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User talk:ColeVan

Hello Former Student!

I'm writing to you because you took a class from me in the past few years at the Art Institute. As of Spring, 2010, I'll not be teaching further classes at AIS for the foreseeable future. (We're parting ways on good terms!) Until now, you've been able to reach my Wikiversity educational resources from my website, but I've decided to delete that link. You can still reach all of those materials here.

If you're interested in what I'm up to in the future (which will include an album in 2010 and a novel in 2011) you can friend my facebook page or drop me an email at info@stevenarntson.info and you'll receive a periodic update about performances, classes, and publications.

If you know any current or former students of mine who might be interested in any of this, please forward this information if you have a moment.

I hope all is well for you.
 * Best! Stevenarntson

Personal Essay
I think there is a good structure here, and the essay is working in some respects. Right now it could use more numbers, especially when it comes to cost. If discussing how much a credit costs at a for profit institution versus a nonprofit, don't stick to generalities: go find out for sure. There are a number of moments here where the essay has a chance to shine, but doesn't get down to brass tacks when it's necessary.

The issue with throwing food out is in interesting one, but may not be apposite to your point, viz. the school is bound by state law, which mandates certain requirements for food preparation that aren't met by students in culinary programs--the food made for class can't even be given away for free, legally.

In revising, sift through and find out where specifics are needed, and what the strongest arguments are. Then follow up on those.

Good start! Best, Stevenarntson

title: User talk:ColeVan


text:
User:Egm6321.f09.team3.diggs/HW7

= 1 Hyperbolic Tangent Equivalent =

Given
$$\frac{x}{2} ln (\frac{1+x}{1-x}) - 1 = x tanh^{-1}(x) - 1$$

Show
The equivalence of the above statement.

Solution
In HW 6, we showed

$$\frac{1}{2} ln (\frac{1+x}{1-x}) = tanh^{-1}(x) $$

Substituting in,

$$ x tanh^{-1}(x) - 1 = x tanh^{-1}(x) - 1$$

which is equivalent.

= 2 Qn as odd/even =

Given
$$Q_n(x) = P_n(x) \cdot tanh^{-1}(x) - 2 \sum \frac{2n-2j+1}{(2n-j+1)j} \cdot P_{n-j}(x)$$

Find
The values for n (2k, 2k+1) for which $$Q_n(x)$$ is odd or even.

Solution
Recall that $$tanh^{-1}(x)$$ is odd. and for n = 2k, $$P_n(x)$$ is even and for n=2k+1, $$P_n(x)$$ is odd.

Therefore, for n = 2k, $$Q_n(x)$$ is odd (because odd * even = odd)

Alternately, for n = 2k+1, $$Q_n(x)$$ is even (because odd * odd = even)

= 3 Plots of Pn and Qn =

Given
$$P_n(x)$$ for n = 0, 1, 2, 3, 4

and

$$Q_n(x)$$ for n = 0, 1, 2, 3, 4

Find
Plot all functions.

Solution
$$P_0(x) = \alpha_0 = 1$$

$$P_1(x) = 2 \mu \alpha_1 = x$$

$$P_2(x) = (- \alpha_1 + 4) = \frac{1}{2}(3x^2 - 1) $$

$$P_3(x) = -4 \mu \alpha_2 + 8 \mu^3 \alpha_3 = \frac{1}{2}(-3x + 5x^3) $$

$$P_4(x) = \alpha_2 - \mu^2 \alpha_3 + 16 \mu^4 \alpha_4 = \frac{1}{8}(3 - 30 x^2 + 35 x^4)$$

$$Q_n(x) = P_n(x) \cdot tanh^{-1}(x) - 2 \sum_{j=1,3,5}^J \frac{2n-2j+1}{(2n-j+1)j} \cdot P_{n-j}(x) $$ where $$ J:=1+2[\frac{n-1}{2}]$$

$$ n=0 $$; $$ J=1 $$

$$Q_0(x) = P_0(x) \cdot tanh^{-1}(x) - 2 \sum_{j=1}^1 \frac{2(0)-2(1)+1}{(2(0)-(1)+1)1} \cdot P_{0-1}(x) $$ $$Q_0(x) =1\cdot tanh^{-1}(x) - 2 (0)= tanh^{-1}(x) $$

$$ n=1 $$; $$ J=1 $$

$$Q_1(x) = P_1(x) \cdot tanh^{-1}(x) - 2 \sum_{j=1}^1 \frac{2 (1) -2(1)+1}{(2(1)-(1)+1)(1)} \cdot P_{1-1}(x)$$

$$Q_1(x) = x \cdot tanh^{-1}(x) - 2 \sum_{j=1}^1 \frac{2 (1) -2(1)+1}{(2(1)-(1)+1)(1)} \cdot (1) = x tanh^{-1}(x)-1 $$

$$ n=2 $$; $$ J=1 $$

$$Q_2(x) = P_2(x) \cdot tanh^{-1}(x) - 2 \sum_{j=1}^1 \frac{2(2)-2(1)+1}{(2(2)-(1)+1)(1)} \cdot P_{(2)-(1)}(x) $$

$$Q_2(x) = \frac{1}{2}(3x^2 - 1) \cdot tanh^{-1}(x) - 2 \sum_{j=1}^1 \frac{2(2)-2(1)+1}{(2(2)-(1)+1)(1)} \cdot x $$

$$Q_2(x) = \frac{1}{2}(3x^2 - 1) \cdot tanh^{-1}(x) -  \frac{5}{2} x $$

$$ n=3 $$; $$ J=3 $$

$$Q_3(x) = P_3(x) \cdot tanh^{-1}(x) - 2 \sum_{j=1,3}^3 \frac{2(3)-2j+1}{(2(3)-j+1)j} \cdot P_{3-j}(x) $$

$$Q_3(x) = P_3(x) \cdot tanh^{-1}(x) - 2 \left [ \frac{2(3)-2(1)+1}{(2(3)-(1)+1)(1)} \cdot P_{3-1}(x) + \frac{2(3)-2(3)+1}{(2(3)-(3)+1)(3)} \cdot P_{3-3}(x)\right] $$

$$Q_3(x) = \frac{1}{2}(-3x + 5x^3) \cdot tanh^{-1}(x) - 2 \left [ \frac{2(3)-2(1)+1}{(2(3)-(1)+1)(1)} \cdot \frac{1}{2}(3x^2 - 1) (x) + \frac{2(3)-2(3)+1}{(2(3)-(3)+1)(3)} \cdot 1 \right] = \frac{1}{2}(-3x + 5x^3) \cdot  tanh^{-1}(x) - (\frac{5}{2}x^3+\frac{1}{3}) $$

$$ n=4 $$; $$ J=3 $$

$$Q_4(x) = P_4(x) \cdot tanh^{-1}(x) - 2 \sum_{j=1,3}^3 \frac{2(4)-2j+1}{(2(4)-j+1)j} \cdot P_{4-j}(x) $$

Q_4(x) = P_4(x) \cdot tanh^{-1}(x) - 2 \left [ \frac{2(4)-2(1)+1}{(2(4)-(1)+1)(1)} \cdot P_{4-1}(x) +  \frac{2(4)-2(3)+1}{(2(4)-(3)+1)(1)} \cdot P_{4-3}(x) \right ]

$$Q_4(x) = \frac{1}{8}(3 - 30 x^2 + 35 x^4) \cdot tanh^{-1}(x) - 2 \left [ \frac{2(4)-2(1)+1}{(2(4)-(1)+1)(1)} \cdot \frac{1}{2}(-3x + 5x^3) +  \frac{2(4)-2(3)+1}{(2(4)-3+1)(1)} \cdot x \right] $$

$$Q_4(x) = \frac{1}{8}(3 - 30 x^2 + 35 x^4) \cdot tanh^{-1}(x) - (\frac{35}{8} x^3-\frac{55}{24}x) $$

Plots:

P(x)

Q(x)

= 4 Proof of Pn and Qn =

Given
$$ = $$

Show
$$ = 0$$

Solution
Recall $$ = \int P_n(x) \cdot Q_n(x) dx$$

Since Pn(x) is even and Qn(x) is odd for any value of n, the integral is zero.

= 5 Distance Proof =

Given
$$(r_{PQ})^2 = (r_P)^2 + (r_Q)^2 - 2r_Pr_Q cos \gamma$$

where $$ cos \gamma = cos \theta_Q cos \theta_P cos(\varphi_Q - \varphi_P) + sin \theta_P sin \theta_P $$

Show
The above relation is true.

Solution
Starting with,

$$(r_{PQ})^2 = \sum (x_Q^i - x_P^i)^2$$

where

$$x_P^1 = r_P cos \theta_P cos \varphi_P$$

$$x_P^2 = r_P cos \theta_P sin \varphi_P$$

$$x_P^3 = r_P sin \theta_P$$

$$x_Q^1 = r_Q cos \theta_Q cos \varphi_Q$$

$$x_Q^2 = r_Q cos \theta_Q sin \varphi_Q$$

$$x_Q^3 = r_Q sin \theta_Q$$

$$(r_{PQ})^2 = (x_Q^1 - x_P^1)^2 + (x_Q^2 - x_P^2)^2 + (x_Q^3 - x_P^3)^2$$

$$(r_{PQ})^2 = (r_Q cos \theta_Q cos \varphi_Q - r_P cos \theta_P cos \varphi_P)^2 + (r_Q cos \theta_Q sin \varphi_Q - r_P cos \theta_P sin \varphi_P)^2 + (r_Q sin \theta_Q - r_P sin \theta_P)^2$$

$$(r_{PQ})^2 = r_Q^2 (cos \theta_Q)^2 (cos \varphi_Q)^2 - 2 r_Q r_P cos \theta_Q cos \theta_P cos \varphi_Q cos \varphi_P + r_P^2 (cos \theta_P)^2 (cos \varphi_P)^2 + r_Q^2 (cos \theta_Q)^2 (sin \varphi_Q)^2 - 2 r_Q r_P cos \theta_Q cos \theta_P sin \varphi_Q sin \varphi_P + r_P^2 (cos \theta_P)^2 (sin \varphi_P)^2 + r_Q^2 (sin \theta_Q)^2 - 2 r_Qr_P sin \theta_Q sin \theta_P + r_P^2 (sin \theta_P)^2$$

$$(r_{PQ})^2 = r_Q^2 (cos \theta_Q)^2 ((cos \varphi_Q)^2 + (sin \varphi_Q)^2) - 2 r_Q r_P cos \theta_Q cos \theta_P (cos \varphi_Q cos \varphi_P + sin \varphi_Q sin \varphi_P)+ r_P^2 (cos \theta_P)^2 ((cos \varphi_P)^2 + (sin \varphi_P)^2) + r_Q^2 (sin \theta_Q)^2 - 2 r_Qr_P sin \theta_Q sin \theta_P + r_P^2 (sin \theta_P)^2$$

$$(r_{PQ})^2 = r_Q^2((cos \theta_Q)^2 + (sin \theta_P)^2) + r_P^2((cos \theta_Q)^2 + (sin \theta_P)^2) - 2r_Q r_P [ cos \theta_Q cos \theta_P cos(\varphi_Q - \varphi_P) + sin \theta_P sin \theta_P ]$$

given the defintion of $$cos \gamma = [...] $$

$$(r_{PQ})^2 = r_Q^2 + r_P^2 - 2r_Q r_P cos \gamma $$

= 6 Binomial Proof =

Given
a. $$(x + y)^r = \sum (r k) x^{r-k}y^k$$

b. $$(r k) = \frac{r(r-1)...(r-k+1)}{k!}$$

Find
$$(1-x)^{-1/2} = \sum \alpha_i x^i$$

where

$$\alpha_i = \frac{1 \cdot 3 \cdot ... \cdot (2i-1)}{2 \cdot 4 \cdot ... \cdot (2i)}$$

