \frac {G M_s}{R_s} $$ is the absolute value of scalar potential of gravitational field at the surface of the star, $$ G $$ is the gravitational constant.

Solar system
For the velocity circulation quantum of a planet in the Solar system can be written:
 * $$ \sigma_p = \omega_p S_p = \frac {4}{5}\pi R^2_p \omega_p = \frac {4}{5}\pi R_p V_p, \ $$

where $$ R_p $$ is the planet radius, $$ V_p $$ is the equatorial rotation speed.

The planetary data are presented in the Table 1.

By its meaning the velocity circulation quantum is proportional to angular momentum of body per unit of mass. We can see that the stellar gravitational torsion flux quantum $$ \Phi_s $$ is close to velocity circulation quanta of the Sun and big planets in the Solar system. With constant mass the gravitational torsion flux is conserved in the same degree as the angular momentum.


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User:Djatsvnit/Three Phase Transformer

It is the three phase system which has been adopted world over to generate, transmit and distribute electrical power. Therefore to change the level of voltages in the system three phase transformers should be used. Three number of identical single phase transformers can be suitably connected for use in a three phase system and such a three phase transformer is called a bank of three phase transformer. Alternatively, a three phase transformer can be constructed as a single unit.

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

title: User:Djatsvnit/Three Phase Transformer


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User talk:Leighblackall/Everything you need to teach and learn online

Initial thoughts

 * As you rewrite, I'd tone down the emotivity i.e., aim to convince by argument/rationale/example rather than strength of personal conviction.
 * I'd probably shift most of this into the body draft - the abstract is really just for summarising the key points.
 * Clarify the title of the paper in relation to abstract - the abstract suggest an LMS critique although the title suggests an explanation of an online learning model. There may even be two papers / chapter here - I fear one might spoil the other? -- Jtneill - Talk - c 10:07, 31 March 2010 (UTC)

 * hmm thanks on all points. Question:
 * Is it inappropriate to write an abstract as a hook, making all sorts of claims and personal convictions that are like a guarantee that the body will be expected to cover with convincing argument/rationale and examples. I can almost see the answer to this.. the emotive tone is too blunt a hook turning editors away. I guess I need to better understand the audience of academic editor. --Leighblackall 10:25, 31 March 2010 (UTC)
 * Well, it can be very journal-specific as to the tone wanted/accepted - I had a quick quiz at the journal (titles look interesting!), but didn't read any abstracts to date. But I wouldn't be too worried about the abstract - it usually gets written last, as a summary of the paper rather than a pitch per se. Mostly journal editors I think will want to see a full paper before deciding whether to reject, ask for a rewrite, or send out to review. Your initial audience is the editor and the reviewers. A radical thesis is fine, but focus on explication of the thesis. -- Jtneill - Talk - c 10:37, 31 March 2010 (UTC)

Acceptance
Dear Leigh,

Thanks for your interest in contributing to the special issue of the International Journal for Educational Integrity (IJEI). We’re delighted to accept your paper proposal.

Your paper stood out for its clear focus on the special issue brief: to explore the implications of digital technologies on educational or academic integrity. We were particularly interested in the way your proposal offered a boundary crossing experiment with scholarly approaches to educational integrity that deliberately hybridises models of knowledge production, and would welcome your contribution of a full paper in this direction.

Some points that you might like to consider include: a discussion of your approach ot copyright and licensing of the material; the difference between open access and paid services; the relation of vidoe to online teaching and learning; whether and how your approach might contribute to a breakdown of the boundaries between higher education institutions and wider audiences. But we look forward to what you come up with!

Just a reminder: the full paper (3-6000 words) deadline is the 1st of July when we will need to send the paper off to external anonymous reviewers. If you have any trouble meeting this deadline, please let us know. The IJEI formatting and referencing style guides can be found at: http://www.unisa.edu.au/EducationalIntegrity/Journal_submission_guidelines.htm

Please don't hesitate to contact us if you have any queries.

best wishes UNISA Mon, Apr 19, 2010


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User:Cormanicus

First year LLB LAW student at the University of South Africa (UNISA)

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Haskell/Basic Haskell

The Haskell Compiler
While there are various implementations of Haskell, for the purposes of this course we will only be using GHC, the Glasgow Haskell Compiler, and any references to compiling or running Haskell will assume a modern version of GHC (version 7.10 or 8).

Installing GHC
TODO: update this section and talk about Cabal and Stack.

Linux
If you're on Linux, you might have a package manager, where you can install GHC. If you're not that lucky you should try and build it from source. Get the source from the website: http://www.haskell.org/ghc/download.html

Using GHC
Now that GHC is installed, let's write a simple "Hello world"-program (We'll explain this in detail later): main = putStrLn "Hello, world!" Put the above in a file called

GHC
To run it with  type: $ ghc HelloWorld.hs Now you should have a file called  which you can run, and it should print: Hello, world! great.

runghc
is very much like, but instead of making an executable file, it simply runs the program, without making any new files.

GHCi
With your installation of GHC you should also have a program called, an interactive version of the Haskell compiler. Interactive interfaces to compilers are often called REPLs or read, eval, print, loops. When run, you should see output similar to: $ ghci GHCi, version 7.10.3: http://www.haskell.org/ghc/  :? for help Prelude> Note: the Prelude is a collection of commonly used functions, like a standard library, that allow us to more easily write Haskell without having to remember to import the same libraries in every program. It is imported by default.

The line Prelude> in GHCI tells us which modules are currently in scope. However we can change it to whatever we like with the set command. For example: Prelude> :set prompt λ> λ> Note: all commands to GHCI are prefixed with a colon. As GHCI says when you start it, you can view these commands with  or.

Users of the Vim text editor may find various commands in GHCI are equivalent, such as  for running shell commands from inside of GHCI. For example: λ>:!uname Linux

Finally it is worth noting that GHCI has a scrollable history (with the arrow keys) and tab completion.

Setting up and becoming familiar with GHCI
For the purposes of learning Haskell, we'll want to change some of GHCI's default settings. Start by turning on type signatures: λ>:set +t Now when we give GHCI input it will print out the type of the expression as well as what it evaluates to! λ>"Hello, world!" "Hello, world!" it :: [Char] The last value given to GHCI is bound to the name, thus we can re-evaluate it by typing: λ>it "Hello, world!" it :: [Char] Finally, it's worth noting that type signatures can be checked without evaluating an expression (which is useful if GHCI doesn't know how to print that type of value (such as functions)). This can be done with :type or :t λ>:t it it :: [Char]

Type signatures
Okay, so now that we've got GHCI to tell us about the types of things, we need to learn what it's actually saying.

Note: GHC and GHCI can have intimidating error messages when you first start. Try to break down the error message into small pieces and follow the types.

