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UNO/Official Rules

This section of the UNO wikibook will detail the official rules of the game, as of the 2018 rules update. The goal of the game is to discard all of the cards in your hand.

Introduction to the Deck
UNO is played using a specially printed deck of 112 cards, including 25 each of four different colours: red, blue, green and yellow.

Each colour has 19 number cards, consisting of one zero and two of one through nine. There are also two per colour of the three action cards - Draw Two, Reverse and Skip.

The deck also includes eight Wild cards - four standard Wilds and four Wild Draw Fours.

UNO sets manufactured post-2018 will also include one Wild Shuffle Hands card and three Wild Customisable Cards.

Basic Gameplay
To begin the game, one player is selected to be the dealer. The dealer shuffles the deck and deals seven cards to each player, setting the remaining cards face down on the table as a draw pile. The top card from the draw pile is flipped over and placed next to the draw pile, face up to start the discard pile. If this starting card is an action or Wild card, the action or Wild is ignored and another card is flipped until a number card comes up.

The player to the dealer's left takes the first turn, then play initially proceeds clockwise.

On a player's turn, that player must play one card from their hand to the discard pile. The card being placed must match the current card on top of the discard pile by having either the same number, colour or symbol. For example, if a yellow 5 is on top of the discard pile, the player must either play a yellow card or any colour 5. Alternatively, the player may put down a Wild card if they have one (this will be explained later).

If a player does not have a card in their hand that can match the card in the discard pile, the player must draw one card from the draw pile. If this card matches the card on top of the discard pile, the player may play the card they just drew as part of their turn. Otherwise, play passes to the next player.

Also, a player may choose not to play a card on their turn if they do not want to. They then draw a card, and they can play that card if they want, but not any others.

Action Cards
When a player plays an action card, an action will be performed corresponding to the type of card. There are seven different types of action cards (five with the pre-2018 deck):

Draw Two
When this card is played the next player in turn order must draw two cards from the draw pile and lose their turn.

Reverse
When this card is played the direction of play reverses and passes in the opposite direction. If play was originally passing clockwise then it changes to passing counterclockwise, and vice versa.

Skip
When this card is played the next player in turn order loses their turn.

Wild
This card can be played on top of any other card. In addition, the player who put down this card must declare one of the four colours to resume play with, and only cards of that colour may be placed on top of the Wild.

Wild Draw Four
The most powerful card in the deck, this card plays like a normal Wild, with the addition that the next player in turn order must draw four cards and lose their turn.

However... there is a catch. A player may only legally play a Wild Draw Four if they do not have any cards in their hand that match the colour of the card on top of the discard pile (however cards with the same number or action symbol are acceptable).

Challenging Wild Draw Fours
If a player suspects a Wild Draw Four was played on them illegally (i.e. the previous player had a colour-matching card), that player may challenge the play. If they so do, the player being challenged must privately show the challenger their hand. If the challenger was correct in their accusation, the guilty player must draw the four cards instead. However, if the challenger was incorrect then they must draw the four cards plus two penalty cards, for six total. Whatever the result of a challenge, the player who played the Wild Draw Four selects the colour that resumes play.

Wild Shuffle Hands
This card is one of two Wilds introduced in the 2018 update. When played, the player who played the card must gather all of the cards in all of the players' hands and shuffle them. Then they must deal the cards out, starting with the player on their left and passing clockwise. However, the current direction of play is retained. The player who played the Wild Shuffle Hands selects the colour that resumes play.

Wild Customisable
This card is the other Wild introduced in the 2018 update. As their name suggests these Wild cards are customisable. They have an empty white space in the centre that allows for a house rule - a reasonable one, mind you - to be written. When a Wild Customisable is played the house rule written on it is performed and then the player who played the Wild Customisable selects the colour that resumes play.

Calling "UNO" and Winning the Game
When a player discards their penultimate card and is left with only one card, they must call "UNO" (Spanish for "one") to alert the others they are about to win. If they forget to call "UNO" and are caught before the next player plays a card, the player who forgot to call "UNO" must draw two penalty cards.

Once a player discards the last card in their hand, they win the game.

Optional Win Condition: Scoring
There is an optional victory condition, which is to play for points. When this victory condition is being used, the player who discards their last card does not win the game instantly - instead, they score points for all of the cards in their opponents' hands, as follows:

Note that if the last card played is a Draw Two or Wild Draw Four, the next player must draw the appropriate number of cards before points are tallied.
 * Number cards are worth their face value.
 * Non-wild action cards are worth twenty points.
 * Wild cards are worth fifty points.

After points are scored, if no player has reached 500 points the deck is shuffled and a new round begins. If a player reaches 500 points, they win the game.

title: UNO/Official Rules


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History of video games/Platforms/PlayStation Portal

Development
The system was previewed as the "PlayStation Q", using the same concept of streaming PlayStation 5 games as the PlayStation Portal would launch with.

Launch
The launch price of the system was announced as $199.99 USD. The device was seen by some as a successor of sorts to the PS Vita, albeit with a different purpose. Another point of comparison made was to the Wii U gamepad.

On August 31, 2023, preorders for the system were opened, with a projected release date of November 15, 2023. Preorders were limited to one device per person.

Around December 21, 2023, the PlayStation Portal had sold out at GameStop in the United States of America according to Tom's Guide. Stock levels also impacted availability in the United Kingdom, with IGN reporting low stocks in early December 2023.

Compute
The local processing is handled by a Qualcomm Snapdragon 662. The actual running of games is left to a networked PlayStation 5 game console.

Display
A LCD measuring 8 in and operating at 60 Hz is used as the display of the device. The screen was touch sensitive.

Audio
The system included a 3.5mm headphone jack, twin speakers and a microphone, though notably it lacked Bluetooth audio support locking in users to Sony's own wireless audio products.

Wireless
The system was supported Wi-Fi 5, with reviewers commonly noting a desire for more advanced Wi-Fi technology in the console given it's dependence on a strong signal for functionality. Notably, the system included an Airplane mode, though this was noted by The Verge as rendering the system moot.

Hardware
The system weighed 1.17 lb. The system includes an integrated 16.6 Watt hour battery.

iFixit and The Verge reported that much of the controller controller was notably easier to repair then a stock DualSense controller.

Games
The PlayStation Portal streams games from a PlayStation 5.

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


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User:Thierry Dugnolle/Python

The language of the machine must adapt to the human being, and not the other way around.

The Python files which generate my animations :

High definition paintbrush

Wave packet2

The whole infinite tree

Zoom on an infinite tree

Cantor Set Expansion

Interference of a particle with itself

Wave packet

Double slit experiment

To make an animation, I make use of imagemagick in a terminal. You can install it with the following command:

If I open a terminal from the folder where my images are, I can convert them in an animation with the following command:

To install Pillow (a package needed for these files to work), you might need the following commands:

To edit and run my Python files, I make use of Pycharm. You can download it for free. If you make use of Pycharm, click on the mouse right button on 'PIL' at the top of the file before you run it. Then click on 'Show context actions' with the left button, and on 'Install package Pillow', with the same button.

title: User:Thierry Dugnolle/Python


text: User:Thierry Dugnolle/Python/Double-slit-experiment


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User:Thierry Dugnolle/Python/Wave-packet

A gaussian wave packet. The color (yellow green blue) indicates the phase of the wave function $$\psi$$, its intensity indicates $$| \psi | ^2 / | \psi |_{max} ^2$$. This wave function could represent the motion of a quantum particle. The wave function is $$\psi(x,y,t)=\psi(x,t) \psi(y,t)$$, $$k_{0x}= k_0$$, $$k_{0y}=0$$, $$ \psi (x,t) = (\frac{2a ^2}{\pi}) ^{1/4} \frac{e ^{i \phi}}{(a ^4 + \frac{4 \hbar ^2 t ^2}{m ^2}) ^{1/4}} e ^{i k_0 x} exp [ - \frac{(x - \frac{\hbar k_0}{m} t ) ^2 }{a ^2 + \frac{2 i \hbar t}{m} } ]$$ where $$ \phi = - \theta - \frac{\hbar k_0 ^2}{2 m} t$$ and $$tg (2 \theta) = \frac{2 \hbar t}{m a ^2}$$ (source: Cohen-Tannoudji, Diu & Laloë, Quantum Mechanics, complement GI, §3-a)


text: Category:Book:UNO

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text: Talk:Marathi language portal

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text:
Quantum Chemistry/Example 28

Question
For an electron in a 3D cube with a length of 6.00 Å, what is: (a) the energy of its state? (b) the degeneracy of this energy state? (c) the total number of nodal planes for a particle in the $${n_\text{x}}=4$$, $${n_\text{y}}=5$$, and $${n_\text{z}}=3$$?

Solution
(a) The mass of an electron must be known to determine the energy of the particle. To determine the energy state of an electron in a 3D box, the equation that relates the energy levels of a particle in a cube must be used with every variable in its SI units. The mass of an electron is known to be $${9.1093837\text{×}10^{-31} \text{kg}}$$. Planck's constant is known to be $${6.62607015\text{×}10^{-34} \text{m²·kg·s⁻¹}}$$. The length of the box is $${6.00\text{x}10^{-10}\text{m}}$$ since one angstrom is known to be $$10^{-10}\text{m}$$. The energy of the electron in the cube can be calculated as follows,

 * $${E}=\left(\frac{h^2}{8 m L^2} \right)\left({n_\text{x}^2 + n_\text{y}^2 + n_\text{z}^2}\right)$$

 * $${E}=\left(\frac{\left(6.62607015\text{×}10^{-34} \text{m²·kg·s⁻¹}\right)^2}{8 \text{×} \left(9.1093837\text{×}10^{-31} \text{kg} \right) \text{×} \left(6.00 \text{x} 10^{-10} \text{m} \right)^2} \right)\left({{4^2} + {5^2} + {3^2}}\right)$$

 * $${E}=\left(1.68\text{×}10^{-19} \text{J} \right)\left(50\right)$$

 * $${E}=8.38\text{×}10^{-18} \text{J} $$

(b) Degeneracy is defined as an energy state with an identical energy to that of a particle with a different set of quantum numbers. In this question, the energy of degenerate states must equal the following,

 * $${E}=\left(\frac{h^2}{8 m L^2} \right)\left({{4^2} + {5^2} + {3^2}}\right)=\left(\frac{50 h^2}{8 m L^2} \right)$$

To determine the degeneracy of a system, the simplest method is to use a matrix to ensure a systematic process is followed. In this case, the sum of the square of all quantum numbers must equal 50. Therefore, the matrix is as follows,

 * {| class="wikitable" style="text-align: center; width: 300px; height: 150px;"

! $${n_\text{x}}$$ ! $${n_\text{y}}$$ ! $${n_\text{z}}$$ ! $${n_\text{x}^2+n_\text{y}^2+n_\text{z}^2} $$
 * 4 || 5 || 3 || 4² + 5² + 3² = 50
 * 4 || 3 || 5 || 4² + 3² + 5² = 50
 * 5 || 3 || 4 || 5² + 3² + 4² = 50
 * 5 || 4 || 3 || 5² + 4² + 3² = 50
 * 3 || 4 || 5 || 3² + 4² + 5² = 50
 * 3 || 5 || 4 || 3² + 5² + 4² = 50
 * }
 * 5 || 4 || 3 || 5² + 4² + 3² = 50
 * 3 || 4 || 5 || 3² + 4² + 5² = 50
 * 3 || 5 || 4 || 3² + 5² + 4² = 50
 * }
 * 3 || 5 || 4 || 3² + 5² + 4² = 50
 * }

This results in the identification of 6 different sets of quantum numbers, and thus, this energy state is said to be 6-fold degenerate.