Solution
Substitute b into a, since r is not an integer, but is any real value.

$$(x + y)^r = \sum \frac{r(r-1)...(r-k+1)}{k!} \cdot x^{r-k}y^k$$

$$y = 1$$, so $$y^k=1$$ for all values of k.

$$(x + 1)^r = \sum \frac{r(r-1)...(r-k+1)}{k!} \cdot x^{r-k} $$

$$r = -\frac{1}{2}$$, Substitute in:

$$(x + 1)^{-\frac{1}{2}} = \sum \frac{-\frac{1}{2}(-\frac{1}{2}-1)...(-\frac{1}{2}-k+1)}{k!} \cdot x^{-\frac{1}{2}-k} $$

Now all for -x:

$$(-x + 1)^{-\frac{1}{2}} = \sum \frac{-\frac{1}{2}(-\frac{1}{2}-1)...(-\frac{1}{2}-k+1)}{k!} \cdot (-x)^{-\frac{1}{2}-k} $$

let $$i = -\frac{1}{2}-k$$ to get

$$(1-x)^{-\frac{1}{2}} = \sum \frac{(2i-1)!}{(2i)!} \cdot x^i $$

Note that $$-x^i = (-1)^i \cdot x^i$$, which is combined into the fractional factorial.

therefore,

$$(1-x)^{-\frac{1}{2}} = \sum \alpha_i \cdot x^i $$

where $$\alpha_i = \frac{(2i-1)!}{(2i)!}$$, as expected.

= 7 Expressions for Pn =

Given
$$\frac{1}{\sqrt{A(\mu, \rho)}} = \sum \alpha_i (2\mu \rho - \rho^2)^i$$

Find
The expressions for $$P_3$$, $$P_4$$, $$P_5$$ using the expansion

Solution
$$\frac{1}{\sqrt{A(\mu, \rho)}} = \alpha_0 + \alpha_1 \cdot (2 \mu \rho - \rho^2) + \alpha_2 \cdot (2 \mu \rho - \rho^2)^2 + \alpha_3 \cdot (2 \mu \rho - \rho^2)^3 + \alpha_4 \cdot (2 \mu \rho - \rho^2)^4 + \alpha_5 \cdot (2 \mu \rho - \rho^2)^5$$

where

$$(2 \mu \rho - \rho^2)^2 = 4 \mu^2 \rho^2 - 4 \mu \rho^3 + \rho^4$$

$$(2 \mu \rho - \rho^2)^3 = 8 \mu^3 \rho^3 - 8 \mu^2 \rho^4 + 2 \mu \rho^5 - 4 \mu^2 \rho^4 + 4 \mu \rho^5 + \rho^6$$

$$(2 \mu \rho - \rho^2)^4 = 16 \mu^4 \rho^4 - 16 \mu^3 \rho^5 + 4 \mu^2 \rho^6 - 8 \mu^3 \rho^5 + 8 \mu^2 \rho^6 + 2 \mu \rho^7 -    8 \mu^3 \rho^5 + 8 \mu^2 \rho^6 - 2 \mu \rho^7 + 4 \mu^2 \rho^6 - 4 \mu \rho^7 - \rho^8$$

$$(2 \mu \rho - \rho^2)^5 = 32 \mu^5 \rho^5 - 32 \mu^4 \rho^6 + 8 \mu^3 \rho^7 - 16 \mu^4 \rho^6 + 16 \mu^3 \rho^7 + 4 \mu^2 \rho^8 - 16 \mu^4 \rho^6 + 16 \mu^3 \rho^7 - 4 \mu^2 \rho^8 + 8 \mu^3 \rho^7 - 8 \mu^2 \rho^8 - 2 \mu \rho^9 -    16 \mu^4 \rho^6 + 16 \mu^3 \rho^7 - 4 \mu^2 \rho^8 + 8 \mu^3 \rho^7 - 8 \mu^2 \rho^8 + 2 \mu \rho^9 + 8 \mu^3 \rho^7 - 8 \mu^2 \rho^8 + 2 \mu \rho^9 - 4 \mu^2 \rho^8 + 4 \mu \rho^9 + \rho^10$$

gather by $$\rho$$:

$$\frac{1}{\sqrt{A(\mu, \rho)}} = \alpha_0 + 2 \mu \alpha_1 \cdot \rho + (- \alpha_1 + 4) \rho^2 + (-4 \mu \alpha_2 + 8 \mu^3 \alpha_3) \cdot \rho^3 + (\alpha_2 - \mu^2 \alpha_3 + 16 \mu^4 \alpha_4) \cdot \rho^4 + (6 \mu \alpha_3 - 24 \mu^3 \alpha_4 + 32 \mu^5 \alpha_5) \cdot \rho^5 + ...$$

From Eqn 7, pg 38-4,

$$\alpha_0 = 1$$

$$\alpha_1 = \frac{1}{2}$$

$$\alpha_2 = \frac{3}{8}$$

$$\alpha_3 = \frac{5}{16}$$

$$\alpha_4 = \frac{35}{128}$$

$$\alpha_5 = \frac{63}{256}$$

Therefore,

$$P_0(x) = \alpha_0 = 1$$

$$P_1(x) = 2 \mu \alpha_1 = x$$

$$P_2(x) = (- \alpha_1 + 4) = \frac{1}{2}(3x^2 - 1)$$

$$P_3(x) = -4 \mu \alpha_2 + 8 \mu^3 \alpha_3 = \frac{1}{2}(-3x + 5x^3)$$

$$P_4(x) = \alpha_2 - \mu^2 \alpha_3 + 16 \mu^4 \alpha_4 = \frac{1}{8}(3 - 30 x^2 + 35 x^4)$$

$$P_5(x) = 6 \mu \alpha_3 - 24 \mu^3 \alpha_4 + 32 \mu^5 \alpha_5 = \frac{1}{8} (15 x - 70 x^3 + 63 x^5)$$

as expected.

= Contributing Team Members =

Angela Diggs Egm6321.f09.team3.diggs 20:21, 6 December 2009 (UTC)

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

title: User:Egm6321.f09.team3.diggs/HW7


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User talk:SergeyJ

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Physics/Essays/Fedosin/Selfconsistent electromagnetic constants

Selfconsistent electromagnetic constants is the full set of fundamental constants of classical electromagnetism that are selfconsistent and determine the external definitions of different physical quantities (and its fundamental dimensions), and therefore – the resulting set of the Maxwell's equations. The constants are confirmed by the fact that they work in any systems of measurement and are part of vacuum constants.

The primary set of electromagnetic constants is:
 * 1) the first electromagnetic constant ($$c $$), which is the speed of light or speed of the electromagnetic waves in free space; $$c = 299792458 $$ metres per second.
 * 2) the second electromagnetic constant, which is the impedance of free space $$ Z_0 = 376.73031...$$ Ω.

The secondary set of electromagnetic constants is:

1. the electric constant or vacuum permittivity:
 * $$\varepsilon_0 = \begin{cases} \frac{10^7}{4\pi c^2} = 8.85418782\cdot 10^{-12} \quad \text {F/m}, & \mbox{(SI units)} \\ \frac{1}{4\pi}, & \mbox{(Cgs units)} \end{cases} $$

2. the magnetic constant or vacuum permeability:
 * $$\mu_0 = \begin{cases} 4\pi \cdot 10^{-7} \quad \text {H/m}, \quad \text{Wb/(A m)}, \quad \frac {\text{N}} {A^2}, & \mbox{(SI units)} \\ \frac{4\pi}{c^2}, & \mbox{(Cgs units)} \end{cases} $$

Both, primary and secondary sets of electromagnetic constants are selfconsistent, because they are connected by the following relations:
 * $$\frac{1}{\sqrt{\varepsilon_0\mu_0}} = c ,$$
 * $$\sqrt{\frac{\mu_0}{\varepsilon_0}} = \begin{cases} Z_0 =\frac{1}{c \varepsilon_0} =c \mu_0 = c \cdot 4\pi \cdot 10^{-7}\quad \Omega, & \mbox{(SI units)} \\ Z^{ Cgs }_0 = \frac{4\pi}{c} = 4.19169\cdot 10^{-10} \quad \text {s/cm}, & \mbox{(Cgs units)} \end{cases}$$

Note that in the Cgs units $$\varepsilon_0, \mu_0 \ $$ and $$ Z_0 \ $$ are in the "latent form" and therefore are not defined evidently, but they are the same as defined above. Furthermore, the values of impedance of free space in the SI units and Cgs units are connected by the following relation:
 * $$ Z_0^{Cgs} = 4\pi \varepsilon_0\cdot Z_0^{SI} \ $$

Connection with other constants
The electromagnetic constants may be found in many equations and also connect with other constants. Introducing the Planck constant $$ h $$ and the elementary charge $$ e $$ we find:

the fine structure constant $$\alpha = \frac{e^2}{2\varepsilon_0 hc} $$,

the von Klitzing constant $$R_K = \frac{h}{e^2} $$,

the impedance of free space $$Z_0 =2 \alpha R_ K $$.

Another example is the strong gravitational constant $$\Gamma= \frac{e^2}{4 \pi \varepsilon_0 m_p m_e }$$,

where $$ ~ m_p $$ – the mass of proton, $$ ~ m_e $$ – the mass of electron.

History
There is the delicate problem of electromagnetic constants in the classical electromagnetism up to now. Actually, in the CGS units only two constants: $$c \ $$ (speed of light) and $$4\pi \ $$ are used, but in the SI units there are four constants: $$\varepsilon_0 \ $$ (electric constant), $$\mu_0 \ $$ (electric constant), $$c \ $$ ( speed of light) and $$ Z_0 \ $$ (impedance of free space). Furthermore, the impedance of free space was introduced by Stratton only in the 1941, which are widely used in the applied physics. But the second set ($$\varepsilon_0 \ $$ and $$\mu_0 \ $$) is mostly considered as "artificial" ones, that have no physical meaning, and used only for the sake of dimension consistency of the physical quantities (such as in electrostatic induction with $$\varepsilon_0 \ $$, and in electromagnetic induction with $$\mu_0 \ $$).