The notation  indicates a type signature and can be pronounced as is of type or is a. Thus the English equivalent to  is "Hello, World" is a String. But wait, wasn't the type of    ? Yes! Haskell uses type synonyms to try and keep things simple whenever possible. You can find out information about various Haskell terms with the  or   command. So when we investigate  we find out that it's the same as  : λ>:i String type String = [Char] 	-- Defined in ‘GHC.Base’

title: Haskell/Basic Haskell


text:
Talk:Connectivism

What happened to the Connectivism and Connective Knowledge page? And the wiki? Anyone know? --Bnleez 14:33, 31 March 2010 (UTC)

title: Talk:Connectivism


text: User talk:Yuki Konno

title: User talk:Yuki Konno


text:
User talk:Melos

 Hello Melos, 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. 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.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
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 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 18:20, 31 March 2010 (UTC)

title: User talk:Melos


text: User talk:Willking1979

title: User talk:Willking1979


title: User:Willking1979


text:
User talk:Jredmond

 Hello Jredmond, 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. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random random project.
 * Browse everything on 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Gbaor 12:20, 14 August 2008 (UTC)

 Hi , I am Percy. Nice to meet you. I love the beach, swimming, fishing, and I am currently doing some research at Wikiversity on oceanography. I am also learning to play piano. What do you like? Can I be your mascot?

title: User talk:Jredmond


title: File:Egm6341.s10.mtg35.djvu


title: File:Egm6341.s10.mtg36.djvu


text:
User:Egm6341.s10.team3.heejun/HW6

=  (10) Run Kessler's code to reproduce his table, and Complete HW p. 30-2 =

Problem Statement
$$ \displaystyle Follow\, Kessler's\, code\, line\, by\, line\, to\, produce\, (P_2,P_3)\, (P_4,P_5)\, (P_6,P_7)\, and\, put\, comments\, in\, his\, code\, $$

Ref: Lecture Notes [[media:Egm6341.s10.mtg30.djvu|p.30-2]] and [[media:Egm6341.s10.mtg37.djvu|p.37-1]] Ref: Trapezoidal rule error

Solution

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

 * }
 * }
 * }
 * }

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

$$ f=1 \,\,\, g=2$$ $$ f=f.*g.*(g+1) $$ yields f=6. $$ fracsum(-1*cn,cd.*f) $$ yields fracsum(-1, 6) Now looking into the fracsum function,
 * $$ c_1 $$ = -1

div=gcd(round(n),round(d))

will yield div = 1. because, round(-1) = -1 round(6) = 6 gcd(-1,6) = 1.

n=round(n./div); will give n=1

d=round(d./div); will give d=6

Next, for k=1:length(d) dsum=lcm(dsum,d(k)); end

will yield dsum = 6.

nsum=dsum*sum(n./d); is, nsum = 6*sum(1/6) = 6*(1/6) =1.

div=gcd(round(nsum),round(dsum)); gives div = 1.

So. nsum = 1 and  dsum =6 Hence $$ c_3 = \frac{1}{6} $$

Now going back, [newcn newcd] = [1 6] cn=[cn;newcn]; cd=[cd;newcd]

cn = [-1;1]; cd=[1;6]

f=[f;1]; So, f=[6;1]

and

g=[2+g(1);g]; which means, g = [2+2, 2] = [4;2]

[newpn,newpd]=fracsum((g-1).*cn,f.*cd); i.e, fracsum(-3,6) and fracsum(-1,1)

Again repeating the exercise for fracsum as specified above will give, would yield, $$-\frac{1}{2} \,\,\, and  \frac{1}{6} $$ respectively. Hence,

$$p_2(1) = -\frac{1}{2} + \frac{1}{6} = -\frac{1}{3} $$

So this explains the way to calculate $$ c_3 \,\,\, and p_2(1) $$.

The other constants and the values of polynomial at t=1 can be similarly calculated. It is to be noted that once one constant is found the succeeding constants can be calculated from the previous ones.

 * }

=  (11) Verification of results for the question 10 of HW 5 =

Problem Statement
$$ \displaystyle Compare\, our\, results\, to\, the\, results\, of\, Team4\, $$

$$ \displaystyle i)\, Evaluate\, the\, given\, circumference\, formular\, with\, Comp. Trap,\, Romberg\, and\, Clencurt\, $$

$$ \int_{\theta=0}^{\theta=2\pi} dl = C $$

$$ \displaystyle Where\,\,\,\, \begin{align} dl &=d\theta [r^2+(\frac{dr}{d\theta})^2]^(\frac{1}{2})\\ r(\theta) &= \frac{1-e^2}{1-ecos(\theta)} \\ e &= sin(\frac{\pi}{12}) \\\end{align}\ $$

Ref: Lecture Notes [[media:Egm6341.s10.mtg25.djvu|p.25-2]] and [[media:Egm6341.s10.mtg30.djvu|p.30-3]]

$$ \displaystyle ii)\, The\, complete\, elliptic\, integral\, of\, the\, second\, kind\, method\, $$

$$ \displaystyle C = 4a E (e) $$

$$ \displaystyle E(e) = \int_{0}^{\pi /2} [1-e^2sin^2(\theta)]^{(\frac{1}{2})} d\theta $$

Ref: Team 4 in HW 4 [|problem_11] and Wikipedia[|Elliptic_integral]

Solution
$$ \displaystyle i)\, Summary\, of\, Results\, given\, by\, Team4\, and\, Team3\, $$

$$ \displaystyle \dagger\, Note:\,\, In\, the\, result\, of\, Clencurt,\, X\, means\, ocillating\, $$

$$ \displaystyle ii)\, Comparision\, $$

$$ \displaystyle a)\, The\, big\, difference\, was\, caused\, by\, the\, calculation\, of\, error.\, $$ $$ \displaystyle :\, Team 4\, computed\, I_n\, to\, the\, error\, 10^{-10}\, b/w\, the\, exact\, I\, and\, I_n.\, $$ $$ \displaystyle \,\, However,\, Team 3\, computed\, I_n\, to\, the\, error\, 10^{-10}\, b/w\, I_{n-1}\, and\, I_n.\, $$ $$ \displaystyle \,\, In\, order\, to\, clearly\, know\, the\, exact\, I,\,\, Team 3\, directly\, computed\, I\, with\, Quad\, again\, $$

$$ \displaystyle b)\, Team 4\, exactly\, found\, I_n\, with\, Clencurt\, but\, the\, result\, of\, Team 3\, is\, oscillating\, on\, the\, place\, for\, 10^{-15}\, $$

$$ \displaystyle c)\, Correction\, for\, Clencurt\, and\, 2nd\, method\, $$ $$ \displaystyle :\, Since\, the\, Clencurt's\, result\, of\, Team 3\, is\, going\, in\, busy\, mode\, and\, the\, input\, of\, 2nd\, method\, was\, not\, correctly\, uploaded,\, it\, is\, not\, easy\, to\, clearly\, see\, the\, results.\, $$ $$ \displaystyle Thus,\, the\, inputs\, for\, above\, two\, are\, attached\, below\, again.\, $$

$$ \displaystyle c-1)\, Clencurt\, $$

$$ \displaystyle c-2)\, 2nd\, method\, $$

$$ \displaystyle iii)\, Analyzing\, the\, Results\, of\, Clencurt\, $$

$$ \displaystyle The\, oscillating\, on\, the\, place\, for\, 10^{-15}\, is\, caused\, by\, the\, difference\, b/w\, I_{exact}\, and\, I_{cl}\, in\, the\, result\, of\, team 3.\, $$ $$ \displaystyle Thus,\, we\, verified\, the\, Clencurt's\, result\, with\, a\, different\, order\, of\, errors\, $$

$$ \displaystyle a)\, Correctional\, Clencurt\, $$

$$ \displaystyle b)\, The\, difference\, when\, I_{exact}\, -\, I_{cl}\, <\, 10^{-8}\, is\, 7.591901329817574*10^{-9}.\, $$ $$ \displaystyle This\, value\, is\, pretty\, small\, and\, can\, be\, thought\, that\, the\, Clencurt\, integration\, close\, up\, to\, the\, I_{exact},\, the\, Quad\, integration.\, $$

title: User:Egm6341.s10.team3.heejun/HW6


text:
User talk:Jnnix

 Hello Jnnix, 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. 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.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
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 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --AFriedman (talk) 00:47, 1 April 2010 (UTC)