(c) To determine the number of nodal planes, each axis must be considered individually. Mathematically, to calculate the number of nodal planes associated with the x-axis, the following equation is used,
 * $${N_{\text{nodal planes x-axis}}=n_\text{x}-1}$$

Therefore, in this example, the number of nodal planes in x-axis is,
 * $${N_{\text{nodal planes x-axis}}=4-1=3}$$

Similarly, for the y-axis and the z-axis, the number of nodal planes is,
 * $${N_{\text{nodal planes y-axis}}=n_\text{y}-1=5-1=4}$$
 * $${N_{\text{nodal planes z-axis}}=n_\text{z}-1=3-1=2}$$

Therefore, the total number of nodal planes in this system is 9. This was determined by summing the number of nodal planes associated with each individual axis.

title: Quantum Chemistry/Example 28


text:
Quantum Chemistry/Example 29

Quantum Mechanical Harmonic Oscillator Wavefunction
A system undergoing harmonic motion around an equilibrium is known as a harmonic oscillator.

In quantum chemistry, the harmonic oscillator refers to a simplified model often used to describe how a diatomic molecule vibrates. This is because it behaves like two masses on a spring with a potential energy that depends on the displacement from the equilibrium, but the energy levels are quantized and equally spaced. The potential energy $$V(x) = \frac{1}{2}kx^2  $$ is non-zero  and can theoretically range from $$x =[-\infty \text{, } \infty] $$.

The wavefunction for the quantum harmonic oscillator is given by the Hermite polynomials multiplied by the Gaussian function. The general form of the wavefunction is:

$$\psi_v= N_v \cdot H_v \left (\sqrt{\frac{mw}{\hbar}}x \right) \cdot \exp\left( \frac{-mw}{2\hbar}x^2 \right) $$

With:

$$v = \text{Quantum number} $$

$$N_v = \text{Normalization factor}$$

$$H_v= v\text{-th Hermite polynomial} $$

The first four Hermite polynomials are:

$$\begin{align} H_0(x) &= 1, \\ H_1(x) &= 2x, \\ H_2(x) &= 4x^2 - 2, \\ H_3(x) &= 8x^3 - 12x. \\ \end{align} $$

$$m = \text{Mass of particle} $$

$$w = \text{Angular frequency of the oscillator} $$

$$\hbar = \text{Reduced Planck's constant}  $$

$$x=\text{Position}  $$

Normalization of a Wavefunction
The probability of finding the particle in any state is given by the square of the wavefunction. Therefore normalizing a wavefunction in quantum mechanics means ensuring that the total probability of finding a particle in all possible positions is equal to 1. A normalized wavefunction is one that satisfies the normalization condition:

$$\int_{-\infty}^{\infty} \mid \psi (x) \mid^2 dx =1 $$

Normalization is important because it ensures that the probability of finding the particle somewhere in space is 100%.

Example
Show the derivation of the normalization factor of the v=1 state of the harmonic oscillator beginning from the unnormalized wavefunction.

$$\psi_v= N_v \cdot H_v \left (\sqrt{\frac{mw}{\hbar}}x \right) \cdot \exp\left( \frac{-mw}{2\hbar}x^2 \right) $$

$$N_{v}^{2} \int_{-\infty}^{\infty} H_{v}^{2} \left( \sqrt{\frac{mw}{\hbar}}x \right) \cdot \exp\left( \frac{-mw}{\hbar}x^2 \right) dx = $$

$$\text{Let } y=\left (\sqrt{\frac{mw}{\hbar}} \right)x $$

$$N_{v}^{2} \int_{-\infty}^{\infty} H_{v}(y) H_{v}(y) \cdot \exp\left( -y^2 \right) \sqrt{\frac{\hbar}{mw}} dy = $$

$$N_{v}^{2} \sqrt{\frac{\hbar}{mw}} (-1)^{v} \int_{-\infty}^{\infty} H_{v}(y) \frac{d^{v}}{dy^{v}} \exp\left( -y^2 \right) dy = $$

$$N_{v}^{2} \sqrt{\frac{\hbar}{mw}} \int_{-\infty}^{\infty}\exp(-y^{2}) \frac{d^{v}}{dy^{v}} H_{v}(y) dy = $$

$$N_{v}^{2} \sqrt{\frac{\hbar}{mw}} 2^{v}v!\sqrt{\pi} = $$

$$N_{v}=\frac{1}{\sqrt{2^{v}v!}} \left( \frac{mw}{\pi \hbar}\right)^{1/4} $$

Sub in v=1

$$N_{1}=\frac{1}{\sqrt{2^{1}1!}} \left( \frac{mw}{\pi \hbar}\right)^{1/4} =\frac{1}{\sqrt{2}} \left( \frac{mw}{\pi \hbar}\right)^{1/4} $$

Check
Prove that $$\psi_{1} $$ is normalized (using notation from class)

$$\psi_{1} = \left( \frac{4 \alpha^3 }{\pi} \right)^{1/4} x \exp\left( \frac{-\alpha x^2}{2} \right) $$, where $$\alpha = \left( \sqrt{\frac{k\mu}{\hbar^{2}}} \right)  $$

$$\int_{-\infty}^{\infty} \mid \psi_{1}\mid^2 dx = \left( \frac{4 \alpha^3 }{\pi} \right)^{1/2} \int_{-\infty}^{\infty} x^2 \exp^{-\alpha x^2} dx = \left( \frac{4 \alpha^3 }{\pi} \right)^{1/2} \left( \frac{1}{2 \alpha} \left( \frac{\pi}{\alpha} \right)^{1/2} \right) = 1 $$

title: Quantum Chemistry/Example 29


text:
Quantum Chemistry/Example 30

Energy in the particle in a 1D box model
Energy in quantum mechanical systems is quantized, unlike in classically mechanical systems, where the energy can take any value. The energy of a quantum mechanical system may only hold specific discrete values, which are known as s. Consider the model for the 1D. In this model, the possible discrete energy levels are given by the relation,

$$ The ground state of any quantum mechanical system is the state with the lowest possible energy (otherwise known as the of the system). Defined in the equation for the energy levels of a particle in a 1D box, the quantum number $$n$$ can hold any integer value equal to or greater than one and as such, the ground state of this model occurs when $$n=1$$. All energy levels above the ground state are referred to as excited states. There are an infinite number of these states and for the particle in a 1D box, are defined by the quantum number $$n$$, like the ground state. The first excited state is the energy level one above the ground state, in which $$n=2$$, the second excited state is the energy level one above the first excited state, where $$n=3$$, and so forth.

Particle transitions between states
A particle in a 1D box can transition between energy levels by the means of three different processes, whose probability can be measured by. The transitional processes involve electromagnetic radiation in the form of photons. They are the following:

The energy of a photon can be determined by the relationship between a photon's frequency of oscillation and energy, known as the , $$ In quantum chemistry, it is often more convenient to express frequency in terms of wavenumber ($$\tilde{\nu}$$), which has units of $$\text{cm}^{-1}$$ compared to $$\text{s}^{-1}$$. There is a simple conversion as frequency and wavenumber are related to the speed of light by,
 * Spontaneous emission: The spontaneous decay of a particle from a higher energy state to a lower energy state, emitting a photon of the transition energy.
 * Stimulated emission: The decay of a particle from a higher energy state to a lower energy state stimulated by the presence of a photon of the same energy as the transition.
 * Photon absorption: The promotion of a particle from a lower energy state to a higher energy state caused by the absorption of a photon of the transition energy.
 * $$\tilde{\nu}=\frac{\nu}{c} \, \text{, where} \ c \ \text{is the speed of light in cm/s.}$$

As such, the Planck relation can be rewritten as, $$ This relation allows the calculation of the energy of a photon involved in one of the transitions between states, as the energy of the transition will be equal to the energy of the photon, whether it is the emitted photon in spontaneous emission, the stimulating photon in stimulated emission or the absorbed photon in the absorption transition.

Example
What is the wavenumber ($${\tilde{\nu}}_{photon}$$) of electromagnetic radiation emitted when a proton in a one-dimensional box with length 472 nm decays from the fifth excited state to the fourth excited state?

SOLUTION: This transition is a spontaneous emission where the energy of the emitted photon can be determined by the difference between the energy levels of the transition,

 * $$\begin{align}

E_{photon} & = \Delta{E} \\ & = E_j - E_i, \\ & \text{where} \ i \ \text{and} \ j \ \text{are the final state and the excited state, respectively.} \\ \end{align}$$

As this transition occurs between the fourth and fifth excited states, $$i$$ and $$j$$ will be 5 and 6, respectively. From the energy levels of a particle in a 1D box,
 * $$\begin{align}

E_6 - E_5 & = \frac{h^2 6^2}{8 m_p L^2} - \frac{h^2 5^2}{8 m_p L^2} \\ & =\frac{11 h^2}{8m_p L^2}, \\ & \text{where} \ m_p \ \text{is the mass of a proton in kg and} \ L \ \text{is the given length of the box in m,} \ (1 \ \text{nm}=1\cdot10^{-9}\text{m})\text{.} \\ \end{align} $$ Substituting these values into the above equation gives,
 * $$\begin{align}

E_{photon} & =\frac{11(6.62607015\cdot10^{-34}\,\text{m}^2\text{kg/s})^2}{8(1.67262192\cdot 10^{-27}\,\text{kg})(472\cdot10^{-9}\,\text{m})^2} \\ & = 1.62 \cdot 10^{-27} \, \text{J} \\ \end{align} $$ Using the wavenumber variation of Planck's relation, the wavenumber of a photon of this exact energy can be determined and expressed in convenient units of $$\text{cm}^{-1}$$.

 * $$\begin{align}

\tilde{\nu}_{photon} & =\frac{E_{photon}}{hc}\text{, where}\ h\ \text{is Planck's constant and}\ c\ \text{is the speed of light expressed in cm/s.} \\ & =\frac{1.62\cdot10^{-27}\,\text{J}}{(6.62607015\cdot10^{-34}\,\text{m}^2\text{kg/s})(2.99792458\cdot10^{10}\,\text{cm/s})} \\ & =8.16 \cdot 10^{-5} \, \text{cm}^{-1} \\ \end{align}$$

title: Quantum Chemistry/Example 30


text:
Quantum Chemistry/Example 31

Write an example problem related to the conversion between wavelength, frequency, energy and wavenumber of electromagnetic radiation. Show each step in detail and explain the conversion.

Example: Carbon monoxide shows a sharp peak in its IR spectrum at 2143 cm-1.

a) Calculate the frequency and wavelength of the molecule's vibration.