However, with the discovery of the quantum Hall effect by von Klitzing (1981) the theorists paid serious attention to the physical essence of resistance (or impedance), which is due to the charges or fluxes. Actually, Yakymakha (1989) first introduced the magnetic coupling constant, defined through the magnetic monopole, and in the 1994 for the first time the impedance of free space was observed in the quantum 2D-electron system at the silicon- dioxide interface of the serial MOSFETs. Further, Tsu and Datta (2003) considered for the first time the new interpretation of the wave function in the Schrodinger equation, defined through the impedance of free space. Increasing attention to the impedance of free space as part of the general problem of the characteristic impedance was shown by Zel’dovich (2008).

Electromagnetic fields
The main conception of the Cgs units is defined on the primary nature of electromagnetic fields. So, here we have the same dimensions for electric and magnetic fields:
 * $$[E] = [D] = [H] = [B] = L^{-1/2}M^{1/2}T^{-1} \ $$

Contrary to the Cgs units, the SI units have different dimensions of the electromagnetic fields (in vacuum):
 * $$D = \varepsilon_0E \ $$
 * $$B = \mu_0H, \ $$

which is based on the different dimensions of electric and magnetic charges:
 * $$[e]^{SI} = \ $$Coulomb,
 * $$[q_m]^{SI} = \ $$J/A.

In the general case, when the space is filled by matter, these definitions are changed:
 * $$D = \varepsilon_0 \varepsilon_r E \ $$

 * $$B = \mu_0\mu_r H, \ $$

where $$\varepsilon_r \ $$ is the relative permittivity, and $$\mu_r \ $$ is the relative permeability.

In the electromagnetic wave propagation process we have the following relationships between electric and magnetic fields:
 * $$\sqrt{\mu_r}\mathbf{H} = \sqrt{\varepsilon_r}\mathbf{E} \ $$ (Cgs units)
 * $$\sqrt{\mu_0\mu_r}\mathbf{H} = \sqrt{\varepsilon_0\varepsilon_r}\mathbf{E}. \ $$ (SI units)

Note that, in the Cgs units it is hard to define the wave impedance, and therefore it is often said that there are no any wave impedance. But using the generalized definition of the wave impedance in the form:
 * $$Z = \sqrt{\frac{\mu_0\mu_r}{\varepsilon_0\varepsilon_r}}, \qquad  Z^{ Cgs } =\frac{4\pi }{c} \sqrt{\frac{\mu_r}{\varepsilon_r}},  $$

we can rewrite the above equations for the wave in the general form:
 * $$\mathbf{E} = \frac{Z^{ Cgs }}{Z^{ Cgs }_0}\mathbf{H} \ $$ (Cgs units)
 * $$\mathbf{E} = Z \mathbf{H}, \ $$ (SI units)

where the fact of the same dimensions of electric and magnetic fields in the Cgs units is considered.

Reactive parameters
The same problem of dimensions equality is presented in the Cgs units for reactive parameters. Actually, the standard capacitance is defined as:
 * $$C = \frac{Q}{V}, \ $$

where the dimension of electric charge in Cgs units is $$[Q] = L^{3/2}M^{1/2}T^{-1} \ $$, and the dimension of electric voltage is $$[V] = L^{1/2}M^{1/2}T^{-1} \ $$. So, capacitance in the Cgs units has dimension of the length $$[C] = L. \ $$ Furthermore, the standard inductance is defined as:
 * $$L = c\frac{\Phi}{I}, \ $$

where the dimension of magnetic flux is $$[\Phi] = L^{3/2}M^{1/2}T^{-1} \ $$, and the dimension of electric current in the Cgs units is $$[I] = L^{3/2}M^{1/2}T^{-2} \ $$. So, inductance has the same dimension of the length $$[L] = L \ $$.

LC circuit
The main problem in the Cgs units is the LC circuit resonance parameters. Actually, the natural values of the resonance frequency ($$\omega_R \ $$) and characteristic impedance ($$ Z_R \ $$) in a lossless line are working well in the SI units only:
 * $$\omega_R = \frac{1}{\sqrt{LC}}\ $$
 * $$ Z_R = \sqrt{\frac{L}{C}}. \ $$

But in the Cgs units characteristic impedance is dimensionless and angular frequency is reverse square of the length. Therefore, theoretics which prefer Cgs units, when considering LC circuit use the SI units.

So, redefinition of them through the electromagnetic constants is needed:
 * $$\omega_R = \frac{c}{\sqrt{LC}}\ $$
 * $$ Z_R = Z^{ Cgs }_0\sqrt{\frac{L}{C}}. \ $$

Maxwell equations
Considering the following relationships between electromagnetic constants:
 * $$\varepsilon_0 = \frac{1}{c Z_0}, \quad Z^{ Cgs }_0 = \frac{4\pi }{c}, $$
 * $$\mu_0 = \frac{Z_0}{c}.$$

In the Cgs units, macroscopic Maxwell's equations can be rewritten in the normalized form:
 * $$ \nabla \times \mathbf{H} = Z^{ Cgs }_0 \mathbf{J}_f + \frac{1}{c} \frac{\partial \mathbf{D}} {\partial t}$$
 * $$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}} {\partial t}$$
 * $$\nabla \cdot \mathbf{B} =0$$
 * $$\nabla \cdot \mathbf{D} = c Z^{ Cgs }_0 \rho_f .$$

where $$\rho_f \ $$ is the free electric charge 3D-density, and $$ J_f \ $$ is the current density of free charges.

Note that in this normalized form there are only the primary electromagnetic constants included (without $$4\pi \ $$).

Coulomb force
The electric Coulomb's Law for two elementary charges $$e \ $$ is defined as:
 * $$F = \frac{1}{4\pi \varepsilon_0}\cdot \frac{e^2}{r^2}. \ $$

In the Cgs units we have:
 * $$F^ {Cgs} = \frac{e^2}{r^2}. \ $$

The magnetic force between two fictitious elementary magnetic charges can be defined as follows:
 * $$F_m = \frac{1}{4\pi \mu_0}\cdot \frac{q_m^2}{r^2}, \ $$

where $$q_m = \frac{h}{e}$$ is the magnetic charge. The same in the Cgs units is:
 * $$F^{ Cgs }_m = \frac{g_0^2}{r^2}, \ $$

where
 * $$g_0 = \frac{q_m}{Z^{ Cgs }_0} = \frac{\hbar c}{2e} \ $$

is the normalized magnetic charge (or Dirac's monopole in the Cgs units). Furthermore, electric and magnetic charges in the Cgs units have the same dimensions:
 * $$[g_0] = [e] = L^{3/2}M^{1/2}T^{-1} \ $$

and could be compared:
 * $$\frac{g_0}{e} = \frac{\hbar c}{2e^2} = \frac{1}{2\alpha^{Cgs} } = \sqrt{\frac{\beta^{Cgs} }{\alpha^{Cgs} }}=2 \beta^{Cgs}, \ $$

where $$\alpha^{Cgs} = \frac{e^2}{\hbar c} \ $$ is the electric  fine structure constant in the Cgs units, and $$\beta^{Cgs} = \frac{1}{4\alpha^{Cgs} } = \frac{\hbar c}{4e^2} \ $$ is the magnetic coupling constant in the Cgs units for the fictitious magnetic charges.

Thus, the relationship between Coulomb forces will be:
 * $$\frac{ F^{ Cgs }_m }{F^{ Cgs }} = \frac{g^2_0}{e^2} = \frac{1}{4 (\alpha^{Cgs})^2} = \frac{\beta^{Cgs} }{\alpha^{Cgs} } =4(\beta^{Cgs})^2 \ $$

which is the same as in the SI units:
 * $$\frac{ F_m }{F} = \frac{\varepsilon_0 q^2_m}{\mu_0e^2} = \frac{1}{4\alpha^2} = \frac{\beta }{\alpha} =4 \beta^2,$$

where $$ \beta =\frac {\varepsilon_0 h c}{2 e^2}. $$

Quanta of action
In consistence to the Quantum Electromagnetic Resonator approach, the charge multiplication (electric and magnetic) should be equal to the quant of action:
 * $$e \cdot g_0 = h, \ $$

where $$e \ $$ is the electric charge, $$g_0 \ $$ is the magnetic charge, and $$h \ $$ is the Planck constant (or the quant of action).

There are no problems in the SI units, where $$g_0 =q_m= h/e \ $$, but in the Cgs units we have the same dimensions of the charges:
 * $$[e] = [g_0]. \ $$

Therefore, to restore the self consistence of the Cgs units we should to consider the second electromagnetic constant $$Z^{ Cgs}_0 \ $$:
 * $$ Z^{ Cgs}_0 \cdot (e g_0) = h, \ $$

which is an analog of the uncertainty principle in the quantum mechanics.

Quantum Hall effect
Simple theory presented by Laughlin to explain QHE used the following definition of the adiabatic strip current in the Cgs units:
 * $$I = c\cdot \frac{\partial U}{\partial \phi} = \frac{c}{L_l}\frac{\partial U}{\partial A}, \ $$

where $$\phi = L_lA \ $$ is the magnetic flux, $$A \ $$ is the vector potential, and $$L_l \ $$ is the strip length. Using the following changes of total energy $$U \ $$ and magnetic flux between Landau levels:
 * $$\Delta U = (n+\frac {1}{2}) e V \ $$
 * $$\Delta \phi = \frac{hc}{e} = \phi_l, $$

we obtain the following current:
 * $$I = c\cdot \frac{\Delta U}{\Delta \phi} = (n+\frac {1}{2}) \frac{e^2}{h}V, \ $$

where $$n = 1,2,3,... \ $$, and $$ V\ $$ is effective potential of the level. Note that, this magnetic flux quantum $$\phi_l \ $$ is different from Dirac monopole:
 * $$\phi_l = 4\pi g_0 = \frac{hc}{e}. \ $$

Photon as quantum resonator
Let us consider $$C_p \ $$ and $$L_p \ $$ as quantum capacitance and inductance of free photon in the SI units. We shall suppose that characteristic impedance of photon equals to the impedance of free space:
 * $$ Z_p =Z_o= \sqrt{\frac{L_p}{C_p}} = \sqrt{\frac{\mu_0}{\varepsilon_0}}. \ $$

Then the resonance frequency will be:
 * $$\omega_p = \frac{1}{\sqrt{L_pC_p}} = 2\pi \nu_p = \frac{2\pi c}{\lambda_p}, \ $$

where $$\lambda_p \ $$ is wavelength of photon. The solution of these two equations will be:
 * $$C_p = \frac{\lambda_p}{2\pi c Z_0} = \frac{\lambda_p \varepsilon_0}{2\pi } =\frac{\varepsilon_0}{2\lambda_p}S_p \ $$
 * $$L_p = \frac{\lambda_p Z_0}{2\pi c }= \frac{\lambda_p \mu_0}{2\pi } =\frac{\mu_0}{2\lambda_p}S_p, \ $$

where $$S_p = 4\pi r_p^2 = \frac{\lambda_p^2}{\pi}$$ and $$r_p = \frac{\lambda_p}{2\pi}$$ is the photon intrinsic radius.