 Woof! My name is Jack Russell. I am a dog and a Wikiversity mascot. I am pretty new around Wikiversity. Perhaps we can learn together! Tail wag...

title: User talk:Jnnix


title: File:WikiversityPresentation02-2010.pdf


text:
Force Field Analysis: Figure

Back to ID Homepage >  Force Field Analysis >  Definition >  FFA Figure >  FFA’s  Function >  References

Force field analysis is usually presented in a figure although there are many ways to draw a figure. This figure below is one of the representations of force field analysis. Pay attention to that the organization is currently at ‘a’ and wants to move to the situation of ‘b.’ Several forces operating within the organization or outside the environment may make movement towards ‘b’ desirable or undesirable.

Forces for Change VS. Forces against Change
Think about the example of Harry Potter and say we are expecting that Harry defeated Voldemort. Then probably a stronger power, a fatal magic, and support from his families are the needed effects that can help achieve this expectation. If these factors happened, they could be viewed as driving forces that support and lead Harry to his goal. On the other hand, Voldemort’s power is viewed as restraining forces that resist or decrease Harry’s power.

The same concept can be applied to any force field analysis figure, and both driving and restraining forces are represented by arrows with opposite directions. The strength of each force is represented by the length of its representative arrow. As a result, in the organization development, the forces favoring the proposed change or keeping it going are called driving forces, and the forces resisting change or keeping the status quo are called restraining forces.

According to Lewin’s point, organizations are systems in which the current situation is not static but dynamic with forces working in opposite directions. There are always both driving forces that push for change and restraining forces that act against change in any situation.

Let’s review a case study for practice and see how force field analysis is applied in this bicycle manufacturer - A case study for practicing FFA

Click the Next button to practice and review the case.

title: Force Field Analysis: Figure


text:
Instructional design/Force field analysis/A case study for practicing FFA

Back to ID Homepage > ID force field analysis > What is force field analysis? > How force field analysis is presented in a figure? > How force field analysis is used?

Your Task for the Case
Here is a case regarding Huffy Corporation's evaluation on its current strategy. Suppose that you are a consultant who is working on assessing Huffy's strategic decision. Your client, a manager in the administration department, provided you some examples of external forces and internal forces collected and analyzed from the annual reports and wanted you to identify forces for change and forces resisting change from these external and internal factors.

The Case of Huffy
The 1982 sales of bicycles in the United States dropped approximately 40 per cent. Sales were at the lowest level in 15 years. Huffy Corporation, the United States’ largest manufacturer of bicycles, received 90 per cent of its revenues from bicycle sales. Given the decline in sales and the pessimistic projections for the short-term future, Huffy was forced to evaluate its current strategy. It was necessary for Huffy to decide whether to remain with its current strategy for selling bicycles (its major product) through mass retailers (its major outlet) or to consider a diversification strategy.

External Forces

One of the general changes in society impacting many businesses in the U.S. is the increasing birth rate. Where there were slightly over three-million children born in 1975, the U.S. Department of Health and Human Service estimates the birth rate will increase to 4.5 million children per year for 1985 to 1990. This ‘baby boom echo’ is in large part the result of children from the post World-War II ‘baby boom’ starting families. The delay in starting families by this group has created an increased disposable income per child, making investments in infant’s and children’s products potentially attractive. Yet with their emphasis on bicycles it would be a number of years before the new births represent potential customers for Huffy. Being able to market products for infants and toddlers thus is a pressure encouraging Huffy to undertake a different strategy than was used in the past.

Another pressure to change strategies was the increased interest in physical fitness. The physical fitness interest is relevant to Huffy as a producer of bicycles, but it is also of interest to all firms interested in producing physical fitness related equipment and supplies. Given Huffy’s contacts with mass retails, diversification into other products related to sporting goods and physical fitness has potential strategic fit.

A significant force for many smaller firms (including Huffy) considering diversifying into physical fitness products is the entry of firms with large resource bases into the market. West Bend Company and Campbell Soup have both aggressively entered the market. West Bend expects sporting goods to account for 20 per cent of its sales within one year of entry. Campbell Soup increased the number of outlets selling its sporting goods products from 60 to 1500 outlets in five months. Campbell’s sees the diversification as a part of its ’health and well-being’ theme. The entry of large firms into the market for sporting goods and fitness products may serve as a significant force against movement into the market by Huffy.

Another force against some diversification strategies is Huffy’s strong association with mass retailers. The association of the Huffy name with mass markets and discount sales may prove a barrier to producing or marketing premium quality products through specialty shops. While such market may not represent the potential sales volume of mass markets, higher profit margins may make such diversification strategies attractive.

A final external force favoring Huffy’s diversification from its concentration on bicycles is competition from imports. The Bicycle Manufacturers’ Association projected a 30 per cent increase in bicycle sales in the U.S. for 1984. However, nearly all of the increase was expected to result from imported cycles. The increased competition from imports is an especially salient force for a single product company such as Huffy where 90 per cent of sales were from bicycles. The threat of imports is one force causing Huff’s management to undertake a diversification strategy designed to reduce bicycle sales to less than 50 per cent of corporate sales.

Internal Forces

There were also a number of forces within Huffy that were relevant to the selection and implementation of diversification strategies. One of the major internal pressures for change was Huffy’s strong research and development department, the Huffy Tech Center. Using the Tech Center’s new technology, U.S. cyclists won two gold, two silver and a bronze medal in the 1984 Olympics on bicycles produced by Huffy. They were the first Olympic medals won by U.S. cyclists since 1912. Huffy Tech Center has also allowed the firm to introduce innovative new products in sporting goods, in tricycles and in other youth-oriented products.

Huffy’s response to the decreased sales of 1982 provided a strong internal base from which to diversity. In response to the sales decline, Huffy closed two production facilities and modernized other facilities to produce the same number of bicycles with fewer personal and at a lower per unit cost. This move provided the firm a strengthened profit margin and existing facilities in which to produce new products.

The major internal force opposing diversification efforts is the limited experience of Huffy management. The firm’s management team has a proven record of successfully marketing bicycles through mass retailers. The ability of existing management to successfully market a more diversified product line through other retail outlet (e.g. specialty shops) was a major consideration in diversifying from its basic bicycle business.

Your Analysis
According to the definition and examples we talked about earlier, you might now be able to tell your client what the forces for change are and what the forces resisting change are by completing the following questions. {These are the external forces influencing Huffy's strategic decision, please choose the one(s) that work(s) for changes. - Name associated with mass markets. + Rising birth rates. + Public interest in physical fitness. - Entry of firm with larger resources bases. + Pressure from imports
 * type="[]"}

{These are the internal forces influencing Huffy's strategic decision, please choose the one(s) against changes. + Limited management experience. - Strong research and development efforts. + Distribution channels limited to mass retailers. - Modern production facilities with excess capacity.
 * type="[]"}

Click the Next button to continue.
 * Check your results of analysis to see if they correspond with this graphic.[[Image: FFAF2.jpg |500px|center|Force impacting Huffy’s diversification strategy]]


text:
Making Change Successful

Back to ID Homepage > ID force field analysis > What is force field analysis? > How force field analysis is presented in a figure? > How force field analysis is used?