The question gives us the wavenumber which can be converted to frequency through the equation:

$$ v = \widehat{v} * c$$

where v is the frequency, ṽ is the wavenumber and c is the speed of light.

$$ v = \widehat{v} * c$$

$$ v = $$ (2143cm-1) * (2.99792458*1010cm s-1)

= 6.42455237494*1013 s-1

= 64.24 THz

To find the wavelength of the vibration we can use the equation:

$$ \hat{v}$$= $$ {1 \over \lambda} $$

where $$ \lambda$$ is the wavelength.

$$ \hat{v}$$= $$ {1 \over \lambda} $$

This equation can be rearranged to solve for wavelength:

$$ \lambda$$= $$ {1 \over \hat{v}} $$

= $$ {1 \over2143 cm^{-1} } $$

= 4.666356*10-4 cm

This should be converted to nm since wavelength is usually written in nm.

λ = 4.666356*10-4 cm * $$ {1nm \over(1*10^{-7} cm)} $$

= 4.6*103nm

b) Calculate the energy of carbon monoxide at its ground state.

To find the energy of a molecule at its ground state we can use the equation:

$$ E = hv_0 (v+\left ( \frac{1}{2} \right ))$$

where E is the energy, h is Planck's constant, $$ v_0 $$ is the frequency of the ground state, and $$ v$$ is the quantum number of the energy level.

We can use this equation since carbon monoxide's vibrations act as a harmonic oscillator.

$$ E = hv_0 (v+\left ( \frac{1}{2} \right ))$$

$$ E = h (6.424* 10^{13} s^{-1} )$$$$  (0+\left ( \frac{1}{2} \right ))$$

$$ E = 2.12847674 * 10^{-20} J $$

c) Calculate the wavelength of a photon that excites an electron from the ground state up 2 levels.

In this case, the quantum number v is equal to 2. We can use the same equation used in b) to first solve the change in energy caused by the photon.

$$ E = hv_0 (v+\left ( \frac{1}{2} \right ))$$

$$ E = h (6.424* 10^{13} s^{-1} )$$$$  (2+\left ( \frac{1}{2} \right ))$$

$$ E = 1.06423837*10^{-19} J$$

Now that we have found the change in energy we can calculate the wavelength of the photon using the equation:

$$ E = \left ( \frac{hc}{\lambda} \right )$$

Rearrange the equation to solve for λ:

$$ \lambda = \left ( \frac{hc}{E } \right )$$

$$ \lambda = \left ( \frac{hc}{1.06423837*10^{-19} J } \right )$$

$$ \lambda = 0.0001866542 cm $$

Convert the wavelength to nm.

$$ \lambda = 0.0001866542 cm * \left ( \frac{1 nm}{1*10^{-7}cm} \right ) $$

$$ \lambda = 1.86*10^{-6} nm $$

Therefore, a photon that is able to cause a transition from ground state to v = 2 must have a wavelength of 1.86 * 10-6 nm.

title: Quantum Chemistry/Example 31


text:
Quantum Chemistry/Example 32

The Wavefunction of a Particle in a One-Dimensional Box
Despite the wavefunction having very little physical interpretation, the solution to the wavefunction of a particle is beneficial in order to determine the probability of such particle existing in a given area. When deriving the equation for the wavefunction of a particle in a one-dimensional box, we first begin by defining the Hamiltonian operators (i.e., kinetic and potential energy) for the given system, and substituting these values into the Schrodinger equation.

In quantum mechanics, the Schrodinger equation is given as, $$

where $$\hat{H}$$ is the Hamiltonian operator, $$\hat{T}$$ is the kinetic energy operator, $$\hat{V}$$ is the potential energy operator, $$\psi$$ is the wavefuntion, and $$E$$ is the total energy of the system. The first equation is a simplification of the second equation, since $$\hat{H}=\hat{T}+\hat{V}$$. Mathematically, the wavefunction $$\psi$$ is an eigenfunction of the Hamiltonian operator $$\hat{H}$$ with an eigenvalue of $$E$$.

Defining the Hamiltonian
For the case of a particle in a one-dimensional box, its potential energy is equal to zero within the constraints of such box (i.e., $$0\le x \le L$$), but the potential energy of the particle is infinite outside of these constraints: $$

Additionally, the kinetic energy operator in the $$ x $$ dimension is given as $$\hat{T} = -\frac{{\hslash}^2}{2m} \frac{{d}^2}{{dx}^2}$$. Therefore, since $$V(x)=0$$ inside of the box, the values defined for $$\hat{T}$$ and $$\hat{V}$$ can be substituted into the Schrodinger equation, which simplifies to   $$\frac{{d}^2\psi(x)}{{dx}^2}=-\frac{2E\cdot m}{{\hslash}^2}\cdot\psi(x)$$.

Boundary Conditions of the Wavefunction
The boundary conditions must then be identified for a particle in a one-dimensional box. The constraints of the box have been previously defined as the position of the particle, $$ x $$, being contained within a box of length $$ L $$. This means that the particle cannot exist when $$ x=L $$ or when $$ x=0 $$. The boundary conditions for the value of the wavefunction must therefore be $$ \psi(0)=0 $$ and $$ \psi(L)=0 $$.

General Solution
This is a second-order linear homogenous equation with respect to $$ \psi(x) $$, and has a general solution of

$$ \psi(x)=A\cdot \sin(k\cdot x)+B\cdot \cos(k\cdot x) $$, where $$ k=\frac $$

Thus, the solution for the given second-order linear homogenous equation is

$$ \psi(x)=A\cdot \sin\left( \frac\cdot x \right)+B\cdot \cos\left( \frac\cdot x \right) $$

To determine the specific solution for this wavefunction, the constants $$ A $$ and $$ B $$ must be found.

Determining the Unknown Variables
By substituting the first boundary condition that $$ \psi(0)=0 $$ into the general solution of the wavefunction, the value of $$ B $$ may be found.

$$ \psi(0)=A\cdot \sin\left( \frac\cdot 0 \right)+B\cdot \cos\left( \frac\cdot 0 \right) $$

$$ \psi(0)=A\cdot \sin(0)+B\cdot \cos(0)=0 $$

$$ A\cdot 0+B\cdot 1=0 $$

$$ \therefore B=0 $$

We now have $$ \psi(x)=A\cdot \sin\left( \frac\cdot x \right) $$. The second boundary condition, $$ \psi(a)=0 $$, may be applied.

$$ \psi(L)=A\cdot \sin\left( \frac\cdot L \right)=0$$

The value of A cannot be equal to zero, otherwise the value of the wavefunction would be equal to zero at any position of $$ x $$. So, $$ \sin\left( \frac\cdot L \right)=0 $$.

The sine function is periodic, therefore, there are multiple values of $$ x $$ at which $$ \sin(x)=0 $$. The values of x in which this is true are integer multiples of $$ \pi $$. Thus, $$ \frac\cdot L= n\pi $$. This can be further simplified by noting that the sine function is symmetric, therefore, the negative value of some $$ n $$ will have the same wavefunction as its positive value.

Additionally, substituting $$ n=0 $$ into our above equation would result in a value of 0 for the wavefunction at every position.

$$ \psi(x)=A\cdot \sin(0\cdot \pi\cdot x)=A\cdot \sin (0)=0 $$ Therefore, $$ n\geq 1 $$.

We can then plug $$ \frac= \frac{n\pi}{L} $$ back into our wavefunction equation, which gives $$ \psi(x)=A\cdot \sin \left(\frac{n\pi x}{L}\right) $$

The second property of a wavefunction is that it is normalized, meaning that the integral of the square of the wavefunction (i.e., the probability distribution) over all space must be equal to 1. We can now apply this to the above function to determine the constant value of $$ A $$.

$$ \int_0^L (\psi(x))^2 dx=1 $$

$$ \int_0^L A^2 \sin^2\left(\frac{n\pi x}{L}\right) dx=1 $$

$$ A^2 \int_0^L \sin^2\left(\frac{n\pi x}{L}\right) dx=1 $$

The tabulated solution to this integral gives a constant value for $$ A $$ as

$$ A = \sqrt{\frac{2}{L}} $$

Therefore, the finalized specific solution of the wavefunction for a particle in a one-dimensional box is as follows.

$$ \psi(x)=\sqrt{\frac{2}{L}}\sin\left(\frac{n\pi x}{L}\right) $$, where $$ n=1,2,3... $$

Example
The wavefunction of an electrion moving along a platinum wire with length $$ a$$ is given by $$ \psi(x)=B(x^3-3x^2+2x)$$, where $$ x $$ is the position of the electron. Outside the boundaries of this wire, the value of the wavefunction is zero ($$ \psi(x)=0 $$). Determine the equation of the wavefunction of this electron by calculating $$ B $$, the normalization constant, in terms of $$ a $$. Is this normalized wavefunction a valid wavefunction? Explain why or why not.

As previously mentioned, one of the properties of a wavefunction is that it must be normalized. When normalizing the wavefunction, a normalization constant appears. Therefore, to determine the normalization constant $$ B $$ for this wavefunction, we must integrate over all space and set it equal to 1.

$$ \int_0^L (\psi(x))^2 dx=1 $$

In this case, the length of the wire is an arbitrary constant $$ a $$. Thus, $$ L=a $$. Additionally, the equation for the wavefunction is $$ B(x^3-3x^2+2x)$$, which can be substituted in for $$ \psi(x) $$.

$$ \int_0^a (B(x^3-3x^2+2x))^2 dx=1 $$

$$ B^2\int_0^a x^6+9x^4+4x^2 dx=1 $$

$$ B^2\left[\frac{x^7}{7}+\frac{9x^5}{5}+\frac{4x^3}{3}\right]_0^a=1 $$

$$B^2 \left(\frac{a^7}{7}+\frac{9a^5}{5}+\frac{4a^3}{3}\right)=1 $$

$$ B^2=\frac{1}{\frac{15a^7+329a^3}{105}} $$

$$ \therefore B= \sqrt{\frac{105}{15a^7+329a^3}} $$

To ensure that this is a valid wavefunction, one of two properties have been satisfied: the function is normalized. We must now ensure that the boundary conditions are valid as well (i.e., $$ \psi(0)=0 $$ and $$ \psi(a)=0 $$).

$$ \psi(0)=\sqrt{\frac{105}{15a^7+329a^3}}\cdot 0 = 0 $$

The first boundary condition is valid.

$$ \psi(a)=\sqrt{\frac{105}{15a^7+329a^3}}(a^3-3a^2+2a)\neq 0 $$

The value of the wavefunction at $$ x=a $$ will never be equal to zero, since the length of the wire is always a nonzero value. Thus, because this wavefunction disobeys the second property of $$ \psi(0)=0 $$ and $$ \psi(a)=0 $$, it is not considered a valid wavefunction.

title: Quantum Chemistry/Example 32


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This books is a book of manual arts that use the metaphysics as a principal topic or theme, it explores the use of sewing machines and 3D printing. Metaphysical artcrafts (discuss • contribs) 21:45, 25 August 2023 (UTC)

