OpenLLM-France/wikimedia huggingface dataset:
# Introduction to Nynorsk/Introduction

Nynorsk is a North Germanic language of the West Scandinavian branch. Its closest relatives are Bokmål, Swedish and Danish. Some mutual intelligibility with Faroese exists, and many words in Icelandic can be recognised with little effort.
This book intends to provide a rough outline for the Nynorsk language, and help the reader from the state of standing on bare ground to having a sense of basic familiarity with the language.
# Introduction to Oceanography/Authors

| Oz "Fisheye" | Martin Hoecker-Martinez |
# Java Swings

This book is about the Java Swing technology. It does not teach you Java from tip to toe, instead it concentrates on how to create GUI using the Java programming language. Hence you must have already known how to program with Java if this book should become useful to you. You must know how to write Java programs using a text editor or IDE. You must know how to compile and run your Java programs. It is better if you have created and successfully run your own Java project.
Content v • d • e
* Java Swing
* Overview
* AWT
* Dive into Swings
* First Examples
* Swing Top Level Containers
* Swing Layouts
* Event Handling
* MVC architecture
* Responsive Swing Application
* Large Examples
Appendix
# Java Programming/Unchecked Exceptions

* Navigate Exceptions topic:( v • d • e )
* Throwing and catching exceptions
* Checked exceptions
* Unchecked exceptions
* Preventing NullPointerException
* Stack trace
* Nesting exceptions (chained exceptions)
Unchecked, uncaught or runtime exceptions are exceptions that can be thrown without being caught or declared:
* Code section 6.12: Throwing an exception without declaring it or catching it.
* public void futureMethod {
* throw new RuntimeException("This method is not yet implemented");
...however, you can still declare and catch such exceptions. Runtime exceptions are not business exceptions. They are usually related to hard-coded issues like data errors, arithmetic overflow, divide by zero etc. In other words, errors that can't be worked around nor anticipated. The most famous (and feared) runtime exception is the NullPointerException.
A runtime exception must be or inherit from the RuntimeException class or the Error class.
Sometime it is desirable to catch all exceptions for logging purposes, then throw them back in. For example, in servlet programming when an application server calls the server getLastModified, we want to monitor that no exceptions happened during the serving of the request. The application has its own logging separate from the server logging so the runtime exceptions would just go through without being detected by the application. The following code checks all exceptions, logs them and throws them back again.
* Code section 6.13: Logging an exception.
* public long getLastModified(HttpServletRequest req) {
* try {
* return getTimeStamp;
* } catch(RuntimeException e) {
* log.error("Error during handling post request", e);
* throw e;
In the above code, all business logic exception are handled in the getTimeStamp method. Runtime exceptions are caught for logging purposes, and then thrown back to the server to be handled.
# Java Swings/Java Swing

* Java Swing
* Overview
* AWT
* Dive into Swings
* First Examples
* Swing Top Level Containers
* Swing Layouts
* Event Handling
* MVC architecture
* Responsive Swing Application
* Large Examples
Appendix
Java Swing is a library/toolkit released by Oracle as a part of Java language which enables Java programmers to create GUIs and rich client applications.

## Success Stories

There are many applications written in Java, and a new one pops up every day. Here are some examples:

### NetBeans

NetBeans is a Integrated Development Environment (IDE) written completely using Java. Because of Java's portability, it can run on any platform, as long as Java is installed. Initially it was only a Java IDE, but now it supports many languages like C, C++, Python, and PHP, to name a few.

## JFC

Swing is a part of Java Foundation classes (JFC). JFC consists of the following modules

### Swing GUI Components

Java Swing Components are components for the Graphical User Interfaces of Applications. Some examples of Swing GUI components are lists, combo-boxes, labels, text areas, editor panes, buttons, menus, etc. Many components have built-in features such as print, drag & drop, sort, open file, save file, etc.

### Pluggable Look-and-Feel (PLAF) Support

The Look and Feel module defines how all of the components in the application look. Each Java Swing Application has an entirely separate L&F from the rest of the applications on the computer, including other Java Applications. Some examples of L&Fs are: Nimbus (really new), Metal, Aqua(Macs only), Windows Aero & Windows Classic (Windows only), and Motif(Highly customizable by the User of the Application). There are also many third-party Look and Feels available.