When you are jogging and there comes a strong wind against you, you must exert more force to keep your pace. Also, to Harry, he should either strengthen himself or decrease Voldemort’s power so that it would be possible to defeat the opponent.

Now you might have ideas of how to make your change successful. That is that the driving forces must exceed the restraining forces, and this can be achieved by
 * Increasing the forces for the change, or
 * Reducing the forces against the change.

In the following picture, you see the sum of each driving force and restraining force. It is important for you to set a time frame and give suggestions to help your organization or client move from current state to a state where change is favorable.

Click the Next button to continue.

title: Making Change Successful


text:
User:Ladyofshallot

Margaret L. Clarke
Margaret L Clarke is an independent scholar in the field of Canadian western history with specific focus on the history of the fur trade and the development of the Metis people and nation. She uses techniques from Family History Studies and Demography to construct models of pre-settlement communities in the Canadian west.

MASTER’S THESIS TITLE: “RECONSTITUTING THE FUR TRADE COMMUNITY OF THE ASSINIBOINE BASIN, 1793-1810.”  Thesis Advisor: Dr. Jennifer S.H. Brown, Ph.D.

Margaret also wrote and distributed a newsletter called Canada Tree, focusing on Metis and fur trade family reconstitution and issues of ethnicity and personal identity. The website built around around that publication is at A more recent effort, focusing on Social Justice issues is:

Published articles:
CANADA TREE NEWSLETTER: FOUNDER AND EDITOR, (SEPTEMBER, 1993). An Organ for Fur Trade History and genealogical research.

ARTICLES “The Family of John Lyons: Comments on “Using Canadian Census Records to Trace Ethnic Origin and Family Relationships” Generations, Vol. 21, No. 2, June 1996.

Review Article: Blair Stonechild and Bill Waiser, “Loyal till Death” (Calgary, Fifth House Ltd., 1997) in Prairie Forum, fall 1998.

Book Review: Penny van Toorn, Rudy Weibe and the Historicity of the Word (Edmonton: University of Alberta Press, 1995) in Manitoba History, autumn, 1996.

PAPERS "Weaving the Web: Relating Missionaries and Fur Traders." Land Under Foot Museums Network Seminar, January 20, 2003.

“Skinning the Narrative: Closer analysis of the Story of Fish Creek.” Prairie Forum, fall, 2002.

“The Daughters of Edward McKay and Caroline Cook.” Unsettled Pasts: Reconceiving the West Through Women’s History. Women's History Conference, Calgary, June 2002

"The Battle of Fish Creek NHS: a Review of Sources" for Parks Canada, April, 2001.

"Frenchman Butte: a survey of accounts" for Parks Canada, October, 2000.

“Themes in the Historiography of the First Nations Involvement in 1885” for Parks Canada, January, 1998.

“Sitting Bull’s Wedding Gift: The McKays’ Relations with the Dakotas.”  Presented at the 30th Northern Great Plains History Conference, Brandon, Manitoba, September 30, 1995.

“John Richards McKay’s SpyGlass: the larger community.” Presented at the Rupert’s Land Colloquium, May 25 - 27, 1994, Edmonton, Alberta.

“The History of Cold Lake Provincial Park: a focus paper” for Cold Lake Provincial Park, August, 1985.

WORKS IN PROGRESS “A Boy’s Own Summer, 1862” a screenplay, based on archival research.

The People of the Assiniboine Basin: Metis Genesis, thesis to book.

“Georgie, I Loved You: A Woman’s Story.” A screenplay based on family history.

An Aboriginal History of Central Alberta. Begun with support from the Healing Foundation.

“South of Us” an Oral History”, for Alberta History.

title: User:Ladyofshallot


text:
User talk:Ladyofshallot

 Hello Ladyofshallot, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 03:12, 1 April 2010 (UTC)

Welcome Molly
You are off to a good start.

Have you looked at any of the schools to see where your material might fit in?

There are a number of roles you can play here.

 * There is the student for life, that uses Wikiversity as their alma mater
 * There is the teacher who prepares courses for your interest area
 * There is the researcher doing either secondary or Original research
 * There is the publishing role where information on your work gets diseminated to the world
 * There are projects to help the program along, including support roles for others
 * There is the Editor role, where you work your way through portions of the site, and add a little repair here and there
 * There is the Illustrator role, where you find pictures that fit a particular page, and add them
 * The list is virtually endless, and limited mostly by your imagination

I was just looking and the school of Social sciences has demography, and Cultural studies in it.

--Graeme E. Smith 05:20, 1 April 2010 (UTC)

title: User talk:Ladyofshallot


text:
Udayana University

Udayana University is a public university in Denpasar, Bali, Indonesia. It was established on September 29, 1962. Its current rector is Dr. dr. I Made Bakta, SpPD (KHOM).

History
Udayana University was established by the Act of Minister of Higher Education Republic of Indonesia No.104/1962, on 9th of Agustus 1962. It was after being an initial period as part of Airlangga University since 29 September 1958. So that making it the first university to be established in Bali Province. With 4 courses in 1962, Udayana University has developed a wide range of courses in Arts and Literatures, Medical Sciences, Law, Economy, Engineering, Agriculture, Animal Husbandry, Mathematics and Natural Sciences, Veterinary Sciences, Agricultural Technology, Tourism Studies and Social and Political Sciences.

About Udayana University
Udayana University (Universitas Udayana) is the oldest and the largest public university in Bali and a major centre for university graduates from throughout the Indonesia and one of a nationally and internationally distinguished institution of higher education. The University is currently home to over 19,000 students-10% of which are postgraduates.

In 2006 – 2007, The Udayana University confirmed its position as leading university in Indonesia among “50 Promising Universities” published by the government. In 2008, Udayana University continues to be the University of Choices for Bali and increasingly the nation’s, based on a survey carried out by a national magazine “Tempo” which ranked the Udayana University among 15 most favorite universities in Indonesia. In 2009, Udayana University has also reached top 11 universities in Indonesia and rank 3450 webomatrics (June 2009). Udayana University is committed to produce highly employable graduates and researchers of the highest quality possible. In both its teaching and research, the University has strong links with local and international institutions, including government bodies, business, industries, and the professional organizations. The Udayana University undertakes innovative research projects in the field of biotechnology and biosciences, medical sciences and social sciences. Udayana University is fortunate in its location. Bali, a well-known tourist destination with population of 3.5 millions, has been named one of the best island to visit in the world. It should be a very comfortable place for study.

Why Study at Udayana University? Udayana University (Unud) offers excellent opportunities for study and research at many levels; diploma, undergraduate, master and doctorate programs. Students are able to pursue through both coursework and research program.

Experience of Unique Culture Bali is unique because of its tourism and hospitality industries are stronger compared to those in other regions in Indonesia. Its beautiful scenery, its people, its culture and traditions have made Bali popular for decades. A perfect combination of well-known Balinese culture and its rich diversity of peoples provide a dynamic learning environment, which will in turn stimulate creativity and innovation.

