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Physics/Essays/Fedosin/Quantum Hall composite resonator

The Quantum Hall composite resonator (QHCR) is a topological object with quantum reactive parameters (C and L), that as expected has fixed resonant frequency, due to the odd number of electrons which are moving in the homogenous magnetic field B. QHCR in a two-dimensional system of electrons has characteristic impedance proportional to the von Klitzing constant $$R_K = h/e^2 $$ = 25,812.807449(86) Ω, the odd number of electrons ($$j = 3,5,7,...$$) and inversely to the Landau level number ($$i = 1,2,3,...$$):
 * $$ Z = \sqrt{\frac{L}{C}} = \frac{j}{i} R_K \ .$$

History
The discovery of the Quantum Hall effect (QHE) by Klaus von Klitzing in 1980 was completely unexpected, as nobody considered that a macroscopic physical value such as electrical resistance could quantized. Robert B. Laughlin proposed a simple quantum theory in 1981, which explained the quantization of resistance in terms of one-electron filling of Landau levels in a strong magnetic field which caused the electrons to move in circles. Furthermore, the semiclassical Hall current in this approach is due to the adiabatic derivative of the total system energy by magnetic flux through the closed loop. This approach, however, does not take into consideration the electric fields, which can be strong in certain conditions (especially in semiconductor devices such as MOSFETs), and does nothing with the reactive parameters of the Quantum LC circuit formed.

The situation becomes more complicated when Horst Ludwig Stormer, Daniel C. Tsui, and Arthur Gossard discovered the fractional quantum Hall effect. The simple quantum theory of Laughlin would consider the "carriers" of fractional charge, as composite fermions. Further developments was made by S.H. Simon in 1998. In this approach, Landau levels are filled by composite fermions which have fractional charges, as the QHE Laughlin model has. The Laughlin-Jain-Simon approach is the dominant view now, but some physicists strongly criticize it. For example, Keshav N. Shrivastava thought that quasiparticles form the quantum of magnetic flux ($$~\phi_0 = \frac{h}{e} $$), which could be connected to an electron forming a compound state with some magnetic and electric flux quantum. The theory of such quasiparticles could not be derived from the first principles.

Furthermore, M.I. Dyakonov described the current situation as being inconvenient: on one hand, there are many experimental facts which confirm the idea of composite fermions that takes part in the "singular" theoretical approach to the phenomenon, which hints at the physical reality of the idea, but on the other hand, nobody can theoretically justify the existence of these free quasiparticles.

However, there is another approach to the FQHE. At the beginning of the 21st century, Raphael Tsu proposed a new conception of quantum mechanics in which the characteristic impedance plays the dominant role. This dominance was illustrated in the quantum oscillator problem by Yakov Zel'dovich in 2008.

But Tsu and Zel'dovich were not the firsts. It so happens that there is a little interest in macroscopic properties such as resistance, capacitance, and inductance in the modern quantum electrodynamics. Furthermore, these properties are neglected even in classical electrodynamics, in favour of concepts such as electric and magnetic fields. For example, Maxwell equations are formulated in terms of fields and so the resulting solutions only include fields. "Field approaches" in electrodynamics that consider "point charges" leads to mathematical singularities (renormalization problems) when the interaction radius trends to zero. Furthermore, these singularities are present in quantum electrodynamics too, where power methods are developed to compensate them. In applied physics, reactive parameters such as capacitance and inductance are used instead of fields.

The present day situation (without proper development of the theory of reactive parameters such as inductance, capacitance and electromagnetic resonator) impedes developments of information technologies and quantum computing.The mechanical harmonic oscillator was studied in the early 1930s, when the quantum theory was first developed. However, the quantum consideration of the LC circuit was started only by Louisell in 1973. Since then, there were no practical examples of quantum capacitances and inductances, therefore this approach did not received much consideration. Theoretically correct introductions of the quantum capacitance for QHE, based on the density of states, were first presented by Serge Luryi in 1988. However, Luryi did not introduce the quantum inductance, and this approach was not considered in the quantum LC circuit and resonator. One year later, O.L. Yakymakha considered an example of the series and parallel QHE LC circuits (both integer and fractional) and their characteristic impedances. However he did not consider the Schrodinger equation for the quantum LC circuit.

For the first time, both quantum values, capacitance and inductance, were considered by Yakymakha in 1994, during spectroscopic investigations of MOSFETs at the very low frequencies (sound range). The flat quantum capacitances and inductances here had thicknesses about Compton wavelength of electron and its characteristic impedance – the wave impedance of free space. Three year later, Devoret presented a complete theory of the quantum LC circuit (applied to the Josephson junction). Possible application of the quantum LC circuits and resonators in quantum computations were considered by Devoret in 2004.

Quantum Hall resonator (QHR)
Magnetic length of the resonator is:
 * $$l = \sqrt{\frac{\hbar}{eB}}, \ $$

where $$\hbar \ $$ is the reduced Planck constant, $$e \ $$ is the elementary charge, and $$B  \ $$ is the external homogenous magnetic field.

Surface scaling parameter is:
 * $$S = 2\pi l^2 = \frac{h}{eB}. \ $$

Cyclotron frequency is:
 * $$\omega_c = \frac{eB}{m}, \ $$

where $$m \ $$ is the effective electron mass in solids.

QHR density of states (DOS) is:
 * $$D = \frac{1}{S \hbar \omega_c} = \frac{m}{2\pi \hbar^2}. \ $$

DOS quantum capacitance is:
 * $$C = q^2 D S, \ $$

where $$q $$ is the induced electric charge of the resonator.

DOS quantum inductance is:
 * $$L = \phi^2 D S, \ $$

where $$ \phi $$ is the induced magnetic flux.

Maximal value of the capacitance energy is:
 * $$W_C = \frac{q^2}{2C} = \frac{1}{2D S}. \ $$

Maximal value of the inductance energy is:
 * $$W_L = \frac{ \phi^2}{2L} = \frac{1}{2D S}. \ $$

QHR resonance frequency is:
 * $$\omega = \frac{1}{\sqrt{L C}} = \frac{1}{q \phi D S}. \ $$

The standard quantum oscillator has the following eigenvalues of the Hamiltonian:
 * $$W_n = \hbar \omega_0(n + 1/2), \ $$

where at $$n = 0 \ $$ we shall have zero oscillation:
 * $$W_0 = \hbar \omega_0/2. \ $$

QHR energy conservation law (at n = 0) is:
 * $$W_{QR} = \frac{1}{2}\hbar \omega = \frac{\hbar}{2q \phi D S} = \frac{1}{2D S}, \ $$

which yields the following relationship between $$q $$  and  $$\phi $$ (an analogue of uncertainty principle ):
 * $$q \phi = \hbar. \ $$

QHR characteristic impedance:
 * $$ Z = \sqrt{\frac{L}{C}} = \frac{ \phi }{q} = R_K \ $$.

The solution of these two equation yields the following values for $$q $$  and  $$\phi $$:
 * $$q = \frac{e}{\sqrt{2\pi}} \ $$
 * $$ \phi = \frac{\phi_0}{\sqrt{2\pi}}, \ $$

where $$ \phi_0= h/e \ $$ is the  magnetic monopole.

 * $$C = q^2 D S = 2 \alpha \cdot \frac{\varepsilon_0}{\lambda_0}S \ ,$$
 * $$L = \phi ^2 D S = 2 \beta \cdot \frac{\mu_0}{\lambda_0}S, \ $$

where $$\alpha \ $$  is the electric fine structure constant], $$\beta = \frac{1}{4\alpha} \ $$ is the magnetic coupling constant, $$\varepsilon_0 \ $$ is the electric constant, $$\mu_0 \ $$ is the vacuum permeability, and $$\lambda_0 = \frac{h}{ mc} \ $$ is the Compton wavelength of electron. Note that, the QHR resonance frequency takes the values of cyclotron frequency here:
 * $$\omega = \frac{1}{\sqrt{L C}} = \frac{eB}{m} = \omega_c. \ $$

Constant magnetic field
Let us consider the standard QHE for one electron filling Landau levels step by step at constant magnetic field $$B_1 = const \ $$ and increasing electric field $$E_1 = variable. \ $$ At the first Landau level surface electron concentration will be:
 * $$n_{1} = \frac{1}{S_{1}} = \frac{eB_1}{h}. \ $$

First Landau level energy is:
 * $$W_{L1} = \hbar \omega_{c1}, \ $$

where $$\omega_{c1} \ $$ is the cyclotron frequency due to the constant magnetic field $$B_1 \ $$.

With increasing filling number $$i_1 = 1, 2, 3,... \ $$ we shall have the following parameters of QHR:

Surface electron concentration is:
 * $$n_{i} = i_1 n_{1}. \ $$

Landau level energy is:
 * $$W_{Li} = i_1 W_{L1}. \ $$

Density of states is:
 * $$D_{i} = \frac{n_{i}}{W_{Li}} = D_{1}. \ $$

Induced effective electric charge is:
 * $$q_{i} = i_1 q_{1}. \ $$

DOS quantum capacitance is:
 * $$C_{i} = \frac{ q_{i}^2}{ W_{Li} } = i_1 C_{1}. \ $$

So, we have the parallel connection of “elementary resonator” quantum capacitances in that case.

Induced magnetic flux is:
 * $$ \phi_i = \phi_1. \ $$

DOS quantum inductance is:
 * $$L_{i} = \frac { \phi_1^2}{ W_{Li} } =\frac{1}{i_1}L_{1}. \ $$

So, we have the parallel connection of “elementary resonator” quantum inductances in that case.

Characteristic impedance is:
 * $$ Z_{i} = \sqrt{\frac{L_{i}}{C_{i}}} = \frac{1}{i_1}\sqrt{\frac{L_{1}}{C_{1}}} = \frac{1}{i_1} Z_{1}. \ $$

Resonance frequency is:
 * $$\omega_{i} = \frac{1}{\sqrt{L_{i}C_{i}}} = \frac{1}{\sqrt{L_{1}C_{1}}} = \frac{eB_1}{m} = \omega_{c1}. \ $$

Thus, in the constant homogenous magnetic field with one electron filling Landau level we shall have the following conservating parameters:
 * $$D_{i}= const, \quad \omega_{i} = const. \ $$

Constant electric field
Let us consider the other case when electric field is constant ($$E_2 = (E_1)_{max} = const \ $$), and increasing magnetic field:
 * $$B_1 \le B_2 \le j_2\cdot B_1 = 2B_1, \ $$

where $$j_2 \ $$ is the maximal number of electron on Landau level.

The maximum number of Landau level is taken as:
 * $$i_2 = (i_1)_{max} = k = 3. \ $$

For the sake of the unitary consideration it is need to redefine parameters of the first stage future composite resonator. Surface electron concentration is:
 * $$n_{i2} = n_{i1} = k\cdot n_{1}. \ $$

Landau level energy is:
 * $$W_{Li2} = k\cdot W_{L1}. \ $$

Density of states is:
 * $$D_{i2} = D_{i1} = D_{1}. \ $$

Induced charge is:
 * $$q_{i2} = k\cdot q_{1}. \ $$

DOS quantum capacitance is:
 * $$C_{i2} = C_{i1} = k\cdot C_{1}. \ $$

Induced magnetic flux is:
 * $$ \phi_{i2} = \phi_{i1} = \phi_1. \ $$

DOS quantum inductance is:
 * $$L_{i2} = k\cdot L_{1}. \ $$

Characteristic impedance is:
 * $$ Z_{i2} = \frac{1}{k} Z_{1}. \ $$

Resonance frequency is:
 * $$\omega_{i2} = \omega_{i1} = \omega_{c1}. \ $$

Thus, we are ready to consider the second case at $$j_2 =2 \ $$, $$i_2 = 2 \ $$ and $$B_2 = j_2B_1 = 2B_1 \ $$. Note that with increasing magnetic field to $$B_2 = 2B_1 \ $$ the second electron from the second Landau level goes to the first Landau level filled by the first electron, and the third electron goes to the second Landau level. So, we have the composite resonator with two filled Landau levels.