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text: Talk:Old Norse/Grammar/Pronouns

title: Talk:Old Norse/Grammar/Pronouns


text: Talk:Old Norse/Noun Declension

title: Talk:Old Norse/Noun Declension


text: Talk:Old Norse/Numerals

title: Talk:Old Norse/Numerals


text: Talk:Old Norse/Pronouns

title: Talk:Old Norse/Pronouns


text: Talk:Onondaga/Basics

title: Talk:Onondaga/Basics


text: Talk:Onondaga/Weather

title: Talk:Onondaga/Weather


text: Talk:Palembang

title: Talk:Palembang


text: Talk:Pashto/Introduction

title: Talk:Pashto/Introduction


text: Talk:Palembang/How to use this book

title: Talk:Palembang/How to use this book


text: Talk:Palembang/Lessons/Alphabet

title: Talk:Palembang/Lessons/Alphabet


text: Talk:Palembang/Why learn Palembang?

title: Talk:Palembang/Why learn Palembang?


text: Talk:Pashto/Salaam - سلام - Your first Pashto conversation


text: Talk:Persian/Lesson 8/man

title: Talk:Persian/Lesson 8/man


text: Talk:Plains Cree/Numbers

title: Talk:Plains Cree/Numbers


text: Talk:Plains Cree/Simple Words

title: Talk:Plains Cree/Simple Words


text: Talk:Polish/Exercises - Introductory declension


text: Talk:Polish/Introduction

title: Talk:Polish/Introduction


text: Talk:Polish/List of Words

title: Talk:Polish/List of Words


text: Talk:Polish/Na kursie

title: Talk:Polish/Na kursie


text: Talk:Polish/Nominative case

title: Talk:Polish/Nominative case


text: Talk:Polish/Nouns - Gender

title: Talk:Polish/Nouns - Gender


text: Talk:Polish/Nouns - Number

title: Talk:Polish/Nouns - Number


text: Talk:Portuguese/Contents/BP Introduction


text: Talk:Proto-Finnic

title: Talk:Proto-Finnic


text: Talk:Proto-Finnic/Later phonological changes


text: Talk:Proto-Finnic/Nominal cases

title: Talk:Proto-Finnic/Nominal cases


text: Talk:Proto-Finnic/Nouns and adjectives

title: Talk:Proto-Finnic/Nouns and adjectives


text: Talk:Proto-Finnic/Phonology

title: Talk:Proto-Finnic/Phonology


text: Talk:Proto-Germanic

title: Talk:Proto-Germanic


text: Talk:Proto-Germanic/Nouns and adjectives


text: Talk:Proto-Germanic/Pronouns and numbers


text: Talk:Proto-Germanic/Pronunciation

title: Talk:Proto-Germanic/Pronunciation


text: Talk:Proto-Mongolic

title: Talk:Proto-Mongolic


text: Talk:Proto-Mongolic/Alphabet

title: Talk:Proto-Mongolic/Alphabet


text: Talk:Proto-Turkic

title: Talk:Proto-Turkic


text: Talk:Proto-Turkic/Abilities, future tense and present continuous


text: Talk:Proto-Turkic/Alphabet

title: Talk:Proto-Turkic/Alphabet


text: Talk:Proto-Turkic/Basics

title: Talk:Proto-Turkic/Basics


text: Talk:Proto-Turkic/Contributors

title: Talk:Proto-Turkic/Contributors


text: Talk:Proto-Turkic/Converbs and sentence formation


text: Talk:Proto-Turkic/Equative, instrumental and imperatives


text: Talk:Proto-Turkic/Genitive, accusative and dative cases


text: Talk:Proto-Turkic/History of Proto-Turkic language


text: Talk:Proto-Turkic/Introduction

title: Talk:Proto-Turkic/Introduction


text: Talk:Proto-Turkic/Locative-ablative case and plurality


text: Talk:Proto-Turkic/Optatives, necessitatives and questions


text: Talk:Proto-Turkic/Past tenses and vowel harmony


text: Talk:Proto-Turkic/Phonology

title: Talk:Proto-Turkic/Phonology


text: Talk:Proto-Turkic/Pronouns and numbers

title: Talk:Proto-Turkic/Pronouns and numbers


text: Talk:Proto-Turkic/Suffixes used to create new words with new meanings


text: Talk:Proto-Turkic/Verbals

title: Talk:Proto-Turkic/Verbals


text: Talk:Proto-Turkic/Vocabulary

title: Talk:Proto-Turkic/Vocabulary


text: Talk:Proto-Turkic/Vocabulary 2

title: Talk:Proto-Turkic/Vocabulary 2


text: Talk:Provençal/Dates

title: Talk:Provençal/Dates


text: Talk:Provençal/Introductions

title: Talk:Provençal/Introductions


text: Talk:Provençal/Pronunciation

title: Talk:Provençal/Pronunciation


text: Talk:Provençal/Vocabulary

title: Talk:Provençal/Vocabulary


text: Talk:Prussian

title: Talk:Prussian


text: Talk:Prussian/Accusative Nouns

title: Talk:Prussian/Accusative Nouns


text: Talk:Prussian/Adjective Chart

title: Talk:Prussian/Adjective Chart


text: Talk:Prussian/Clothes Vocabulary

title: Talk:Prussian/Clothes Vocabulary


text: Talk:Prussian/Dative Nouns

title: Talk:Prussian/Dative Nouns


text: Talk:Prussian/Food Vocabulary

title: Talk:Prussian/Food Vocabulary


text: Talk:Prussian/Genitive Nouns

title: Talk:Prussian/Genitive Nouns


text: Talk:Prussian/Lesson 1

title: Talk:Prussian/Lesson 1


text: Talk:Prussian/Nominative Nouns

title: Talk:Prussian/Nominative Nouns


text: Talk:Prussian/Nouns Chart

title: Talk:Prussian/Nouns Chart


text: Talk:Prussian/Personal Pronouns Chart

title: Talk:Prussian/Personal Pronouns Chart


text: Talk:Prussian/Possessive Pronouns Chart

title: Talk:Prussian/Possessive Pronouns Chart


text: Talk:Prussian/Present Verb Conjugation

title: Talk:Prussian/Present Verb Conjugation


text: Talk:Prussian/Pronunciation

title: Talk:Prussian/Pronunciation


text: Talk:Prussian/Prussian - English Vocabulary List


text: Talk:Punjabi/Conversation/ExpressingEmotions


text: Talk:Punjabi/Conversation/IntroducingYourself


text: Talk:Punjabi/Conversation/MakingTelephonicInquiries


text: Talk:Punjabi/Conversation/Parting

title: Talk:Punjabi/Conversation/Parting


text: Talk:Punjabi/Conversation/PlacingTelephonicOrder


text: Talk:Punjabi/Conversation/Shopping

title: Talk:Punjabi/Conversation/Shopping


text: Talk:Punjabi/Culture

title: Talk:Punjabi/Culture


text: Talk:Punjabi/Dictionary/ਣ

title: Talk:Punjabi/Dictionary/ਣ


text: Talk:Punjabi/Dictionary/ਪ

title: Talk:Punjabi/Dictionary/ਪ


text: Talk:Punjabi/Dictionary/ਵ

title: Talk:Punjabi/Dictionary/ਵ


text: Talk:Punjabi/Grammar/Adverb

title: Talk:Punjabi/Grammar/Adverb


text: Talk:Punjabi/Grammar/Conjunction

title: Talk:Punjabi/Grammar/Conjunction


text: Talk:Punjabi/Grammar/Parts of speech

title: Talk:Punjabi/Grammar/Parts of speech


text: Talk:Punjabi/Gurmukhi/Practice

title: Talk:Punjabi/Gurmukhi/Practice


text: Talk:Punjabi/Gurmukhi/Practice/ਅ

title: Talk:Punjabi/Gurmukhi/Practice/ਅ


text: Talk:Punjabi/Gurmukhi/Practice/ਕ

title: Talk:Punjabi/Gurmukhi/Practice/ਕ


text: Talk:Punjabi/Gurmukhi/Practice/ਖ

title: Talk:Punjabi/Gurmukhi/Practice/ਖ


text: Talk:Punjabi/Gurmukhi/Practice/ਗ

title: Talk:Punjabi/Gurmukhi/Practice/ਗ


text: Talk:Punjabi/Gurmukhi/Practice/ਘ

title: Talk:Punjabi/Gurmukhi/Practice/ਘ


text: Talk:Punjabi/Gurmukhi/Practice/ਙ

title: Talk:Punjabi/Gurmukhi/Practice/ਙ


text: Talk:Punjabi/Gurmukhi/Practice/ਚ

title: Talk:Punjabi/Gurmukhi/Practice/ਚ


text: Talk:Punjabi/Gurmukhi/Practice/ਛ