Extensive Choices of Subjects As a leading university, Udayana University offers exciting opportunities for more than 100 undergraduate and graduate degree programs, with expert and specialist staffs and researchers with global reputation.

Study Part-Time Our programs allow the students for studying part time while on employment.

Study Skills Udayana University believes in its potential in developing independent, creative and analytical thinking but remains committed in practicing their existing indigenous knowledge. To assist the students in their studies, Udayana University offers qualified academic staffs, quality library, modern laboratories, computer, and internet access and other technologies relevant to the students’ courses.

Schools
The university has 11 faculties:

Logo
Udayana University Logo named Widya Cakra Pawartana which in Bali culture means the rotation wheel science based on pancasila (Indonesian basic static). The meaning of the symbols are:
 * Tangible a circle that has a wheel "cakra", in the middle there is padma (lotus) with eight pieces of leaf which symbolizes the eight corners of the wind, which symbolizes the sanctity of God Almighty based of first principle of Pancasila.
 * The wheel "cakra" has four fingers symbolizing strength iron from the four principles of Pancasila.
 * The outside of the circle radius of the wheels are decorated with 54 (fifty four) as points ratna jewel in accordance with a given set of Udayana science.
 * The color is golden yellow emblem Udayana University with a blue base color. Golden yellow color symbolizes the rising sun and the blue color symbolizes the sky.

Flag
Udayana's University flag rectangular with a ratio of 3 (three) vs. 2 (two) basic color blue, in the middle there is a colored symbol Unud golden yellow.

Banner of Faculty

 * School of Letter, the color is white.
 * School of Medicine, the color is green.
 * School of Law, the color is red.
 * School of Engineering, the color is black.
 * School of Economics, the color is orange.
 * School of Agriculture, the color is chocolate.
 * School of Ranch, the color is purple.
 * School of Mathematic and Natural Sciences, the color is silver.
 * School of Animal Medicine, the color is lilac.
 * School of Agricultural Technology, the color is verdant.
 * School of Tourism, the color is pink.
 * School of Peace and Democracy, the color is maroon.
 * Post Graduate, the color is blue.

Nias Campus
Jl. Nias was the original campus of Udayana University which was established in 1958. The most opulent of this campus is the fabulous statue of Saraswati, the goddess of knowledge, a monument to love science and technology. It is now home for Faculty of Letters and and Postgraduate Programs (Master and Doctorate) of Cultural Studies.

Sudirman Campus
Sudirman campus is in the heart of Denpasar, located within easy distance of major sights of the city. It is home for Postgraduate Programs and Medical Sciences Faculty. The early days of the campus saw field of Palm trees planted along the front corridor, so that making the campus known as “Campus of Palm” or in Bahasa called “Kampus Palma”.

The campus has grown in number and facilities. This includes GDLN, an information and communication technology facilities to assist with our work and strengthen the connections with. which allows all university member to access distance tutorial and conference

Bukit Jimbaran Campus
Udayana University has 3 campuses. The main campus, Bukit Jimbaran,built in 1986 located at 25 kilometers to the south of Denpasar, is relatively new campus which is set in a large complex and designed like a town. Facilities include health clinic, university library, sport centre, post office, guesthouse and university housing. International Hospital, shopping centre, lake and leisure facilities are being made available soon. The facilities are available to everyone in the university community and also, where applicable, to the broader community. The campus is close to Ngurah Rai International Airport, only 10 minutes drive from the airport and major tourism sites of Kuta and Nusa Dua.

title: Udayana University


text:
Gospel of John (CBS)/Week 8

This is the last week of the Book of Signs. There will be a Unit Test this week, then we will move on to the Epilogue next week.

Assignments

 * 1) Read John 20:1-31
 * 2) Write a well developed response that expands upon this week's topic.
 * 3) Finish the Study Guide
 * 4) Complete this week's unit test

Discussion
This week's discussion will be held at TIME on DATE in the AWF virtual universe, Agape World at the AWF School facility. There is a section on the talk page where you can post topics and questions for us to go over. If you are unable to make it, your questions can also be posted in a separate section to the talk page, where I will do my best to answer them shortly.

Chapter 20
''The sepulchre found to be empty. (1-10) Christ appears to Mary. (11-18) He appears to the disciples. (19-25) The unbelief of Thomas. (26-29) Conclusion. (30,31)''

Verses 1-10 If Christ gave his life a ransom, and had not taken it again, it would not have appeared that his giving it was accepted as satisfaction. It was a great trial to Mary, that the body was gone. Weak believers often make that the matter of complaint, which is really just ground of hope, and matter of joy. It is well when those more honoured than others with the privileges of disciples, are more active than others in the duty of disciples; more willing to take pains, and run hazards, in a good work. We must do our best, and neither envy those who can do better, nor despise those who do as well as they can, though they come behind. The disciple whom Jesus loved in a special manner, and who therefore in a special manner loved Jesus, was foremost. The love of Christ will make us to abound in every duty more than any thing else. He that was behind was Peter, who had denied Christ. A sense of guilt hinders us in the service of God. As yet the disciples knew not the Scripture; they Christ must rise again from the dead.

Verses 11-18 We are likely to seek and find, when we seek with affection, and seek in tears. But many believers complain of the clouds and darkness they are under, which are methods of grace for humbling their souls, mortifying their sins, and endearing Christ to them. A sight of angels and their smiles, will not suffice, without a sight of Jesus, and God's smiles in him. None know, but those who have tasted it, the sorrows of a deserted soul, which has had comfortable evidences of the love of God in Christ, and hopes of heaven, but has now lost them, and walks in darkness; such a wounded spirit who can bear? Christ, in manifesting himself to those that seek him, often outdoes their expectations. See how Mary's heart was in earnest to find Jesus. Christ's way of making himself known to his people is by his word; his word applied to their souls, speaking to them in particular. It might be read, Is it my Master? See with what pleasure those who love Jesus speak of his authority over them. He forbids her to expect that his bodily presence look further, than the present state of things. Observe the relation to God, from union with Christ. We, partaking of a Divine nature, Christ's Father is our Father; and he, partaking of the human nature, our God is his God. Christ's ascension into heaven, there to plead for us, is likewise an unspeakable comfort. Let them not think this earth is to be their home and rest; their eye and aim, and earnest desires, must be upon another world, and this ever upon their hearts, I ascend, therefore I must seek the things which are above. And let those who know the word of Christ, endeavour that others should get good from their knowledge.

Verses 19-25 This was the first day of the week, and this day is afterwards often mentioned by the sacred writers; for it was evidently set apart as the Christian sabbath, in remembrance of Christ's resurrection. The disciples had shut the doors for fear of the Jews; and when they had no such expectation, Jesus himself came and stood in the midst of them, having miraculously, though silently, opened the doors. It is a comfort to Christ's disciples, when their assemblies can only be held in private, that no doors can shut out Christ's presence. When He manifests his love to believers by the comforts of his Spirit, he assures them that because he lives, they shall live also. A sight of Christ will gladden the heart of a disciple at any time; and the more we see of Jesus, the more we shall rejoice. He said, Receive ye the Holy Ghost, thus showing that their spiritual life, as well as all their ability for their work, would be derived from him, and depended upon him. Every word of Christ which is received in the heart by faith, comes accompanied by this Divine breathing; and without this there is neither light nor life. Nothing is seen, known, discerned, or felt of God, but through this. After this, Christ directed the apostles to declare the only method by which sin would be forgiven. This power did not exist at all in the apostles as a power to give judgment, but only as a power to declare the character of those whom God would accept or reject in the day of judgment. They have clearly laid down the marks whereby a child of God may be discerned and be distinguished from a false professor; and according to what they have declared shall every case be decided in the day of judgment. When we assemble in Christ's name, especially on his holy day, he will meet with us, and speak peace to us. The disciples of Christ should endeavour to build up one another in their most holy faith, both by repeating what they have heard to those that were absent, and by making known what they have experienced. Thomas limited the Holy One of Israel, when he would be convinced by his own method or not at all. He might justly have been left in his unbelief, after rejecting such abundant proofs. The fears and sorrows of the disciples are often lengthened, to punish their negligence.