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User talk:Lolalita

 Hello Lolalita, 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.
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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 24 November 2009 (UTC)

title: User talk:Lolalita


text:
User talk:BP83

 Hello BP83, 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

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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. --Mu301Bot 08:18, 24 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 24 November 2009 (UTC)

title: User talk:BP83


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User talk:Brian217

 Hello Brian217, 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

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 * Give feedback about your initial observations
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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. --Mu301Bot 08:18, 24 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 24 November 2009 (UTC)

title: User talk:Brian217


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User talk:Rahinecono

 Hello Rahinecono, 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

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 24 November 2009 (UTC)

title: User talk:Rahinecono


text:
User:Msafiri~enwikiversity

Hello world

This is the user page of msafiri.

Karibu!

I'll edit this when I have time.

title: User:Msafiri~enwikiversity


text:
Physics/Essays/Fedosin/Fine structure constant

In physics, the fine structure constant (usually denoted α, the Greek letter alpha) is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity, it has constant numerical value in all systems of units. Arnold Sommerfeld introduced the fine-structure constant in 1916.

The current recommended value of α is 7.29735257×10−3.

Definition
Some equivalent definitions of α in terms of other fundamental physical constants are:

 * $$\alpha = \frac{e^2}{4 \pi \varepsilon_0 \hbar c} = \frac{m_{S}^2}{4 \pi \varepsilon_g \hbar c}= \frac{e^2 c \mu_0}{2 h} = \frac{k_\mathrm{e} e^2}{\hbar c} = \frac {Z_0}{2R_K} = \left(\frac{e}{q_p}\right)^2 = \left(\frac{m_S}{m_P}\right)^2 = \frac{G_s M_p M_e}{\hbar c} = \frac {1}{4\beta } ,$$

where:
 * e is the elementary charge;
 * h is the Planck constant;
 * ħ = h/2π is the Dirac constant or reduced Planck constant;
 * c is the speed of light in vacuum;
 * ε0 is the electric constant;
 * mS is the Stoney mass;
 * $$ \varepsilon_g = \frac {1 }{4 \pi G} $$ is the gravitoelectric gravitational constant of selfconsistent gravitational constants;
 * $$~ G $$ is the gravitational constant;
 * µ0 is the vacuum permeability;
 * ke is the Coulomb constant;
 * RK is the von Klitzing constant;
 * Z0 is the impedance of free space;
 * qp is the Planck charge;
 * mP is the Planck mass;
 * Mp is the mass of proton;
 * Me is the mass of electron;
 * Gs is the strong gravitational constant;
 * β is the magnetic coupling constant.

In electrostatic cgs units, the unit of electric charge, the statcoulomb, is defined so that the Coulomb constant, ke, or the permittivity factor, 4πε0, is 1 and dimensionless. Then the expression of the fine structure constant becomes the abbreviated
 * $$\alpha = \frac{e^2}{\hbar c} $$

an expression commonly appearing in physics literature.

Bohr model
In the Bohr model of hydrogen atom α is connected to the atom parameters for the first energy level
 * $$~ \alpha = \frac {v_B}{c} ,$$

where $$~ v_B $$ is the speed of electron’s matter at the Bohr radius $$ ~a_B $$.

On the other hand
 * $$~\alpha = \frac {\lambda_0 }{2\pi a_B } = \sqrt {\frac {r_e}{ a_B} } = 4 \pi a_B  R_\infty,$$

where $$~\lambda_0 \ $$ is the Compton wavelength of the electron, $$~ r_e \ $$ is the classical electron radius, $$~ R_\infty $$ is the Rydberg constant for wavelength.

The next equation for α is
 * $$~ \alpha = \sqrt {\frac {\Phi_{e}}{\Phi_0 }} ,$$

where $$~ \Phi_0 = \frac{h}{2 e} $$ is the magnetic flux quantum, $$~ \Phi_e = B S_B = \frac { \mu_0 e }{4 \pi a_B }\sigma_e $$ is the electron magnetic flux for the first energy level, $$ ~B $$ is the magnetic field in electron disc with flat surface area $$~ S_B = \pi a_B^2 $$, and $$~ \sigma_e = \frac{h}{2 M_e} $$ is velocity circulation quantum for electron.

Another equation for α is

 * $$~ \alpha = \sqrt {\frac {\Phi_{eg}}{\Phi_p }} ,$$

where $$~ \Phi_p = \frac{h}{2 M_p} = 1.98 \cdot 10^{-7}$$ m2/s

is the strong gravitational torsion flux quantum, which is related to proton and to its velocity circulation quantum,

and the strong gravitational electron torsion flux for the first energy level of hydrogen atom is
 * $$~ \Phi_{eg} = \Omega S_B = \frac { G_s h }{2c^2 a_B }, $$

while $$~ \Omega $$ is the gravitational torsion field of strong gravitation in electron disc.

The Bohr model for hydrogen system at the level of star introduces α in such way:

 * $$~\alpha = \frac {G M_{ps} M_{\Pi } }{\hbar_s C_s}, $$

where $$~ M_{ps} $$ and $$~ M_{\Pi } $$ – mass of the star-analogue of proton and the planet-analogue of electron, respectively, $$~ \hbar_s $$ – stellar Dirac constant, $$~ C_s $$ – characteristic speed of stars matter.


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File:HelpScreenshot.jpg

Summary
Screen capture from the VUE website displaying the User Guide page.

title: File:HelpScreenshot.jpg


text:
Physics/Essays/Fedosin/Magnetic coupling constant

In physics, the magnetic coupling constant, or magnetic fine structure constant (usually denoted β, the Greek letter beta) is a fundamental physical constant, characterizing the strength of the magnetic force interaction. The numerical value of β is the same in all system of measurement, because β is a dimensionless quantity: $$\beta = 34.258999743$$. The constant β was proposed by Yakymakha in 1989.

Definition
The standard definition of the magnetic coupling constant is:
 * $$ \beta = \frac {\varepsilon_0 h c}{2 e^2} = \frac {h}{2 \mu_0 c e^2}, $$

where:
 * $$~ \varepsilon_0 $$ is the electric constant;
 * $$~h $$ is the Planck constant;
 * $$~c$$ is the speed of light in vacuum;
 * $$~ e$$ is the elementary charge;
 * $$~\mu_0$$ is the vacuum permeability.

In the Cgs units magnetic coupling constant is: $$\beta^{Cgs} =  \frac{\hbar c}{4e^2} .\ $$

Magnetic charge quantization
It is known, that magnetic charge (and magnetic flux) has the property to be quantized:
 * $$ q_n = n \cdot q_m, \ $$

where $$n = 1,2,3,... $$ is the integer number and $$ q_m =h/e $$ is the fictitious elementary magnetic charge. The conception of magnetic monopole was first hypothesized by Pierre Curie in 1894, but the quantum theory of magnetic charge started with a 1931 paper by Paul Dirac. In this paper, Dirac showed that the existence of magnetic monopoles was consistent with Maxwell's equations only in case of charge quantization, which is observed.

Magnetic force
Coulomb law for the fictitious magnetic charges is:
 * $$F = \frac{1}{4\pi \mu_0}\cdot \frac{q_{n1} q_{n2} }{r^2}, \ $$

where $$ q_{n1} = n_1 q_m $$ and $$ q_{n2} = n_2 q_m $$ are two interacting magnetic charges. At $$n_1 = n_2 = 1 $$ we shall have the minimal magnetic force:
 * $$F_m = \frac{\beta \hbar c}{r^2}, \ $$

from which it is seen that $$\beta $$ is magnetic coupling constant.

In the general case, when we know the magnetic charges, Coulomb force could be rewritten as:
 * $$F = F_m\cdot n_1n_2. \ $$

Gravitational torsion force
The "static" Stoney mass is defined as:
 * $$m_S = e \sqrt{\frac{\varepsilon_g}{\varepsilon_o}} = 1.85927\cdot 10^{-9} \ $$ kg,

where
 * $$\varepsilon_g = \frac{1}{4\pi G} \ $$ is the gravitoelectric gravitational constant, $$G \ $$ is the gravitational constant.

Similar to the elementary magnetic charge the fictitious gravitational torsion mass could be defined:
 * $$ m_{\Omega} = \frac{h}{m_S}. \ $$

Newton law for the gravitational torsion masses is:
 * $$F_{\Omega } = \frac{1}{4\pi \mu_{g0}}\cdot \frac{ m_{\Omega}^2}{r^2} = \beta_g \cdot \frac{\hbar c}{r^2}, \ $$

where $$\beta_g = \frac {\varepsilon_g h c}{2 m_S^2} = \frac {h}{2c \mu_{g0} m_S^2} \ $$ is the gravitational torsion coupling constant for the gravitational torsion mass $$ m_{\Omega } \ $$, and $$\mu_{g0} = \frac{4\pi G}{c^2} \ $$ is the gravitomagnetic gravitational constant.

In the case of equality of the above forces $$F_m \ $$ and $$ F_{\Omega}\ $$, we shall get the equality of the coupling constants for magnetic field and gravitational torsion field:
 * $$\beta = \beta_g = \frac{1}{4 \alpha}, \ $$

where $$\alpha \ $$ is the fine structure constant as the coupling constant of electrostatic interaction.

From the stated above, it is evident that the magnetic coupling constant (magnetic fine structure constant) is the constant, which defines the force interactions (magnetic, gravitational, etc.) in the Stoney scale. Therefore, this dimensionless constant could be named as the Stoney scale dynamic force constant (with the following designation: $$\beta_S \ $$).


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User:Seacer

Hi :)

title: User:Seacer


text:
User talk:B9 hummingbird hovering/Blog/Learning Tibetan Weblog/Pushing the envelope2

Due to the warmer weather & my increasing facility of health yielded from prostrations to our Sun the source of light, illumination and life in our solar-system and the transmission of energy to our Planet and with thanksgiving to the glorious ensealment of prana in my bodymind I have been fortunate to re-engage bodywork and vinyasa yoga sadhana & as a result will resume with refining an English rendering of Jigme Lingpa's Heart Essence Nundro. I was fortunate in being emailed a university thesis on Trul Khor, the Wikipedia article I will iterate as well. The Trul Khor article was my first fledgling offering to the Community and I have progressed it little since commencement. Sri Sri Sri B9hummingbirdhoverin'æ•ω•ॐ 14:12, 24 November 2009 (UTC)


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UTPA STEM/CBI Courses/Mechatronics/Basic Electronics

Course Title: MECE-4320 Mechatronics

Lecture Topic: Basic Electronics

Instructor: Horacio Vasquez

Institution: UTPA

Backwards Design
Course Objectives

 * Primary Objectives- By the end of this challenge, students will be able to:
 * Read a schematic and make basic electronic circuits using resistors and LEDs.
 * Understand and use breadboards, power supplies, and digital multimeters (DMMs).
 * Understand and use units in basic electronics

 * Sub Objectives- The objectives will require that students be able to:
 * Use breadboards and power supplies.
 * Measure resistance, voltage, and current using a DMM.
 * Connect and measure resistors in parallel and series.
 * Apply Ohm’s Law.
 * Understand and use LEDs.
 * Understand and apply Kirchhoff voltage law.
 * Compute power and energy consumption by resistors and LEDs.

