OpenLLM-France/wikimedia huggingface dataset:
# Electronics Fundamentals/Transistor Circuit
## Analysis

    $V_{B}=V_{i}{\frac {R_{2}}{R_{2}+R_{1}}}$
    $V_{E}=V_{B}-0.7=V_{B}$
    $I_{E}={\frac {V_{E}}{R_{4}}}={\frac {V_{B}}{R_{4}}}$
    $I_{C}=I_{E}$
    $V_{C}=I_{C}R_{4}$
    $V_{C}=V_{i}[1-({\frac {R_{3}}{R_{4}}})({\frac {R_{2}}{R_{2}+R_{1}}})]$
* Khi R$_3$ = Khi R$_4$
    $V_{C}=V_{i}(1-{\frac {R_{2}}{R_{2}+R_{1}}})$
    $V_{C}=0$ khi R$_2$ >> R$_1$
    $V_{C}=1$ khi R$_2$ = 0
Trăng si tơ hoạt động như Công Tắc Điện Tử . Công tắc đóng khi R$_2$ = 0 . Công tắc mở khi R$_2$ >> R$_1$
* Khi R$_2$ >> R$_1$
    $V_{C}=V_{i}(1-{\frac {R_{3}}{R_{4}}})$
    $V_{C}=0$ khi R$_3$ = R$_4$
    $V_{C}=1$ khi R$_3$ = 0
    $V_{C}=-1$ khi R$_3$ = 2R$_3$
    $V_{C}=-n$ khi R$_3$ = (n+1)R$_3$
Trăng si tơ hoạt động như Khuếch Đại Điện Âm . Với Khuếch đại n R$_3$ = (n=1) R$_4$

## Summary

    $V_{C}=V_{i}[1-({\frac {R_{3}}{R_{4}}})({\frac {R_{2}}{R_{2}+R_{1}}})]$
* Khi R$_2$ >> R$_1$ then
    $V_{C}=V_{i}(1-{\frac {R_{3}}{R_{4}}})$
    $V_{C}=-n$ khi R$_3$ = (n+1)R$_3$
Transistor operates as Inverting amplifier
* Khi R$_3$ = Khi R$_4$, then
    $V_{C}=V_{i}(1-{\frac {R_{3}}{R_{4}}})$
    $V_{C}=0$ khi R$_2$ >> R$_1$
    $V_{C}=1$ khi R$_2$ = 0
Transistor operates as a closed switch when R$_2$ >> R$_1$ as a opened switch when R$_2$ = 0
# Electronics Handbook/Circuits/High-pass Filter
## High Pass Filter

Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency

## RC Configuration
### Vo / Vi

    ${\frac {V_{o}}{V_{i}}}={\frac {Z_{R}}{Z_{R}+Z_{C}}}={\frac {R}{{\frac {1}{j\omega C}}+R}}={\frac {j\omega CR}{1+j\omega CR}}=j\omega T{\frac {1}{1+j\omega T}}$
    T = RC

### Frequency Response

    ω = 0ω = ${\frac {1}{RC}}$ω = 00 $V_{o}=0$$V_{o}=V_{i}/2$$V_{o}=V_{i}$
Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency

## RL Configuration
### Vo/Vi

    ${\frac {V_{o}}{V_{i}}}={\frac {Z_{L}}{Z_{R}+Z_{L}}}={\frac {j\omega L}{R+j\omega L}}=j\omega T{\frac {1}{1+j\omega T}}$ .
    $T={\frac {L}{R}}$

### Frequency Response

    ω = 0$\omega ={\frac {R}{L}}$ω = 00 $V_{o}=V_{i}$$V_{o}=V_{i}$$V_{o}=0$
Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency .

## Summary

* High Pass Filter Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency
* High Pass Filter can be constructed from RC or RL
* High Pass Filter has a general formula
    ${\frac {V_{o}}{V_{i}}}=j\omega T{\frac {1}{1+j\omega T}}$
    T = RC = R / L
* Angle Difference Tan θ = j ω T
# Electronics Fundamentals/Semi Conductor Devices/Transistor/NPN Transistor
## NPN Transistor

NPN Transistor is a Semi Conductor Device made from Semi Conductor materials which has 3 pins Base, Collector, Emmiter forming 2 junctions namely BE and CE

## NPN Transistor

NPN Transistor is made by joining one Positive-Typed Semi Conductor in between two Negative-Typed Semi Conductors
# Electronics Fundamentals/Semi Conductor Devices/Transistor/PNP Transistor
## PNP Transistor

PNP Transistor is a Semi Conductor Device made from Semi Conductor materials which has 3 pins Base, Collector, Emmiter forming 2 junctions namely BE and CE

## Construction

PNP Transistor is made by joining one Nagative-Typed Semi Conductor in between two Positive-Typed Semi Conductors
# Electronics Handbook/Circuits/Current Divider
## Current Divider

If two elements are in parallel, the voltage across them must be the same, but the current divides according to the resistances. A simple circuit with two (or more) resistors in parallel with a source is called a current divider.
Figure B: Parallel Resistors.

## Mathmatic Formula

If a voltage V appears across the resistors in Figure B with only $R_{1}$ and $R_{2}$ for the moment then the current flowing in the circuit, before the division, i is according to Ohms Law.
    $i={\frac {V}{R_{eq}}}$
Using the equivalent resistance for a parallel combination of resistors is
    $i={\frac {V(R_{1}+R_{2})}{R_{1}R_{2}}}$ (1)
The current through $R_{1}$ according to Ohms Law is
    $i_{1}={\frac {V}{R_{1}}}$ (2)
Dividing equation (2) by (1)
    $i_{1}={\frac {iR_{2}}{R_{2}+R_{1}}}$
Similarly
    $i_{2}={\frac {iR_{1}}{R_{2}+R_{1}}}$
In general with n Resistors the current $i_{x}$ is
    $i_{x}={\frac {iR_{1}R_{2}\cdots R_{n}}{(R_{2}\cdots R_{n}+\cdots +R_{1}\cdots R_{n-1})R_{x}}}$
Or possibly more simply
    ${\frac {i_{x}}{i}}={\frac {R_{eq}}{R_{x}}}$
Where
    $R_{eq}={\frac {R_{1}\cdots R_{n}}{R_{2}\cdots R_{n}+\cdots +R_{1}\cdots R_{n-1}}}$
# Electronics Handbook/Circuits/LC Series
## LC Series Configuration

Picture

## Circuit Analysis
### Circuit's Impedance

    $Z=Z_{L}+Z_{C}$
    Z = ω L /_90 + ${\frac {1}{\omega C}}$/_-90
* $Z_{L}>Z_{C}$
    Z = Z_L - Z_C/_90
* $Z_{L}<Z_{C}$
    Z = Z_C - Z_L/_-90
* $Z_{L}=Z_{C}$
    Z = 0 /_ 0

### Natural Response

    $L{\frac {dI}{dt}}+{\frac {1}{C}}\int Idt=0$
    ${\frac {dI}{dt}}+{\frac {1}{LC}}\int Idt=0$
    ${\frac {d^{2}I}{dt^{2}}}+{\frac {1}{LC}}=0$
    $s^{2}=-{\frac {1}{LC}}$
    s = ± ${\sqrt {-{\frac {1}{LC}}}}t$ = ± j ${\sqrt {\frac {1}{LC}}}t=\pm j\omega t$
The Second Ordered Equation has two imaginary roots
    $I=e^{j}\omega t+e^{-}j\omega t$
    $I=ASin\omega t$
The natural response of the LC series is a Sinusoidal Wave . Therefore, LC series can be used as a Sin Wave Oscillator

### Resonance Response

Resonance occurs in the circuit when $Z_{L}-Z_{C}=0.V_{C}+V_{L}=0$
* $Z_{C}=Z_{L}$
    $\omega L={\frac {1}{\omega C}}$
    $\omega ={\sqrt {\frac {1}{LC}}}$
* $V_{L}+V_{C}=0$
    $V_{L}=-V_{C}$
At Resonance, the LC series has the capability to generate Standing Wave Oscillation