### Accessibility API

Not all humans are perfect. There is a good chance that a disabled person might not be able to use your program/application, so your program must be accessible to him or her. Java Foundation Classes Accessibility API enables you to create programs that are accessible to disabled people by providing them with screen readers, braille displays, etc., so that they can get information from the User Interface.

### Java 2D API

The Java 2D API provides a rich set of graphics classes and utilities for drawing 2D graphics. It can even generate output for printers.

### Internationalization

English is not the only language on this planet. Many people don't know any other language than their native tongue. Hence, when a programmer writes an application he/she must consider how to release it in as many languages as possible. Java i18n (there are 18 letter's between 'i' and 'n' in Internationalization) helps programmers develop applications in various different languages, so that you can target a global audience.

## Reference

http://docs.oracle.com/javase/tutorial/uiswing/start/about.html
# LMIs in Control/pages/LMI for Schur Stabilization

LMIs in Control/pages/LMI for Schur Stabilization

## The System

We consider the following system:
${\begin{aligned}x(k+1)=Ax(k)+Bu(k)\end{aligned}}$
where ${\begin{aligned}x\in \mathbb {R} ^{n}{\text{and}}u\in \mathbb {R} ^{r}\end{aligned}}$, are the state vector and the input vector, respectively. Moreover, the state feedback control law is defined as follows:
${\begin{aligned}u(k)=Kx(k)\end{aligned}}$
Thus, the closed-loop system is given by:
${\begin{aligned}x(k+1)=(A+BK)x(k)\end{aligned}}$

## The Data

    ${\begin{aligned}{\text{Given matrices}}\quad A\in \mathbb {R} ^{n\times n}{\text{,}}\quad B\in \mathbb {R} ^{n\times r}\quad {\text{, and the scalar}}\quad 0<\gamma \leq 1.\end{aligned}}$

## The Optimization Problem

Find a matrix ${\begin{aligned}K\in \mathbb {R} ^{r\times n}\end{aligned}}$ such that,
${\begin{aligned}||A+BK||_{2}<\gamma \end{aligned}}$
According to the definition of the spectral norms of matrices, this condition becomes equivalent to:
${\begin{aligned}(A+BK)^{T}(A+BK)<\gamma ^{2}I\end{aligned}}$
One can use the Lemma 1.2 in [1] page 14, the aforementioned inequality can be converted into:
${\begin{aligned}{\begin{bmatrix}-\gamma I&(A+BK)\\(A+BK)^{T}&-\gamma I\end{bmatrix}}<0\\\end{aligned}}$

## The LMI: LMI for Schur stabilization

Title and mathematical description of the LMI formulation.
       ${\begin{aligned}{\text{min}}\;\quad \gamma :&\\{\text{s.t.}}\quad {\begin{bmatrix}-\gamma I&(A+BK)\\(A+BK)^{T}&-\gamma I\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

This problem is a special case of Intensive Disk Region Design (page 230 in [1]). This problem may not have a solution even when the system is stabilizable. In other words, once there exists a solution, the solution is robust in the sense that when there are parameter perturbations, the closed-loop system's eigenvalues are not easy to go outside of a circle region within the unit circle [1].

## Implementation

A link to Matlab codes for this problem in the Github repository:
https://github.com/asalimil/LMI-for-Schur-Stability

## Related LMIs

LMI for Hurwitz stability

## External Links

A list of references documenting and validating the LMI.
* - LMI in Control Systems Analysis, Design and Applications
# LMIs in Control/pages/LMI for Matrix Norm Minimization

LMIs in Control/pages/LMI for Matrix Norm Minimization

## The System

    ${\begin{aligned}A(x)=A_{0}+A_{1}x_{1}+...+A_{n}x_{n}\end{aligned}}$
Note that ${\begin{aligned}A_{i},\quad i=1,2,...,n\end{aligned}}$ are symmetric matrices.

## The Data

    ${\begin{aligned}A_{0},A_{1},...,A_{n}\quad {\text{are given matrices.}}\end{aligned}}$

## The Optimization Problem

Find
${\begin{aligned}x=[x_{1}\quad x_{2}...x_{n}]\end{aligned}}$
to minimize,
${\begin{aligned}J(x)=||A(x)||_{2}\end{aligned}}$
According to Lemma 1.2 in [1] page 11, the following statements are equivalent
${\begin{aligned}A^{T}A-t^{2}I\leq 0\iff {\begin{bmatrix}-tI&A\\A^{T}&-tI\end{bmatrix}}\leq 0\\\end{aligned}}$