 * Difficulties- Students may have difficulty:
 * Correctly using the correct relationships and units between voltage, current, and resistance.
 * Correctly using breadboards, color code wiring, and power supplies to implement basic electronic circuits.
 * Correctly using DMMs to measure current, voltage, and other parameters because not only they need to know the correct lead connections but also setting the knob of the DMM to the right place and range.

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * There are many applications that use basic electronic circuits including resistors and LEDs: traffic lights, flash lights, street lights, monitoring systems, video game systems, etc. [[Image:RBG-LED.jpg|thumb|right|LEDs]]
 * Learning the mentioned concepts and acquiring hands-on experience in basic electronics are intended to be the first steps to encourage students to pursue a career in a STEM field, such as electronics, semiconductors, measurements and instrumentation, mechatronics, and control systems.

Model of Knowledge

 * Concept Map
 * Electronic components
 * Resistors, light emitting diodes (LEDs), and power supplies.
 * Parallel and series connection of resistors.
 * Units.
 * Symbols and diagrams.
 * Electronics Instruments
 * Breadboards and DMMs.
 * Measuring resistance, voltage, and current.
 * Ohm’s Law
 * Voltage, Current, and Resistance.
 * LEDs
 * Polarity, current limits, and connection requirements.
 * Power consumption and energy utilization.

 * Content Priorities
 * Enduring Understanding
 * Resistors
 * LEDs and their correct connections.
 * Using a breadboard.
 * Ohm’s Law.

 * Important to Do and Know
 * Correctly using a DMM
 * Worth Being Familiar with
 * Understanding power supplies.
 * Computing power and energy consumption by resistors and LEDs.
 * Kirchhoff voltage law.

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Pre-test.
 * Group activities:
 * Adding resistors in series and parallel. Use Ohm’s law to determine expected currents and voltages in resistor circuits.
 * Study LEDs and ways of connecting them.
 * Compute power and energy consumption.
 * Lab Work
 * Using a breadboard.
 * Create circuits, measure currents, and voltages.
 * Validate Ohm’s law and Kirchhoff’s voltage law.
 * Explain the results of the hands-on activities and the reasons why the system might not function properly.

 * Summative Assessment
 * Conclusions and answers to handout questions.
 * Solution to the Challenge.
 * Post-test

Legacy Cycle
OBJECTIVE

 * Goal  - By the end of this challenge, students will be able to:
 * Read a schematic and make basic electronic circuits using resistors and LEDs.
 * Understand and use breadboards, power supplies, and digital multimeters (DMMs).

THE CHALLENGE
 * Sub Objectives- The objectives will require that students be able to:
 * Use breadboards and power supplies.
 * Measure resistance, voltage, and current using a DMM.
 * Connect and measure resistors in parallel and series.
 * Apply Ohm’s Law.
 * Understand and use LEDs.
 * Understand and apply Kirchhoff voltage law.
 * Compute power and energy consumption by resistors and LEDs.

You are working for a videogame company and they are going to release a new system. You supervisor wants you to inspect LED circuits that are malfunctioning. It is your job to get the circuit up and running in order to meet the deadline to release the system. The company is planning to sell millions of games and your future job and salary depend on executing such plan at perfection.

GENERATE IDEAS

Students are requested to brainstorm and write down ideas about the challenge, requirements to solve the challenge, importance of finding a solution, difficulties, and limitations.

MULTIPLE PERSPECTIVES The following link presents some information about LED applications: LED lights!

Common applications of LEDs: traffic lights, computers, and toys. Which other ones? Included information form different sources to demonstrate the importance of the challenge and engage students in solving it.

RESEARCH & REVISE

Present Lectures and handouts. Students need to study the lecturers and the handouts before doing the hands-on activity.

TEST YOUR METTLE

 * i. Students do experiments (work in the lab to learn through hands-on activities).
 * ii. Instructors ask questions in order for students to explain their experimental results and understanding of concepts.
 * iii. Post-test.
 * iv. Answer the questions in the handout.

GO PUBLIC

 * i.	Students demonstrate to the instructor and other students how their electronic circuits work.
 * ii.	Students turn in the results and conclusions, including possible solutions to the challenge.
 * iii.	Show pictures, videos, presentations.

Pre-Lesson Quiz

 * Back to Topic: Instructional Design > User Testing of E-Learning Courses > Analyzing the Results

Knowledge Check 1
Read the user testing data and then indicate whether it is quantitative or qualitative by selecting the appropriate radio button. When you are finished making your selection, click the "Submit" button.

{The units of electrical resistance are Amperes. - TRUE + FALSE
 * type=""}

{Current multiplied by resistance equals Power! - TRUE + FALSE
 * type=""}

{Voltage equals current divided by resistance. - TRUE + FALSE
 * type=""}

{To measure current a voltimeter has to be connected in parallel with the current path. - TRUE + FALSE
 * type=""}

{Did you answer correctly the first 4 questions. + TRUE - FALSE
 * type=""}

{Should you study more in this class? + TRUE - FALSE
 * type=""}

Knowledge Check 2
Read the user testing data and then indicate whether its severity by selecting the appropriate radio button. For the purposes of this exercise, you have already confirmed each item's veracity. When you are finished making your selection, click the "Submit" button.

{Free body diagram is: - a rigid body connected with only a roller. + a rigid body or a particle that has been isolated but it shows all external forces acting on it. - It is a dynamic event. - a particle connected to cables - a rigid body attached to another rigid body with a fixed connection - a rigid body or a particle that has no forces acting on it - N/A
 * type=""}
 * you need to study more


text:
Bandpass Modulation/Demodulation techniques

Bandpass Modulation or Passband Modulation refers to modulation of signal over a carrier frequency. In these techniques the signal to be transmitted is sent by modulating either one or more of the three properties of carrier wave. And accordingly they are classified into diffrent categories as

1. Amplitude Modulation - In this the amplitude of carrier wave is modulated by the message signal. It can be expressed mathematically as $$s(t) = Am(t)*cos(wt)$$

here Am is the modulating signal and w is the angular frequency of carrier.

2. Angle Modulation - In this the angle of carrier wave is modulated by the message signal. This is further divided into two types:

s(t) = cos(wt + Φ(t))

a. Frequency Modulation b. Phase Modulation

In practical digital communication systems, phase modulation frequently combined with amplitude modulation is used over Frequency modulation, as they provide better performance.


text:
User:Dry.eats/Numerical Solution: Spoon in Hot Tea

The solution of the temperature profile of a spoon in hot tea can be approximated by a rod. It is assumed that half of the rod is in one medium at temperature, $$T_0$$, of 80 C and the other half of the rod is in another medium at temperature, $$T_\infty$$, of 20 C. The spoon is approximated by a rod that is 10 cm long, has a cross sectional area, $$A_c$$, of approximately 0.2 cm^2 and a perimeter, $$P$$, of approximately 2 cm.

The governing equations are

$$A_c k \frac{d^2T}{dx^2} - h_c P (T-T_0) = 0$$ from x = 0 to L/2

$$A_c k \frac{d^2T}{dx^2} - h_c P (T-T_\infty) = 0$$ from x = L/2 to L

with adiabatic boundary conditions defined by

$$\left.\frac{dT}{dx}\right|_{x=0}=0$$

and

$$\left.\frac{dT}{dx}\right|_{x=L}=0$$

where $$T$$ is the temperature, $$k$$ is the conductivity, $$h_c$$ is the convective heat transfer coefficient.

The difference in materials can be seen by calculating the temperature profile for metals with different thermal conductivity $$k$$ such as silver and stainless steel. The thermal conductivity of silver is 400 W/m^2/K while the thermal conductivity of stainless steel is 15 W/m^2/K. With silver having the greater thermal conductivity, one would suppose that it would conduct heat better, thus resulting in a hotter spoon handle. The results and MATLAB code for this analysis are found below.

Numerical Solution with MATLAB
clear all; close all; clc;

%Geometric Parameters l = 0.1; %m Ac = 0.2/10000; %m^2 P = 0.02; %m

%Computational Parameters n = 10; %number of points h = l/n; %cell size %Locations of points + boundaries i = 1:(n); x(i) = 0.5*h + h*(i-1); x = [0 x l];

%Thermal Parameters k(1) = 15; %W/(m^2*K) - Stainless Steel k(2) = 400; %W/(m^2*K) - Silver hc(1:n/2) = 1000; %W/(m^2*K) hc(n/2+1:n) = 10; %W/(m^2*K) Tinf(1:n/2) = 80; %353; %K Tinf(n/2+1:n) = 20; %293; %K for i = 1:2 %Compute coefficients of super-diagonal, sub-diagonal, and diagonal l(1:n) = k(i)*Ac/(h^2); d(1:n)= -(2*k(i)*Ac/(h^2)+hc*P); u(1:n) = k(i)*Ac/(h^2); %Implement zero flux boundary conditions d(1) = -(k(i)*Ac/(h^2)+hc(1)*P); d(n) = -(k(i)*Ac/(h^2)+hc(n)*P); %Compute Source term b = -hc'.*P.*Tinf'; %Create tridiagonal matrix A = spdiags([l;d;u]',-1:1,n,n); %Solve linear system for temperature t = zeros(n,1); t = A\b; %Boundary conditions at end of fin tTip0 = 1/8*(9*t(1)-t(2)); tTipN = 1/8*(9*t(n)-t(n-1)); t = [tTip0 t' tTipN]; T(i,:) = t; end

%Plot Statements plot(x,T(1,:),'-d',x,T(2,:),'--*') xlabel('x position (m)'); ylabel('Temperature (C)'); title('Temperature Profile Along Length of Spoon in Hot Tea'); legend('Stainless Steel','Silver'); Dry.eats 18:04, 24 November 2009 (UTC)


text:
The Big Bang Theory

The Big Bang theory is an effort to explain what happened at the very beginning of our universe. Discoveries in astronomy and physics have shown beyond a reasonable doubt that our universe did in fact have a beginning. Prior to that moment there was nothing; during and after that moment there was something: our universe. The big bang theory is an effort to explain what happened during and after that moment.

According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know.

After its initial appearance, it apparently inflated (the "Big Bang"), expanded and cooled, going from very, very small and very, very hot, to the size and temperature of our current universe. It continues to expand and cool to this day and we are inside of it: incredible creatures living on a unique planet, circling a beautiful star clustered together with several hundred billion other stars in a galaxy soaring through the cosmos, all of which is inside of an expanding universe that began as an infinitesimal singularity which appeared out of nowhere for reasons unknown. This is the Big Bang theory.

Big Bang Theory - Common Misconceptions There are many misconceptions surrounding the Big Bang theory. For example, we tend to imagine a giant explosion. Experts however say that there was no explosion; there was (and continues to be) an expansion. Rather than imagining a balloon popping and releasing its contents, imagine a balloon expanding: an infinitesimally small balloon expanding to the size of our current universe.

