OpenLLM-France/wikimedia huggingface dataset:
# Georgia Water/Statewide Plan/Advisory Committees

* Water Policy
* Management
* Information
* Planning
* Statewide Plan
* Regional Plans
* References
Chapter 6. Statewide Plan
          6.4. Public Participation
             6.4.1. Advisory Committees

### Statewide Advisory Committee

* Role of SAC
* Membership
* Meetings
* Public participation

### Technical Advisory Committees

* Role of TACs
* Membership
* Meetings
* Public participation
* List of TACs by topic

### Basin Advisory Committees

* Role of BACs
* Membership
* Meetings
* Public Participation
* List of BACs
   * Savannah and Ogeechee Rivers
   * Satilla, Suwannee and St. Marys Rivers
   * Oconee, Ocmulgee and Altamaha Rivers
   * Flint and Ochlockonee Rivers
   * Chattahoochee River
   * Coosa, Tallapoosa, Tennessee Rivers
   * Georgia Coastal Area (Floridan Aquifer)
# Georgia Water/Statewide Plan/Statewide Advisory Committee

* Water Policy
* Management
* Information
* Planning
* Statewide Plan
* Regional Plans
* References

## Overview

"How was the state advisory group formed? What is it charged to do?
When the advisory committees were formed, the major purposes of the Statewide Advisory Committee (SAC) were identified as follows:
* Provide early input to EPD and the Water Council on the description of Georgia’s over-arching goals for water management, water management objectives, and the array of new policy tools identified for development in the first water plan;
* Screen draft policy tool recommendations, for statewide applicability, before EPD submits them to the Water Council.
To accomplish these purposes, the SAC includes organizations with statewide perspectives and water-related interests that reflect Georgia’s geographic, economic, cultural, jurisdictional, and water resources realities. Governor Perdue and the Water Council identified such organizations and then, as Water Council Chair, the EPD Director formally asked each organization to name individuals from their ranks to represent the organization’s views on the SAC. ‘At-large’ individuals were also identified for their broad knowledge or expertise concerning water issues statewide." (quoted from: SAC Discussion Paper, 10-20-06, pg.7)

## References

Statewide Advisory Committee's discussion packet for meeting of November 6, 2006. (SAC Discussion Paper, 10-20-06)
# Georgia Water/Statewide Plan/Technical Advisory Committees

* Water Policy
* Management
* Information
* Planning
* Statewide Plan
* Regional Plans
* References
TECHNICAL ADVISORY COMMITTEES for GEORGIA'S COMPREHENSIVE STATEWIDE WATER RESOURCES MANAGEMENT PLAN

### Role of TACs

"The Technical Advisory Committees are topic-specific groups of technical experts assembled to provide technical input – as needed – in discussions of specific new policy tools." (The Carl Vinson Institute of Government will provide discussion papers on the range of options for the new water management policy tools.) These "advisory committees are for advisory purposes only" and are not decision-making in nature. "Their only role is to receive information and help evaluate that information and provide some understanding on whether or not proposals will work in target areas."
"A technical advisory committee will be assembled to ascertain what technical questions on (a) topic must be asked and answered."

### Membership

"The Technical Advisory Committees are topic-specific groups of technical experts assembled to provide technical input – as needed – in discussions of specific new policy tools. These technical advisors have extensive expertise and are actively participating and/or researching the topic being addressed. TAC members represent diverse abilities and bring a broad range of scientific/technical experience and regional knowledge to EPD in this planning process."

### Public Participation

"... in additional to the formal advisory bodies, there will also need to be a series of town hall type meetings throughout the state in the later stages of the planning process."

### List of TACs

List of Technical Advisory Committees (from June 7, 2005, minutes of Georgia Water Council)
* Water Conservation TAC (appointed September 2005 )
* Water ReUse TAC (appointed September 2005 )
* Water Use Efficiency TAC
* Interbasin Transfers TAC
* Septic Systems TAC
* Instream Flow TAC (appointed Dec.2005)
* Water Supply Reservoirs TAC
* Aquifer Storage, Usage and Recovery TAC
* Stormwater Management TAC
# Circuit Theory/Progressive Simplification

Progressive simplification is to simplify the circuit around the device interested in.
# Circuit Theory/Shorted Resistors