## Summary

LC series has a second order equation of current with two imaginaries roots
    $I(t)=e^{j\omega t)+e^{-j\omega t)$
Which generates Sin Wave Oscillation
    $I(t)=ASin\omega t$
    $\omega ={\sqrt {\frac {1}{T}}}$
    T = LC
At resonance, Impedance of Inductor and Capacitor cancel out
    Z$_L$ = Z$_C$
    $\omega ={\sqrt {\frac {1}{LC}}}$
Which generates Standing Wave Oscillation
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...Ngf6/5. dxe5/5...dxe5/6. Ng5
## 6.Ng5

This simple move forces resignation since Black cannot guard f7.
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7/6. Bxf7/6...Kf8/7. Ne6
## 7.Ne6+

This simple move forks the queen and leaves white up material to the good.

## Theory table

| 7 | |
| Kxf7 Nxd8+ | +- |
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7/6. Bxf7/6...Kf8/7. Ne6/7...Kxf7
## 7...Kxf7

This move captures the bishop, but drops the queen with check. Unfortunately, it is his only legal move.

## Theory table

| 8 | |
| Nxd8+ | +- |
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7/6. Bxf7/6...Kxf7
## 6...Kxf7

This move accepts the sacrifice. White needs to find another brilliant move to win.

## Theory table

| 7 | 8 | 9 | |
| Ne6!! Kxe6 | Qd5+ Kf6 | Qf5# | 1-0 |
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7/6. Bxf7/6...Kf8
## 6...Kf8

This move declines the sacrifice, but actually makes white's winning combination easier. The simple Ne6+ forks the king and queen.

## Theory table

| 7 | 8 | |
| Ne6+ Kxf7 | Nxd8+ | +- |
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7
## 5...Be7?

The position after 1. e4 e5 2. Nf3 d6 3. d4 Nd7 4. Bc4 exd4 5. Nxd4 is a critical juncture for Black. The seemingly natural move 5...Be7? is a blunder, and 5...Ngf6 is a safer and superior alternative.
White can exploit the blunder with 6. Bxf7+!, intending to win the Black's queen with 7. Ne6 and 8. Nxd8+.
The move Bxf7+ is beneficial for several reasons:
* It sets up the Ne6 threat, prevents the defense of e6 with fxe6, and captures the black pawn on f7.
* The white knight on d4 can move to e6 to capture the black queen on d8.
* The white knight threatens the black queen on d8.
* White utilizes the a2-g8 diagonal to capture the black pawn on f7.
* Additionally, White can consider playing Qd5, while Black can play g6 and use the 8th rank to control the square d8 with the rook on h8.

## Theory table

1. e4 e5 2. Nf3 d6 3. d4 Nd7 4. Bc4 exd4 5. Nxd4 Be7?
| | 6 | 7 | 8 | 9 |
| Hanham Variation | Bxf7+!! Kxf7 | Ne6!! Kxe6 | Qd5+ Kf6 | Qf5# | 1-0 |
When contributing to this Wikibook, please follow the Conventions for organization.
Bibliography
* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
* Kaufman, Larry (2004). The Chess Advantage in Black and White. ISBN 0-8129-3571-3.
* Panov, Vasily (1973). Teoría de Aperturas, Tomo I: Aperturas Abiertas - Aperturas Semiabiertas. ISBN 84-270-0132-0.
* Schiller, Eric (2002). Standard Chess Openings. ISBN 1-58042-048-6.