Another misconception is that we tend to image the singularity as a little fireball appearing somewhere in space. According to the many experts however, space didn't exist prior to the Big Bang. Back in the late '60s and early '70s, when men first walked upon the moon, "three British astrophysicists, Steven Hawking, George Ellis, and Roger Penrose turned their attention to the Theory of Relativity and its implications regarding our notions of time. In 1968 and 1970, they published papers in which they extended Einstein's Theory of General Relativity to include measurements of time and space.1, 2 According to their calculations, time and space had a finite beginning that corresponded to the origin of matter and energy."3 The singularity didn't appear in space; rather, space began inside of the singularity. Prior to the singularity, nothing existed, not space, time, matter, or energy - nothing. So where and in what did the singularity appear if not in space? We don't know. We don't know where it came from, why it's here, or even where it is. All we really know is that we are inside of it and at one time it didn't exist and neither did we.

Big Bang Theory - Evidence for the Theory What are the major evidences which support the Big Bang theory?

First of all, we are reasonably certain that the universe had a beginning. Second, galaxies appear to be moving away from us at speeds proportional to their distance. This is called "Hubble's Law", named after Edwin Hubble (1889-1953) who discovered this phenomenon in 1929. This observation supports the expansion of the universe and suggests that the universe was once compacted. Third, if the universe was initially very, very hot as the Big Bang suggests, we should be able to find some remnant of this heat. In 1965, Radioastronomers Arno Penzias and Robert Wilson discovered a 2.725 degree Kelvin (-454.765 degree Fahrenheit, -270.425 degree Celsius) Cosmic Microwave Background radiation (CMB) which pervades the observable universe. This is thought to be the remnant which scientists were looking for. Penzias and Wilson shared in the 1978 Nobel Prize for Physics for their discovery. Finally, the abundance of the "light elements" Hydrogen and Helium found in the observable universe are thought to support the Big Bang model of origins.

Big Bang Theory - The Only Plausible Theory? Is the standard Big Bang theory the only model consistent with these evidences? No, it's just the most popular one. Internationally renown Astrophysicist George F. R. Ellis explains: "People need to be aware that there is a range of models that could explain the observations….For instance, I can construct you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations….You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that."4

In 2003, Physicist Robert Gentry proposed an attractive alternative to the standard theory, an alternative which also accounts for the evidences listed above.5 Dr. Gentry claims that the standard Big Bang model is founded upon a faulty paradigm (the Friedmann-lemaitre expanding-spacetime paradigm) which he claims is inconsistent with the empirical data. He chooses instead to base his model on Einstein's static-spacetime paradigm which he claims is the "genuine cosmic Rosetta." Gentry has published several papers outlining what he considers to be serious flaws in the standard Big Bang model.6 Other high-profile dissenters include Nobel laureate Dr. Hannes Alfvén, Professor Geoffrey Burbidge, Dr. Halton Arp, and the renowned British astronomer Sir Fred Hoyle, who is accredited with first coining the term "the Big Bang" during a BBC radio broadcast in 1950.

Big Bang Theory - What About God? Any discussion of the Big Bang theory would be incomplete without asking the question, what about God? This is because cosmogony (the study of the origin of the universe) is an area where science and theology meet. Creation was a supernatural event. That is, it took place outside of the natural realm. This fact begs the question: is there anything else which exists outside of the natural realm? Specifically, is there a master Architect out there? We know that this universe had a beginning. Was God the "First Cause"? We won't attempt to answer that question in this short article. We just ask the question:

Does God Exist?

title: The Big Bang Theory


text:
User talk:Baf

Welcome
 Hello Baf, 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.
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 * Find out about research activities on Wikiversity.

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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 20:28, 24 November 2009 (UTC) Additionally, thanks for spotting and removing the unhelpful content from Topic:Calculus. Adambro 20:28, 24 November 2009 (UTC)

title: User talk:Baf


text:
User talk:EnKi

Just Testing =D -- EnKi 20:52, 24 November 2009 (UTC)

Questions
Where do i go to translate pages? i'm looking to translate eng to swe --EnKi 21:34, 24 November 2009 (UTC)

What are Categories really? --EnKi 21:38, 24 November 2009 (UTC) Ok i found out now XD --EnKi 21:42, 24 November 2009 (UTC) Cool you can do this =D --EnKi 21:42, 24 November 2009 (UTC) test

Your talk:
You talk here so i can separate me from you (Questions can be answered up there =D)

title: User talk:EnKi


text:
User:EnKi

Nothing here yet...

will edit when i have time

title: User:EnKi


text:
Advanced Java/Dependency

In Java, a dependency is a package requirement for your program.

If you restrict yourself only to code within your program, then you can construct a JAR file with all the necessary code. However, if you code requires a third-party library (e.g. an improved widget interface), it will not be included in the JAR file simply by compiling your code.

title: Advanced Java/Dependency


text:
Talk:Complex numbers

Blanking page as it is a duplicate of Complex Numbers

title: Talk:Complex numbers


text:
User:BruceFlanders

My full name is Robert Bruce Flanders

title: User:BruceFlanders


text: User:IlliniGradResearch

title: User:IlliniGradResearch


text:
User:The Banshee

Hello! I'm known as The Banshee around the web... Feel free to e-mail me at stargo25[at]gmail[dot]com, though I'm not sure what you'd E-mail me about...

Any way, I'm artist and a student.

title: User:The Banshee


text: File:Resultant Forces .png

title: File:Resultant Forces .png


text: File:Deformed.png

title: File:Deformed.png


text:
Talk:Painting/Oils

This is the talk page for "Oils".

title: Talk:Painting/Oils


text:
Template talk:MathDeps

This list needs better organisation. Graemeb1967 07:03, 25 November 2009 (UTC) We're working on it.

 * Is there any reason why there are no Portal: Namespace in these areas? Saml214 (discuss • contribs) 15:55, 13 July 2023 (UTC)

title: Template talk:MathDeps


text:
User talk:Dariant3

 Hello Dariant3, 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

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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. --Mu301Bot 08:18, 25 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 November 2009 (UTC)

title: User talk:Dariant3


text:
User talk:Katknave

 Hello Katknave, 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

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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. --Mu301Bot 08:18, 25 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 November 2009 (UTC)

title: User talk:Katknave


text:
User talk:Bridgerg

 Hello Bridgerg, 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

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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. --Mu301Bot 08:18, 25 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 November 2009 (UTC)

title: User talk:Bridgerg


text:
User talk:Jasonghuna

 Hello Jasonghuna, 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

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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. --Mu301Bot 08:18, 25 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 November 2009 (UTC)

title: User talk:Jasonghuna


text:
User talk:Christine 933

 Hello Christine 933, 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.
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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. --Mu301Bot 08:18, 25 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 November 2009 (UTC)

title: User talk:Christine 933


text:
User talk:Tarunuday

 Hello Tarunuday, 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.
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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. --Mu301Bot 08:18, 25 November 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 November 2009 (UTC)

title: User talk:Tarunuday


text:
User:Linguist 16601

"Nenhum residente dira: Estou doente." Isaías 33:24

Queira conhecer mais sobre a esperança maravilhosa pelo futuro como predito na Bíblia?

Es realidades de hoje são guerra, crime fome, doença velhice - para mencionar apenas alumas. Contudo, á uma razão para esperança. Contemplando o futuro, a Bíblia fala de "novos céus e uma nova terra que aguardamos segundo a sua [de Deus] promessa, e nestes há de morar a justiça". 2 Pedro 3:13; Isaías 65:17

www.watchtower.org

title: User:Linguist 16601


text:
Talk:Genetics/How to access the genome databases

iam new but really want to excess to human genome database so any  one intrested contact me


text:
Talk:Brazilian Portuguese/Lesson 3

Have you considered mentioning that it is not necessary to use the indefinite article 'um(a)' for professions?Redcamarocruiser 15:36, 25 November 2009 (UTC)

title: Talk:Brazilian Portuguese/Lesson 3


text:
User:Kaihsu/EUlawA5

Constitutional and institutional law of the European Union.

Section A: The European Union institutional outline.

Chapter 5: Competences and subsidiarity.

Notes by Kaihsu Tai, 2010-04-22.

Competences
The constitutional status quo (including case law) on competences has been restated/codified (however imperfectly) in Articles 3 to 6 TFEU.

Implied powers
The Union has implied authority to conclude agreements with third-parties after it had exercised internal power in the policy area; this is exclusive competence for the Union insofar as that the Member State no longer has power to alter the scope of common rules; such agreement can be sui generis acts when expedient: ERTA case 22/70. This is now codified within Article 3(2) TFEU: ‘The Union shall also have exclusive competence for the conclusion of an international agreement when its conclusion is provided for in a legislative act of the Union or is necessary to enable the Union to exercise its internal competence, or in so far as its conclusion may affect common rules or alter their scope.’

The Union has implied power indispensable in carrying out tasks conferred by the Treaties such as social and immigration policy: Germany v Commission 281/85.

Open-ended power under Article 352 TFEU (ex 308 TEC) can be relied upon for customs union if necessary powers not provided elsewhere: Hauptzollamt Bremerhaven v Massey-Ferguson 8/73. Open-ended power under Article 352 cannot serve as the basis for tasks not defined by the Treaties: Opinion 2/94 (ECHR).

While the European Community does not have express competence as legislator in criminal law, ‘When the application of effective, proportionate and dissuasive criminal penalties by the competent national authorities is an essential measure for combating serious environmental offences, the Community legislature may require the Member States to introduce such penalties in order to ensure that the rules which it lays down in that field are fully effective.’: Commission v Council C-176/03 (as restated in Commission v Council C-440/05).

Legal basis
‘[T]he choice of the appropriate legal basis has constitutional significance. Since the Community has conferred powers only, it must tie the agreement that it seeks to conclude to a Treaty provision which empowers it to approve such a measure’: Opinion 1/08 (General Agreement on Trade in Services).

When a policy area can be based on two Articles with different procedures, both need to be fulfilled: Commodity Coding case 165/87. But when procedural provisions conflict, one has to be chosen as the sole legal basis: Titanium Dioxide C-300/89; distinguish from Commodity Coding.

Article 352 TFEU (ex 308 TEC) cannot be relied upon when a more specific legal basis provides for the specific power and rule of procedure: Tariff Preference case 45/86.

Decision 2004/496 (EU-USA Passenger Name Record Agreement) cannot have been validly adopted on the basis of Article 114 TFEC (approximation of laws; ex 95 TEC) and Article 25 of Directive 95/46 (protection of individuals with regard to the processing of personal data and on the free movement of such data): Parliament v Council C-317/04.

Provisions adopted based on TEU that could have been validly adopted on EC Treaty infringes ex Article 47 TEU: Commission v Council C-440/05 (ship-source pollution). Similarly, a measure cannot base itself on the Common Foreign and Security Policy if it could properly be adopted on the basis of the EC Treaty: Commission v Council C-91/05 (small arms).

Subsidiarity
The principle of subsidiarity was pleaded by Germany but not considered in the Tobacco Advertising case C-376/98; rather the Court ruled that Parliament and Council lacked competence to impose an overall ban on tobacco advertising, not within the indispensable power for completing the internal market. The harmonization of laws for human health was an express exclusion in the Treaty. (A later, narrower Directive 2003/33/EC replacing the annulled Directive 98/43/EC was held to be compatible with Article 114 TFEU: Germany v Parliament and Council C-380/03.)

The principle of subsidiarity cannot be relied upon to annul a measure if the Treaty provides for the competence expressly: Working Time Directive case C-84/94.