A wire in the left circuit is shorting the 100Ω resistor. All current will bypass the resistor and travel through the short. The voltage across the 100Ω resistor is going to be zero. The 100Ω resistor is not impacting the circuit. For analysis purposes, the 100Ω resistor can be removed.
The real world wire is going to have some resistance, and a tiny trickle of current will go through the resistor. The exact magnitude is going to depend upon the amount of resistance in the wire. The ideal math would involve infinity. So typically the assumption of a short is done by redrawing the circuit. This is why redrawing circuits when making assumptions (such as removing a resistor because of the short) is important.
# Circuit Theory/Resources
## Further reading

Pages listed here are sources of further information on the topic of electric circuits, or are additional subjects that may be of interest for a reader of this book. Many of the resources listed here are sources of information, and this may be treated as a bibliography for this wikibook.

### Wikibooks

* Wikibooks: Electronics
* Wikibooks: Signals and Systems
* Wikibooks: Digital Circuits
* Wikibooks: Circuit Idea
The following Wikibooks list Circuit Theory as a prerequisite:

### Other Resources

* Horowitz and Hill, The Art of Electronics, Second Edition, Cambridge University Press, 1989. ISBN 0521370957
* US Navy, Basic Electrity, Dover, 1970. ISBN 0486209733
* US Navy, Basic Electronics, Dover, 1973. ISBN 0486210766
* Comer and Comer, Fundamentals of Electronic Circuit Design, John Wiley & Sons, 2003. http://www.wiley.com/college/comer/ ISBN 0471410160
* Dorf and Svoboda, Introduction to Electric Circuits, Sixth Edition, John Wiley & Sons, 2004. ISBN 0471447951
# Circuit Theory/Series Resistance
## Series Resistance

Two or more resistor can be connected in series to increase the total resistance . The Total Resistance is equal to the sum of all the resistor's resistance . The total resistance In Series connected circuit Current and voltage will be reduced
    $R_{tot}=R_{1}+R_{2}+R_{3}+...+R_{n}\,$

## Series Impedance

A branch is defined as any group of resistors, capacitors and inductors that can be circled with only two wires crossing the circle boundary.
A branch connects two, non-trivial nodes or junctions.
Within a branch the components are said to be "in series."
Consider a branch containing a Resistor, Capacitor and Inductor.
Say the driving function or source is
    $V_{s}=10*cos(22400t+30^{\circ })$
    $V_{s}=10*e^{-5000t}cos(22400t+30^{\circ })$
There is just one current, $I$.

## Symbolic Derivation

The terminal equations are:
    $\mathbb {V} _{r}=\mathbb {I} *R$
    $\mathbb {V} _{L}=\mathbb {I} *j\omega L$ or $\mathbb {V} _{L}=\mathbb {I} *sL$
    $\mathbb {I} =\mathbb {V} _{c}*j\omega C$ or $\mathbb {I} =\mathbb {V} _{c}*sC$
There are no junction equations and the loop equation is:
    $\mathbb {V} _{r}+\mathbb {V} _{L}+\mathbb {V} _{c}-\mathbb {V} _{s}=0$
Solving the terminal equations for voltage, substituting and then dividing by $\mathbb {I}$ yields:
    ${\frac {\mathbb {V} _{s}}{\mathbb {I} }}=R+j\omega L+{\frac {1}{j\omega C}}$
    ${\frac {\mathbb {V} _{s}}{\mathbb {I} }}=R+sL+{\frac {1}{sC}}$
In terms of impedance, if:
    $Z=R+j\omega L+{\frac {1}{j\omega C}}$
    $Z=R+sL+{\frac {1}{sC}}$
Then:
    ${\frac {\mathbb {V} _{s}}{\mathbb {I} }}=Z$
In general, impedances add in series like resistors do in the time domain:
    $Z=\sum R_{i}+\sum j\omega L_{i}+\sum {\frac {1}{j\omega C_{i}}}$
    $Z=\sum R_{i}+\sum sL_{i}+\sum {\frac {1}{sC_{i}}}$

## Numeric Example

In rectangular form:
    $Z=100+.15714j$
    $Z=80.508+2.2759j$
In polar form (remember impedance is not a phasor, it is a concept in the phasor or complex frequency domain):
    $Z=100.0001\angle 0.0016(0.09^{\circ })$
    $Z=80.5402\angle 0.0283(1.6193^{\circ })$