title: Talk:Punjabi/Gurmukhi/Practice/ਛ


text: Talk:Punjabi/Gurmukhi/Practice/ਜ

title: Talk:Punjabi/Gurmukhi/Practice/ਜ


text: Talk:Punjabi/Gurmukhi/Practice/ਝ

title: Talk:Punjabi/Gurmukhi/Practice/ਝ


text: Talk:Punjabi/Gurmukhi/Practice/ਞ

title: Talk:Punjabi/Gurmukhi/Practice/ਞ


text: Talk:Punjabi/Gurmukhi/Practice/ਟ

title: Talk:Punjabi/Gurmukhi/Practice/ਟ


text: Talk:Punjabi/Gurmukhi/Practice/ਠ

title: Talk:Punjabi/Gurmukhi/Practice/ਠ


text: Talk:Punjabi/Gurmukhi/Practice/ਡ

title: Talk:Punjabi/Gurmukhi/Practice/ਡ


text: Talk:Punjabi/Gurmukhi/Practice/ਢ

title: Talk:Punjabi/Gurmukhi/Practice/ਢ


text: Talk:Punjabi/Gurmukhi/Practice/ਣ

title: Talk:Punjabi/Gurmukhi/Practice/ਣ


text: Talk:Punjabi/Gurmukhi/Practice/ਤ

title: Talk:Punjabi/Gurmukhi/Practice/ਤ


text: Talk:Punjabi/Gurmukhi/Practice/ਥ

title: Talk:Punjabi/Gurmukhi/Practice/ਥ


text: Talk:Punjabi/Gurmukhi/Practice/ਦ

title: Talk:Punjabi/Gurmukhi/Practice/ਦ


text: Talk:Punjabi/Gurmukhi/Practice/ਧ

title: Talk:Punjabi/Gurmukhi/Practice/ਧ


text: Talk:Punjabi/Gurmukhi/Practice/ਨ

title: Talk:Punjabi/Gurmukhi/Practice/ਨ


text: Talk:Punjabi/Gurmukhi/Practice/ਪ

title: Talk:Punjabi/Gurmukhi/Practice/ਪ


text: Talk:Punjabi/Gurmukhi/Practice/ਫ

title: Talk:Punjabi/Gurmukhi/Practice/ਫ


text: Talk:Punjabi/Gurmukhi/Practice/ਬ

title: Talk:Punjabi/Gurmukhi/Practice/ਬ


text: Talk:Punjabi/Gurmukhi/Practice/ਭ

title: Talk:Punjabi/Gurmukhi/Practice/ਭ


text: Talk:Punjabi/Gurmukhi/Practice/ਮ

title: Talk:Punjabi/Gurmukhi/Practice/ਮ


text: Talk:Punjabi/Gurmukhi/Practice/ਯ

title: Talk:Punjabi/Gurmukhi/Practice/ਯ


text: Talk:Punjabi/Gurmukhi/Practice/ਰ

title: Talk:Punjabi/Gurmukhi/Practice/ਰ


text: Talk:Punjabi/Gurmukhi/Practice/ਲ

title: Talk:Punjabi/Gurmukhi/Practice/ਲ


text: Talk:Punjabi/Gurmukhi/Practice/ਵ

title: Talk:Punjabi/Gurmukhi/Practice/ਵ


text: Talk:Punjabi/Gurmukhi/Practice/ਸ

title: Talk:Punjabi/Gurmukhi/Practice/ਸ


text: Talk:Punjabi/Gurmukhi/Practice/ਹ

title: Talk:Punjabi/Gurmukhi/Practice/ਹ


text: Talk:Punjabi/Gurmukhi/Practice/ੜ

title: Talk:Punjabi/Gurmukhi/Practice/ੜ


text: Talk:Punjabi/Gurmukhi/Practice/ੲ

title: Talk:Punjabi/Gurmukhi/Practice/ੲ


text: Talk:Punjabi/Gurmukhi/Practice/ੳ

title: Talk:Punjabi/Gurmukhi/Practice/ੳ


text: Talk:Punjabi/Numbers

title: Talk:Punjabi/Numbers


text: Talk:Punjabi/Vocabulary/Festivals

title: Talk:Punjabi/Vocabulary/Festivals


text: Talk:Punjabi/Vocabulary/Jewellery

title: Talk:Punjabi/Vocabulary/Jewellery


text: Talk:Punjabi/Vocabulary/Seasons

title: Talk:Punjabi/Vocabulary/Seasons


text: Talk:Quechua/A1/Lesson 1

title: Talk:Quechua/A1/Lesson 1


text: Talk:Quenya/Duodecimal Numerals

title: Talk:Quenya/Duodecimal Numerals


text: Talk:Quenya/Texts in Quenya

title: Talk:Quenya/Texts in Quenya


text: Talk:Quenya/Texts in Quenya/Aiya María

title: Talk:Quenya/Texts in Quenya/Aiya María


text: Talk:Quenya/Texts in Quenya/Eldar ataformaiti


text: Talk:Quenya/Texts in Quenya/Hríveressë

title: Talk:Quenya/Texts in Quenya/Hríveressë


text: Talk:Quenya/Texts in Quenya/I Yessessë

title: Talk:Quenya/Texts in Quenya/I Yessessë


text: Talk:Quenya/Texts in Quenya/Litany of Loreto


text: Talk:Quenya/Texts in Quenya/Makirya

title: Talk:Quenya/Texts in Quenya/Makirya


text: Talk:Quenya/Texts in Quenya/Namárië - Altariello nainië Loriendessë


text: Talk:Quenya/Texts in Quenya/Ortírielyanna


text: Talk:Quenya/Texts in Quenya/Roccalassen

title: Talk:Quenya/Texts in Quenya/Roccalassen


text: Talk:Quenya/Texts in Quenya/Ríanna

title: Talk:Quenya/Texts in Quenya/Ríanna


text: Talk:Quenya/Texts in Quenya/Átaremma

title: Talk:Quenya/Texts in Quenya/Átaremma


text: Talk:Romanian/Appendix S

title: Talk:Romanian/Appendix S


text: Talk:Romanian/Lesson 11

title: Talk:Romanian/Lesson 11


text: Talk:Romanian/Lesson 12

title: Talk:Romanian/Lesson 12


text: Talk:Romanian/Lesson 6

title: Talk:Romanian/Lesson 6


text: Talk:Romanian/Viitor

title: Talk:Romanian/Viitor


text: Talk:Russian/Appendix/Signs

title: Talk:Russian/Appendix/Signs


text: Talk:Russian/Exercises/Как тебя зовут?

title: Talk:Russian/Exercises/Как тебя зовут?


text: Talk:Russian/Grammar/Adverbs

title: Talk:Russian/Grammar/Adverbs


text: Talk:Russian/Lesson 3/Dative case quiz

title: Talk:Russian/Lesson 3/Dative case quiz


text: Talk:Russian/Lesson 3/This these and those quiz


text: Talk:Russian/Personal Pronouns/Quiz

title: Talk:Russian/Personal Pronouns/Quiz


text: Talk:Russian/Prepositions Instrumental quiz


text: Talk:Russian/Pronouns/Quiz

title: Talk:Russian/Pronouns/Quiz


text: Talk:Russian/Vocabulary/Body Parts

title: Talk:Russian/Vocabulary/Body Parts


text: Talk:Russian/Vocabulary/Cardinal Directions


text: Talk:Russian/Vocabulary/Clothing

title: Talk:Russian/Vocabulary/Clothing


text: Talk:Russian/Vocabulary/Countries

title: Talk:Russian/Vocabulary/Countries


text: Talk:Russian/Vocabulary/Family

title: Talk:Russian/Vocabulary/Family


text: Talk:Russian/Vocabulary/Food

title: Talk:Russian/Vocabulary/Food


text: Talk:Russian/Vocabulary/Music

title: Talk:Russian/Vocabulary/Music


text: Talk:Russian/Vocabulary/Plants and Animals


text: Talk:Sanskrit/Numbers

title: Talk:Sanskrit/Numbers


text: Talk:Sardinian

title: Talk:Sardinian


text: Talk:Sardinian/Alphabet

title: Talk:Sardinian/Alphabet


text: Talk:Sardinian/Articles

title: Talk:Sardinian/Articles


text: Talk:Sardinian/Cardinal numbers

title: Talk:Sardinian/Cardinal numbers


text: Talk:Sardinian/Colours, months and seasons


text: Talk:Sardinian/Interjections

title: Talk:Sardinian/Interjections


text: Talk:Sardinian/Ordinal numbers

title: Talk:Sardinian/Ordinal numbers


text: Talk:Sardinian/Prepositions

title: Talk:Sardinian/Prepositions


text: Talk:Sardinian/Pronounce

title: Talk:Sardinian/Pronounce


text: Talk:Sardinian/Verbs

title: Talk:Sardinian/Verbs


text: Talk:Sardinian/Verbs/All the three conjugations


text: Talk:Sardinian/Verbs/Conjugation of ''ÈSSER''


text: Talk:Sardinian/Verbs/Conjugation of other auxiliary verbs


text: Talk:Sardinian/Verbs/Irregular verbs

title: Talk:Sardinian/Verbs/Irregular verbs


text: Talk:Scottish Gaelic/Grammar

title: Talk:Scottish Gaelic/Grammar


text:
User:TromboneBoi9

Greetings, Wikibooks.

I'm a fluent American English speaker, making some progress in other languages including German, Mandarin Chinese, and Japanese. I've also studied Toki Pona for about a year, and I've been quite active in the language.

I'm mostly into music theory and composition, especially microtonality and alternative tuning systems.

Books I'm contributing to

 * Music Theory
 * possibly a Toki Pona book in the future?