Delegation of powers
Obligations accompanying delegated power, such as the requirement for reasoning, applies to the delegate; delegation of powers cannot be implied by non-specific conferral of tasks; discretionary power cannot be delegated: Meroni case 9/56. This last applies even to Member States: Rey Soda case 23/75.

Reasoning
Acts must state the reasons on which they are based, enough to enable any person concerned to have defend their interests: Brennwein case 24/62. Reasons should not be merely a reference to another act or a judgment: Papiers Peints 73/74.

title: User:Kaihsu/EUlawA5


text:
User:Everlearning

I'm not entirely sure what this page is for, but here it is.

title: User:Everlearning


text:
Ancient Egyptian vocalization project/General principles

For the first three millenia of its history, Egyptian writing by and large only recorded the consonantal shape of the Egyptian language, giving little indication to the position of vowels, their quality and quantity and any additional features like tone and stress. Without this information, it is nearly impossible to fully appreciate the ancient literature.

The single most important source for filling in the missing information is Coptic, as it is the only stage that systematically records the vowels. Coptic does have some shortcomings, though: All vowels but those of the main stressed syllables of words are often reduced to [e] or [ə] and entire syllables that are indicated in the hieroglyphic writing have disappeared from the language by the time it got recorded in Coptic. Also, many older words and grammatical forms from the time of the Middle Kingdom have already disappeared when Coptic replaces the older literary norms. And finally, even the accented vowels will have changed substantially over the millenia before the Coptic stage so that Coptic vowels can only be an important starting point, but in itself not sufficient for a reconstruction of early stages of the language.

Important additional information is provided by Egyptian words and names that were recorded in the languages of Egypt's neighbours or entered their vocabulary as loan words. Most of these languages recorded vowels (Akkadian, Greek, Meroitic) and can thus be used to give snapshots of how an Egyptian word was pronounced one or even two millenia before the Coptic stage. If Amenophis III's throne name Nb-m3ˤt-Rˤ is transcribed as Ni-ib-mu-a-ri-ia in cuneiform of the Amarna tablets this gives us at least the approximate vowels for nb (lord), m3ˤt (truth) and Rˤ (the sun god) more than a thousand years before the Coptic stage. It also shows us that the H in Coptic ΜΗΙ descends from an older [u] sound.

Putting both pieces of information together one can formulate rules of how the older vowels changed into the Coptic stage and then (although not always unambiguously) how to calculate backwards from the Coptic stage. This extends the scope of words that can be reconstructed for the first and even the second millenium before the common era dramatically.

Another feature that comes in helpful is the paradigmatic nature of the Semitic languages - if the vowel structure for a few infinitives of one class of verbs is known, for example, the same vowels can be assumed for all other infinitives of the same class. The relationship to other Semitic languages may also help in reconstructing grammatical forms or words that have not survived into Coptic but may have close analoga in other languages of the Semitic branch.

Finally, there is also quite a bit of information contained within the Egyptian orthography and literature itself. Examples are puns on words, mistakes in writing one word for its homonym, spelling errors and, more intricately, phonetic complements and other conclusions drawn from the regular spelling itself (e.g. adding a /w/ at the end of ḫpr indicates that the /r/ was already not being pronounced at the time and a change from writing a single /n/ to a double /n/ in certain verb forms may indicate that there was a vowel in between in the double forms )

The following presents a list of the rules that have been found based on the different types of evidence described above. The idea of this list is to facilitate future reconstruction be it from Coptic or from other sources (see: ../List of vocalized forms/).

Abbreviations for commonly used reference works
The following list is meant to make referencing the sources easier (separate endnotes for each example would take up significantly more space). Please use this format and add the page number to make future look-ups easier!

 * AE: A. Loprieno "Ancient Egyptian - A linguistic introduction" Cambridge Univ. Press, 1995
 * EAS: W. Schenkel "Einfuehrung in die Altaegyptische Sprachwissenschaft" Wissenschaftl. Buchgesellschaft, Darmstadt, 1990
 * EP: C. Peust: "Egyptian Phonology" Peust und Gutschmidt, Goettingen, 1999
 * KG: W. Till: "Koptische Grammatik" VEB Verlag Enzyklopaedie, Leipzig, 1970
 * ICG: J. Plumley: "An introductory Coptic grammar" Home & van Thal, London, 1948

Coptic syllable structure
Syllables begin with a consonant - where this doesn't seem to be the case in Coptic, a (weak) consonant is found in the hieroglyphic form (e.g. aleph or ayin).

Syllables can be open (CV) or closed (CVC). Open syllables generally contain a long vowel, closed syllables a short vowel. Apparent violations can usually be explained by the consonants still present in the hieroglyphic writing that have disappeared in the Coptic stage, e.g. ϢѠΠЄ which seems to violate the 'open syllables have long vowels' rule in ΠЄ but can be explained by ḫpr (to become) having a final /r/ in earlier stages of the language. Note that the general rule can only be upheld if we accept consonants from significantly earlier stages into the model. This is equivalent to saying that the Coptic rule about the relation between vowel quantity and syllable type is actually a New Kingdom Egyptian rule. This assumption (if correct) makes this rule very useful for the reconstruction of the Egyptian language of the New Kingdom.

Evolution of Precoptic vowels into Coptic
Vowels of the tone syllable

[a] in closed syllables generally → O, but before ˤ,h,ḥ,ḫ, h → A (exception: before ˤ with vowel doubling → A or O)

[a:] in open syllables generally → ω, but after M, N → ΟΥ (exception: → ω before 2.Pl -TN)

&c. - under construction :-)


text:
User:Welkin.Shibboleth/Czech 000

= Beginning Czech =

{| cellpadding="10" cellspacing="5" style="width: 99%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="background-color: Cornsilk; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" |

Ahoj and welcome to the beginning Czech course. In this first series we will explore some basic Czech grammar and ways to hold a simple conversation in Czech. This course is in the first stages of construction, so please feel free to correct any errors you find or to add content.

Dobré den !
 * style="width: 60%; background-color: #fffff0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" |
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Czech 000
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Česká republika
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The Czech Republic is a landlocked nation in central Europe. It is a highly developed nation, and an economic powerhouse, especially among former Comecon nations.
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Lessons

 * Lesson 1 :  Introducing Yourself
 * Lesson 2 : A Conversation
 * Lesson 3 : Grammar Overview
 * Lesson 4 : Simple cases and tenses

 * }

title: User:Welkin.Shibboleth/Czech 000


text: Survey design/Workshop/Message

title: Survey design/Workshop/Message


text:
User talk:Rojas1114

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title: User talk:Rojas1114


text:
Golf match play

'Match play' is a scoring system for golf in which a player, or team, earns a point for each hole in which they have bested their opponents; this is as opposed to stroke play, in which the total number of strokes is counted over one or more rounds of 18 holes. In professional golf, a small number of notable match play tournaments use the match play scoring system.

Scoring system
Unlike stroke play, in which the unit of scoring is the total number of strokes taken over one or more rounds of golf, match play scoring consists of individual holes won, halved or lost. On each hole, the most that can be gained is one point. Golfers play as normal, counting the strokes taken on a given hole. The golfer with the lowest score on a given hole receives one point. If the golfers tie, then the hole is halved. i.e., in an 18 hole match, the first hole is a par-4 and player 'A' scores a 3 (birdie) and player 'B' score a 4 (par); player 'A' is now 1-up with 17 to play. In the same match on the second hole, a per-5, player 'A' takes 8 strokes and player 'B' takes 5 (par); player 'B' wins the hole and the match is now all square with 16 to play. On the third hole, a per-3, both players take 3 strokes and the match is 'all square' with 15 holes to play. Once a player is 'up' more holes than there are holes remaining to play the match is over. i.e., if after 12 holes player 'A' is 7-up with six left to play, player 'A' is said to have won the match '7 and 6'.

A team that is leading by 'x' holes with 'x' holes remaining is said to be "dormie-x", or simply "dormie", meaning that they need one more halved hole to win the match (or alternately, that the other team must win all the remaining holes outright in order to halve the match). i.e., if player 'A' is 2-up with 2 to play, he is dormie; the worst outcome for player 'A' at that point is a tie, unless the format calls for extra holes to determine a winner.

In a tournament event where the score is all square after the last hole, usually 18 or 36, the players will play on until a player wins a hole (sudden death). In the Ryder Cup and other similar team events, the match is not finished this way, and the teams each receive a half point. In such events there are points accumulated over several days, playing different formats, and the total determines the winner.

Scoring Using Handicaps
Scoring match play using handicaps is not done exactly the same way it is done in a stoke play event. In 18-hole stroke play where player 'A' is a -10 handicap and player 'B' is a -19 handicap, player 'A' gets one stoke off his score on the ten hardest holes (by handicap rating on scorecard); player 'B' gets two strokes off his score on the hardest hole and one stroke off on the other 17.

In match play, player 'A' would play as 'scratch' (zero handicap) and player 'B' would get one stroke off his score on the nine hardest holes. In other words, the 10 handicap becomes zero and the 19 handicap becomes a 9.

In team match play competition, where team 'A' consists of player 'A1' (a -10 handicap), and player 'A2' (a -15 handicap); where team 'B' consists of player 'B1' (a -19 handicap) and player 'B2' (a -30 handicap). Player 'A1' plays as 'scratch'; 'A2' gets one stroke off his score on the five hardest holes; player 'B1' gets one stroke off his score on the nine hardest holes; 'B2' will take 2 strokes off the 2 hardest holes and 1 stroke of the other 16. Exception: the USGA does not restrict the handicap of the low partner but some local clubs and organized tournaments do. i.e, in team play, if no player can have a handicap more than 8 strokes higher than his partner, 'B2' would play as if his or her handicap were -27 (high partners handicap of 19 + 8 = 27).

Tournaments featuring match play
Today, there are few professional tournaments that use match play. They include the biennial Ryder Cup played by two teams, one representing the United States|USA and the other representing Europe; the biennial Presidents Cup for teams representing the United States|USA and International (non-European) players; the WGC-Accenture Match Play Championship]]; and the older Volvo World Match Play Championship, an invitational event which is now part of the European Tour. Formerly, the PGA Championship, one of the Men's major golf championships|majors, used match play, but it changed to a stroke play event in 1958.

Women's professional golf had no event directly comparable to the Accenture Championship until the HSBC Women's World Match Play Championship was introduced in 2005. It also has an event directly analogous to the Ryder Cup, the Solheim Cup. In addition, women's golf now has an event broadly analogous to the Presidents Cup in the Lexus Cup. The U.S. Amateur Championships for both men and women are conducted with two rounds of stroke play to cut the field to 64, and then proceed to a single-elimination match play tournament. All elimination matches are 18 holes except for the final, which is 36 holes.

Strategy
Golfers can employ a slightly different strategy during a match play event, since the scoring is different. The situation in the match and the outcome of each shot already played on a hole will both be taken into account. On the whole match play encourages more aggressive play, especially at the professional level, where a par is not usually good enough to win a hole. Since a very poor result for a hole is no worse than a slightly-below-average result when playing against an opponent with an average score, it often makes sense to accept the higher risk connected with aggressive tactics. However, in some circumstances players will be especially cautious in match play. For instance, one may choose to play more conservatively if the opponent has hit a poor tee shot or is otherwise under pressure to compensate a poor start on a particular hole, reasoning that there is a good chance to win the hole with an average result.