#### External links

* Chargemax Entertainment (2022). Chess For Beginners: Anand & Topalov easily get an edge vs Philidor Hanham variation.
* ChessBase (2023). Philidor Defence.
* Chess Openings for Beginners (2009). Philidor Defense: General Information.
* ChessPathways (2019). PHILIDOR DEFENSE.
* ChessPathways (2019). The Philidor Defense.
* Chess Simplified (2019). Philidor Defence.
* HangingPawns (2019). Introduction to the Philidor Defense.
* Hrishi Chavan (2022). Philidor Defence - Hanham Variation.
* Marsh, Sean (ChessAble) (2021). Chess Opening Basics: The Philidor Defense.
* Miodrag Perunovic (2019). Chess For Beginners: Anand & Topalov easily get an edge vs Philidor Hanham variation.
* Nicolas Skettos (2022). How To Beat The Philidor Defense - Hanham Variation - Black Lion - Chess Opening Traps.
* papachess.com (2024). papachess.com, Nimzowitsch's Unbeatable Weapon: Philidor Defense.
* papachess.com (2024). papachess.com, Philidor Defense: Nimzowitsch Variation, Rellstab Variation, move by move.
* Prem, Krishna (2012). Chess openings - Philidor Defence.
* Sean Lei (2020). My Precious "Philidor". Philidor and Lion Defence Chess.
* Solomon, Ruddell (TheChessGiant) (2021). Chess Openings: Learn to Play the Philidor Defense!.
* The Chess Website (2012). Philidor Defense - Chess Openings.
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7/6. Bxf7
## 6.Bxf7+!!

This move is a crushing sacrifice. Black loses his queen whether he accepts it or declines it.

## Theory table

| 6 | 7 | 8 | |
| Kxf7 Ne6 | Kxe6 Qd5+ | Kf6 Qf5# | 1-0 |
| Kf8 Ne6+ | Kxf7 Nxd8+ | | +- |
# Chess Opening Theory/1. e4/1...e5/2. Nf3/2...d6/3. d4/3...Nd7/4. Bc4/4...exd4/5. Nxd4/5...Be7/6. Bxf7/6...Kf8/7. Ne6/7...Kxf7/8. Nxd8
## 8.Nxd8+

This simple move wins the queen with check. Black is down a decisive amount of material.
# Engineering Tables/Z Transform Properties

| | Time domain | Z-domain | ROC |
| Notation | $x[n]={\mathcal {Z}}^{-1}\{X(z)\}$ | $X(z)={\mathcal {Z}}\{x[n]\}$ | ROC: $r_{2}<|z|<r_{1}\$ |
| Linearity | $a_{1}x_{1}[n]+a_{2}x_{2}[n]\$ | $a_{1}X_{1}(z)+a_{2}X_{2}(z)\$ | At least the intersection of ROC$_1$ and ROC$_2$ |
| Time shifting | $x[n-k]\$ | $z^{-k}X(z)\$ | ROC, except $z=0\$ if $k>0\,$ and $z=\infty$ if $k<0\$ |
| Scaling in the z-domain | $a^{n}x[n]\$ | $X(a^{-1}z)\$ | $|a|r_{2}<|z|<|a|r_{1}\$ |
| Time reversal | $x[-n]\$ | $X(z^{-1})\$ | ${\frac {1}{r_{2}}}<|z|<{\frac {1}{r_{1}}}\$ |
| Conjugation | $x^{*}[n]\$ | $X^{*}(z^{*})\$ | ROC |
| Real part | $\operatorname {Re} \{x[n]\}\$ | ${\frac {1}{2}}\left[X(z)+X^{*}(z^{*})\right]$ | ROC |
| Imaginary part | $\operatorname {Im} \{x[n]\}\$ | ${\frac {1}{2j}}\left[X(z)-X^{*}(z^{*})\right]$ | ROC |
| Differentiation | $nx[n]\$ | $-z{\frac {\mathrm {d} X(z)}{\mathrm {d} z}}$ | ROC |
| Convolution | $x_{1}[n]*x_{2}[n]\$ | $X_{1}(z)X_{2}(z)\$ | At least the intersection of ROC$_1$ and ROC$_2$ |
| Correlation | $r_{x_{1},x_{2}}(l)=x_{1}[l]*x_{2}[-l]\$ | $R_{x_{1},x_{2}}(z)=X_{1}(z)X_{2}(z^{-1})\$ | At least the intersection of ROC of X$_1$(z) and X$_2$($z^{-1}$) |
| Multiplication | $x_{1}[n]x_{2}[n]\$ | ${\frac {1}{j2\pi }}\oint _{C}X_{1}(v)X_{2}({\frac {z}{v}})v^{-1}\mathrm {d} v\$ | At least $r_{1l}r_{2l}<|z|<r_{1u}r_{2u}\$ |
| Parseval's relation | $\sum ^{\infty }x_{1}[n]x_{2}^{*}[n]\$ | ${\frac {1}{j2\pi }}\oint _{C}X_{1}(v)X_{2}^{*}({\frac {1}{v^{*}}})v^{-1}\mathrm {d} v\$ | |
       $x[0]=\lim _{z\rightarrow \infty }X(z)\$, If $x[n]\,$ causal
       $x[\infty ]=\lim _{z\rightarrow 1}(z-1)X(z)\$, Only if poles of $(z-1)X(z)\$ are inside unit circle
# Engineering Thermodynamics