DOS quantum capacitance in that case will be:
 * $$C_{22} = \frac{2}{3}C_{11} = q_{22}^2 D_{22}\frac{1}{n_{22}} = \frac{q_{22}^2}{W_{L22}}, \ $$

where
 * $$C_{11} = q_{11}^2 D_{11}\frac{1}{n_{11}} = \frac{q_{11}^2}{W_{L11}}. \ $$

The total energy of this composite resonator will be:
 * $$W_{L22} = \frac{3}{2}(\frac{q_{22}}{q_{11}})^2 W_{L11} = \frac{3^3}{2}W_{L11}, \ $$

at $$q_{22} = 3q_{11}. \ $$

Density of states will be:
 * $$D_{22} = \frac{n_{22}}{W_{L22}} = \frac{2n_{22}}{27W_{L11}} = \frac{2}{27}\frac{n_{22}}{n_{11}}D_{11}. \ $$

The natural supposition for surface electron density is:
 * $$n_{22} = 3^2\cdot n_{11} \ $$

yields the following value for DOS in that case:
 * $$D_{22} = \frac{2\cdot 9}{27}D_{11} = \frac{2}{3}D_{11}. \ $$

DOS quantum inductance is:
 * $$L_{22} = \frac{3}{2}L_{11}, \ $$

where induced magnetic flux is considered:
 * $$ \phi_{22} = \frac{9}{2} \phi_{11}. \ $$

Characteristic impedance in the case will be:
 * $$ Z_{22} = \sqrt{\frac{L_{22}}{C_{22}}}= \frac{3}{2} Z_{11}. \ $$

Resonance frequency is:
 * $$\omega_{22} = \frac{1}{\sqrt{L_{22}C_{22}}} = 2\omega_{11} = \frac{e}{m}2B_1 = \omega_{c2}. \ $$

Now we are ready to consider the third case at $$j_2 = 3 \ $$, $$i_2 = 1 \ $$ and $$B_2 = j_2 B_1 = 3B_1 \ $$. Note that, with increasing magnetic field to $$B_2 = 3B_1 \ $$ the third electron from the second Landau level goes to the first Landau level filled by the first and second electrons. So, we have the composite resonator with one filled Landau level by three electrons. DOS quantum capacitance in that case will be:
 * $$C_{33} = \frac{1}{3}C_{11} = q_{13}^2 D_{13}\frac{1}{n_{13}} = \frac{q_{13}^2}{W_{L13}}. \ $$

The total energy of this composite resonator will be:
 * $$W_{L13} = 3(\frac{q_{13}}{q_{11}})^2 W_{L11} = 3^3W_{L11}, \ $$

at $$q_{13} = 3q_{11}. \ $$

Density of states will be:
 * $$D_{13} = \frac{n_{13}}{W_{L13}} = \frac{n_{13}}{27W_{L11}} = \frac{1}{27}\frac{n_{13}}{n_{11}}D_{11}. \ $$

The natural supposition for surface electron density is:
 * $$n_{13} = 3\cdot n_{22} = 3^3\cdot n_{11} \ $$

yields the following value for DOS in that case:
 * $$D_{13} = \frac{n_{13}}{W_{L13}} = \frac{n_{11}}{W_{L11}} = D_{11}. \ $$

So, the new composite system returns to the natural 2D- case.

DOS quantum inductance is:
 * $$L_{13} = \frac{3}{1}L_{11}, \ $$

where induced magnetic flux is considered:
 * $$ \phi_{13} = \frac{9}{1} \phi_{11}. \ $$

Characteristic impedance in that case will be:
 * $$ Z_{13} = \sqrt{\frac{L_{13}}{C_{13}}}= \frac{3}{1}\rho_{11}. \ $$

Resonance frequency is:
 * $$\omega_{13} = \frac{1}{\sqrt{L_{13}C_{13}}} = 3\omega_{11} = \frac{e}{m}3B_1 = \omega_{c3}. \ $$

Thus, the composite quantum Hall resonator is formed.

The energy per Landau level is:
 * $$W_{L13} = \hbar \omega_{c3} = 3\hbar \omega_{c1}. \ $$

The energy gap of QHCR:
 * $$\Delta W_{gap} = 3^2\cdot \hbar \omega_{c3} = 3^3\cdot \hbar \omega_{c1}. \ $$

Now the QHCR can be considered as elementary quantum object for the external magnetic and electric fields, independently of its intrinsic structure. Note that, this object is connected to three electrons and could change its state simultaneously.

QHCR and fractional QHE
Now we can consider the s.c. fractional QHE by the composite resonator model formed by three electrons. As in the case of one electron resonator model we should to fix magnetic field:
 * $$B_3 = 3B_1 = const \ ,$$

and increase electric field:
 * $$(E_1)_{max} \le E = variable. \ $$

So, the filling Landau level number $$i_3 = 1, 2, 3,... \ $$ will be connected with three electrons for every Landau level.

Surface electron concentration in the case will be:
 * $$n_{i3} = i_3 n_{13} \ .$$

Density of states will be:
 * $$D_{i3} = \frac{n_{i3}}{W_{i3} } = \frac{i_3n_{13}}{i_3W_{13}} = D_{13}. \ $$

Induced electric charge is:
 * $$q_{i3} = i_3 q_{13} = variable \ . $$

DOS quantum capacitance is:
 * $$C_{i3} = i_3^2q_{13}^2D_{i3}\frac{1}{n_{i3}} = i_3 C_{13} \ .$$

Induced magnetic flux is:
 * $$ \phi_{i3} = \phi_{13} = const. \ $$

DOS quantum inductance is:
 * $$L_{i3} = > \phi_{i3}^2D_{i3}\frac{1}{n_{i3}} = \frac{1}{i_3}L_{13} \ .$$

Characteristic impedance in that case will be:
 * $$ Z_{i3} = \sqrt{\frac{L_{i3}}{C_{i3}}} = \frac{1}{i_3}\sqrt{\frac{L_{13}}{C_{13}}} = \frac{1}{i_3} Z_{13} = \frac{3}{i_3} Z_{11} \ $$

where $$ Z_{11} = R_K \ .$$

QHCR resonance frequency:
 * $$\omega_{i3} = \frac{1}{\sqrt{L_{i3} C_{i3} }} = \frac{1}{\sqrt{L_{13}C_{13}}} = \omega_{13} = 3\omega_{11} \ . $$

Note that, in the general case filling number $$i_3 = 1, 2, 3,... \ $$ could be connected with any odd quantity of filling electrons per Landau level ($$k = 3, 5, 7, 9,... \ $$). However, in those cases we shall have other values for characteristic impedance and resonance frequency:
 * $$ Z_k = \frac{k}{i_3} Z_{11}$$
 * $$ \omega_k = k \omega_{11}. \ $$

Quantum antidot
Resonance electron tunnelling in the Goldman quantum antidot can be investigated experimentally by measuring of the periodic quantization (oscillation) of magnetic and electric fields:
 * $$\Delta B_{ik}\cdot S = \frac{\Delta B_{ik}h}{eB} = \Delta \phi_{ik} \ $$
 * $$\Delta D_{ik}\cdot S = \frac{\Delta D_{ik}h}{eB} = \Delta q_{ik} \ $$

where $$i = 1, 2, 3,... \ $$ is the Landau level number, and $$k = 3, 5, 7,... \ $$ is the electron number of composite resonator.

The electric field in the quantum antidot can be represented through applied voltage:
 * $$\Delta D_{ik} = \varepsilon_0 \varepsilon_r \Delta E_{ik} = \frac{\varepsilon_0 \varepsilon_r}{d_x} \Delta V_{ik} = C_x\Delta V_{ik}, \ $$

where $$\varepsilon_0 \ $$ is the electric constant, $$\varepsilon_r  \ $$ is the relative permittivity, $$d_x \ $$ is the heterojunction thickness, and $$C_x  \ $$ is the heterojunction mesoscopic capacitance per unit area.

The induced electric charge and induced magnetic flux quantization is due to the properties of composite resonator formed in the quantum antidot:
 * $$\Delta q_{ik} = iq_0 = ie \ $$
 * $$\Delta \phi_{ik} = k \phi_0 = k \frac{h}{e}. \ $$

Characteristic impedance of composite resonator is:
 * $$Z_{ik} = \frac{\Delta \phi_{ik}}{\Delta q_{ik}} = \frac{k}{i}R_K = \frac{\Delta B_{ik}}{C_x\Delta V_{ik}}. \ $$

Now we can find out the relationship between electric voltage and magnetic field quantization:
 * $$\Delta V_{ik} = \frac{i}{k}\frac{\Delta B_{ik}}{C_xR_K}. \ $$

Thus, there are no any fractional electric charges in the quantum antidot. The number of tunnelling electron is due to the Landau level number ($$i \ $$). But the number of magnetic charge quantum is due to the electron in the composite resonator ($$k \ $$).

History
First, the unconventional integer QHE was discovered in graphene by Novoselov et. al. and Zhang et al.(2005). Theoretical interpretation was proposed by Sharapov et.al. The point is that conductance quantization has anomaly at the first Landau level, due to a twice smaller degeneracy. Furthermore, the first Landau level is filled by electron and hole quasiparticles simultaneously. Similar phenomena were presented in the classical case in silicon MOSFETs, which are working in the weak inversion mode first considered by Swanson (1972) and further modernized by Yakymakha (1981). The only difference between graphene and silicon devices is that MOSFETs are the unipolar devices (due to the p-n- junctions of source and drain).

The room-temperature quantum galvanomagnetic effects in the 2D-systems consisting of the two sort particles was predicted by Yakymakha (1989)< /ref name =Yakym1>

First experimental confirmation of the room-temperature QHE were obtained in graphene by Novoselov et.al. (2007) . This is due to the highly unusual nature of charge carriers in graphene, which behave as massless relativistic particles (Dirac fermions) and move with little scattering under ambient conditions.

Graphene QHE composite resonator
The standard characteristic impedance of the electron quantum Hall resonator in graphen is:
 * $$ Z_{Rn} = \sqrt{\frac{L_{Rn}}{C_{Rn}}} = \frac{R_K}{g_n}, \ $$

where $$g_n $$ is the electron degeneration number due to the band structure of graphene. The standard characteristic impedance of the hole quantum Hall resonator in graphen is:
 * $$ Z_{Rp} = \sqrt{\frac{L_{Rp}}{C_{Rp}}} = \frac{R_K}{g_p}, \ $$

where $$g_p = g_n = g = 4 $$ is the hole degeneration number due to the band structure of graphene.

At the first Landau level both, electrons and holes are filling the same 2D surface (something like chessboard).

So, the elementary composite resonator here will be formed by one electron and one hole. The total inductance of this resonator will be consisted of the electron and hole inductances connected in series:
 * $$L_{RT} = L_{Rn} + L_{Rp} = 2L_R. \ $$

By analogy, the total capacitance of this resonator will be consisted of the electron and hole capacitances connected in series:
 * $$C_{RT}^{-1} = C_{Rn}^{-1} + C_{Rp}^{-1} = 2C_R^{-1}. \ $$

Thus, the total characteristic impedance of the composite resonator will be as follows:
 * $$ Z_{RT} = \sqrt{\frac{L_{RT}}{C_{RT}}} = \sqrt{\frac{4L_{R}}{C_{R}}} = 2\frac{R_K}{g}, \ $$

where $$g = 4 $$.

The second Landau level is filled by monopolar particles (electrons or holes). Therefore, the total characteristic impedance of the second Landau level will be consisted of the first composite resonator and second standard resonator connected in parallel:
 * $$ Z_{RT2}^{-1} = Z_{RT}^{-1} + Z_{R}^{-1} = \sigma_{Hg}(1 + 1/2), \ $$

where $$\sigma_{Hg} = g/R_K $$ is the quantum conductance for graphene.

For the third Landau level and higher we would have the following total characteristic impedance:
 * $$ Z_{RTi}^{-1} = \sigma_{Hg}(i - 1/2), \quad \quad i = 1,2,3,.. \ $$

where $$i $$ is the Landau level number.

Reference Books

 * Stratton J.A.(1941). Electromagnetic Theory. New York, London: McGraw-Hill.p.615. djvu
 * Детлаф А.А., Яворский Б.М., Милковская Л.Б.(1977). Курс физики. Том 2. Электричество и магнетизм (4-е издание). М.: Высшая школа, "Reference Book on Electricity"  djvu
 * Гольдштейн Л.Д., Зернов Н.В. (1971). Электромагнитные поля. 2- издание. Москва: Советское Радио. 664с. "Electromagnetic Fields" djvu
 * Zyun F. Ezawa: Quantum Hall Effects - Field Theoretical Approach and Related Topics. World Scientific, Singapore 2008, ISBN 978-981-270-032-2
 * Sankar D. Sarma, Aron Pinczuk: Perspectives in Quantum Hall Effects. Wiley-VCH, Weinheim 2004, ISBN 978-0-471-11216-7
 * Composite Fermions, Edited by O. Heinonen, World Scientific, Singapore (1998).