title: User:TromboneBoi9


text: Talk:Scottish Gaelic/Introduction

title: Talk:Scottish Gaelic/Introduction


text: Talk:Scottish Gaelic/Simple Sentences

title: Talk:Scottish Gaelic/Simple Sentences


text: Talk:Serbian/Dialectology

title: Talk:Serbian/Dialectology


text: Talk:Serbian/Introduction

title: Talk:Serbian/Introduction


text: Talk:Serbian/Main Contents/Level 1

title: Talk:Serbian/Main Contents/Level 1


text: Talk:Serbian/Main Contents/Level 1/Lesson 1


text: Talk:Serbian/Main Contents/Level 1/Lesson 11


text: Talk:Serbian/Main Contents/Level 1/Lesson 2


text: Talk:Serbian/Main Contents/Level 1/Lesson 8


text: Talk:Serbian/Main Contents/Level 2

title: Talk:Serbian/Main Contents/Level 2


title: Talk:Sinhala/1.1


title: Talk:Sinhala/1.10


title: Talk:Sinhala/1.3


title: Talk:Sinhala/1.5


title: Talk:Sinhala/1.6


title: Talk:Sinhala/1.8


title: Talk:Sinhala/2.1


title: Talk:Sinhala/2.10


title: Talk:Sinhala/2.2


title: Talk:Sinhala/2.3


title: Talk:Sinhala/2.4


title: Talk:Sinhala/2.5


text: Talk:Sinhala/Alphabet

title: Talk:Sinhala/Alphabet


text: Talk:Slovak

title: Talk:Slovak


text: Talk:Slovak/Introduction

title: Talk:Slovak/Introduction


text: Talk:Slovak/Numbers

title: Talk:Slovak/Numbers


text: Talk:Slovak/Slovak alphabet

title: Talk:Slovak/Slovak alphabet


text: Talk:Slovak/Useful phrases

title: Talk:Slovak/Useful phrases


text: Talk:Slovene/Casing/First-Case

title: Talk:Slovene/Casing/First-Case


text: Talk:Slovene/Nouns

title: Talk:Slovene/Nouns


text: Talk:Slovene/Numbers

title: Talk:Slovene/Numbers


text: Talk:Slovene/Verbs/list

title: Talk:Slovene/Verbs/list


text: Talk:Solresol

title: Talk:Solresol


text: Talk:Solresol/Orthography

title: Talk:Solresol/Orthography


text: Talk:Somali

title: Talk:Somali


text: Talk:Somali/Alphabet

title: Talk:Somali/Alphabet


text: Talk:Somali/Dialects

title: Talk:Somali/Dialects


text: Talk:Somali/Gender

title: Talk:Somali/Gender


text: Talk:Sumerian/List

title: Talk:Sumerian/List


text: Talk:Sumerian/SimpleSigns

title: Talk:Sumerian/SimpleSigns


text: Talk:Swedish/Idrott

title: Talk:Swedish/Idrott


text: Talk:Tagalog/Legends

title: Talk:Tagalog/Legends


text: Talk:Tagalog/Leron-Leron Sinta

title: Talk:Tagalog/Leron-Leron Sinta


text: Talk:Tagalog/Pronouns

title: Talk:Tagalog/Pronouns


text: Talk:Tagalog/Verbs

title: Talk:Tagalog/Verbs


text: Talk:Tahitian

title: Talk:Tahitian


text: Talk:Tahitian/Adjectives

title: Talk:Tahitian/Adjectives


text: Talk:Tahitian/Adverbs

title: Talk:Tahitian/Adverbs


text: Talk:Tahitian/Alphabet and pronunciation


text: Talk:Tahitian/Articles

title: Talk:Tahitian/Articles


text: Talk:Tahitian/Conjunctions

title: Talk:Tahitian/Conjunctions


text: Talk:Tahitian/Date

title: Talk:Tahitian/Date


text: Talk:Tahitian/Determiners

title: Talk:Tahitian/Determiners


text: Talk:Tahitian/Greetings

title: Talk:Tahitian/Greetings


text: Talk:Tahitian/Phrases

title: Talk:Tahitian/Phrases


text: Talk:Tahitian/Possessives

title: Talk:Tahitian/Possessives


text: Talk:Tahitian/Prepositions

title: Talk:Tahitian/Prepositions


text: Talk:Tahitian/Questions

title: Talk:Tahitian/Questions


text: Talk:Tahitian/Sentences

title: Talk:Tahitian/Sentences


text: Talk:Tahitian/Verbs

title: Talk:Tahitian/Verbs


text: Talk:Tahitian/Vocabulario

title: Talk:Tahitian/Vocabulario


text: Talk:Tahitian/Vocabulary

title: Talk:Tahitian/Vocabulary


text: Talk:Tahitian/Weather

title: Talk:Tahitian/Weather


text: Talk:Tahitian/Words

title: Talk:Tahitian/Words


text: Talk:Tajik/Lesson 3

title: Talk:Tajik/Lesson 3


text: Talk:Tajik/Useful Words and Expressions

title: Talk:Tajik/Useful Words and Expressions


text: Talk:Tamil/About

title: Talk:Tamil/About


text: Talk:Tamil/Phonetic Chart

title: Talk:Tamil/Phonetic Chart


text: Talk:Tanchangya/Vocabulary

title: Talk:Tanchangya/Vocabulary


text: Talk:Telugu/Alphabet and Pronunciation

title: Talk:Telugu/Alphabet and Pronunciation


text: Talk:Telugu/Alphabet and Pronunciation/Introduction to consonants


text: Talk:Telugu/Alphabet and Pronunciation/Introduction to vowels


text: Talk:Telugu/Alphabet and Pronunciation/అ ఆ - ఇ ఈ - ఉ ఊ


text: Talk:Telugu/Alphabet and Pronunciation/అ ఆ - ఇ ఈ - ఉ ఊ/Link to Answers


text: Talk:Telugu/Alphabet and Pronunciation/అం అః


text: Talk:Telugu/Alphabet and Pronunciation/ఋ ౠ - ఌ ౡ


text: Talk:Telugu/Alphabet and Pronunciation/ఎ ఏ ఐ - ఒ ఓ ఔ


text: Talk:Telugu/Alphabet and Pronunciation/ఎ ఏ ఐ - ఒ ఓ ఔ/Link to Answers


text: Talk:Telugu/Alphabet and Pronunciation/క ఖ గ ఘ ఙ


text: Talk:Telugu/Alphabet and Pronunciation/క, ఖ, గ, ఘ, ఙ/Link to Answers


text: Talk:Telugu/Animals

title: Talk:Telugu/Animals


text: Talk:Telugu/Colors

title: Talk:Telugu/Colors


text: Talk:Telugu/Fruits

title: Talk:Telugu/Fruits


text: Talk:Telugu/Greetings

title: Talk:Telugu/Greetings


text: Talk:Telugu/Noun

title: Talk:Telugu/Noun


text: Talk:Telugu/Numbers

title: Talk:Telugu/Numbers


text: Talk:Telugu/Pronoun

title: Talk:Telugu/Pronoun


text: Talk:Telugu/Relations

title: Talk:Telugu/Relations


text: Talk:Telugu/Sentence

title: Talk:Telugu/Sentence


text: Talk:Telugu/Talking about oneself

title: Talk:Telugu/Talking about oneself


text: Talk:Telugu/Vegetables

title: Talk:Telugu/Vegetables


text: Talk:Thai/Core vocabulary

title: Talk:Thai/Core vocabulary


text: Talk:Thai/Tone

title: Talk:Thai/Tone


text: Talk:The Latin Language

title: Talk:The Latin Language


text: Talk:The Latin Language/First Declension


text: Talk:The Latin Language/Latin Cases and Gender


text: Talk:The Sakha language

title: Talk:The Sakha language


text: Talk:The Sakha language/Nouns

title: Talk:The Sakha language/Nouns


text: Talk:The Sakha language/Phonology and alphabet


text: Talk:Tibetan/Adjectives

title: Talk:Tibetan/Adjectives


text: Talk:Tibetan/Nouns

title: Talk:Tibetan/Nouns


text: Talk:Tibetan/Pronouns

title: Talk:Tibetan/Pronouns


text: Talk:Tibetan/Verbs

title: Talk:Tibetan/Verbs


text: Talk:Tok Pisin/Amharic

title: Talk:Tok Pisin/Amharic


text: Talk:Tok Pisin/Swedish

title: Talk:Tok Pisin/Swedish


text: Talk:Tokelauan

title: Talk:Tokelauan


text: Talk:Tokelauan/Phrases

title: Talk:Tokelauan/Phrases


text: Talk:Tokelauan/Sentences

title: Talk:Tokelauan/Sentences


text: Talk:Tokelauan/Vocabulary

title: Talk:Tokelauan/Vocabulary


text: Talk:Toki Pona/Constituent order typology


text: Talk:Toki Pona/Morphological typology

title: Talk:Toki Pona/Morphological typology


text: Talk:Turkish/About this book

title: Talk:Turkish/About this book


text: Talk:Turkish/Accusative

title: Talk:Turkish/Accusative


text: Talk:Turkish/Animals

title: Talk:Turkish/Animals


text: Talk:Turkish/Aorist

title: Talk:Turkish/Aorist


text: Talk:Turkish/Big Vocabulary

title: Talk:Turkish/Big Vocabulary


text: Talk:Turkish/Big Vocabulary/Calendar

title: Talk:Turkish/Big Vocabulary/Calendar


text: Talk:Turkish/Big Vocabulary/Family

title: Talk:Turkish/Big Vocabulary/Family


text: Talk:Turkish/Big Vocabulary/Groceries

title: Talk:Turkish/Big Vocabulary/Groceries


text: Talk:Turkish/Big Vocabulary/House

title: Talk:Turkish/Big Vocabulary/House


text: Talk:Turkish/Big Vocabulary/Man

title: Talk:Turkish/Big Vocabulary/Man


text: Talk:Turkish/Causative

title: Talk:Turkish/Causative


text: Talk:Turkish/Compound Verbs

title: Talk:Turkish/Compound Verbs


text: Talk:Turkish/Converbs

title: Talk:Turkish/Converbs


text: Talk:Turkish/Derivation

title: Talk:Turkish/Derivation


text: Talk:Turkish/Grammar/Alphabet and Pronunciation


text: Talk:Turkish/Imperative and Optitative

title: Talk:Turkish/Imperative and Optitative


text: Talk:Turkish/Infinitive

title: Talk:Turkish/Infinitive


text: Talk:Turkish/Kinship

title: Talk:Turkish/Kinship


text: Talk:Turkish/Lesson Nine - Kinship

title: Talk:Turkish/Lesson Nine - Kinship


text: Talk:Turkish/Necessative

title: Talk:Turkish/Necessative


text: Talk:Turkish/Noun Constructions

title: Talk:Turkish/Noun Constructions


text: Talk:Turkish/Passive

title: Talk:Turkish/Passive


text: Talk:Turkish/Pronunciation and Alphabet/Alfabe"Alphabet"


text: Talk:Turkish/imek

title: Talk:Turkish/imek


text: Talk:Tyap

title: Talk:Tyap


text: Talk:Tyap/Adjectives

title: Talk:Tyap/Adjectives


text: Talk:Tyap/Adverbs

title: Talk:Tyap/Adverbs


text: Talk:Tyap/Alphabet

title: Talk:Tyap/Alphabet


text: Talk:Tyap/Articles

title: Talk:Tyap/Articles


text: Talk:Tyap/Conjunctions

title: Talk:Tyap/Conjunctions


text: Talk:Tyap/Interjections

title: Talk:Tyap/Interjections


text: Talk:Tyap/Nouns

title: Talk:Tyap/Nouns


text: Talk:Tyap/Numbering system

title: Talk:Tyap/Numbering system


text: Talk:Tyap/Phonology

title: Talk:Tyap/Phonology


text: Talk:Tyap/Prepositions

title: Talk:Tyap/Prepositions


text: Talk:Tyap/Professions

title: Talk:Tyap/Professions


text: Talk:Tyap/Pronouns

title: Talk:Tyap/Pronouns


text: Talk:Tyap/Tyiet 1/Lesson 1 (Salutations)