This book deals with Engineering Thermodynamics, where concepts of thermodynamics are used to solve engineering problems. Engineers use thermodynamics to calculate the fuel efficiency of engines, and to find ways to make more efficient systems, be they rockets, refineries, or nuclear reactors. One aspect of "engineering" in the title is that a lot of the data used is empirical (e.g. steam tables), since you won't find clean algebraic equations of state for many common working substances. Thermodynamics is the science that deals with transfer of heat and work. Engineering thermodynamics develops the theory and techniques required to use empirical thermodynamic data effectively.
This course forms the foundation for the Heat Transfer course, where the rate and mechanisms of transmission of energy in the form of heat is studied. The concepts can be used in further study including internal combustion engines, refrigeration and air conditioning, and turbomachines to name a few.
Rigorous treatment of the molecular basis will be omitted, in favor of formulations most useful for developing intuition and understanding common technologies. Students of physics will want to pair this text with one on Statistical Mechanics.
* Introduction
* History
* Preface

## Contents

* Thermodynamic Systems
* Zeroth Law
* First Law
* Second Law
* Third Law
* Applications
* Appendix
* Further Reading
# Engineering Tables/Trigonometric Identities

| $\sin ^{2}\theta +\cos ^{2}\theta =1$ | $1+\tan ^{2}\theta =\sec ^{2}\theta$ |
| $\sin \left({\frac {\pi }{2}}-\theta \right)=\cos \theta$ | $\cos \left({\frac {\pi }{2}}-\theta \right)=\sin \theta$ |
| $\sec \left({\frac {\pi }{2}}-\theta \right)=\csc \theta$ | $\csc \left({\frac {\pi }{2}}-\theta \right)=\sec \theta$ |
| $\sin \left(-\theta \right)=-\sin \theta$ | $\cos \left(-\theta \right)=\cos \theta$ |
| $\sin 2\theta =2\sin \theta \cos \theta$ | $\cos 2\theta =\cos ^{2}-\sin ^{2}=2\cos ^{2}\theta -1=1-2\sin ^{2}\theta$ |
| $\sin ^{2}\theta ={\frac {1-\cos 2\theta }{2}}$ | $\cos ^{2}\theta ={\frac {1+\cos 2\theta }{2}}$ |
| $\sin \alpha +\sin \beta =2\sin \left({\frac {\alpha +\beta }{2}}\right)\cos \left({\frac {\alpha -\beta }{2}}\right)$ | $\sin \alpha -\sin \beta =2\cos \left({\frac {\alpha +\beta }{2}}\right)\sin \left({\frac {\alpha -\beta }{2}}\right)$ |
| $\cos \alpha +\cos \beta =2\cos \left({\frac {\alpha +\beta }{2}}\right)\cos \left({\frac {\alpha -\beta }{2}}\right)$ | $\cos \alpha -\cos \beta =-2\sin \left({\frac {\alpha +\beta }{2}}\right)\sin \left({\frac {\alpha -\beta }{2}}\right)$ |
| $\sin \alpha \sin \beta ={\frac {1}{2}}\left[\cos \left(\alpha -\beta \right)-\cos \left(\alpha +\beta \right)\right]$ | $\cos \alpha \cos \beta ={\frac {1}{2}}\left[\cos \left(\alpha -\beta \right)+\cos \left(\alpha +\beta \right)\right]$ |
| $\sin \alpha \cos \beta ={\frac {1}{2}}\left[\sin \left(\alpha +\beta \right)+\sin \left(\alpha -\beta \right)\right]$ | $1+\cot ^{2}=\csc ^{2}$ |
| $e^{j\theta }=\cos \theta +j\sin \theta$ | $\cos \theta ={\frac {e^{j\theta }+e^{-j\theta }}{2}}$ |
| $e^{-j\theta }=\cos \theta -j\sin \theta$ | $\sin \theta ={\frac {e^{j\theta }-e^{-j\theta }}{2j}}$ |
| $\tan \left({\frac {\pi }{2}}-\theta \right)=\cot \theta$ | $\cot \left({\frac {\pi }{2}}-\theta \right)=\tan \theta$ |
| $\tan(-\theta )=-\tan \theta$ | |
| $\tan ^{2}\theta ={\frac {1-\cos 2\theta }{1+\cos 2\theta }}$ | $\tan 2\theta ={\frac {2\tan \theta }{1-\tan ^{2}\theta }}$ |
# Engineering Tables/Z Transform Table