Alternative forms of match play
There is a format of match play called "Irish match play" in which 3 or 4 individuals may compete against each other. A points system is assigned where as an outright win on a hole for a single player constitutes 2 points, a half of the hole for 2 or more players is equal to a single point. This format allows golfers to enjoy the format of hole-by-hole match play in groups larger than 2 people.

Notes and references
USGA Rules-and-Decisions

Hulspil Match play Matchplay Matchspill Lista över golftermer 比洞赛

title: Golf match play


text:
Physics/Essays/Fedosin/Stoney scale

In physics, Stoney scale is the fundamental scale, named after the Irish physicist George Johnstone Stoney, who first proposed the ‘’elementary electric charge’’ in 1881. It defines that fine structure constant $$~\alpha $$ is equal to gravitational coupling constant (and to electric coupling constant) $$~\alpha_S $$ of Stoney scale:

 * $$~\alpha_{S} = \frac{m_S^2}{2hc\varepsilon_g}= \frac{e^2}{2hc\,\varepsilon_0} =\alpha, $$

where
 * $$~ m_S = \sqrt{\frac{e^2}{4\pi \varepsilon_0 G}} $$ is the Stoney mass;
 * $$~e$$ is the elementary charge;
 * $$~\varepsilon_0$$ is the electric constant;
 * $$~G $$ is the gravitational constant;
 * $$~h $$ is the Planck constant;
 * $$~c$$ is the speed of light in vacuum;
 * $$~\varepsilon_g $$ is the gravitoelectric gravitational constant.

There is the dimensionless magnetic coupling constant $$~ \beta =\frac{1} {4\alpha} $$ that could be named as the Stoney scale force constant since it defines the force interactions (electric, gravitational, etc.) in the Stoney scale.

History
Contemporary physics has settled on the Planck scale as the most suitable scale for the unified field theory. The Planck scale was however anticipated by George Stoney. James G. O’Hara pointed out in 1974 that Stoney’s derived estimate of the unit of charge, 10-20 Ampere (later called the Coulomb), was $1/undefined$ of the correct value of the charge of the electron. Stoney used the quantity 1018 for the number of molecules presented in one cubic millimeter of gas at standard temperature and pressure. Using Avogadro constant $6.022$, and the volume of a  mole (at standard conditions) of $22.711 mm^{3}$, we derive, instead of 1018, the estimate $2.652$. So, if Stoney could use the true number of molecules his estimate of the unit of charge was about $1/undefined$ of the correct value of the charge.

For a long time the Stoney scale was in the shadow of the Planck scale (something like a "deviation" of it). However, after intensive investigation of gravitation by using the Maxwell-like gravitational equations during last decades, became clear that Stoney scale is independent scale of matter.

Fundamental units of vacuum
The set of primary vacuum constants is: the speed of light $$~c$$; the electric constant $$~\varepsilon_0$$; the speed of gravity $$~c_g$$ (usually equated to the speed of light); the gravitational constant $$~G $$.

The set of secondary vacuum constants is: The vacuum permeability: $$ \mu_0 = \frac{1}{\varepsilon_0 c^2}\ $$;

The electromagnetic impedance of free space:
 * $$ Z_0 = \mu_0 c = \sqrt{\frac{\mu_0}{\varepsilon_0}}= \frac{1}{\varepsilon_0 c} $$;

The gravitoelectric gravitational constant: $$~\varepsilon_g = \frac{1}{4\pi G } $$;

The gravitomagnetic gravitational constant: $$~\mu_g = \frac{4\pi G }{ c^2_g} $$;

The gravitational characteristic impedance of free space:
 * $$~\rho_g =\sqrt{\frac{\mu_g}{\varepsilon_g}} = \frac{4\pi G }{c_g}.  $$

Note that all Stoney and Planck units are derivatives from the vacuum constants, therefore the last are more fundamental that units of any scale.

If $$c_g =c$$ the above fundamental constants define naturally the following relationship between mass and elementary charge for the Stoney mass:
 * $$m_S = e \sqrt{\frac{\varepsilon_g}{\varepsilon_0}} = e \sqrt{\frac{\mu_0}{\mu_g}} = e \sqrt{\frac{ Z_0}{\rho_g}} \ $$,

and these constants are the base units of the Stoney scale.

Gravitational Stoney units
Stoney mass:
 * $$m_S = e\sqrt{\frac{\varepsilon_g}{\varepsilon_0}} = \sqrt{\alpha} \ m_P = 1.85927\cdot 10^{-9}  \ $$ kg,

where $$m_P \ $$ is the Planck mass.

Stoney gravitational fine structure constant:
 * $$\alpha_S = \frac{m_S^2}{2hc\varepsilon_g} = \alpha = 7.29735257 \cdot 10^{-3} \ $$.

Stoney fictitious gravitational torsion mass:
 * $$ m_{\Omega} = \frac{h}{m_S} = 3.563801 \cdot 10^{-25} \ $$ J s kg−1.

Stoney scale gravitational torsion coupling constant:

$$\beta_g = \frac {\varepsilon_g h c}{2 m_S^2} = \frac {h}{2c \mu_{g0} m_S^2} = \frac{1} {4\alpha} = 34.258999743 \ $$.

Stoney gravitational impedance quantum:
 * $$R_{g} = \frac{ m_{\Omega}}{m_S} = \frac{h}{m_S^2} = 1.91677\cdot 10^{-16} \ $$ J s kg−2.

Electromagnetic Stoney units
Stoney charge:

 * $$q_S = e = 1.602176565 \cdot 10^{-19} \ $$ C.

Stoney electric fine structure constant:

 * $$\alpha_{S} = \frac{q_S^2}{2hc\,\varepsilon_0} = \alpha. \ $$

Stoney fictitious magnetic charge:

 * $$ q_m = \frac{h}{e} = 4.1356675\cdot 10^{-15} \ $$ Wb.

Stoney scale magnetic coupling constant:

 * $$\beta = \frac {\varepsilon_0 h c}{2 e^2} = \frac {h}{2c \mu_{0} e^2} = \frac{1} {4\alpha} = 34.258999743 \ $$.

Stoney electrodynamic impedance quantum:

 * $$R_{e} = \frac{ q_m }{e} = \frac{h}{e^2} = 25,812.807449 \ $$ Ohm

which appears as the von Klitzing constant.

Secondary Stoney scale units
All systems of measurement feature is base units: in the International System of Units (SI), for example, the base unit of length is the meter. In the system of Stoney units, the Stoney base unit of length is known simply as the ‘’Stoney length’’, the base unit of time is the ‘’Stoney time’’, and so on. These units are derived from the presented above primary Stoney units, and arranged in Table 1 so as to cancel out the unwanted dimensions, leaving only the dimension appropriate to each unit. (Like all systems of natural units, Stoney units are an instance of dimensional analysis.)

The keys which are used in the Tables below: L = length, T = time, M = mass, Q = electric charge, Θ = temperature.

Derived Stoney scale units
In any system of measurement, units for many physical quantities can be derived from base units. Table 2 offers a sample of derived Stoney units, some of which in fact are seldom used. As with the base units, their use is mostly confined to theoretical physics because most of them are too large or too small for empirical or practical use and there are large uncertainties in their values.

Table 2: Derived Stoney units

Stoney scale static forces
Electric Stoney scale force:
 * $$F_S(q_S, q_S) = \frac{1}{4\pi \varepsilon_0}\cdot \frac{e^2}{r^2} = \frac{\alpha \hbar c}{r^2}. \ $$

Gravity Stoney scale force:
 * $$F_S(m_S, m_S) = \frac{1}{4\pi \varepsilon_g}\cdot \frac{m_S^2}{r^2} = \frac{\alpha_S \hbar c}{r^2}, \ $$

where $$\alpha_S = \frac{m_S^2}{2hc \varepsilon_g} = \alpha \ $$ is the gravitational fine structure constant.

Mixed (charge-mass interaction) Stoney force:
 * $$F_S(m_S, q_S) = \frac{1}{4\pi \sqrt{\varepsilon_g \varepsilon_0}}\cdot \frac{m_S\cdot e}{r^2} = \sqrt{\alpha_S \alpha}\frac{\hbar c}{r^2} = \frac{\alpha \hbar c}{r^2}. \ $$

So, at the Stoney scale we have the equality of all static forces which describes interactions between charges and masses:
 * $$F_S(q_S, q_S) = F_S(m_S, m_S) = F_S(m_S, q_S) = \frac{\alpha \hbar c}{r^2}. \ $$

Stoney scale dynamic forces
Magnetic Stoney scale force:
 * $$ F_S(q_m, q_m) = \frac{1}{4\pi \mu_0}\cdot \frac{q_m^2}{r^2} = \frac{\beta \hbar c}{r^2}, \ $$

where $$ q_m = \frac{h}{e}\ $$ is the fictitious elementary magnetic charge, $$\beta = \frac{h}{2c\mu_0 e^2} \ $$ is the magnetic coupling constant.

Gravitational torsion force:
 * $$ F_S(m_{\Omega}, m_{\Omega}) = \frac{1}{4\pi \mu_{g0}}\cdot \frac{ m_{\Omega}^2}{r^2} = \frac{\beta_g \hbar c}{r^2}, \ $$

where $$ m_{\Omega} = \frac{h}{m_S} \ $$ is the fictitious gravitational torsion mass, $$\beta_g = \frac {\varepsilon_g h c}{2 m_S^2} = \frac {h}{2c \mu_{g0} m_S^2} =\beta \ $$ is the gravitational torsion coupling constant for the gravitational torsion mass $$ m_{\Omega } \ $$.

Mixed dynamic (magnetic - torsion interaction) force:
 * $$ F_S(q_m, m_{\Omega}) = \frac{1}{4\pi \sqrt{\mu_{g0} \mu_0}}\cdot \frac{ q_m \cdot m_{\Omega}}{r^2} =  \sqrt{\beta_g \beta}\frac{\hbar c}{r^2} = \frac{\beta \hbar c}{r^2}. \ $$

So, at the Stoney scale we have the equality of all dynamic forces which describes interactions between dynamic charges and masses:
 * $$ F_S(q_m, q_m) = F_S(m_{\Omega}, m_{\Omega}) = F_S(q_m, m_{\Omega}) = \frac{\beta \hbar c}{r^2}. \ $$

title: Physics/Essays/Fedosin/Stoney scale


text:
Talk:Introduction to Computers/Security

 * While someone has gone to great lengths to fill in the section, it suffers from serious inaccuracy and readability issues. Will be trying to improve this article over the coming weeks. Renski 08:05, 26 November 2009 (UTC)

I've tried to clean up the content a bit, but it's way to heavy for an into to computers page. Lots of spam deleted. More to come when I'm more lucid. Historybuff 08:07, 5 December 2011 (UTC)

title: Talk:Introduction to Computers/Security