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Physics/Essays/Fedosin/Gravitational characteristic impedance of free space

The Gravitational characteristic impedance of free space, $$\rho_{g0} \ $$ is a physical constant that relates the magnitudes of the gravitational field strength $$\mathbf {\Gamma } $$ and the gravitational torsion field $$\mathbf {\Omega } $$ in covariant theory of gravitation (the gravitoelectric and gravitomagnetic fields in gravitoelectromagnetism) in gravitational radiation travelling through free space:
 * $$\rho_{g0} = \sqrt{\frac{\mu_{g0}}{\varepsilon_g}} = \frac{4\pi G}{c} = \frac {\mu_{g0} \Gamma}{\Omega}= 2.796696\cdot 10^{-18} \mathrm {m^2/(s\cdot kg)}. \ $$

where $$~\varepsilon_g = \frac{1}{4\pi G } = 1.192708\cdot 10^9 \mathrm {kg \cdot s^2 \cdot m^{-3}} $$ is the gravitoelectric gravitational constant in the set of selfconsistent gravitational constants, $$~ G $$ is the gravitational constant, c is the speed of light, $$ \mu_{g0} = \frac{4\pi G}{c^2} = 9.328772\cdot 10^{-27} \mathrm {m / kg} \ $$ is the gravitomagnetic gravitational constant.

As in electromagnetism, the characteristic impedance of free space plays a central role in all radiation problems, such as in a comparison of the radiation resistance of gravity-wave antennas to the value of this impedance in order to estimate the coupling efficiency of these antennas to free space. The numerical value of this impedance is extremely small, but the impedance of all material objects must be “impedance matched” to this extremely small quantity before significant power can be transferred efficiently from gravitational waves to these detectors.

The gravitational characteristic impedance of free space may be connected with other constants:
 * $$\rho_{g0} = 2\alpha \cdot \frac{h}{m_S^2}, \ $$

where $$h \ $$ is the Planck constant, $$\alpha = \frac{e^2}{2\varepsilon_0 hc}$$ is the fine structure constant for the elementary charge $$e \ $$, $$ \varepsilon_0 $$ is the electric constant, $$m_S = e\sqrt{\frac{\varepsilon_g}{\varepsilon_0}} = \frac{e}{\sqrt{4\pi G\varepsilon_0}} \ $$ is the Stoney mass.

The gravitational characteristic impedance of free space for the atoms and nucleons level of matter is:
 * $$ \rho_s = \frac{4\pi G_s }{c} =  6.346\cdot 10^{21} \mathrm {m^2/(s\cdot kg)}, \ $$

where $$ G_s = \frac {e^2}{4 \pi \varepsilon_0 m_p m_e}$$ is the strong gravitational constant, $$ m_p $$ and $$ m_e $$ are the masses of proton and electron.

History
Due to McDonald first who used Maxwell equations to describe gravity was Oliver Heaviside. The point is that in the weak gravitational field the standard theory of gravity could be written in the form of Maxwell-like gravitational equations.

In the 80-ties Maxwell-like equations were considered in the Wald book of general relativity. In the 90-ties Kraus first introduced the gravitational characteristic impedance of free space, which was detailed later by Kiefer, and now by Raymond Y. Chiao, who is developing the ways of experimental determination of the gravitational waves.

Typical gravitational impedance at the megascopic scale
In the general case only planets (with their sattelites) and stars could be considered "as free, as possible" to be used as some "antenna" to the gravitational waves detection. Spherical megascopic bodies have the folloving characteristic impedance:
 * $$\rho_{gs} \approx \frac{v r}{3m}, \ $$

where
 * $$v \ $$ is the equatorial velocity,
 * $$r \ $$ is the spherical body radius and
 * $$m \ $$ is the body mass.

Planetary data were taken from the textbook. As could be seen from the Table, only the Mercury has characteristic impedance close to the free space value.
 * Solar planetary system

Satellites' data were taken from the textbook. As could be seen from the Table, only the Moon has the closest value of characteristic impedance about 12-times greater then for free space.
 * Planet's satellites

In this table designations "O5" and "F5" define stellar types. As it is seen from the Table, some stars could have characteristic impedance value about the same as the impedance of free space.
 * Stars

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


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User talk:Nelsonc5~enwikiversity

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Your account will be renamed
Hello,

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

Unfortunately, your account clashes with another account also called Nelsonc5. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Nelsonc5~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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Renamed
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title: User talk:Nelsonc5~enwikiversity


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User talk:Gcbound

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title: User talk:Gcbound


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User talk:Duinit8

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User talk:Tristan.wolfe

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User talk:Emiliotheplayer

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User talk:S0095109

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User talk:Amzzy101

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User talk:Dshanthi01

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User:Aripnurahman

Arip Nurahman

Curriculum Vitae

Educational Background

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title: User:Aripnurahman


text:
Physics/Essays/Fedosin/Stoney mass

In physics, the Stoney mass ($$m_S$$), is one of the base units in the system of natural units called Stoney units. It is a quantity of mass defined in terms of fundamental physical constants.

The Stoney mass is defined as:
 * $$m_S = e \sqrt{\frac{\varepsilon_g}{\varepsilon_0}} = \sqrt{\alpha} m_P = 1.859\cdot 10^{-9}  \ $$ kg,

where
 * $$\varepsilon_g = \frac{1}{4\pi G} \ $$, and $$G \ $$ is the gravitational constant,
 * $$\varepsilon_0 \ $$ is the electric constant,
 * $$ \alpha \ $$ = (137.035999074)−1 is the electric  fine structure constant,
 * $$ e \ $$ is the elementary charge.

The Stoney mass is $$\alpha^{-1/2} \approx 11.706$$ times less than the Planck mass $$m_P \ $$.

History
Contemporary physics has settled on the Planck scale as the most suitable scale for a unified field theory. The Planck scale was however anticipated by George Stoney.

The Stoney scale has been re-discovered by M. Castans and J. Belinchon, and by Ross McPherson, in connection with the Large number coincidences.

Stoney mass vs elementary electric charge
The elementary charge is a unit of the Stoney scale. The Coulomb force between two such charges is:
 * $$F_{C} = \frac{1}{4\pi \varepsilon_0}\cdot \frac{e^2}{r^2}. \ $$

The Newton force between two Stoney masses is:
 * $$F_{N} = \frac{1}{4\pi \varepsilon_g}\cdot \frac{m_S^2}{r^2}, \ $$

From the equality of the above forces
 * $$F_{C} = F_{N} \ $$

we find out the relationship between Stoney mass and Stoney charge:
 * $$m_S = e \sqrt{\frac{\varepsilon_g}{\varepsilon_0}}. \ $$

Note that, George Stoney first proposed the term electron for the particle with elementary electric charge due to O’Hara and Keller.

title: Physics/Essays/Fedosin/Stoney mass


text:
Physics/Essays/Fedosin/Planck mass

In physics, the Planck mass (mP) is the unit of mass in the system of natural units known as Planck units. It is defined so that

 * $$m_P = \sqrt{\frac{\hbar c}{G}} = 1.2209\cdot 10^{19}\, \text {GeV/c}^2 = 2.17644\cdot 10^{-8}\, \text {kg} \ $$

where c is the speed of light in vacuum, G is the gravitational constant, and h is the reduced Planck constant.

Particle physicists and cosmologists often use the reduced Planck mass, which is

 * $$\sqrt\frac{\hbar{}c}{8\pi G}$$ = 4.341 × 10-9 kg = 2.435 × 1018 GeV/c2.

The added factor of $$1/\sqrt{8\pi} $$ simplifies a number of equations in general relativity.

The name honors Max Planck, who was the first to propose it. The Planck mass is not so far from Stoney mass $$ m_S \ $$ and connect with it through fine structure constant $$\alpha = \frac{e^2}{2\varepsilon_0 hc}$$ in the way: $$ m_P = \frac {m_S} {\sqrt{ \alpha}} \ .$$

Dimensional analysis
The formula for the Planck mass can be derived by dimensional analysis. In this approach, one starts with the three physical constants ħ, c, and G, and attempt to combine them to get a quantity with units of mass. The expected formula is of the form
 * $$m_\text{P} = c^{n_1} G^{n_2} \hbar^{n_3},$$

where $$n_1,n_2,n_3$$ are constants to be determined by matching the dimensions of both sides. Using the symbol L for length, T for time, M for mass, and writing "[x]" for the dimensions of some physical quantity x, we have the following:
 * $$[c] = \mathsf{LT}^{-1} \ $$
 * $$[G] = \mathsf{M}^{-1}\mathsf{L}^3\mathsf{T}^{-2} \ $$
 * $$[\hbar] = \mathsf{M}^1\mathsf{L}^2\mathsf{T}^{-1} \ $$.

Therefore,
 * $$[c^{n_1} G^{n_2} \hbar^{n_3}] = \mathsf{M}^{-n_2+n_3} \mathsf{L}^{n_1+3n_2+2n_3} \mathsf{T}^{-n_1-2n_2-n_3}$$

If one wants dimensions of mass, the following equations must hold:
 * $$-n_2 + n_3 = 1 \ $$
 * $$n_1 + 3n_2 + 2n_3 = 0 \ $$
 * $$-n_1 - 2n_2 - n_3 = 0 \ $$.

The solution of this system is:
 * $$n_1 = 1/2, n_2 = -1/2, n_3 = 1/2. \ $$

Thus, the Planck mass is:
 * $$m_\text{P} = c^{1/2}G^{-1/2}\hbar^{1/2} = \sqrt{\frac{c\hbar}{G}}. $$

Significance
Unlike all other Planck units and most Planck derived units, the Planck mass is a macroscopic amount, having a scale more or less conceivable to humans. For example, the body mass of a flea is roughly 4000 to 5000 mP.

The Planck mass has the Schwarzschild radius equals to its Compton wavelength divided by $$\pi \ $$. The Planck mass is also the mass of the Planck particle, a hypothetical tiny black hole whose Schwarzschild radius equals the Planck length.

The Planck mass is an idealized mass thought to have special significance for quantum gravity when general relativity and the fundamentals of quantum physics become mutually important to describe mechanics.

title: Physics/Essays/Fedosin/Planck mass


text:
Physics/Essays/Fedosin/Quantum Inductance

Quantum Inductance is the physical value that can be obtained from the density of states (DOS) approach, first introduced by Serge Luryi (1988) to describe the 2D-electronic systems in silicon surfaces and AsGa junctions. This inductance is defined through standard density of states in the solids. Quantum inductance can be used in the Quantum Hall effect (integer and fractional) investigations as an approach which uses Quantum LC circuit.

Classical flat inductance
For the standard classical series $$R_dL_dC_d \ $$ circuit the planar inductance can be defined as:
 * $$L_d = \frac{\mu_0 \mu_r S_{xz}N^2}{l_y},$$

where $$\mu_0 \ $$ is the vacuum permeability, $$\mu_r \ $$ is the relative permeability, $$S_{yz} = l_yl_z \ $$ is the MOSFET channel surface, $$S_{xz} = l_xl_z  \ $$ is the channel cross section, $$l_x  \ $$ is the channel depth, $$l_y  \ $$ is the channel length, $$l_z  \ $$ is the channel width, $$N = \frac{l_y}{\lambda_y}  \ $$ is the turn number of the planar induction coil, $$\lambda_y  \ $$ is the helix step of induction coil.

In the quantum limits, unknown parameter could be estimated by the following:
 * $$\lambda_y = \sqrt{\frac{\mu_0\mu_r S_{yz}l_x}{L_d}} $$,

where $$\mu \to 1 \ $$, $$l_x \to \lambda_0 \ $$, $$L_d \to L \approx 7.407\cdot 10^{-2} \ $$ H and $$S_{yz} \to S \approx 1.43\cdot 10^{-7} \ $$ m2. Therefore we shall have the quantum value about Compton wavelength of electron $$ \lambda_0 \ $$:

 * $$\lambda_{y0} = \sqrt{\frac{\mu_0 S \lambda_0 }{L}} \approx 2.426\cdot 10^{-12} $$ m.