Here:
* $u[n]=1$ for $n>=0$, $u[n]=0$ for $n<0$
* $\delta [n]=1$ for $n=0$, $\delta [n]=0$ otherwise
| | Signal, $x[n]$ | Z-transform, $X(z)$ | ROC |
| 1 | $\delta [n]\,$ | $1\,$ | ${\mbox{all }}z\,$ |
| 2 | $\delta [n-n_{0}]\,$ | $z^{-n_{0}}\,$ | $z\neq 0\,$ |
| 3 | $u[n]\,$ | ${\frac {1}{1-z^{-1}}}$ | $|z|>1\,$ |
| 4 | $-u[-n-1]\,$ | ${\frac {1}{1-z^{-1}}}$ | $|z|<1\,$ |
| 5 | $nu[n]\,$ | ${\frac {z^{-1}}{(1-z^{-1})^{2}}}$ | $|z|>1\,$ |
| 6 | $-nu[-n-1]\,$ | ${\frac {z^{-1}}{(1-z^{-1})^{2}}}$ | $|z|<1\,$ |
| 7 | $n^{2}u[n]\,$ | ${\frac {z^{-1}(1+z^{-1})}{(1-z^{-1})^{3}}}$ | $|z|>1\,$ |
| 8 | $-n^{2}u[-n-1]\,$ | ${\frac {z^{-1}(1+z^{-1})}{(1-z^{-1})^{3}}}$ | $|z|<1\,$ |
| 9 | $n^{3}u[n]\,$ | ${\frac {z^{-1}(1+4z^{-1}+z^{-2})}{(1-z^{-1})^{4}}}$ | $|z|>1\,$ |
| 10 | $-n^{3}u[-n-1]\,$ | ${\frac {z^{-1}(1+4z^{-1}+z^{-2})}{(1-z^{-1})^{4}}}$ | $|z|<1\,$ |
| 11 | $a^{n}u[n]\,$ | ${\frac {1}{1-az^{-1}}}$ | $|z|>|a|\,$ |
| 12 | $-a^{n}u[-n-1]\,$ | ${\frac {1}{1-az^{-1}}}$ | $|z|<|a|\,$ |
| 13 | $na^{n}u[n]\,$ | ${\frac {az^{-1}}{(1-az^{-1})^{2}}}$ | $|z|>|a|\,$ |
| 14 | $-na^{n}u[-n-1]\,$ | ${\frac {az^{-1}}{(1-az^{-1})^{2}}}$ | $|z|<|a|\,$ |
| 15 | $n^{2}a^{n}u[n]\,$ | ${\frac {az^{-1}(1+az^{-1})}{(1-az^{-1})^{3}}}$ | $|z|>|a|\,$ |
| 16 | $-n^{2}a^{n}u[-n-1]\,$ | ${\frac {az^{-1}(1+az^{-1})}{(1-az^{-1})^{3}}}$ | $|z|<|a|\,$ |
| 17 | $\cos(\omega _{0}n)u[n]\,$ | ${\frac {1-z^{-1}\cos(\omega _{0})}{1-2z^{-1}\cos(\omega _{0})+z^{-2}}}$ | $|z|>1\,$ |
| 18 | $\sin(\omega _{0}n)u[n]\,$ | ${\frac {z^{-1}\sin(\omega _{0})}{1-2z^{-1}\cos(\omega _{0})+z^{-2}}}$ | $|z|>1\,$ |
| 19 | $a^{n}\cos(\omega _{0}n)u[n]\,$ | ${\frac {1-az^{-1}\cos(\omega _{0})}{1-2az^{-1}\cos(\omega _{0})+a^{2}z^{-2}}}$ | $|z|>|a|\,$ |
| 20 | $a^{n}\sin(\omega _{0}n)u[n]\,$ | ${\frac {az^{-1}\sin(\omega _{0})}{1-2az^{-1}\cos(\omega _{0})+a^{2}z^{-2}}}$ | $|z|>|a|\,$ |
# Engineering Thermodynamics/Further Reading