text: Talk:Tyap/Tyiet 2/Lesson 2

title: Talk:Tyap/Tyiet 2/Lesson 2


text: Talk:Tyap/Verbs

title: Talk:Tyap/Verbs


text: Talk:Tyap/Vocabulary

title: Talk:Tyap/Vocabulary


text: Talk:Ukrainian/Authors & Contributors

title: Talk:Ukrainian/Authors & Contributors


text: Talk:Ukrainian/Diaspora

title: Talk:Ukrainian/Diaspora


text: Talk:Ukrainian/Glossary

title: Talk:Ukrainian/Glossary


text: Talk:Ukrainian/History

title: Talk:Ukrainian/History


text: Talk:Ukrainian/Religion

title: Talk:Ukrainian/Religion


text: Talk:Ukrainian/Texts

title: Talk:Ukrainian/Texts


text: Talk:Ukrainian/Ukrainian Culture/Naming

title: Talk:Ukrainian/Ukrainian Culture/Naming


text: Talk:Urdu/Elementary Urdu

title: Talk:Urdu/Elementary Urdu


text: Talk:Vietnamese/Classifier

title: Talk:Vietnamese/Classifier


text: Talk:Vietnamese/Demonstratives

title: Talk:Vietnamese/Demonstratives


text: Talk:Vietnamese/Kitchen

title: Talk:Vietnamese/Kitchen


text: Talk:Vietnamese/Lesson 3

title: Talk:Vietnamese/Lesson 3


text: Talk:Vietnamese/Lesson 4

title: Talk:Vietnamese/Lesson 4


text: Talk:Vietnamese/Lesson 6

title: Talk:Vietnamese/Lesson 6


text: Talk:Vietnamese/Mythology

title: Talk:Vietnamese/Mythology


text: Talk:Vietnamese/Predicative Adjective

title: Talk:Vietnamese/Predicative Adjective


text: Talk:Vietnamese/Tourism

title: Talk:Vietnamese/Tourism


text: Talk:Vietnamese/Verb index

title: Talk:Vietnamese/Verb index


text: Talk:Volapük/English-Volapük dictionary

title: Talk:Volapük/English-Volapük dictionary


text: Talk:Wu Chinese

title: Talk:Wu Chinese


text: Talk:Wu Chinese/About Wu

title: Talk:Wu Chinese/About Wu


text: Talk:Wu Chinese/Lesson 1

title: Talk:Wu Chinese/Lesson 1


text: Talk:Yoruba/Adjectives

title: Talk:Yoruba/Adjectives


text: Talk:Yoruba/Adverbs

title: Talk:Yoruba/Adverbs


text: Talk:Yoruba/Conjunctions

title: Talk:Yoruba/Conjunctions


text: Talk:Yoruba/Idioms in Yoruba

title: Talk:Yoruba/Idioms in Yoruba


text: Talk:Yoruba/Nouns

title: Talk:Yoruba/Nouns


text: Talk:Yoruba/Phrases in Yoruba

title: Talk:Yoruba/Phrases in Yoruba


text: Talk:Yoruba/Prepositions

title: Talk:Yoruba/Prepositions


text: Talk:Yoruba/Pronouns

title: Talk:Yoruba/Pronouns


text: Talk:Yoruba/Proverbs in Yoruba

title: Talk:Yoruba/Proverbs in Yoruba


text: Talk:Yoruba/Word order in Yoruba

title: Talk:Yoruba/Word order in Yoruba


text: Talk:Aymara/Alphabet

title: Talk:Aymara/Alphabet


text: Talk:Aymara/Prepositions

title: Talk:Aymara/Prepositions


text: Talk:Bahasa Indonesia

title: Talk:Bahasa Indonesia


text: Talk:Bahasa Indonesia/Affixation

title: Talk:Bahasa Indonesia/Affixation


text: Talk:Basic Ancient Greek/Inflected Forms


text: Talk:Basic Ancient Greek/Uninflected Forms


text: Talk:Basque/First Lesson

title: Talk:Basque/First Lesson


text: Talk:Beginners Guide to Ladino

title: Talk:Beginners Guide to Ladino


text: Talk:Beginners Guide to Ladino/Adjectives in Ladino


text: Talk:Beginners Guide to Ladino/Guide to Reading and Writing Ladino


text: Talk:Beginners Guide to Ladino/Ladino Grammar


text: Talk:Beginners Guide to Ladino/Nouns in Ladino


text: Talk:Beginners Guide to Ladino/Verbs in Ladino


text: Talk:Bosnian

title: Talk:Bosnian


text: Talk:Burmese Grammar Guide/Comparison Of Formal And Colloquial Speech


text: Talk:Burmese Grammar Guide/Emphasis Particles


text: Talk:Burmese Grammar Guide/Numbers

title: Talk:Burmese Grammar Guide/Numbers


text:
Talk:Cambodian Language

Nuon Chea/Pol Pot's Suicide!
His convictions on genocide and crimes against humanity stand[odenglish.news/nuon-cheas-genocide-conviction-stands-but-final-judgement-left-unsaid] 5.189.2.183 (discuss) 15:55, 15 April 2024 (UTC)

title: Talk:Cambodian Language


text: Talk:Cambodian Language/Grammar

title: Talk:Cambodian Language/Grammar


text: Talk:Cambodian Language/Introduction

title: Talk:Cambodian Language/Introduction


text: Talk:Cambodian Language/Writing System

title: Talk:Cambodian Language/Writing System


text: Talk:Classical Meitei

title: Talk:Classical Meitei


text: Talk:Classical Meitei/Authors & Contributors


text: Talk:Classical Meitei/Common terms

title: Talk:Classical Meitei/Common terms


text: Talk:Classical Meitei/Verb list

title: Talk:Classical Meitei/Verb list


text: Talk:Globish

title: Talk:Globish


text: Talk:Globish/Lesson I: Alphabet

title: Talk:Globish/Lesson I: Alphabet


text: Talk:Greenlandic/Introducing yourself

title: Talk:Greenlandic/Introducing yourself


text: Talk:Greenlandic/The Greenlandic alphabet


text: Talk:Hong Kong Cantonese

title: Talk:Hong Kong Cantonese


text: Talk:Hong Kong Cantonese/Examples/OK

title: Talk:Hong Kong Cantonese/Examples/OK


text: Talk:Hong Kong Cantonese/Examples/creamy


text: Talk:Hong Kong Cantonese/Examples/fit

title: Talk:Hong Kong Cantonese/Examples/fit


text: Talk:Hong Kong Cantonese/Examples/friend


text: Talk:Hong Kong Cantonese/Examples/juicy

title: Talk:Hong Kong Cantonese/Examples/juicy


text: Talk:Hong Kong Cantonese/Examples/special


text: Talk:Hong Kong Cantonese/Examples/sure

title: Talk:Hong Kong Cantonese/Examples/sure


text: Talk:Hong Kong Cantonese/Examples/up

title: Talk:Hong Kong Cantonese/Examples/up


text: Talk:Hong Kong Cantonese/Introduction

title: Talk:Hong Kong Cantonese/Introduction


text: Talk:How to Teach a Language/Consider Your Audience


text: Talk:How to Teach a Language/English

title: Talk:How to Teach a Language/English


text: Talk:Hungarian/Offensive

title: Talk:Hungarian/Offensive


text: Talk:Høgnorsk/Grammatical genders

title: Talk:Høgnorsk/Grammatical genders


text: Talk:Interlingua/On the Grammar of Interlingua


text: Talk:Interlingua/Profanity

title: Talk:Interlingua/Profanity


text: User:Thierry Dugnolle/Python/Interference of a particle with itself


text:
User:Iketsi/common.js

/** * Direct imagelinks to Commons * * Required modules: mediawiki.util * * @source https://www.mediawiki.org/wiki/Snippets/Direct_imagelinks_to_Commons * @author Krinkle * @version 2022-09-06 */ if ( mw.config.get( 'wgNamespaceNumber', 0 ) >= 0 ) { mw.loader.using( [ 'mediawiki.util' ] ).then( function {		mw.hook( 'wikipage.content' ).add( function ( $content ) { var uploadBaseRe = /^(https:)?\/\/upload\.wikimedia\.org\/wikipedia\/commons/, localFileNSString = mw.config.get( 'wgFormattedNamespaces' )['6'] + ':', localBasePath = new RegExp( '^' + mw.util.escapeRegExp( mw.util.getUrl( localFileNSString ) ) ), localBaseScript = new RegExp( '^' + mw.util.escapeRegExp( mw.util.wikiScript + '?title=' + mw.util.wikiUrlencode( localFileNSString ) ) ),				commonsBasePath = 'https://commons.wikimedia.org/wiki/File:', commonsBaseScript = 'https://commons.wikimedia.org/w/index.php?title=File:';

$content.find( 'a.image, a.mw-file-description' ).attr( 'href', function ( i, currVal ) {				if ( uploadBaseRe.test( $( this ).find( 'img' ).attr( 'src' ) ) ) {					return currVal						.replace( localBasePath, commonsBasePath )						.replace( localBaseScript, commonsBaseScript );				}			} ); } );	} ); }

title: User:Iketsi/common.js


text: User talk:Epicyatra56

title: User talk:Epicyatra56


text: User:Thierry Dugnolle/Python/Cantor Set Expansion


text: User:Thierry Dugnolle/Infinite Binary Tree


text:
Talk:Metaphysical Arts and Crafts/Crystal glove holder

Intention of this practice
The intention of this laboratory practice is to obtain the skills require to design, sew and create a glove that will also serve as a crystal holder. The glove could also hold other objects instead.

The metaphysical side of the practice comes from the energy and radiation that emanates from the crystal and the experience of the user while using a crystal or other object inside the glove, that could be seen as just folk believes.

Another use of the glove would be to serve as part of a custom for the upcoming Samhain and Halloween celebrations. Metaphysical artcrafts (discuss • contribs) 21:49, 26 August 2023 (UTC)


text: User:Thierry Dugnolle/Python/Wave-packet2


text:
User talk:129.63.91.8

Attention:

This, is registered to University of Massachusetts - Lowell and may be shared by multiple users. If the institution uses proxy servers, this IP address may represent many users at many physical computers.

For this reason, a message intended for one person may be received by another. Similarly, an innocent user may be blocked for another user's vandalism. If you are editing from this address and are frustrated by irrelevant messages, you can avoid them by creating an account for yourself. In some cases you may temporarily be unable to create an account due to efforts to deal with vandalism. Caution should be used when blocking this IP or reverting its contributions without checking - if a block is needed, administrators should consider a soft block

Two pages you recently created: Todd in the Shadows/Year-End Justin Bieber Songs and Todd in the Shadows/Year-End Lists/Publish Times have been deleted. They are not suitable for Wikibooks. Please do not add endless lists like this to Wikibooks. Please read Using Wikibooks to find out more about contributing to this project.--Xania   talk 01:23, 27 August 2023 (UTC)

Waiting periods of music videos
This page has been deleted. This is not suitable for Wikibooks. Future bad page creations will result in your IP address being blocked from editing.--Xania   talk 07:58, 23 February 2024 (UTC)

Merriam Webster/Benefit
This page has been deleted. This is Wikibooks, not Wiktionary. Please read Using Wikibooks to learn about this project. Future bad page creations may result in you being blocked from editing.--Xania   talk 03:13, 7 March 2024 (UTC)

Blocked
You cannot edit for 7 days due to disruptive editing. You are welcome to contribute constructively when editing privileges are restored. You may appeal this action with a reasonable argument by adding the text below.

--Xania   talk 03:43, 31 March 2024 (UTC)

title: User talk:129.63.91.8


text:
Python Programming/Cond

It is used to collect 4 numerical data from the user via multi-function keypad. Plus, plus, sum, display results and search...

title: Python Programming/Cond


text: User:Thierry Dugnolle/The whole infinite tree


text:
Modular Arithmetic/Lagrange's Theorem

(WIP)

title: Modular Arithmetic/Lagrange's Theorem


text: Talk:Units of Measurement/Density

title: Talk:Units of Measurement/Density


text:
Metaphysical Arts and Crafts/The sound of silence

This laboratory practice is part of the coursing class; A course as a change that can alter or define an object, person or society. It is an internal or introspective practice, since it requires the person to look an observe its own though process and feelings when interact with external stimuli and the reactions to them.

The universe is a three-dimensional space and to our eyes and mind exists in a fourth dimension, the time, the universe has at least four dimensions, everything moves with inertia, the objects move and change their course

For millennia many cultures defined how to act and react in a given situations using scriptures since they can "speak" 24 hours a day during the whole year, they were used as mass control using fear, belonging, capital punishment and exile to the citizens that do not act as written. Among these first books can be named the Sumerian Epic of Gilgamesh, other civilizations copied their formula to allow their civilizations to flourish. Nowadays mass media is used as a way to program how people is expecting to act and react, in this way they are being converted in a fourth dimensional objects, while at the same time loose their own conscience. This has the power of making people to live more as an object (4D) than a person in full control of its own benefit, desires and future (5D).

Metaphysical aspects of the practice: Speaking has a motivation, it has been programmed by society of by individuals, this speaking make us believe that the talks we speaks and how we speak is what we are, it define us in a trap that keep us being view and identified of that of what we speak, do, act, react or work or how we are currently behaving, this gave us a course that benefits other people o sometimes ourselves, and that we can continue or that we can correct and change at will.

= The practice =

The laboratory consist in a 3 days of practice where the practitioner will observe its own behavior, feelings, reactions of its won body and mind to different stimuli, and the interactions and social dynamic of its relations and environment.

Day one
This is an observational day, we will see the actions and interactions during the day observing the own "desires", the motivations, the triggers and the reactions.