Josephson junction quantum inductance
Electromagnetic induction (Faraday) law is:
 * $$V_{ind} = \frac{\partial \Phi}{\partial t} = -L\frac{\partial I}{\partial t}, \ $$

where $$\Phi \ $$ is magnetic flux, $$L \ $$ is the Josephson junction quantum inductance and $$I \ $$ is the Josephson junction current.

DC Josephson equation for current is:
 * $$I = I_J\cdot \sin \phi, \ $$

where $$I_J \ $$ is the Josephson scale for current, $$\phi \ $$ is the phase difference between superconductors.

Current derivative on time variable will be:
 * $$\frac{\partial I}{\partial t} = I_J \cos \phi \cdot \frac{\partial \phi}{\partial t}. \ $$

AC Josephson equation is:
 * $$\frac{\partial \phi}{\partial t} = \frac{q}{\hbar}V = \frac{2\pi}{\Phi_0}V, \ $$

where $$\hbar \ $$ is the reduced Planck constant, $$\Phi_0 = h/2e $$ is the Josephson magnetic flux quantum, $$q = 2e \ $$ and $$e \ $$ is the elementary charge.

Combining equations for derivatives yields junction voltage:
 * $$V = \frac{\Phi_0}{2\pi I_J}\cdot \frac{1}{\cos \phi}\cdot \frac{\partial I}{\partial t} = L_J\cdot \frac{\partial I}{\partial t}, \ $$

where
 * $$L_J = \frac{\Phi_0}{2\pi I_J}\cdot \frac{1}{\cos \phi} \ $$

is the Deboret (1997) quantum inductance.

DOS quantum inductance
In the general case 2D-density of states (DOS) in a solid can be defined by the following:
 * $$D_{2D} = \frac{m^*}{2\pi \hbar^2} \ $$,

where $$m^* = \xi m_e \ $$ is current carriers effective mass in a solid, $$m_e \ $$ is the electron mass, and $$\xi \ $$ is a dimensionless parameter, which considers band structure of the solid. So, the quantum inductance can be defined as follows:
 * $$L_Q = \phi_0^2 \cdot D_{2D} \cdot S = \frac {h^2}{e^2} \cdot D_{2D} \cdot S = k \xi \cdot L_{Q0},$$

where $$\phi_0 = h/e \ $$ is the magnetic flux quantum, $$S = k S_0 $$ is the resonator surface area, $$S_0 = \frac {\lambda^2_0}{2 \pi } $$ is the elementary surface area, $$ k  $$ is the coefficient of area, $$L_{Q0} = 2 \beta \cdot L_{QY} \ $$ is the elementary quantum inductance, and another ideal quantum inductance is:
 * $$L_{QY} = \mu_0 \lambda_0 = 3.04899 \cdot 10^{-18} \ $$ H,

where $$\mu_0 \ $$ is the  vacuum permeability, $$\beta = \frac{1}{4\alpha} \ $$ is the magnetic coupling constant, $$\alpha \ $$ is the fine structure constant  and $$ \lambda_0 = \frac{h}{m_e c} \ $$ is the Compton wavelength of electron.

Quantum inductance in quantum Hall effect
The quantum inductance in the QHE mode will be:
 * $$L_{QA} = \frac{ \phi_0^2 \cdot D_{2D}}{n_B} \ $$,

where the carrier concentration per unit area in magnetic field $$ B \ $$ is:
 * $$n_B = \frac{eB}{h} .\ $$

By analogy, the quantum capacitance in the QHE mode will be:
 * $$C_{QA} = \frac{ C_{QL}}{n_B} \ $$,

where
 * $$C_{QL} = e^2\cdot D_{2D} = \xi \cdot C_{q0}, $$

is DOS definition of the quantum capacitance per unit area according to Luryi, and $$C_{q0} = 4\pi \alpha \cdot C_{qY} \ $$ is the elementary quantum capacitance per unit area at $$\xi = 1 \ $$, and another ideal quantum capacitance per unit area is:

 * $$C_{qY} = \frac{\varepsilon_0}{\lambda_0} = 3.6492417 \ $$ F/m2,

where $$\varepsilon_0 \ $$ is the electric constant.

The standard wave impedance definition for the QHE LC circuit can be presented as:

 * $$ \rho_Q = \sqrt{\frac{L_{QA}}{C_{QA}}} = \sqrt{\frac{\phi_0^2}{e^2}} = R_K \ $$,

where $$R_K = \frac{h}{e^2} = 25.812813 k\Omega \ $$ is the von Klitzing constant for resistance.

The standard resonant frequency definition for the QHE LC circuit can be presented as:

 * $$\omega_Q = \frac{1}{\sqrt{L_{QA}C_{QA}}} = \frac{\hbar \omega_c}{\phi_0e} = \frac{\omega_c}{2\pi}$$,

where $$\omega_c = \frac{eB}{m^*} \ $$ is the standard cyclotron frequency in the magnetic field $$ B \ $$.

Quantum inductance per unit of area in a quantum dot
The first quantum inductance, based on the density of states approach was introduced by Wang et al. (2007) . These authors modernized Buttiker approach (1993) considering quantum dot (QD, labeled by “I”), placed over the metallic electrode (ME, labeled by “II”), and quantum capacitance. The quantum dot has the injected charge and induced charge per unit of area:

 * $$Q_I = Q_I^{inj} + Q_I^{ind} \ $$,

where injection charge is:
 * $$Q_I^{inj} = e^2 D_I v_I \ $$,

and induced charge is:
 * $$Q_I^{ind} = -e^2D_I V_I \ $$.

Therefore the resulting charge will be

 * $$Q_I = e^2D_I (v_I - V_I) = C_0 (V_I - V_{II}) = C_{\mu} (v_I - v_{II}) \ $$,

 * $$Q_{II} = - Q_I = e^2D_{II} (V_{II} - v_{II}) \ $$,

where $$D_I \ $$ and $$D_{II} \ $$ are frequency dependent density of states for QD and ME, $$v_I \ $$ and $$v_{II}  \ $$ are the external AC potentials applied to the QD and ME and $$ C_{\mu}\ $$ is a frequency dependent capacitance per unit of area connected with the potentials; $$ V_I  \ $$ and $$ V_{II} \ $$ are the proper frequency dependent electric potentials due to QD and ME, and $$ C_0 \ $$ is a capacitance per unit of area connected with the potentials.

From the above we can obtain the following equation for the quantum capacitance per unit of area of the considered quantum system:

 * $$\frac{e^2}{C_{\mu}} = \frac{e^2}{C_0} + \frac{1}{D_I} + \frac{1}{D_{II} } \ $$.

The quantum density of states for QD as a function of frequency $$ \omega \ $$ can be expressed as:
 * $$ D_I(\omega) = \frac{\Gamma_L}{2\pi \hbar \omega (\hbar \omega + i\Gamma_L)} \left [ \frac{1}{2} \ln \frac{\Delta^2}{\Delta_+\Delta_-}  - i (\arctan \frac{\Delta E - \hbar\omega}{\Gamma_L/2}

- \arctan {\frac{\Delta E + \hbar \omega}{\Gamma_L/2} }) \right ], $$

where $$\Delta = \Delta E^2 + \Gamma_L^2/4 ,\ $$ and $$\Delta_{\pm } = (\Delta E \pm \hbar \omega)^2 + \Gamma_L/4, \ $$ and $$\Delta E = E_F - E_0 .\ $$

For the quantum capacitor at low frequencies, there exists a charge relaxation resistance: $$R_q = \frac{h}{2e^2 \ }$$, for a single channel plate. Therefore, the considered system has the charge build-up time per unit of area due to the RC-time:

$$\tau_{RC} = R_qC_{\mu} \ $$.

However, the complexity of the density of states quantum capacitance produces another dwell time parameter $$\tau_d \ $$ per unit of area, due to the quantum inductance. Actually, the general expression for quantum capacitance per unit of area can be expanded into a Taylor series to second order in frequency:

 * $$C_{\mu}(\omega) = C_{\mu 0} + i\omega C_{\mu 0}^2\frac{h}{2e^2} - \omega^2C_{\mu 0}^3\frac{h^2}{4e^4} + \omega^2C_{\mu 0}^2\frac{h^2}{12\pi \Gamma_Le^2} \ $$,

where $$C_{\mu}(\omega =0) =C_{\mu}(0) = C_{\mu 0} \ $$ on the right hand side is the static electrochemical capacitance.

For a classical RLC circuit with capacitance $$C_{\mu 0} \ $$, resistance $$R_q \ $$ and inductance $$L_q \ $$, the dynamic conductance is

 * $$G(\omega) = \frac{-i\omega C_{\mu 0}}{1 - \omega^2L_qC_{\mu 0}-i\omega C_{\mu 0}R_q} \ $$,

Expanding this expression in power series of $$\omega \ $$, we obtain

 * $$G(\omega) = -i\omega C_{\mu 0} + \omega^2C_{\mu 0}^2R_q + i\omega^3C_{\mu 0}^3R_q^2 - i\omega^3 C^2_{\mu 0}L_q \ $$.

Since a capacitor conductance $$G(\omega) = -i\omega C_{\mu}(\omega) \ $$, we obtain the following values for quantum resistance and inductance per unit of area:

 * $$R_q = h/2e^2 = R_K/2 \ $$,
 * $$L_q = \frac{h^2}{12\pi e^2\Gamma_L} = \frac{h R_K}{12\pi \Gamma_L} \ $$,

where $$ R_K = \frac{h}{e^2} \ $$ is the von Klitzing constant.

Let us consider in more detail obtained values of reactive parameters of the system per unit of area:
 * $$C_{\mu} = \frac{e^2}{12 \pi \Gamma_L} ,\ $$
 * $$L_q = \frac{h R_K}{12\pi \Gamma_L}= 2\pi R_ K\frac{m_e}{h} = 2 \beta \frac{L_{QY}}{S_0 } ,\ $$
 * $$\tau_d = \frac{4\hbar}{\Gamma_L}, \ $$
 * $$\omega_q = \frac{1}{ \sqrt{C_{\mu} L_q}} = \frac{12 \pi \Gamma_L}{h} ,\ $$
 * $$\rho_q = \sqrt{\frac{L_q}{C_{\mu}}} = R_K, \ $$

where line width function:
 * $$\Gamma_L = \frac{h^2}{24\pi^2m_e} = \frac{1}{12\pi}\frac{1}{D_{2D}} .\ $$

So, we have the first definition of quantum inductance for the DOS.

Semi-classical serial RLC circuit
In the general case the characteristic impedance of RLC circuit can be defined as:
 * $$Z_d = \sqrt{R_d + (\frac{1}{\omega C_d} - \omega L_d)^2} \ $$.

The resonant parameters of the RLC circuit (without dissipation, when $$ R_d =0\ $$ and $$ Z_d =0\ $$ ) will be:
 * $$\omega_d = \frac{1}{\sqrt{L_dC_d}} \ $$,
 * $$\rho_d = \sqrt{\frac{L_d}{C_d}} \ $$.

Semi-classical inductance and capacitance could be defined through the quantum values by the following: $$L_d = L_0 + \Delta L \ $$ and $$C_d = C_0 + \Delta C \ $$.

So, the resulting value of quantum resonant impedance will be: $$\rho_0 = \sqrt{\frac{L_0}{C_0}} = \sqrt{\frac{\mu_0}{\varepsilon_0}} \ $$ (impedance of free space).

Let us consider in more detail the semi-classical wave impedance in the form:

 * $$\rho_d = \sqrt{\frac{L_d}{C_d}} = \sqrt{\frac{L_0 + \Delta_L}{C_0 + \Delta_C}} \ $$.

Expanding this expression in power series of $$\Delta_C \ $$ and $$\Delta_L \ $$, we shall obtain for the first order:
 * $$\rho_d = \rho_0[1 + \frac{1}{2}(\frac{\Delta_L}{L_0} - \frac{\Delta_C}{C_0})] \ $$.

Considering that $$\Delta_L = L_d - L_0 \ $$ and $$\Delta_C = C_d - C_0 \ $$, the semi-classical wave impedance can be rewritten as:
 * $$\rho_d = \rho_0[1 + \frac{1}{2}(\frac{L_d}{L_0} - \frac{C_d}{C_0})] \  $$.

Experimental results
The first semi-classical resonant LC circuit was discovered by Yakymakha (1994) during MOSFET spectroscopic investigation in the frequency band 100H – 20kH. Obtained value for the cycle resonance frequency (5088 rad/s), permits to make estimations for the quantum reactive MOSFETs parameters. Quantum capacitance was defined as:

 * $$C_{0X} = \frac{\varepsilon_0S_{MOS}}{\lambda_0}\cdot \frac{\lambda_{CX}}{\lambda_0} \ $$

where $$S_{MOS} \ $$ is the MOSFET surface area and $$\lambda_{CX} \ $$ is the flat quantum capacitance thickness.