Further reading and resources:
* Kostic, M. (2008). Sadi Carnot’s Ingenious Reasoning of Ideal Heat-Engine Reversible Cycles (Proceedings of the 4th IASME/WSEAS International Conference on ENERGY, ENVIRONMENT, ECOSYSTEMS and SUSTAINABLE DEVELOPMENT (EEESD'08), Algarve, Portugal, June 11–13, 2008. In NEW ASPECTS OF ENERGY, ENVIRONMENT, ECOSYSTEMS and SUSTAINABLE DEVELOPMENT (Editors: T. Panagopoulos, T. Noronha Vaz, M. D. Carlos Antunes) ed.). WSEAS Press. pp. 159–166. ISBN 978-960-6766-71-8. (full text)
* Thermodynamics
* Engineering Thermodynamics - A Graphical Approach by Dr. Israel Urieli, Ohio University Dept of Mechanical Engineering
# Engineering Thermodynamics/Preface
## Goals

Thermodynamics is the study of the relationships between HEAT (thermos) and WORK (dynamics). Thus, it deals with energy interactions in physical systems. Classical thermodynamics can be stated in four laws called the zeroth, first, second, and third laws respectively. The laws of thermodynamics are empirical, i.e., they are deduced from experience, and supported by a large body of experimental evidence.
The topic of thermodynamics is taught in Physics and Chemistry courses as part of the regular curriculum. This book deals with Engineering Thermodynamics, where concepts of thermodynamics are used to solve engineering problems. Engineers use thermodynamics to calculate the fuel efficiency of engines, and to find ways to make more efficient systems, be they rockets, refineries, or nuclear reactors.
Thermodynamics is the science that deals with transfer of heat and work.
Engineering thermodynamics develops the theory and techniques required to use empirical thermodynamic data effectively. However, with the advent of computers most of these techniques are transparent to the engineer, and instead of looking data up in tables, computer applications can be queried to retrieve the required values and use them in calculations. There are even applications which are tailored to specific areas which will give answers for common design situations. But thorough understanding will only come with knowledge of underlying principles, and the ability to judge the limitations of empirical data is perhaps the most important gain from such knowledge.
One aspect of "engineering" in the title is that a lot of the data used is empirical (e.g. steam tables), since you won't find clean algebraic equations of state for many common working substances.
This book is a work in progress. This course forms the foundation for the Heat Transfer course, where the rate and mechanisms of transmission of energy in the form of heat is studied.