## Notes

* Calculations like this are only necessary when trying to find out what is going on in one little part of the circuit ... and Kirchhoff would take too long. This was true in the past, but given the modern capabilities of matLab and mupad, the importance of the series concept may diminish.
* It appears that the exponential term decreases the overall magnitude and increases the reactance ... increases in the inductive direction with the exponential term.
* The V/I ratio sets up/prepares for the transfer function discussion later.
# Fundamentals of Physics/Energy from the Nucleus

P=N(V^2) V=(P/N)^(1/2)
# Fundamentals of Physics/Fluid Mechanics

Any substance that flows is called a fluid. In other words fluids cannot undergo shearing or tensile stress. This chapter is dedicated to studying about the behavior (mechanism) of fluids. Fluid mechanism is a vital science and is used in hydraulic engineering, aviation etc. There are two major branches in fluid mechanics, namely, fluid statics which is the study of fluid in a stationary state and fluid dynamics which is the study of fluid when its flowing, like what happens when water flows? So lets dive into fluid mechanics.
Fluids are readily able to flow because their intermolecular forces are comparatively week at room temperatures. Fluids do not have any specific shape and take the shape of the container into which they are filled. Fluids like air has no definite shape and are extremely turbulent.

## Pressure

All fluids exert a force on any substance that's immersed in them. This is called pressure. Pressure compresses any object that is immersed in a fluid. Pressure in a fluid can be measured using a device as shown in figure 15-1. This device consists of a evacuated cylinder with a tight fitting piston. The piston's inward movement into the cylinder is resisted by the spring.
When the cylinder is immersed in the water, force acts upon the piston and pushes it inside the cylinder. If we had calibrated the spring properly, we could tell how much pressure is exerted on the piston by measuring its position in the cylinder.
Lets see how to calculate pressure. Mathematically pressure is equal to the force exerted on a object per unit area. That is
$P={\frac {F}{A}}N/m^{2}$
So lets say that radius of the piston is $r$ meters, then pressure is
$P={\frac {F}{\pi r^{2}}}$
Let say the piston has moved inward about a distance of $x$ meters from its normal position. Then the force on piston is equal to
$F=Kx$
Where K is a constant. Hence pressure is
$P={\frac {Kx}{\pi r^{2}}}N/m^{2}$
The unit of force is Newtons ($N$) and unit for area is meter-square ($m^{2}$). Pressure is force per unit area and hence has the unit Newton per meter-square ($N/m^{2}$). In honor of the great mathematician Blaise Pascal, pressure is called Pascal.
# Fundamentals of Physics/Circular Motion and Other Applications of Newton's Laws

In the last chapter, five types of forces were mentioned. Those forces are: `normal force, friction, tension, weight, and drag. In this chapter, we will focus on three types of forces: friction, drag, and centripetal acceleration. These forces are all forces that we encounter in our daily lives, and there are plenty of examples highlighting the importance of these forces. For example, a race car must be designed so that it encounters minimal air resistance as it moves along the track. In addition, the tires must be specially manufactured so that there is minimal friction between the tires and the track.

## Friction

Friction is a force that always opposes all motion; it always acts in a direction exactly opposite to that in which an object is moving (or trying to move), and typically comes when the object rubs or drags against another object as it moves. It is defined as ${\vec {f}}=\mu {\vec {N}}$ where $\mu$ is the coefficient of friction, and ${\vec {N}}$ is the normal force acting on the object. There are two types of friction, static and kinetic, also known as sliding friction. Static friction is the amount of initial force required to move an object, and kinetic friction is the amount of force required to sustain motion in an object. Because of this, static friction is always greater than or equal to kinetic friction.

## Drag

Drag is similar to friction, in the sense that it always acts in the direction opposite of motion, but unlike friction, drag occurs from air or water. Thus, the air resistance experienced by a race car is a type of drag.
# Fundamentals of Physics

Physics is an essential subject for many professions like astronomy, engineering, rocket science, architecture, and so on. A good free text book is absolutely essential. A book like Fundamentals of Physics ISBN 978-0-471-32000-5 by Halliday, Resnick, and Walker is the standard for many schools and colleges. This wikibook project is to create a similar kind of book with far greater quality. Please join us to educate the world.