Quantum inductance was defined as:

 * $$L_{0X} = \frac{\mu_0S_{MOS}}{\lambda_0}\cdot \frac{\lambda_{LX}}{\lambda_0} \ $$,

where $$\lambda_{LX} \ $$ is the flat quantum inductance thickness.

Experimental results prove that flat quantum inductance and capacitance thicknesses were about the Compton wavelength of electron:
 * $$\lambda_{CX} = \lambda_{LX} = \lambda_0 \ $$.

Quantum Hall Effect
The first attempts were made by Cage and Jeffery (1996) to consider QHE devices as resonant LC circuit. These investigations were made due to the program of the AC-measuring resistor standards. However, the considered model used only classical approach to the reactive parameters of the Landau levels.


text:
Talk:Obstetrics and Gynecology/Gestational Trophoblastic Disease

Can a Gestational Trophoblastic disease occur in a non-molar pregnancy? The symtomps are very similar to this disease but pathological reports on the tissues are negative for molar or partial molar pregnancy.


text:
User:Smatthan

Susanna Matthan, Home based educator, Lincolnshire, United Kingdom. --Susanna Matthan 18:01, 23 November 2009 (UTC)

title: User:Smatthan


text:
User:Egm6321.f09.Team2/HW7

Homework Assignment #7 - due Wednesday, 12/9, 22:00 UTC

Problem 1
p. 37-1 Show $$Q_1(x)={1\over 2}xln\Bigg({{1+x}\over {1-x}}\Bigg)-1=xtanh^{-1}x-1$$

$$\frac{1}{2}xln(\frac{1+x}{1-x})-1=xtanh^{-1}x-1$$

Add 1 to both sides and divide by x: $$\frac{1}{2}ln(\frac{1+x}{1-x}) = tanh^{-1}x$$

Assume: $$y = tanh^{-1}(x)$$

Then: $$x = tanh (y) = \frac{e^y - e^{-y}}{e^y + e^{-y}}$$

Cross-multiply: $$ xe^y + xe^{-y} = e^y - e^{-y}$$

Multiply through by e^y: $$ x(e^y)^2 + x = (e^y)^2 - 1 $$

Re-arrange terms: $$ e^{2y} = \frac{1+x}{1-x}$$

Square root of both sides: $$ e^y = \sqrt{\frac{1+x}{1-x}}$$

To solve for y, take the natural log: $$ y = ln{(\sqrt{\frac{1+x}{1-x}})}$$ $$ y = \frac{1}{2}ln(\frac{1+x}{1-x})$$

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

Problem 2
p. 37-1 1) Using $$Q_ \left( x \right) =P_ \left( x \right) {\it tanh^{-1}} \left( x \right) -2\,\sum _{j=1,3,5}^{J}{\frac { \left( 2\,n-2\,j+1 \right) P_ \left( x \right) }{ \left( 2\,n-j+1 \right) j}} $$ show when $$Q_n$$ is even or odd depending on "n"

2) Plot $$[P_0,\ P_1,\ ...,\ P_4]\ and\ [Q_0,\ Q_1,\ ...,\ Q_4]$$

1) Using the properties of even and odd number and functions, one can determine if $$Q_n \!$$ is even or odd. The product of an odd and even function is odd. The product of two odd functions is even. The sum of two odd functions is odd. The sum of two even functions is even. The sum of an even and odd number is odd. The sum of two odd numbers is even. Constant multiples of a function do not change its evenness or oddness.

For $$n=2k\!$$ (even number) $$P_{2k}(x)\!$$ is even and $$tanh^{-1}(x)\!$$ is odd. Therefore, the left-hand side of $$Q_{2k}(x)\!$$ is odd. On the right side, $$2k-j\!$$ is odd because $$j\!$$ is odd. This means $$P_{2k-j}(x)\!$$ is odd, so the summation is odd. Therefore, the right-hand side of $$Q_{2k}(x)\!$$ is odd. The end result is that $$Q_{2k}(x)\!$$ is odd.

For $$n=2k+1\!$$ (odd number) $$P_{2k+1}(x)\!$$ is odd. Since $$tanh^{-1}(x)\!$$ is still odd, the left-hand side of $$Q_{2k+1}(x)\!$$ is even. On the right side, $$2k+1-j\!$$ is even because $$j\!$$ is odd. This means $$P_{2k+1-j}(x)\!$$ is even, so the summation is even. Therefore, the right-hand side of $$Q_{2k+1}(x)\!$$ is even. The end result is that $$Q_{2k+1}(x)\!$$ is even.

2) $$P_n\!$$

$$Q_n\!$$

Problem 3
Describe why $$=0\!$$

Since $$Pn\!$$ has opposite parity to $$Qn\!$$ for the same choice of $$n\!$$ and the product of an odd and even function is odd, this means the inner product will be equal to zero. The inner product is zero due to the property of odd functions, i.e. the integral of an odd function over a discrete boundary [-A,A] is zero.

Problem 4
p. 37-3 Given $$-\int_{-1}^{+1}L_m\Big[(1-x^2)L'_n\Big]'dx+n(n+1)\int_{-1}^{+1}L_mL_ndx=0$$

Using integration by parts show

$$-\int_{-1}^{+1}(1-x^2)L'_nL'_mdx+n(n+1)=0$$

Integration by parts follows the form,

 * $$\int_{b}^{b}u\, dv=[uv]_{a}^{b}-\int_{a}^{b}v\, du$$

Taking the first term on the left-hand side and separating it by,

 * $$u=L_m \!$$
 * $$dv = [(1-x^2)L_n']'\, dx$$

we can find that,

 * $$du=L_m'\, dx \!$$
 * $$v=[(1-x^2)L_n'] \!$$

This yields,

 * $$\int_{-1}^{1}L_m[(1-x^2)L_n']'\, dx = [L_mL_n'(1-x^2)]_{-1}^{1}-\int_{-1}^{1}(1-x^2)L_n'L_m'\, dx$$

Since $$1-x^2$$ is zero at $$-1$$ and $$1$$, the result is,

 * $$\int_{-1}^{1}L_m[(1-x^2)L_n']'\, dx = -\int_{-1}^{1}(1-x^2)L_n'L_m'\, dx$$

Using $$\!$$ to denote the inner product, the original equation can now be written as,

 * $$-\int_{-1}^{1}(1-x^2)L_n'L_m'\, dx+n(n+1)=0$$

Problem 5
p. 38-2 Given $$(r_{PQ})^2=\sum_{i=1}^3(x_Q^i-x_P^i)^2$$ Where $$x_P^1=r_Pcos\theta_Pcos\phi_P$$, $$x_P^2=r_Pcos\theta_Psin\phi_P$$, $$x_P^3=r_Psin\theta_P$$

$$x_Q^1=r_Qcos\theta_Qcos\phi_Q$$, $$x_Q^2=r_Qcos\theta_Qsin\phi_Q$$, $$x_Q^3=r_Qsin\theta_Q$$

Show $$(r_{PQ})^2=r_p^2+r_Q^2-2r_Pr_Qcos\gamma$$

where $$ cos\gamma=cos\theta_Qcos\theta_Pcos(\phi_Q-\phi_P)+sin\theta_Qsin\theta_P$$

$$(r_{PQ})^2=\sum_{i=1}^3(x_Q^i-x_P^i)^2$$

$$(r_{PQ})^2= \left( x_{1{Q}}-x_{1{P}} \right) ^{2}+ \left( x_{2{Q}}-x_{2{P}}\right) ^{2}+ \left( x_{3{Q}}-x_{3{P}} \right) ^{2}$$

$$(r_{PQ})^2={x_{1{Q}}}^{2}-2\,x_{1{Q}}x_{1{P}}+{x_{1{P}}}^{2}+{x_{2{Q}}}^{2}-2\,x_{2{Q}}x_{2{P}}+{x_{2{P}}}^{2}+{x_{3{Q}}}^{2}-2\,x_{3{Q}}x_{3{P}}+{x_{3{P}}}^{2}$$

 * $$={r_}^{2} \left( \cos \left( \theta_ \right) \right) ^{2}

\left( \cos \left( \phi_ \right) \right) ^{2}-2\,r_\cos \left( \theta_ \right) \cos \left( \phi_ \right) r_ \cos \left( \theta_ \right) \cos \left( \phi_ \right)$$
 * $$ +{r_}^{2} \left( \cos \left( \theta_ \right) \right) ^{2} \left(\cos \left( \phi_ \right)  \right) ^{2}+{r_}^{2} \left( \cos \left( \theta_ \right)  \right) ^{2} \left( \sin \left( \phi_ \right)  \right) ^{2}-2\,r_\cos \left( \theta_ \right)

\sin \left( \phi_ \right) r_\cos \left( \theta_ \right) \sin \left( \phi_ \right)$$
 * $$ +{r_}^{2} \left( \cos \left( \theta_ \right) \right) ^{2} \left( \sin \left( \phi_ \right)  \right) ^{2}+{r_}^{2} \left( \sin \left( \theta_ \right)  \right) ^{2}-2\,r_\sin \left( \theta_ \right) r_\sin \left( \theta_ \right) +{r_}^{2} \left( \sin \left( \theta_ \right)  \right) ^{2}$$

Combine terms;

 * $$={r_}^{2}+ \left (\,\cos \left( \theta_ \right) \cos

\left( \theta_ \right) \cos \left( \phi_ \right) \cos \left( \phi_ \right)-2\, \cos \left( \theta_ \right) \cos \left( \theta_ \right) \sin \left( \phi_ \right) \sin \left( \phi_ \right) -2\,\sin \left( \theta_ \right) \sin \left( \theta_ \right) \right)r_r_+{r_}^{2} $$

 * $$={r_}^{2}+{r_}^{2}-2r_r_(\,\cos \left( \theta_ \right) \cos

\left( \theta_ \right) \cos \left( \phi_ \right) \cos \left( \phi_ \right)+\, \cos \left( \theta_ \right) \cos \left( \theta_ \right) \sin \left( \phi_ \right) \sin \left( \phi_ \right) +\,\sin \left( \theta_ \right) \sin \left( \theta_ \right)) $$

 * $$={r_}^{2}+{r_}^{2}-2r_r_[\,\cos \left( \theta_ \right) \cos

\left( \theta_ \right)[ \cos \left( \phi_ \right) \cos \left( \phi_ \right)+ \sin \left( \phi_ \right) \sin \left( \phi_ \right)] +\,\sin \left( \theta_ \right) \sin \left( \theta_ \right)]$$

Using the identity: $$\cos \left( a \right) \cos \left( b \right) +\sin \left( a \right) \sin \left( b \right)=\cos \left( a-b \right)$$

We can further reduce
 * $$={r_}^{2}+{r_}^{2}-2r_r_[\,\cos \left( \theta_ \right) \cos

\left( \theta_ \right)[ \cos \left( \phi_-\phi_ \right)] +\,\sin \left( \theta_ \right) \sin \left( \theta_ \right)] $$

Substitute $$ cos\gamma=cos(\theta_Q)cos(\theta_P)cos(\phi_Q-\phi_P)+sin(\theta_Q)sin(\theta_P)$$

Yields  $$(r_{PQ})^2=r_p^2+r_Q^2-2r_Pr_Qcos\gamma$$

Problem 6
p. 38-4

Use $$(x+y)^r=\sum_{k=0}^\infty{n\choose k}x^{r-k}y^k$$ and $${n\choose k}={r(r-1)...(r-k+1)\over k!}$$

to show

$$(1-x)^{-1/2}=\sum_{i=0}^\infty\alpha_ix^i$$ and $$\alpha_i={1*3*...(2i-1)\over 2*4*...(2i)}$$

Start by making variables match-up:

$$(1-x)^{-1/2}=\sum_{k=0}^\infty\alpha_kx^k$$ and $$\alpha_k={1*3*...(2k-1)\over 2*4*...(2k)}$$

$$\frac{1}{(1-x)^{1/2}} = \sum_{k=0}^\infty\alpha_kx^k$$

Working from: $$(x+y)^r=\sum_{k=0}^\infty{r\choose k}x^{r-k}y^k$$

Assume: $$x = 1$$, $$ y = -x $$ ,  $$ r = \frac{1}{2}$$

As 1 to any power is still 1, we are left with:

$$\frac{1}{(1-x)^{1/2}} = \sum_{k=0}^\infty{r\choose k}-x^k$$

$${r\choose k} = {r-k+1\choose k}$$

$$\frac{1}{(1-x)^{1/2}}=\sum_{k=0}^\infty{r-k+1\choose k}-x^k$$

$$\frac{1}{(1-x)^{1/2}}=\sum_{k=0}^\infty{\frac{1}{2}+k-1\choose k}x^k$$

$$\frac{1}{(1-x)^{1/2}}=\sum_{k=0}^\infty{k-\frac{1}{2}\choose k}x^k$$

Simplfying the complex fraction / choose function:

$$\frac{1}{(1-x)^{1/2}}=\sum_{k=0}^\infty{2k-1\choose 2k}x^k$$

Defining: $$\alpha_i={(2i-1)\choose (2i)} = {(2k-1)\choose (2k)}$$, with k defined from 0 to $$\infty$$

When $$k=0$$, $$\alpha_0=1$$; $$k=1,\alpha_1=\frac{1}{2}$$; $$k=2,\alpha_2=\frac{3}{8}$$, etc.

 $$(1-x)^{-1/2}=\sum_{i=0}^\infty\alpha_ix^i$$

Problem 7
p.39-2

Continue the power series development of $${1\over\sqrt{A(\mu,\rho)}}=\alpha_0+\alpha_1(2\mu\rho-\rho^2)+\alpha_2(2\mu\rho-\rho^2)^2+....$$ to find $$P_3(\mu),\ P_4(\mu),\ P_5(\mu)$$

Compare to the results obtained on p.31-3.