Second day
The second two days will be 2 days of silence: We will live our day with our inner best intentions, and at the same time we will allow to not speak or speak the minimum necessary and use that time to identify provocations, triggers, cultural traps and to plan an re-plan our present and future for our personal growth. We are going to study how are we acting, how are we being, how are we feeling and any external control or misuse of this elements, this will allow us to identify how are we acting and will allow to redefine ourselves and to make some changes to act in our personal safety, growth and benefit.

Third day
We will improve the practice of the second day.

= Results =

Observation: This practice will allow us to identify unseen controls that were placed in our mental process using culture control, "friendship" and conversations with the objective of make us believe and even speak ideas or believes that where not original part of our way of thinking or behaving, in order to attain the change of perspective of the intended target, giving in this way a change of course or route to the direction that we originally were en-routed, using our own brain, mental processes and talks to generate a inertia to think, believe and behave in ways that benefits a third parting for fun of economic interest, and at the same time make us loose the choose of better options or futures for our won personal, educational, professional or financial benefit.

= See also =

Metaphysical artcrafts laboratory


text:
Talk:Metaphysical Arts and Crafts/The sound of silence

Motivation for the creation of this laboratory practice
The intention of this practice is to allow the practitioner to retake control of its own behavior, and of the present and future of its life for its own benefit. Metaphysical artcrafts (discuss • contribs) 18:03, 28 August 2023 (UTC)


text: Talk:Adventist Adventurer Awards and Answers/Alphabet Fun


text:
User talk:BTWEvans

Welcome
Welcome, BTWEvans!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally.

--Xania   talk 01:22, 29 August 2023 (UTC)

title: User talk:BTWEvans


text:
Public Digital Backbone/2. History in the Making

= 2. History in the Making = Introduction:

India's journey in building an extensive digital infrastructure stands out as a remarkable achievement on the global stage. Here we chronicle the nation's strides in this domain, highlighting the catalysts for change, the challenges faced, and the milestones achieved. The aim is to provide a comprehensive overview of India's success story and its implications for other countries aiming to build similar infrastructures.

*

'''"India is going from an offline, informal, low productivity, multiple set of micro economies to a single online, formal, high productivity mega-economy. And this is the trend of the next 20 years..." -Nandan Nilekani, Founding Chairman of Aadhaar Project.'''

“There is now a major move afoot to take this model to 50 countries in five years,” Nilekani said, speaking at the B20 Summit in the national capital. “So over the next few years, you will see the proliferation of how this new way of thinking about digital infrastructure at population scale, using an open architecture, is going to be more and more ubiquitous and prevalent around the world,” Nilekani said.

India, a land of diverse cultures, traditions, and languages, has always held a spirit of adaptability at its core. As the world hurtled into the digital age, India too began crafting its path, resulting in the formidable ascent of digital public infrastructure. The journey is as much about technological innovation as it is about reimagining governance.

The Starting Block: Aadhaar

Our tale begins with an ambitious project in 2009 – Aadhaar. India decided to give a unique identification number to each of its 1.3 billion residents. Critics wondered: could a nation with vast illiterate populations, lacking basic amenities, pull off such an ambitious feat?

Yet, by 2017, over a billion people had their biometric data registered. An anecdote often shared is of an elderly woman in a remote village, who for the first time had an identity outside her family – her Aadhaar card. For many, it wasn’t just an ID; it was a symbol of belonging.

Banking the Unbanked: Jan Dhan Yojana

Aadhaar paved the way for Jan Dhan Yojana in 2014, aiming to ensure financial inclusion. With the Aadhaar card as identification, millions opened their first bank accounts. In a poignant moment, a vegetable vendor in Bihar expressed his joy saying, "For the first time, a bank recognized me."

A Tryst with Digital Transactions: UPI

The Unified Payments Interface (UPI) story is nothing short of revolutionary. Launched in 2016, it made digital transactions as easy as sending a text. A tea seller in Pune amusingly recalled, "People used to ask for change, now they just ask for my UPI ID!" By 2021, UPI recorded transactions worth 5 trillion rupees in a single month.

A Transparent Approach: GST and e-Way Bill

2017 marked a landmark year with the introduction of the Goods and Services Tax (GST), aiming to unify the nation's complex tax structure. The accompanying e-Way Bill system ensured real-time tracking of goods movement. A cloth merchant from Rajasthan fondly remembers the pre-GST era, jesting, "We had more tax calculations than cloth patterns! Now it's simpler."

Towards a Digital Health Revolution: National Digital Health Mission

2020 was a challenging year for the world. But amidst the pandemic, India announced the National Digital Health Mission. With a vision to digitize health records and ensure efficient health service delivery, this initiative promised a future where medical consultations, prescriptions, and records would all be a click away.

Digital Literacy: Bridging the Digital Divide

While these initiatives created waves, the grassroots movement of digital literacy deserves a mention. Rural digital literacy campaigns transformed young children into village heroes. A popular story speaks of a 12-year-old teaching her grandmother to video-call her son in the city, bridging miles and generations.

As India continues to stride towards a digital future, these anecdotes remind us that at the heart of this transformation is the common citizen. Their stories, their adaptations, and their aspirations. With each digital step, India isn't just adopting technology; it's crafting history.


text:
Public Digital Backbone/3. India Stack:Plumbing for the Internet Age

= 3. India Stack: Plumbing for the Internet Age =

Introduction:

India Stack represents a suite of groundbreaking digital services that have transformed the subcontinent's digital landscape. From the world's largest biometric system to real-time payment platforms, we provide here an in-depth exploration of the elements that make up India Stack, emphasizing their individual and collective impact on the country's digital revolution

*

Overview of India Stack components
India Stack is a comprehensive digital infrastructure initiative by the Indian government, designed to foster innovation and streamline services across the country. It comprises key components like Aadhaar, a unique identity number for residents; UPI, a real-time inter-bank transaction system; eKYC for electronic identity verification; eSign for digital signatures; DigiLocker for storing and sharing personal documents; the Consent Layer for user-controlled data sharing; Account Aggregator for seamless access to financial data; and FASTag, an electronic toll collection system. Together, these tools aim to transition India towards a presence-less, paperless, and cashless service delivery model, enhancing transparency and efficiency in both governance and the private sector.

Aadhaar: Biometric Identification
Aadhaar is India's flagship program that provides a unique 12-digit identification number to its residents based on their biometric and demographic information. Initiated by the Unique Identification Authority of India (UIDAI), the program is one of the largest biometric identification systems globally. Biometric data collected for Aadhaar includes fingerprints, iris scans, and a facial photograph. This biometric data, combined with demographic information like name, date of birth, and address, ensures a unique identity for each individual. The primary objective of Aadhaar is to eliminate duplicates and fake identities and to enable various public and private services in a streamlined manner. The biometric nature of Aadhaar ensures secure identity verification, reducing fraud and ensuring that benefits and services reach the genuine beneficiaries.

UPI: Real-Time Payment System
UPI, or Unified Payments Interface, is a revolutionary real-time payment system developed by the National Payments Corporation of India (NPCI). It facilitates instant inter-bank transactions by enabling funds transfer between two bank accounts through a mobile platform. UPI allows users to link multiple bank accounts to a single mobile application, merging several banking features into one seamless interface. Payments can be made using a unique UPI ID, mobile number, or even by scanning QR codes. The platform also supports features like scheduling payments and checking account balance. With its simple and efficient user experience, UPI has transformed the digital payments landscape in India, promoting a move towards a cashless economy.

DEPA: Data Empowerment and Protection Architecture
DEPA, or the Data Empowerment and Protection Architecture, is an innovative framework introduced in India to redefine the way personal data is shared and consumed. The primary objective of DEPA is to empower individuals to have control over their own data, ensuring that it's used for their benefit while also protecting their privacy.

1. Data Empowerment: DEPA emphasizes the principle that individuals have rights over their data. It provides mechanisms through which individuals can securely access and share their information with entities that offer services, leading to better financial and health outcomes, among others.

2. Data Protection: While ensuring data fluidity, DEPA also places paramount importance on privacy and security. The framework ensures that data is shared only after receiving explicit consent from individuals, and it is transmitted through encrypted channels to prevent misuse.

3. Account Aggregators (AAs): Within the DEPA framework, AAs play a pivotal role. They are neutral entities that facilitate the secure and consented sharing of data between data providers (like banks) and data consumers (like lending institutions). Individuals can instruct AAs to retrieve and share their data without the actual data ever being seen or stored by the AAs.

4. Consent Artifacts: These are digital records of individual consents, capturing the specifics of permission given (like the type of data, purpose, duration, etc.). Consent artifacts ensure that data is used only for purposes the individual has explicitly agreed to.

DEPA aims to strike a balance between the transformative potential of a data-driven economy and the individual's data rights and privacy. The framework forms a significant component of the India Stack, enabling more transparent, efficient, and user-centric digital services across sectors.

Evolution and impact of India Stack

The evolution and impact of India Stack is a remarkable journey that has reshaped the landscape of digital services and governance in India. Let's delve into its evolution and the subsequent effects:

Evolution:

1. Aadhaar (2009): The inception of India Stack began with the launch of Aadhaar by the Unique Identification Authority of India (UIDAI). It provided a 12-digit unique identity number based on biometric and demographic data to Indian residents.

2. eKYC and eSign (2012 and 2015): With the foundation laid by Aadhaar, eKYC (Electronic Know Your Customer) was introduced to simplify identity verification processes for businesses, followed by eSign, which enabled digital signatures based on Aadhaar.

3. Unified Payments Interface (UPI) (2016): The NPCI launched UPI, providing an instant real-time payment system that connected different bank accounts into a single mobile application.

4. DigiLocker (2016): Aimed at digitizing and democratizing document storage and sharing, DigiLocker was launched, allowing citizens to securely store and share digital versions of critical documents.

5. DEPA and Account Aggregators (2018 onwards): The concept of DEPA introduced data empowerment and protection, with Account Aggregators becoming crucial intermediaries for consented data sharing.

Impact:

1. Financial Inclusion: India Stack, especially UPI and eKYC, has played a significant role in expanding financial services to previously unbanked or underbanked segments of the population.

2. Paperless Transactions: With eSign and DigiLocker, paper-based processes have been drastically reduced, leading to faster service delivery and reduced costs for businesses and government.

3. Transparency and Efficiency: Data-driven components like Account Aggregators foster transparency, reducing fraud and ensuring that benefits reach the intended recipients.

4. Boost to Digital Economy: UPI's success has catalyzed the growth of numerous fintech startups and digital services in India, propelling the nation towards a cashless economy.

5. User Empowerment: DEPA and Consent Layer ensure that individuals have control over their data, fostering trust and encouraging more users to engage with digital services.

6. Government Services: Various government services, from subsidies to scholarships, now leverage India Stack components for efficient, transparent, and direct benefit transfers.

India Stack's evolution represents a progressive and integrated approach to addressing India's challenges using digital infrastructure. Its impact has been transformative, affecting various sectors, from finance to health, and empowering both businesses and consumers in the digital age.


text:
User talk:2600:387:C:2C15:0:0:0:1

--Xania   talk 06:53, 29 August 2023 (UTC)

title: User talk:2600:387:C:2C15:0:0:0:1