## Chapters

* Physics and Measurement
* Motion in One Dimension
* Vectors
* Motion in Two Dimensions
* Forces and Motion - I
* Forces and Motion - II
* Work and Kinetic Energy
* Potential Energy and Conservation of Energy
* Linear Momentum and Collisions
* Rotation of a Rigid Object About a Fixed Axis
* Rolling Motion and Angular Momentum
* Static Equilibrium and Elasticity
* Oscillatory Motion
* The Law of Gravity
* Fluid Mechanics
* Wave Motion
* Sound Waves
* Superposition and Standing Waves
* Temperature
* Heat and the First Law of Thermodynamics
* The Kinetic Theory of Gases
* Heat Engines, Entropy, and the Second Law of Thermodynamics
* Electric Fields
* Gauss's Law
* Electric Potential
* Capacitance and Dielectrics
* Current and Resistance
* Direct Current Circuits
* Magnetic Fields
* Sources of the Magnetic Field
* Faraday's Law
* Inductance
* Alternating-Current Circuits
* Electromagnetic Waves
* The Nature of Light and the Laws of Geometric Optics
* Geometric Optics
* Interference of Light Waves
* Diffraction and Polarization
* Relativity
* All About Atoms
* Conduction of Electricity in Solids
* Nuclear Physics
* Energy from the Nucleus
* Quarks, Leptons, and the Big Bang
# Fundamentals of Physics/Forces and Motion - II

In the previous chapter, three forces were discussed: weight, tension and normal force. In this chapter we will discuss in detail friction, drag, and centripetal acceleration. All of these forces are commonly observed in motion, and there are several real world examples of them. For instance, a race car must be engineered so that it encounters minimal friction with the track, as well as minimal air drag as it races. However, the tires of the car must be designed so that some friction is encountered. If the tires were frictionless, the car would not be able to slow down when making a high-speed turn, and would end up crashing.

## Types of Forces

In this chapter, we will focus on three other forces: friction, drag, and circular motion.

### Friction

Friction is a force that always opposes all motion; it always acts in a direction exactly opposite to that in which an object is moving (or trying to move), and typically comes when the object rubs or drags against another object as it moves. It is defined as ${\vec {f}}=\mu {\vec {N}}$ where $\mu$ is the coefficient of friction, and ${\vec {N}}$ is the normal force acting on the object. There are two types of friction, static and kinetic, also known as sliding friction. Static friction is the amount of initial force required to move an object, and kinetic friction is the amount of force required to sustain motion in an object. Because of this, static friction is always greater than or equal to kinetic friction.

### Drag

Drag is like friction in that it always acts in a direction opposite to that in which an object is moving, but comes from fluids such as air and water, through which an object might be moving. This relationship is documented in the equation $D-F_{g}={\vec {F}}$, because the vectors representing drag and motion are in opposite directions. Since drag occurs in the presence of fluids, air resistance is a form of drag. Drag is related by the equation $D={\frac {1}{2}}CpAv^{2}$, where $C$ is the drag coefficient, $A$ is the effective surface area that encounters the resistance, $p$ is the fluid density, and $v$ is the object's speed.

### Circular Motion

Imagine a person whirling a yo-yo around in circles. The yo-yo has a string of length 10 cm, and a constant speed. While the speed is constant, the velocity however, is not. This is because velocity has a direction, and in circular motion, the direction is always changing. An easy way to understand this is to think of a circle with several points on it. Using the points, draw tangent lines on the circle. These tangent lines represent the different velocities, all of which have varying directions, even though their speed may be the same. Remember that speed is the magnitude, or absolute value of velocity. A general equation gives the centripetal acceleration in terms of the velocity and the radius: $a={\frac {v^{2}}{R}}$
# LMIs in Control/Linear matrix inequalities and control theory/pages/Fundamentals of Matrix and LMIs/Basic Matrix Theory
## Basic Matrix Notation

Consider the complex matrix $A\in \mathbb {C} ^{n\times m}$.
       $A={\begin{bmatrix}a_{11}&\dots &a_{1m}\\\vdots &\ddots &\vdots \\a_{n1}&\dots &a_{nm}\end{bmatrix}}\in \mathbb {C} ^{n\times m}$
Transpose of a Matrix
The transpose of $A$, denoted as $A^{T}$ or $A'$ is:
       $A^{T}={\begin{bmatrix}a_{11}&\dots &a_{n1}\\\vdots &\ddots &\vdots \\a_{1m}&\dots &a_{nm}\end{bmatrix}}\in \mathbb {C} ^{m\times n}.$
Adjoint of a Matrix
The adjoint or hermitian conjugate of $A$, denoted as $A^{*}$ is:
       $A^{*}={\begin{bmatrix}a_{11}^{*}&\dots &a_{n1}^{*}\\\vdots &\ddots &\vdots \\a_{1m}^{*}&\dots &a_{nm}^{*}\end{bmatrix}}\in \mathbb {C} ^{m\times n}.$
Where $a_{nm}^{*}$ is the complex conjugate of matrix element $a_{nm}$.
Notice that for a real matrix $A\in \mathbb {R} ^{n\times m}$, $A^{*}=A^{T}$.