Contributing Team Members
--Joe Gaddone 20:16, 30 November 2009 (UTC) --Matt Walker --Egm6321.f09.Team2.sungsik 02:22, 4 December 2009 (UTC) --Kumanchik 17:58, 9 December 2009 (UTC)

title: User:Egm6321.f09.Team2/HW7


text:
Introduction to Italian/Lesson 11

Can and must are covered in this section.

Potere
The infinitive potere is an irregular verb meaning can or may. Technically it is an auxiliary verb and so must be paired with an infinitive. Per esempio: Io posso mangiare una foccacina se ho voglia (I can eat a scone if I want to). Potere is, as previously stated, and irregular verb. Here is a conjugation chart:

Dovere
Dovere is an irregular verb meaning must or have (have as in I have to...). Like potere it is an auxiliary verb used with an infinitive: Io devo mangiare una foccacina (I must eat a scone) Io devo prendere del tè con la mia foccacina (I must have some tea with my scone) Here is the conjugation chart for dovere:

NB. When dovere is used in a conditional tense it means should or should have.

title: Introduction to Italian/Lesson 11


text:
Alternative Analysis

 * [[File:Redirect arrow.svg]] Home | Learning Theories | Instructional Design and eAuthoring | ePortfolio | Storyboard | Wiki Analysis | Communication Tools | Resources Analysis | Accessibility | Glossary

PMI Analysis
We consider that a PMI (Plus, Minus, Interesting) analysis is the first step in our project. An initial PMI analysis will provide us valuable information regarding Wikis as a tool in our group elearning experience. We want to offer a clear view of our tool selection where, we will discuss the pros and cons of the wiki, and why should be used as an elearning resource.

Plus Analysis

 * 1) Anyone can edit, and edition is instantaneous,easy to use and learn and people located all over the world can edit.
 * 2) Possible to revert back to a previous version and access to web publishing to non-technical people.
 * 3) Can be used for a wide range of applications.
 * 4) No licensing cost to installing an institutional wiki.
 * 5) Very versatile tool, that can be adjusted and accommodated to any kind of teaching and learning.
 * 6) Many possibilities to include designs, images, videos, etc.
 * 7) Allows for HTML language what provides huge possibilities
 * (Hart, 2006)

Minus Analysis

 * 1) Being an open resource does not assurance the quality of content, therefore entries are not necessarily reliable.
 * 2) Spontaneous thoughts, content have to be filtered to avoid prohibited material.
 * 3) Anonymous entries, very difficult to verify the source (more issues with quality)
 * 4) Collaborative /Cooperative Paradigm as the resource is strongly based on high levels of coordination free rider problem.
 * 5) Technology issues, requires to be comfortable with computers.
 * 6) Organization, updating, compiling, etc. A lot of work needs to be done.
 * 7) Challenges regarding structure, contents, ideas, etc. and how they should be included in the wiki.
 * 8) Wikis do not show as easily when information was documented or in what order.
 * (Woolf, 2006).

Interesting Analysis

 * 1) Resource with great potential to be used in elearning
 * 2) Great flexibility and adaptability
 * 3) Minimum requirements, everyone can learn how to use it very quickly
 * 4) Great tool to facilitate: Creativity, Development of New Ideas, Collaboration
 * 5) Controls can be implemented to prevent vandalism
 * 6) Content remains alive: as technology improves, knowledge changes, new techniques appear, etc. it is possible to update the resource accordingly.
 * 7) Imagination is the limit.
 * 8) Ideal resource to use to connect with groups based in different countries, different cultures, etc.

SWOT Analysis
SWOT analysis is a strategic planning tool that is exceedingly valuable. It involves identifying strengths, weaknesses, opportunities and threats. After the PMI analysis is done, it is very important to condense all the information into a SWOT (Strength, Weaknesses, Opportunities, Threats), thus we are able to connect all the valuable information that help us to decide if the wiki is the optimal resource for our project.

Strengths
sometimes, in chronological order.
 * 1) Openness and accessibility.
 * 2) Facilate to work with others
 * 3) Creates knowledge and communities
 * 4) Usability.
 * 5) Anonymity of authorship.
 * 6) Public ownership.
 * 7) Cloning acceptable.
 * 8) It is a free tool.
 * 9) Organized by the context, by links and,

Opportunities

 * 1) Motivate Collaboration
 * 2) Versatile Tool
 * 3) Longlife Learning
 * 4) Growing and flexible resource
 * 5) Comprehensive
 * 6) Share knowledge, resources, experiences.
 * 7) Everyone is smarter than anyone alone
 * 8) Encorage learning and critical thinking
 * 9) Large audience
 * 10) Virtual Community

Weaknesses

 * 1) Difficulties to trust content
 * 2) Used to repeat work
 * 3) Content is constantly changing
 * 4) Not professionally edited
 * 5) Need close control to prevent vandalism

Threats

 * 1) Users can erase content
 * 2) Vandalism
 * 3) Copyright, intellectual property issues
 * 4) Taken as the only source of information
 * 5) Content can be spammed
 * 6) Constraints to the tool
 * 7) Openness (no login required)

The main conclusions derived from our analysis are presented in the Wiki Analysis main page, please return to the main page to read about it.

title: Alternative Analysis


text:
Introduction to Italian/Lesson 12

This section will deal with past tense verbs.

More Avere Phrases
In Northern Italy and especially in informal and spoken Italian the past tense is formed using the verb avere (have) and the past participle in the same way as the English present perfect tense (have + past participle). Note, however, that some verbs are not used with avere but are instead used with essere (be). Typically the English phrases I ate 10 scones or I have eaten 10 scones would translate as Io ho mangiato dieci foccacine. Forming the past tense in this way is the easiest way for non-natives because it requires only knowing the present tense forms of avere (or in some cases essere) and the past participle of the verb you're using. There is also a separate past tense which is more common in written Italian and Southern Italy.

Conjugating in the Past Tense
When conjugating an -are word in the past tense, use the appropriate present tense avere conjugation followed by the verb you are using. Append the suffix -ato. Per essemple: Io ho mangiato una foccacina. Tu hai mangiato una foccacina. Lui ha mangiato una foccacina. Noi abbiamo mangiato una foccacina. Voi avete mangiato una foccacina. Loro hanno mangiato una foccacina. In a sense it's basically a different infinitive.

IMPERFECT PAST VERB TO BE
Io ero. Tu eri. Lui era. Noi eravamo. Voi eravate. Loro erano.

PAST TENSE VERB TO BE
Io sono stato. Tu sei stato. Lui è stato. Noi siamo stati. Voi siete stati. Loro sono stati.

IMPERFECT PAST VERB TO HAVE
Io avevo. Tu avevi. Lui aveva. Noi avevamo. Voi avevate. Loro avevano.

Past tense, verb "to have"

 * Io ho avuto.
 * Tu hai avuto.
 * Lui ha avuto.
 * Noi abbiamo avuto.
 * Voi avete avuto.
 * Loro hanno avuto.

Conjugating Other Verbs in the Past Tense
At the time of writing I am unaware of any rule for conjugating -ere and -ire words in the past tense. I believe it works only on a word-by-word basis. That being said, I will certainly update this if I discover otherwise.

title: Introduction to Italian/Lesson 12


text:
Comparative Teaching of Old Greek and Latin/Lesson 03 Part 2

Comparative Teaching of Old Greek and Latin Lesson 03 Part 2

Translated from the Greek Wikipedia|Wikiversity: "Συγκριτική διδασκαλία των κλασικών γλωσσών / (Comparative Teaching of the Classical Languages)"

'''LESSON 03  PART 2. The substantives of male gender. Masculine substantives.'''

3.2.	Analyse and translate the texts:

(Each text should be separated in periods, each period in sentences and each sentence should be  analyzed grammatically  and syntacticly and after be translated.)

OLD GREEK

3.2.1. Arrian's Alexander's Anabasis, 1, 13, 2-3.

'''Ἐν τούτῳ δ’ Ἀλέξανδρος προὐχώρει ἐπὶ τὸν Γρανικὸν  ποταμὸν συντεταγμένῳ τῷ στρατῷ, διπλῆν μὲν τὴν φάλαγγα  τῶν ὁπλιτῶν τάξας, τοὺς δ’ ἱππέας  κατὰ τὰ κέρατα ἄγων, τὰ  σκευοφόρα δὲ  κατόπιν ἐπιτάξας ἕπεσθαι. Τοὺς δὲ προκατασκεψομένους τὰ τῶν πολεμίων ἦγεν αὐτῷ Ἡγέλοχος, ἱππέας μὲν ἔχων τοὺς σαρισσοφόρους, τῶν δὲ ψιλῶν εἰς πεντακοσίους. Καὶ Ἀλέξανδρός τε οὐ πολὺ ἀπεῖχε τοῦ ποταμοῦ τοῦ Γρανικοῦ καὶ οἱ ἀπὸ τῶν σκοπῶν σπουδῇ ἐλαύνοντες ἀπήγγελλον ἐπὶ τῷ Γρανικῷ πέραν τοὺς Πέρσας ἐφεστάναι τεταγμένους ὡς ἐς μάχην. Ἔνθα δὴ Ἀλέξανδρος μὲν τὴν στρατιὰν πᾶσαν συνέταττεν ὡς μαχουμένους. Παρμενίων δὲ προσελθὼν λέγει Ἀλεξάνδρῳ τάδε:'''

'''Vocabulary - comments. Analysis in detail''

(Substantives will be given and  should  be learned with  their genitive, adjectives  and pronouns with the three genders, adverbs with the three degrees and  verbs with  their initial  tenses - in Latin  the present, the perfect, the supine and the present  infinitive.) '''The text has five periods. We first find the sentences and clauses of each period, the infinitives and the participles, if there exist any, and then the main basic terms, that is to say, the verb, the subject, the direct object, the indirect object, the predicative, provided that of course they exist. The remaining words will be determinations, depending on the kind of word and the term that it determines.'''

Main basic terms of the 1st period: Ἐν τούτῳ …ἕπεσθαι.