Verses 26-29 That one day in seven should be religiously observed, was an appointment from the beginning. And that, in the kingdom of the Messiah, the first day of the week should be that solemn day, was pointed out, in that Christ on that day once and again met his disciples in a religious assembly. The religious observance of that day has come down to us through every age of the church. There is not an unbelieving word in our tongues, nor thought in our minds, but it is known to the Lord Jesus; and he was pleased to accommodate himself even to Thomas, rather than leave him in his unbelief. We ought thus to bear with the weak, ( romans 15:1 romans 15:2 ). This warning is given to all. If we are faithless, we are Christless and graceless, hopeless and joyless. Thomas was ashamed of his unbelief, and cried out, My Lord and my God. He spoke with affection, as one that took hold of Christ with all his might; "My Lord and my God." Sound and sincere believers, though slow and weak, shall be graciously accepted of the Lord Jesus. It is the duty of those who read and hear the gospel, to believe, to embrace the doctrine of Christ, and that ( 1 John 5:11 )

Verses 30-31 There were other signs and proofs of our Lord's resurrection, but these were committed to writing, that all might believe that Jesus was the promised Messiah, the Saviour of sinners, and the Son of God; that, by this faith, they might obtain eternal life, by his mercy, truth, and power. May we believe that Jesus is the Christ, and believing may we have life through his name.

Unit Test
The Unit Test will be similar to the last Unit Tests. There will be 25 free response questions drawn from information covered in readings and lessons for this unit. Many of the questions may be reworded study questions, so the study guide is your friend :). Attempt to make significant progress on the questions from the study guide this week, especially those which relate to this weeks topic. Once this course is approved and the Moodle page is set up, a link will be placed here.

title: Gospel of John (CBS)/Week 8


text:
File talk:WikiversityPresentation02-2010.pdf

interesting. Hillgentleman | //\\ |Talk 06:42, 1 April 2010 (UTC)
 * Thanks. I was thinking that some pages could link to it.  Any ideas?  --AFriedman (talk) 03:55, 4 April 2010 (UTC)
 * It could help to look at: Presentations or In the media or Category:Wikiversity publicity, Erkan Yilmaz uses the Chat (try) 09:41, 4 April 2010 (UTC)

Deletion
None of the images are necessary for the presentation's content and it's relatively trivial to take them out. Why not give a period of time that allows for removal of the images, rather than the standard speedy delete? --AFriedman (talk) 20:25, 7 April 2010 (UTC)
 * So you can take these out and re-upload? --Gbaor 16:31, 14 June 2010 (UTC)


text:
Portal:Agape World Fellowship/Programs/Christian Leadership/Related

The Agape World Fellowship School will not be offering any other programs at this time. Please suggest any program you would like to see developed on the main talk page.


text:
Portal:Agape World Fellowship/Programs/Christian Leadership/Resources

 * All About God Servant Leadership
 * Teal Trust. Christian Leadership World


text:
Talk:Protective relays

This infomatiuon is applicable to Inverse-time over curent relays only. There is a myriad of relays without built it time delay and such distiction shoul be made. Case in point are device 21, 87, 50, 32 ...

title: Talk:Protective relays


text:
User:BRUTE

 * My page on Meta

title: User:BRUTE


text:
User talk:BRUTE

 Hello BRUTE, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Adambro 08:51, 1 April 2010 (UTC)

title: User talk:BRUTE


text:
User:Auro.001

My name is Augustön. I am from Minnesota,USA

title: User:Auro.001


text:
User talk:Auro.001

 Hello Auro.001, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. Erkan Yilmaz uses the Chat (try) 12:25, 1 April 2010 (UTC)

 Hi , I am Percy. Nice to meet you. I love the beach, swimming, fishing, and I am currently doing some research at Wikiversity on oceanography. I am also learning to play piano. What do you like? Can I be your mascot?

title: User talk:Auro.001


text:
How to use SPSS/Entering data

To create a variable to enter into the data, just click on the column that starts with var001 when SPSS is initially opened. You can also start a new data set or open an existing one depend on what you need. To enter in data into SPSS, you must realize what the survey or your actual data is trying to tell you. This sounds simple, but can be frustrating to first timers. If you are wanting to compare the bench press weight vs fixed weight bench press you must consider several factors.

What level of measurement is the variable:

Nominal- No ranking what so ever. Such as, all variables are equal and unranked. An example would be: Did you use a bench press? Yes or no? The answers cannot be ranked.

Ordinal- All variables and values and can be ranked. However, the data itself is in groups. An example would be: How much can you bench press? 0-120 121-150 151-200 201+. The answers are grouped, but they have the advantage that they can be ranked.

Interval- The data itself can be written down as a number and can be any value except zero. For example: Please write down how old you are. Obviously, it is impossible for a person to write down 0. The person will more than likely write a number higher than 0 or else it shouldn't be in the data.

Ratio- is a variable in which a number of any value can be written down including zero. For example, Please write how many pounds you can bench press. The respondent can answer with any value they choose including zero.

Now that you know the level of measurement for the variable, you can decide how many columns you would like to break a question up into. Sometimes its beneficial to have a question that is check all that apply on a survey, but when you code it you might consider breaking into a bunch of dichotomous variables like yes or no responses that are coded as 1 or 2. Also, it's helpful if you write on the survey what you expect to code each response as from a value that is 0 to 1000000000 or higher if needed. Generally, just keep must variables that are ordinal or nominal down to 10 categories/values.