## Important Properties of Matricies

Hermitian, Self-Adjoint, and Symmetric Matricies
A square matrix $A\in \mathbb {C} ^{n\times n}$ is called Hermitian or self-adjoint if $A=A^{*}$.
If $A\in \mathbb {R} ^{n\times n}$ is Hermitian then it is called symmetric.
Unitary Matricies
A square matrix $A\in \mathbb {C} ^{n\times n}$ is called unitary if $A^{*}=A^{-1}$ or $A^{*}A=I$.

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/Linear matrix inequalities and control theory/pages/Fundamentals of Matrix and LMIs/Fundamentals of Matrix and LMI/Basic Matrix Theory
## Basic Matrix Notation

Consider the complex matrix $A\in \mathbb {C} ^{n\times m}$.
       $A={\begin{bmatrix}a_{11}&\dots &a_{1m}\\\vdots &\ddots &\vdots \\a_{n1}&\dots &a_{nm}\end{bmatrix}}\in \mathbb {C} ^{n\times m}$
Transpose of a Matrix
The transpose of $A$, denoted as $A^{T}$ or $A'$ is:
       $A^{T}={\begin{bmatrix}a_{11}&\dots &a_{n1}\\\vdots &\ddots &\vdots \\a_{1m}&\dots &a_{nm}\end{bmatrix}}\in \mathbb {C} ^{m\times n}.$
Adjoint of a Matrix
The adjoint or hermitian conjugate of $A$, denoted as $A^{*}$ is:
       $A^{*}={\begin{bmatrix}a_{11}^{*}&\dots &a_{n1}^{*}\\\vdots &\ddots &\vdots \\a_{1m}^{*}&\dots &a_{nm}^{*}\end{bmatrix}}\in \mathbb {C} ^{m\times n}.$
Where $a_{nm}^{*}$ is the complex conjugate of matrix element $a_{nm}$.
Notice that for a real matrix $A\in \mathbb {R} ^{n\times m}$, $A^{*}=A^{T}$.

## Important Properties of Matricies

Hermitian, Self-Adjoint, and Symmetric Matricies
A square matrix $A\in \mathbb {C} ^{n\times n}$ is called Hermitian or self-adjoint if $A=A^{*}$.
If $A\in \mathbb {R} ^{n\times n}$ is Hermitian then it is called symmetric.
Unitary Matricies
A square matrix $A\in \mathbb {C} ^{n\times n}$ is called unitary if $A^{*}=A^{-1}$ or $A^{*}A=I$.

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/Linear matrix inequalities and control theory/pages/Fundamentals of Matrix and LMIs/Notion of Matrix Positivity
## Notation of Positivity

A symmetric matrix $A\in \mathbb {R} ^{n\times n}$ is defined to be:
positive semidefinite, $(A\geq 0)$, if $x^{T}Ax\geq 0$ for all $x\in \mathbb {R} ^{n},x\neq \mathbf {0}$.
positive definite, $(A>0)$, if $x^{T}Ax>0$ for all $x\in \mathbb {R} ^{n},x\neq \mathbf {0}$.
negative semidefinite, $(-A\geq 0)$.
negative definite, $(-A>0)$.
indefinite if $A$ is neither positive semidefinite nor negative semidefinite.

## Properties of Positive Matricies

* For any matrix $M$, $M^{T}M>0$.
* Positive definite matricies are invertible and the inverse is also positive definite.
* A positive definite matrix $A>0$ has a square root, $A^{1/2}>0$, such that $A^{1/2}A^{1/2}=A$.
* For a positive definite matrix $A>0$ and invertible $M$, $M^{T}AM>0$.
* If $A>0$ and $M>0$, then $A+M>0$.
* If $A>0$ then $\mu A>0$ for any scalar $\mu >0$.

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.