προὐχώρει: he was going, verb of the sentence, third singular person, imperfect indicative, active voice,   Ἀλέξανδρος:  subject of the verb as well as  of the temporal participles τάξας, ἄγων, ἐπιτάξας, initial tenses:   τάσσω, ἔτασσον, τάξω,  ἔταξα, τέταχα,  ἐτετάχειν, of the same root: τάγμα = battalion, σύνταγμα = regiment, ταγός (leader), τακτικός, ταξίδι, τάξη, παράταξη, ταΐζω, ταγή, τάμα, τάξιμο, νομοταγής,   τὴν φάλαγγα = phalanx: direct object of the temporal  participle τάξας = when he arrayed, τοὺς ἱππέας= the cavalry men: direct object of the temporal participle  ἄγων= when he led,  ἕπεσθαι: present infinitive, object of the temporal participle ἐπιτάξας = when he ordered, initial tenses, ἕπομαι= follow,  ἕπομαι, εἱπόμην, ἕψομαι, ἑσπόμην, ἠκολούθηκα, ἠκολουθήκειν, of the same root: επόμενος= next, συνεπής= consequent, ασυνεπής, sequor, consecu’tio, seque’ntia= a kind of religious hymn, stuctures: ἕπομαί τινι, ἕπομαι ἐπί τινα,    σκευοφόρα= transporting means: subject of the infinitive, διπλῆν= double: predicative to φάλαγγα,  διπλοῦς, διπλῆ, διπλοῦν: double, numeral, of the same root:  δύο= two, δεύτερος= second, διπλοῦς, διπλάσιος, δίς= twice, δυάς, δευτεραῖος,  μέν, δέ: contrasting conjunctions, they are used as transitive conjunctions here.

Determinations of the first period:

(Determinations are all remaining words of the sentence except conjunctions and interjections which are only recognized grammatically)

ἐν τούτῳ: in the meantime, prepositional determination denoting time, ἐπὶ τὸν ποταμόν: to the river, prepositional determination denoting place, τὸν Γρανικόν: River Granicus, a river in Asia Minor, adjectival determination  (The geographical main names with article when they accompany geographic terms and agree with them in gender, number and case are adjectival determinations, otherwise are appositions),  τῷ στρατῷ: with the army, dative denoting escort,  τῶν ὁπλιτῶν: of the soldiers, genitive denoting contents to φάλαγγα,   συντεταγμένῳ: orderly, predicative determination to τῷ στρατῷ, κατὰ τὰ κέρατα: at the wings, at the borders of the battle array, prepositional determination denoting place,  κατόπιν: the, adverbial determination denoting place.

Analysis of the second period: Τοὺς δὲ προκατασκεψομένους … εἰς πεντακοσίους.

ἦγεν: he led, verb, initial tenses: ἄγω, ἦγον, ἄξω, ἤγαγον, ἀγίοχα and ἦχα, ἠγιόχειν  and ἤχειν, of the same root:  αγωγή= education, αγωγός= pipe, conductor, άγημα, αγέλη, παρείσακτος, ξεναγός, σύναξη, ago, actor,  structures: ἄγω τινά,  ἄγω ἐπί τινα,  εἴς τινα,  πρός τινα, circumlocutions:  ἄγω καὶ φέρω (to plunder), ἄγω  εἰς δίκην,  ἄγω ἐπὶ τοὺς δικαστάς,  ἄγω σπονδάς, σχολήν ἄγω, ἡσυχίαν ἄγω, ἄγομαι  φόνου, ἄγομαι γυναῖκα (to be married), κακῶς ἠγμένος, ἔχων:  by having, participle denoting manner, initial tenses:   ἔχω, εἶχον, ἕξω and σχήσω, ἔσχον, ἔσχηκα, ἐσχήκειν,  aorist B': σχῶ, σχοίην, σχές, σχεῖν, σχών, of the same root: έξη= the habit, ευεξία= good health, εξής,  σχολή, σχέδιο, σχήμα, σχέτλιος, οχυρός, ανεκτός, ὄχος (vehicle), ένοχος, εξοχή,  τοὺς σαρισσοφόρους: those soldiers having long javelins, object of the participle  ἔχων,   ἱππέας: as cavalry men, apposition to σαρισσοφόρους, τοὺς  προκατασκεψομένους:  those who were going to spy, adjectival participle, object to  ἦγεν, initial tenses:  σκοπῶ,  ἐσκόπουν, σκέψομαι,  ἐσκεψάμην, ἔσκεμμαι,  ἐσκέμμην,   perfect tense: ἔσκεμμαι, ἔσκεψαι, ἔσκεπται, ἐσκέμμεθα, ἔσκεφθε, ἐσκεμμένοι  εἰσί, of the same root:  σκοπός= purpose, σκοπιά= watch tower, σκόπιμος, σκόπελος, σκέπτομαι= think, σκέψη= thought, σκέμμα, sco’pulus,   τὰ τῶν πολεμίων: things about the enemies, object of the participle προκατασκεψομένους,  τῶν δὲ ψιλῶν: of the soldiers having light armament,  genitive denoting divided whole,   εἰς πεντακοσίους: about five hundred, prepositional object to the participle  ἔχων.

Analysis of the third period: καὶ Ἀλέξανδρός … ἐς μάχην.

ἀπεῖχεν, ἀπήγγελον: he was not far, they were saying, verbs of the two sentences, initial tenses: ἀπαγγέλλω, ἀπήγγελλον, ἀπαγγελῶ, ἀπήγγειλα, ἀπήγγελκα, ἀπηγγέλκειν, of the same root: ἄγγελμα= anouncement, άγγελος= messenger, εισαγγελέας= public prosecutor, ἀγγελτήρ, τοῦ ποταμοῦ: of the river, object to ἀπεῖχε,   τοῦ Γρανικοῦ:  adjectival determination to τοῦ     ποταμοῦ,  ἐλαύνοντες: by running, participle denoting manner,  σπουδῇ: quickly, hastily, adverbial (with noun) determination denoting time or manner  οἱ ἀπὸ τῶν σκοπῶν: the spies, subject to participle ἐλαύνοντες,  ἐφεστάναι: they had been arrayed for battle, infinitive, object to  ἀπήγγελλον, infinitive of crisis, i.e translated by ὅτι,  ἐφεστάναι τεταγμένους= they had been arrayed for battle,  initial tenses: ἐφίσταμαι, ἐφιστάμην, ἐπιστήσομαι, ἐπέστην ἐφέστηκα, ἐφεστήκειν,  τεταγμένους: participle denoting manner, ἐπὶ τῷ Γρανικῷ: at the river Granicos, prepositional determination denoting place (stopping at a place),  ὡς ἐς μάχην: to fight, prepositional determination denoting purpose.

Analysis of the fourth and fifth period: Ἔνθα … τάδε.

συνέττατεν, λέγει: he was organizing, he says, verbs of the two sentences, initial tenses: συντάττω, συνέταττον, συντάξω,  συνέταξα, συντέταχα, συνετετάχειν, λέγω, ἔλεγον, λέξω and ἐρῶ, ἔλεξα and εἶπον and εἶπα, εἴρηκα, εἰρήκειν, of the same root:   λόγος= speech, συλλογή= collection, εκλογή= election, λογάς, λογάδην, εκλεκτός, ανθολογία, lego, le’ctio, colle’ctio,   πᾶσαν: the whole, all, predicative determination,   ἔνθα: then, that time, adverbial determination of time,  ὡς μαχουμένους: in order they fight, participle denoting purpose,  προσελθὼν: after he had come, participle denoting time, initial tenses:  ἔρχομαι, ᾖα and ᾔειν, εἶμι, ἦλθον, ἐλήλυθα, ἐληλύθειν,  Ἀλεξάνδρῳ: to Alexander, indirect object.

LATIN

3.2.2. From the old reading-book of the Latin language, 8.

(The accentual marks will enter for facilitation of reading until the thirtieth fifth course.)

'''Ro’mulus et Remus Romam aedificave’runt. Ro’mulus Remum neca’vit, quod muros novi o’ppidi vitupera’verat. Quamquam Ro'mulus Remun neca’verat, tamen fortu’na Ro’mulo secu’nda erat; nam multos po’pulos bello armi’sque supera’vit  et terram fini’timam occupa’vit et o’ppida expugna’vit. Nu’merus femina’rum in novo o’ppido parvus erat. I΄taque Ro’mulus Roma’nis fe’minas dolo para’vit. Sabi’nos enim et Sabi’nas et fi’lias sabino’rum ad ludos pu’blicos invita’vit et inter ludos Roma’ni fi’lias Sabino’rum raptave’runt.'''

'''Vocabulary - comments. Analysis in detail.'''

'''The text has seven periods. We first find the sentences and clauses, the infinitives and the participles, if there exist any, and then the main basic terms, that is to say, the verb, the subject, the direct object, the indirect object, the predicative, provided that of course they exist. The remaining words will be determinations, depending on the kind of word and the term that it determines.'''

Main basic terms of the first period: Ro’mulus… aedificave’runt.

aedificave’runt: they built, verb of the sentence, initial tenses: aedi’fico, -a’vi, -a’tum, -a’re, Ro’mulus, Remus: subjects of the verb, et: and, copulative conjunction, synomyms: ac, atque, que, Romam: Rome, object of the verb.

Determinations of the first period: None.

Analysis of the second period: Ro’mulus … vitupera’verat.

neca’vit: he killed, verb of the main clause, perfect indicative, vitupera’verat: he had accused, verb of the subordinate clause of reason beginning by quod, past perfect indicative, initial tenses: neco, -a’vi, -a’tum, -a’re, to kill, vitu’pero, -a’vi, -a’tum, -a’re, to accuse, of the same root:, nex, -cis, νέκυς, νεκρός= dead, quod: because, conjunction of reason, synonyms: quo’niam, quia, cum, muros: the city-walls, murus, -i, masculine noun of the second declension, o’ppidi: of the city, (here, of Rome), possessive genitive to muros, novi: of the new, adjective, novus, -a, -um, rece’ntior, novi’ssimus, adjectival determination to o’ppidi, novus, of the same root: nova’cula (razor), nova’lis, nova’tor, nove’llus (lad), novo (renew, renovate), νέος.

Analysis of the third semiperiod: Quamquam … secu’nda erat.

neca’verat: he had killed, verb of the concessive clause beginning with quamquam, erat: it was, verb oh the main clause, indicative imperfect: eram, eras, erat, era’mus, era’tis, erant, quamquam: though, concessive conjunction, synonyms: etsi, tamen: but, but yet, fortu’na: fortu’na, -ae: feminine noun of the first declension, the luck, the fate, secunda: predicative, secu’ndus, -a, -um, favourable.

Analysis of the fourth semiperiod: nam multos … expugna’vit.

nam: for, conjunction of reason, it introduces a main clause, it always enters in the beginning, supera’vit, he won, he beat, perfect indicative, occupa’vit, he occupied, he besieged, perfect indicative, expugna’vit, he conquered, perfect indicative: verbs of the three main clauses, su’pero= win, beat, expu’gno= besiege, o’ccupo= conquer, su’pero, same stem with the Greek preposition ὑπέρ, in Latin super, po’pulos: populations, po’pulus, -i, masculine noun of the second declension, object to supera’vit, multos: many, a lot of, multus, -a, -um, much, adjectival determination to po’pulos, bello, armi’sque by war and arms, ablatives of manner, que, and, copulative conjunction, et: and, copulative conjunction, terram: earth, country, land, terra, -ae, object to occupa’vit, fini’timam: neigbouring, fini’timus, -a, -um, adjectival determination to terram.

Analysis of the fifth period: Nu’merus… parvus erat.

nu’merus: the number, nu’merus, -i, masculine noun of the second declension, femina’rum: of the women, in novo o’ppido, in new city, in: preposition structured with ablative, to show stopping at a place, and accusative to show movement, motion to a place, parvus: small, parvus, -a, -um, parvus erat, he was small.

Analysis of the sixth period: i'taque … para’vit.

i΄taque: therefore, conlusive conjunction, it introduces main clauses, Roma’nis: to Romans, dative, indirect object to  para’vit, fe’minas: women, accusative,  fe’mina, -ae, f, direct object to  para’vit, dolo: by deceit, dolus, -i, masculine noun of the second declension, ablative denoting manner, from the Greek word δόλος, of the same root: δολερός, δολιότητα.

Analysis of the seventh period: Sabi’nos … raptave’runt.

invita’vit, raptave’runt: he invited, he carried away, verbs of the two main clauses, initial tenses: i'nvito, -a'vi, -a'tum, a're, rapto, -a'vi, -a'tum, -a're < ra’pio, ra’pui, raptum, ra’pere,  Sabi’nos et Sabi’nas: Sabine men and women, fi’lias: the daughters, fi'lia, -ae, f, daughter, fi’lius, -i, m, son,  enim: for, conjunction of reason, it always introduces a main clause, it usually enters after a word, never at the beginning of the sentence, it is like the Greek conjunction  γάρ, ad: preposition structured with accusative, to, in,   it denotes direction, ad ludos pu’blicos: to public games, fights, ludus, -i, game, fight, pu’blicus, -a, -um, public, inter ludos: during the games, inter, preposition structured with accusative and denoting "between, during".