To create a variable to enter into the data, just click on the column that starts with var001 when SPSS is initially opened. You can also start a new data set or open an existing one depend on what you need. Keep clicking on the columns and entering in all the variables and changing their names as needed. Next, you'll notice a bunch of rows with numbers on the left side. These numbers are each individual case or survey response. Just enter in the values for each question the respondent filled out on a survey and put it into the corresponding column and case number. As a hint, it helps to number each individual survey before entering in your data. On the variable view page, you can edit many things about each variable such as what level of measurement it is, assign a label, enter in which value is, and even change the name.

title: How to use SPSS/Entering data


text:
Talk:Wikiversity open letter project

It isn't real clear where exactly to add one's name to the list. Jon Awbrey 15:04, 1 April 2010 (UTC)

title: Talk:Wikiversity open letter project


text:
User talk:Slashme

 Hello Slashme, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 16:52, 1 April 2010 (UTC)

Pre-reading for week 2
Hi! I noticed your recent contributions to Pre-reading for week 2. What would be a more descriptive name for this resource? Is there a course it should be associated with? -- Dave Braunschweig (discuss • contribs) 19:00, 3 March 2016 (UTC)

I think I found it at Human vision and function/Part 1: Perception of objects/Pre-reading for Topic 2. I've moved the content there. If you want or need to go back to previous content, you can find it on the History page. Let me know if you have any questions. -- Dave Braunschweig (discuss • contribs) 19:05, 3 March 2016 (UTC)

I just created a new version of a picture that was used in the course, and contributed it. I have no involvement in the actual curation of the content, so I don't mind if it gets moved anywhere. Thanks! --Slashme (discuss • contribs) 21:22, 3 March 2016 (UTC)

title: User talk:Slashme


text: Educational Media Awareness Campaign/Geography: General/POTD 5


title: File:Egm6341.s10.mtg37.djvu


text:
User:Romaine/monobook.js

mw.loader.load('//nl.wikipedia.org/w/index.php?title=User:Romaine/insertmonobook.js&action=raw&ctype=text/javascript');

title: User:Romaine/monobook.js


text: File:Addie model.jpg

title: File:Addie model.jpg


text: File:Rapid prototyping.jpg

title: File:Rapid prototyping.jpg


text:
User:UTECH

Welcome to the School of Engineering and Technology Founded in 1993, UTECH is one of the most private and prestigious graduate engineering schools in TunisIa. We prepare professionals who are ready to meet the challenges of the global marketplace in information’s technology. The programs at UTECH University’s School of Engineering and Technology lead to Licence’s and Master’s degrees in computer engineering, Communication Networks,  management, marketing and business The courses on offer at Telecom Bretagne cover the following advanced topics: •	Communication networks •	Computer science •	Web technologies •	Network security •	Mobile communications •	Signal and image processing •	Turbocodes (Telecom Bretagne invention, see our Turbocodes section) •	Speech recognition and synthesis •	Underwater acoustics •	Integrated circuit design •	Antennas and propagation •	Optical networks •	Management •	IT marketing and business Through their studies and experiences here, students receive a strong, general education background in and out of the classroom. Using the training they receive, students are more aware of their social responsibilities to the community. As professionals, they can appreciate the importance of continuing professional development and lifelong learning. The School’s faculty members and students have multidisciplinary scholarly and teaching. The School emphasizes open-ended problem solving in all its programs. We prepare the workforce that will create the ideas of the future and apply them to improve society. Join us in building your future – and help us build the technology future for our nation and world!

title: User:UTECH


text:
Utech

Link to any subpages this page might have

 Welcome to UTECH, the School of Engineering and Technology Founded in 1993, UTECH is one of the most private and prestigious graduate engineering schools in TunisIa. We prepare professionals who are ready to meet the challenges of the global marketplace in information’s technology.

The programs at UTECH University’s School of Engineering and Technology lead to Licence’s and Master’s degrees in computer engineering, Communication Networks,  management, marketing and business

The courses on offer at UTECH cover the following advanced topics:

•	Communication networks •	Computer science •	Web technologies •	Network security

•	Mobile communications

•	Signal and image processing •	Speech recognition and synthesis •	Underwater acoustics

•	Integrated circuit design

•	Antennas and propagation •	Optical networks •	Management •	IT marketing and business

Through their studies and experiences here, students receive a strong, general education background in and out of the classroom. Using the training they receive, students are more aware of their social responsibilities to the community. As professionals, they can appreciate the importance of continuing professional development and lifelong learning.

The School’s faculty members and students have multidisciplinary scholarly and teaching.

The School emphasizes open-ended problem solving in all its programs. We prepare the workforce that will create the ideas of the future and apply them to improve society.

Join us in building your future – and help us build the technology future for our nation and world!

title: Utech


text:
User talk:UTECH

 Hello UTECH, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 13:48, 2 April 2010 (UTC)

Note
Your page on Utech is overly promotional. While we allow some discussions about universities, we are not an advertising site. Please tone down accordingly. Ottava Rima (talk) 13:48, 2 April 2010 (UTC)

title: User talk:UTECH


text: Survey research and design in psychology/Abbreviations


text:
User talk:WijnhovenF

 Hello WijnhovenF, 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. 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.

 * 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.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 14:06, 2 April 2010 (UTC)

title: User talk:WijnhovenF


text:
Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

title: Degrees of freedom (statistics)


text:
User:Romaine/vector.js

mw.loader.load('//nl.wikipedia.org/w/index.php?title=User:Romaine/insertvector.js&action=raw&ctype=text/javascript');

title: User:Romaine/vector.js


text: File:Temp.ogg

title: File:Temp.ogg


text:
User:Egm6341.s10.Team4.nimaa&m/HW6

= Problem 2: Rate of momentum change for optimal control problem =

Given
Envisage the below figure as free body diagram of an aircraft:

.

likewise consider the shown axes and vectors, for $$\displaystyle v+dv $$ at $$\displaystyle t+dt $$:

.

Find
Show that $$\displaystyle dp_{\bar y}=mvd\gamma $$.

Solution
According to the above figure, we can survey these two cases at $$\displaystyle t $$ and $$\displaystyle t+dt $$, the velocity of the aircraft after $$\displaystyle dt $$ will reach to $$\displaystyle v+dv $$ and the angle between the aircraft and horizontal axis will reach to the $$\displaystyle \gamma+d\gamma $$. Thus, regarding $$\displaystyle d\gamma $$ generated angle between two velocity vectors, we can write:

 * $$\displaystyle

d\gamma\approxeq sin(d\gamma)=\frac{dv_{\bar y}}{v+dv} $$

 * $$\displaystyle

\Rightarrow dv_{\bar y}=v.d\gamma+dv.d\gamma $$

The amount of $$\displaystyle dv.d\gamma $$ can be neglected in front of $$\displaystyle v.d\gamma $$.

 * $$\displaystyle

\Rightarrow dv_{\bar y}=v.d\gamma $$

On the other hand, momentum is defined as $$\displaystyle p=mv $$. So, we have:

dp_{\bar y}=d(m.v_{\bar y})=v_{\bar y}.dm+m.dv_{\bar y} $$

Assuming the amount of $$\displaystyle dm $$ to be negligible in front of changes in velocity;

dp_{\bar y}=d(m.v_{\bar y})=m.dv_{\bar y} $$

Finally, we can summarize the answer as:

dp_{\bar y}=m.dv_{\bar y}=m.v.d\gamma $$

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

$$\displaystyle dp_{\bar y}=m.v.d\gamma $$
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }.
 * }.

Author
Solved and typed by - Egm6341.s10.Team4.nimaa&m 03:08, 3 April 2010 (UTC) .