## Chapters

* The first chapter is an introduction to thermodynamics, and presents the motivation and scope of the topic.
* The second chapter, Thermodynamic Systems, defines some basic terms which are used throughout the book. In particular, the concepts of system and processes are discussed.
   * The zeroth law is stated and the concept of temperature is developed.
* The next chapter, First Law, develops ideas required for the statement of the first law of thermodynamics.
* Second Law deals with heat engines and the concept of entropy.
* Applications of the tools developed in the previous chapters are illustrated, including the use of thermodynamics in everyday engineering situations.
* The Appendix gives a list of tables for some commonly used properties.
# English-Hanzi/Yoga perfects your posture

Special:search/yoga prefix:English-Hanzi/
Special:search/posture prefix:English-Hanzi/
Your head is like a bowling ball—big, round, and heavy. When it’s balanced directly over an erect spine, it takes much less work for your neck and back muscles to support it. Move it several inches forward, however, and you start to strain those muscles. Hold up that forward-leaning bowling ball for eight or 12 hours a day and it’s no wonder you’re tired. And fatigue might not be your only problem. Poor posture can cause back, neck, and other muscle and joint problems. As you slump, your body may compensate by flattening the normal inward curves in your neck and lower back. This can cause pain and degenerative arthritis of the spine.
你的 头 像 一个 保龄球 - 大，圆，重。当 它 直接 在 直立 的 脊柱 平衡，你的 脖子 和 背部 肌肉 需要 少得多 的 工作 支持 它。然而，向前 移动 几 英寸，你的 肌肉 开始 受 压力。头部 每天 保持 8 到 12小时 的 前倾，难怪 你 累 了。疲劳 可能 不是 你 唯一 的 问题。姿势 不佳 可能 导致 背部，颈部 等 肌肉 和 关节 问题。当 你 疲倦 时，你的 身体 会 弄平 通常 向内 曲 的 脖子 和 下背部。这 可 引起 脊柱 的 疼痛 和 退化性 关节炎。
# English-Hanzi/Yoga builds muscle strength

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Strong muscles do more than look good. They also protect us from conditions like arthritis and back pain, and help prevent falls in elderly people. And when you build strength through yoga, you balance it with flexibility. If you just went to the gym and lifted weights, you might build strength at the expense of flexibility.
强壮 的 肌肉 不仅 看起来 不错。它们 还 保护 我们 免受 关节炎 和 背痛 的 影响，并 帮助 防止 老年人 跌倒。当 你 通过 Yoga 建立 力量，平衡 的 灵活性。如果 你 只 去 健身房 举重，你 可能会 牺牲 灵活性 来 建立 力量。
# English-Hanzi/Yoga increases your blood flow

Yoga gets your blood flowing. More specifically, the relaxation exercises you learn in yoga can help your circulation, especially in your hands and feet. Yoga also gets more oxygen to your cells, which function better as a result. Twisting poses are thought to wring out venous blood from internal organs and allow oxygenated blood to flow in once the twist is released. Inverted poses, such as Headstand, Handstand, and Shoulderstand, encourage venous blood from the legs and pelvis to flow back to the heart, where it can be pumped to the lungs to be freshly oxygenated. This can help if you have swelling in your legs from heart or kidney problems. Yoga also boosts levels of hemoglobin and red blood cells, which carry oxygen to the tissues. And it thins the blood by making platelets less sticky and by cutting the level of clot-promoting proteins in the blood. This can lead to a decrease in heart attacks and strokes since blood clots are often the cause of these killers.
yoga 促进 血液 流动。更 具体地 说，yoga 的 松弛 运动 可 帮助 血液 流通，尤其是 手 和 脚。 yoga 使 更多 氧气 供给 细胞，使 血液 循环得 更好。扭曲 的 姿势 被 认为 拧出 内部 器官 的 静脉 血液，并且 一旦 扭曲 被 放松 就 能 让 带氧 血液 流入。倒立 的 姿势，如 头倒立，手倒立，和 肩倒立，促进 腿部 和 骨盆 的 静脉 血液 流回 心脏，然后 被 心脏 pump 到 肺部 补充 新鲜 氧气。这 对 如果 心脏 或 肾脏 问题引起 的 腿部 肿胀 有 帮助。 yoga 还 提高 血红蛋白 和 红细胞 的 水平，它们 把 氧气 携带 到 组织。并且 它 通过 使 血小板 不 粘 和 通过 降低 血液 中 凝血 蛋白 的 水平 来 使 血液 变 稀。这 可 减少 心脏病 发作 和 中风，血凝块 通常 是 这些 致命 疾病 的 原因。