To continue look at: ../Lesson 03 Part 3/ To see the Introduction look at: ../Introduction/


text:
Children, Schools and Families Bill

Introduction
The Children Schools and Families Bill (CSF Bill) was published in November 2009 represents a major threat to the home education community in England. The purpose of this page is:
 * to discuss the Bill, Explanatory Notes and associated Impact Assessment
 * to suggest any Amendments.

Summary of the Bill
Schedule 1 of The CSF Bill introduces an annual registration scheme, effectively a licence, for Home Educated children. Parents would have to apply an advance plan for their children’s education every year in order to remain on the ‘register’ and Local Authorities would have extensive powers to refuse or revoke registration on a variety of grounds. This reverses the fundamental principle in English law that parents are responsible for the education of their children.

Under the proposals, Local Authorities would have wide powers to monitor home educated families and children. The proposed system includes mandatory annual visits and requests for unaccompanied interviews with children.

The CSF Bill has been described as a "skeleton" with further regulation to be issued on how many of the proposals would work in practise. Future guidance would be issued for Local Authorities on the ‘registration’, monitoring and inspection regime but MPs are being asked to approve the Bill without having sight of this guidance. This exposes Home Educators to huge uncertainty as rules could be changed significantly in the future.

Passage of the Bill through Parliament undefined
19 November 2009: The CSF Bill was published and had its First Reading in the House of Commons

26 November 2009: As part of six days of debate on the Queen's Speech, the House of Lords debated Education. Lord Lucas spoke in support of Home Educators. His speech can be found here.

In closing the debate, Baroness Royall of Blaisdon reaffirmed the Government's committment to registration and monitoring. Her comments are here. Column 576 Para 5.

8 December 2009: Petitions were presented to the House of Commons by MPs from all over the country (transcript).

16 December 2009: MPs break for Christmas.

5 January 2010: MPs return to the House of Commons after their Christmas break.

11 January 2010: Second Reading of the CSF Bill in the House of Commons (transcript).

After the Second Reading, a Public Bill Committee of MPs will be appointed to scrutinise the CSF Bill. The following information came from the House of Commons Scrutiny Unit: ''“The public bill committee will not be appointed till after the second reading debate [...] The number of MPs on a public bill committee varies. It is usually 16 or 18 plus 2 chairmen. The whips of each party decide which members are on which committee so I don't think you are able to influence the decision.”''

19 January 2010: Public Bill Committee hearing. Fiona Nicholson of EO has been invited to give evidence.

General Election 2010 The date has yet to be announced. There is a handy ready reckoner here on the UK Parliament site here:

April 2011: Proposed implementation date if the CSF Bill becomes law.

How to Oppose the Bill
Write to your MP

Write to your MP asking them to raise your concerns with the Minister.

Here is a leaflet with some key points.

They Work for You - Find your MP.

Make a Written Submission about the Bill

Written submissions can be made any time after the Bill has been published. Details can be found here.

Sign this Petition and circulate the link

http://petitions.number10.gov.uk/Home-ed-families/

Lobbying the Lords

According to Lord Lucas - a great supporter of Home Education - the time to involve the Lords is once the Bill has had its Third Reading in the Commons. Lord Lucas has some helpful information about lobbying the Lords on his blog here.

Ian Appleby has created an excellent database to help us lobby the Lords. It is here: Lords Database The database can be edited universally so please update it as you contact people.

Possible amendments to the Bill
/Explanatory notes for Amendments/

/Amendments to Section 19A of Schedule 1/

/Amendments to Section 19B of Schedule 1/

/Amendments to Section 19C of Schedule 1/

/Amendments to Section 19D of Schedule 1/

/Amendments to Section 19E of Schedule 1/

/Amendments to Section 19F of Schedule 1/

/Amendments to Section 19G of Schedule 1/

/Amendments to Section 19H of Schedule 1/

/Amendments to Section 19I of Schedule 1/

/Proposed new Section 19J of Schedule 1/

/Amendments to Section 437 of EA 1996/

/Amendments to Section 442 of EA 1996/

/Amendments to Section 443 of EA 1996/

/Amendments to Section 176 of EA 2002/

/Wish-list for Amendments/

Amendments proposed to the Bill Committee

 * 1) Amendments up to 19 January 2010
 * 2) Amendments proposed on 19 January 2010

History of the Home Education proposals in the Bill
In January 2009, Graham Badman was asked by the Government to carry out a Review of Elective Home Education in England. His report - published in June 2009 - was accepted in full by the Government but triggered widespread opposition from home educators and from 43 MPs who signed an Early Day Motion put forward by MP Mark Field.

In the wake of complaints from home educators, the Children Schools and Families Select Committee ordered an inquiry into the Badman Review. Submissions to that inquiry can be viewed here.

Before publication of the inquiry report, home educators rallied around lobbying MPs and produced their own report called Right to Reply, which was presented to MPs at a mass lobby of Parliament on 13 October 2009. A month later, MP Graham Stuart formed an All-Party Parliamentary Group on Home Education. In the House of Lords, Lord Lucas has also been supporting home educators.

The Impact Assessment (referenced below) was published in November 2009 and it used inaccurate percentages to calculate the benefit/cost ration of the CSF bill as regards home education (see Bullet Point Expose below). An Impact Assessment is used to inform the rationale behind any changes in legislation and forms the basis for the legislation proposed in Scedule 1 of the CSF bill.

The Select Committee published it's inquiry on the 16th December 2009 http://www.parliament.uk/parliamentary_committees/csf/csfpn101209.cfm

MPs and Lords who support Home Education
MP Mark Field:

 * tabled a Westminster Hall Debate on 9 June 2009 "to express home educators' deep concerns about the Badman Review".

 * tabled Early Day Motion 1785 on 1 July 2009.

MP Graham Stuart:
 * took an active part in the CSF Select Committee Inquiry into the Badman Review on 12 and 14 October 2009.

 * spoke in the House of Commons Debate on the Address (i.e. debate on the Queen's Speech) on 19 November 2009.

 * set up an All-Party Parliamentary Group on Home Education. (See details below)

 * has received assurance from MP Michael Gove (Shadow Secretary of State for Children, Schools and Families) that the Conservative Party will oppose the provisions for compulsory registration of home educated children in the Children Schools and Families Bill.

Lord Lucas:
 * co-ordinated a record-breaking presentation of Parliamentary Petitions to the House of Commons at 10.27pm on 8 December 2009. Seventy MPs presented petitions from 120 constituencies. Graham Stuart said: "If enacted, the Government's proposals will, for the first time in our history, tear away from parents and give to the state the responsibility for a child's education."

 * made a speech in the House of Lords on 26 November 2009 and continues to ask pertinent questions of Lady Delyth Morgan regarding refused Freedom of Information requests.

Here is a list of those MPs who spoke up in support of home educators at the first All Party Parliamentary Group on Home Education on 6 January 2010: Notes from the meeting made by home educators can be found here: Wikiversity page devoted to APPG on Home Education

Graham Stuart, Conservative MP for Beverley and Holderness

Susan Kramer, Liberal Democrat MP for Richmond Park

Charlotte Atkins, Labour MP for Staffordshire Moorlands

Anne Milton, Conservative MP for Guildford

Dave Anderson, Labour MP for Blaydon

Sandra Gidley, Liberal Democrat MP for Romsey

Oliver Heald, Conservative MP for North East Herts

Eleanor Lang, Conservative MP for Epping Forest

John Hemming, Liberal Democrat MP for Birmingham Yardley

David Howarth, Liberal Democrat MP for Cambridge

Kate Hoey, Labour MP for Vauxhall

All-Party Parliamentary Group on Home Education
Chairman Graham Stuart (Conservative)

Deputy Chairman Lord Lucas (Conservative)

Secretary Tim Farron (Liberal Democrat)

Treasurer David Drew (Labour)

The full list of members of the APPG as of 26th November 2009 is:

Conservative Richard Benyon, Peter Bottomley, Douglas Carswell, Graham Brady, Alistair Burt, Stephen Crabb, Philip Davies, Mark Field, Robert Goodwill, Cheryl Gillan, Michael Gove, Oliver Heald, Julie Kirkbride, Mark Lancaster, Lord Lucas, Anne Milton, Mark Pritchard, John Randall, Andrew Selous, Graham Stuart, Charles Walker, Bill Wiggin

Labour Celia Barlow, Karen Buck, Richard Caborn, Jim Cunningham, Parmjit Dhanda, David Drew, Kate Hoey, Kelvin Hopkins, George Howarth, Brian Jenkin, Andy Love, Austin Mitchell, Paddy Tipping, Dr Desmond Turner, Lynda Waltho

Liberal Democrat Annette Brooke, Tim Farron, Sandra Gidley, John Hemming, Paul Holmes, David Howarth, Mark Hunter, John Leech, Jo Swinson

The first meeting of the APPG took place on 6 January 2010. Notes from the meeting made by home educators can be found here: Wikiversity page devoted to APPG on Home Education

Related Publications
Children Schools and Families Bill

Children Schools and Families Bill

Children Schools and Families Bill Explanatory Notes

Children Schools and Families Bill Equalities Impact Assessment, page 73-75

Children Schools and Families Bill Impact Assessment, page 83-90,

Early Day Motions

MP Mark Field's Early Day Motion

MP Oliver Letwin's Early Day Motion

CSF Select Committee

CSF Select Committee: Submissions to Inquiry

CSF Select Committee: Report into Elective Home Education published 19 December 2009

Other Documents

Elective Home Education: Guidelinesfor Local Authorities 2007

Right to Reply: The original version presented to MPs can be found here. An updated version can be seen here. (this page is not yet complete)

Critique of Impact Assessment for Children, Schools and Families Bill, (EHE). Dr Ben Anderson

Children, Schools and Families Bill: Legal Analysis.

BULLET POINT EXPOSE of the Statisitcs used to inform the Impact Assessment. http://docs.google.com/fileview?id=0B4_d0FTV62i4Mzg2YjNkNDEtNGNlMy00NWQ5LWEwYmMtMDgzOWFmODE4NGE4&hl=en_GB

title: Children, Schools and Families Bill


text:
Talk:Children, Schools and Families Bill

Who came up with the idea of a Wikipage?
MP Graham Stuart is working hard to represent the views of the home education community in Parliament. In November 2009, he was instrumental in setting up an All-Party Parliamentary Group on Home Education. He suggested that home educators set up a Wiki site and although I have never done such a thing before, there is a first time for everything!

Claire Blades 20:59, 23 November 2009 (UTC)

Are you going to post the relevant sections of the Bill so that comments/amendments etc can be posted?

--

I am not sure of the best way to do this. Do you think it would work if we looked at each section in Schedule 1 separately like this:

19A Maintenance of home education register
(1)A local authority in England shall maintain a register for the purpose of monitoring the provision of education to children of compulsory school age in their area who are not educated at a school or under section 19. (2)Regulations may make provision about maintenance of the register. (3)The regulations may, in particular, make provision about amendment of the register. (4)In this Act—“home-educated child” means a child all of whose education is provided otherwise than at a school, and not under section 19; “home education register” means a register maintained under this section. Claire Blades 21:22, 24 November 2009 (UTC)

Yes. Also the explanatory notes that are applicable. --Rose 17:32, 26 November 2009 (UTC)

It gets complicated because the format of an amendment is to describe words to be added/removed/changed. I think each clause needs a separate section, and each suggestion needs three parts: the text of the amendment, how the clause will appear when modified, and a brief explanation of what it achieves. This way we can check that the proposed amendment matches the final text and have some idea of its purpose.

Llondel 22:34, 12 December 2009 (UTC)

How to discuss amendments
I agree with Llondel's plan about how to organise proposed amendments on here. But can it be done? Won't it make the main page unreasonably long?

We can copy across Llondel's amendments to here. Will be a big job, I reckon.

Shall I start with 19A and see how it goes?

Danigreenhouse 20:04, 16 December 2009 (UTC)

Obvious NPOV violation
Is obvious. KATMAKROFAN (discuss • contribs) 22:31, 31 October 2016 (UTC)

 * Wikiversity has no NPOV requirement. -- Dave Braunschweig (discuss • contribs) 23:36, 31 October 2016 (UTC)


text:
User:Tldmonitronics

Using this site to gain extra knowledge while running my own business. No time for real classes so I would like to learn at my own rate to add on to my associates degree.

title: User:Tldmonitronics