= Problem 7: Expression for Hermitian interpolation at $$\displaystyle t_{i+\frac{1}{2}} $$ =

Given
Consider the Hermitian interpolation by the following equation (on slide [[media:Egm6341.s10.mtg35.djvu|35-2]]):
 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle z(s)=\sum_{i=0}^3 c_is^i

 * }
 * }

Find
Show the following expression can be obtained for $$\displaystyle z'_{i+\frac{1}{2}} $$:

 * $$\displaystyle

z_{i+\frac{1}{2}}=z(s=\frac{1}{2})=\frac{1}{2}(z_i+z_{i+1})+\frac{h}{8}(f_i-f_{i+1}) $$

Solution
By differentiating from the equation for $$\displaystyle z(s) $$, we will attain:

 * $$\displaystyle

z'(s)=\sum_{i=1}^3 ic_is^{i-1} $$

Now, we can compute the followings:

 * $$\displaystyle

z_i=z(s=0)=\sum_{i=0}^3 c_i(0)^i=c_0+0+0+0=c_0 $$

 * $$\displaystyle

z_{i+1}=z(s=1)=\sum_{i=0}^3 c_i(1)^i=c_0+c_1+c_2+c_3 $$

 * $$\displaystyle

z'_i=z'(s=0)=\sum_{i=1}^3 ic_i(0)^{i-1}=c_1+0+0=c_1 $$

 * $$\displaystyle

z'_{i+1}=z'(s=1)=\sum_{i=1}^3 ic_i(1)^{i-1}=c_1+2c_2+3c_3 $$

 * $$\displaystyle

\dot{z}=\frac{dz}{dt}=\frac{dz}{ds}\times\frac{ds}{dt}=z'\times\frac{1}{h} $$

 * $$\displaystyle

\Rightarrow h(f_i-f_{i+1})=h(\dot{z}_i-\dot{z}_{i+1})=(z'_i-z'_{i+1}) $$

 * $$\displaystyle

\Rightarrow \frac{h}{8}(f_i-f_{i+1})=\frac{h}{8}(\dot{z}_i-\dot{z}_{i+1})=\frac{1}{8}(z'_i-z'_{i+1}) $$

 * $$\displaystyle

\Rightarrow\begin{cases} z_i+z_{i+1}=2c_0+c_1+c_2+c_3 \\ f_i-f_{i+1}=-2c_2-3c_3 \end{cases} $$

 * $$\displaystyle

\Rightarrow\begin{cases} \frac{1}{2}(z_i+z_{i+1})=c_0+\frac{1}{2}c_1+\frac{1}{2}c_2+\frac{1}{2}c_3 \\ \frac{h}{8}(f_i-f_{i+1})=-\frac{1}{4}c_2-\frac{3}{8}c_3 \end{cases} $$

 * $$\displaystyle

\Rightarrow\frac{1}{2}(z_i+z_{i+1})+\frac{h}{8}(f_i-f_{i+1})=c_0+\frac{1}{2}c_1+\frac{1}{2}c_2+\frac{1}{2}c_3-\frac{1}{4}c_2-\frac{3}{8}c_3=c_0+\frac{1}{2}c_1+\frac{1}{4}c_2+\frac{1}{8}c_3 $$

The acquired foregoing equation is equal to RHS of the expression. Now, we can compute the LHS of it as:

 * $$\displaystyle

LHS=z_{i+\frac{1}{2}}=z(s=\frac{1}{2})=\sum_{i=0}^3 c_i(\frac{1}{2})^i=c_0\times 1+c_1\times\frac{1}{2}+c_2\times\frac{1}{4}+c_3\times\frac{1}{8}=c_0+\frac{1}{2}c_1+\frac{1}{4}c_2+\frac{1}{8}c_3 $$

 * $$\displaystyle

\Rightarrow LHS=RHS $$

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

$$\displaystyle z_{i+\frac{1}{2}}=z(s=\frac{1}{2})=\frac{1}{2}(z_i+z_{i+1})+\frac{h}{8}(f_i-f_{i+1}) $$
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }.
 * }.

Author
Solved and typed by - Egm6341.s10.Team4.nimaa&m 04:15, 3 April 2010 (UTC) .

= Problem 8: Expression for derivative of Hermitian interpolation at $$\displaystyle t_{i+\frac{1}{2}} $$ =

Given
Consider the Hermitian interpolation by the following equation (on slide [[media:Egm6341.s10.mtg35.djvu|35-2]]):
 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle z(s)=\sum_{i=0}^3 c_is^i

 * }
 * }

Find
Show the following expression can be obtained for $$\displaystyle z'_{i+\frac{1}{2}} $$:

 * $$\displaystyle

z'_{i+\frac{1}{2}}=z'(s=\frac{1}{2})=-\frac{3}{2}(z_i-z_{i+1})-\frac{1}{4}(z'_i+z'_{i+1}) $$

Solution
By differentiating from the equation for $$\displaystyle z(s) $$, we will attain:

 * $$\displaystyle

z'(s)=\sum_{i=1}^3 ic_is^{i-1} $$

Now, we can compute the followings:

 * $$\displaystyle

z_i=z(s=0)=\sum_{i=0}^3 c_i(0)^i=c_0+0+0+0=c_0 $$

 * $$\displaystyle

z_{i+1}=z(s=1)=\sum_{i=0}^3 c_i(1)^i=c_0+c_1+c_2+c_3 $$

 * $$\displaystyle

z'_i=z'(s=0)=\sum_{i=1}^3 ic_i(0)^{i-1}=c_1+0+0=c_1 $$

 * $$\displaystyle

z'_{i+1}=z'(s=1)=\sum_{i=1}^3 ic_i(1)^{i-1}=c_1+2c_2+3c_3 $$

 * $$\displaystyle

\Rightarrow\begin{cases} z_i-z_{i+1}=c_0-(c_0+c_1+c_2+c_3)=-c_1-c_2-c_3 \\ z'_i+z'_{i+1}=2c_1+2c_2+3c_3 \end{cases} $$

 * $$\displaystyle

\Rightarrow\begin{cases} -\frac{3}{2}(z_i-z_{i+1})=\frac{3}{2}c_1+\frac{3}{2}c_2+\frac{3}{2}c_3\\ -\frac{1}{4}(z'_i+z'_{i+1})=-\frac{1}{2}c_1-\frac{1}{2}c_2-\frac{3}{4}c_3 \end{cases} $$

 * $$\displaystyle

\Rightarrow -\frac{3}{2}(z_i-z_{i+1})-\frac{1}{4}(z'_i+z'_{i+1})=(\frac{3}{2}-\frac{1}{2})c_1+(\frac{3}{2}-\frac{1}{2})c_2+(\frac{3}{2}-\frac{3}{4})c_3=c_1+c_2+\frac{3}{4}c_3 $$

The acquired foregoing equation is equal to RHS of the expression. Now, we can compute the LHS of it as:

 * $$\displaystyle

LHS=z'_{i+\frac{1}{2}}=z'(s=\frac{1}{2})=\sum_{i=1}^3 ic_i(\frac{1}{2})^{i-1}=1\times c_1\times (\frac{1}{2})^{1-1}+2\times c_2\times (\frac{1}{2})^{2-1}+3\times c_3\times (\frac{1}{2})^{3-1}=c_1+c_2+\frac {3}{4}c_3 $$

 * $$\displaystyle

\Rightarrow LHS=RHS $$

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

$$\displaystyle z'_{i+\frac{1}{2}}=z'(s=\frac{1}{2})=-\frac{3}{2}(z_i-z_{i+1})-\frac{1}{4}(z'_i+z'_{i+1}) $$
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }.
 * }.

Author
Solved and typed by - Egm6341.s10.Team4.nimaa&m 04:23, 3 April 2010 (UTC) .

title: User:Egm6341.s10.Team4.nimaa&m/HW6


text:
User talk:Sahfan

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title: User talk:Sahfan


title: File:HW-6.2.jpg


title: User:Egm6341.s10.Team2/HW6