## The LMI: Minimization of Maximum Eigenvalue of a Matrix

Mathematical description of the LMI formulation:
       ${\begin{aligned}{\text{min}}\;\quad t:&\\{\text{s.t.}}\quad {\begin{bmatrix}-tI&A(x)\\A(x)^{T}&-tI\end{bmatrix}}\leq 0\\\end{aligned}}$

## Conclusion:

This problem is a slight generalization of the eigenvalue minimization problem for a matrix.
${\begin{aligned}x_{i},\quad i=1,2,...,n\quad {\text{and}}\quad t>0\end{aligned}}$ are parameters to be optimized

## Implementation

A link to Matlab codes for this problem in the Github repository:
https://github.com/asalimil/LMI-for-Matrix-Norm-Minimization

## Related LMIs

LMI for Matrix Norm Minimization
LMI for Schur Stabilization

## External Links

A list of references documenting and validating the LMI.
* - LMI in Control Systems Analysis, Design and Applications
# LMIs in Control/pages/LMI for the Observability Grammian

LMI for the Observability Grammian
Observability is a system property which says that the state of the system $x(T)$ can be reconstructed using the input $u(t)$ and output $y(t)$ on an interval $[0,T]$. This is necessary when knowledge of the full state is not available. If observable, estimators or observers can be created to reconstruct the full state. Observability and controllability are dual concepts. Thus in order to investigate the observability of a system we can study the controllability of the dual system. Although system observability can be determined with multiple methods, one is to compute the rank of the observability grammian.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t),\\y(t)&=Cx(t)+Du(t),\\x(0)&=x_{0},\end{aligned}}$
where $x(t)\in \mathbb {R} ^{n}$, $u(t)\in \mathbb {R} ^{m}$, at any $t\in \mathbb {R}$.

## The Data

The matrices necessary for this LMI are $A$ and $C$.

## The LMI:LMI to Determine the Observability Grammian

$(A,B)$ is observable if and only if $Y>0$ is the unique solution to
       $AY+YA^{T}+C^{T}C<0$,
where $Y$ is the observability grammian.

## Conclusion:

The above LMI attempts to find the observability grammian $Y$of the system $(A,C)$. If the problem is feasible and a unique $Y$ is found, then the system is also observable. The observability grammian can also be computed as: $Y=\int _{0}^{\infty }e^{A^{T}s}C^{T}Ce^{As}ds$. Due to the dual nature of observability and controllability this LMI can be determined by determining the controllability of the dual nature, which results in the above LMI. The Observability and Controllability matricies are written as ${\mathcal {O}}$ and ${\mathcal {C}}$ respectively. They are related as follows:
       ${\mathcal {O}}(C,A)={\mathcal {C}}(A^{T},C^{T})^{T}$
       ${\mathcal {C}}(A,B)={\mathcal {O}}(B^{T},A^{T})^{T}$
Hence $(C,A)$ is observable if and only if $(A^{T},C^{T})$ is controllable. Please refer to the section on controllability grammians.

## Implementation

This implementation requires Yalmip and Sedumi.
https://github.com/eoskowro/LMI/blob/master/Observability_Gram_LMI.m

## Related LMIs

Stabilizability LMI
Hurwitz Stability LMI
Detectability LMI
Controllability Grammian LMI

## External Links

A list of references documenting and validating the LMI.
* 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 Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013, Section 6.1.1 and Table 6.1 pp. 166–170, 192.
* A Course in Robust Control Theory: a Convex Approach, - by Geir E. Dullerud and Fernando G. Paganini, Springer, 2011, Section 2.2.3, pp. 71-73.
# LMIs in Control/pages/LMI for System H2 Norm

${H_{2}}$-norm of System
The ${H_{2}}$-norm is conceptually identical to the Frobenius (aka Euclidean) norm on a matrix. It can be used to determine whether the system representation can be reduced to its simplest form, thereby allowing its use in performing effective block-diagram algebra.

## The System

Suppose we define the state-space system$G:{L_{2}}\rightarrow {L_{2}}{\text{ by }}y=Gu$ if:
    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)+Du(t)\\\end{aligned}}$
where $A\in \mathbb {R} ^{mxm}$, $B\in \mathbb {R} ^{mxn}$, $C\in \mathbb {R} ^{pxm}$, and $D\in \mathbb {R} ^{qxn}$ for any $t\in \mathbb {R}$. Then the ${H_{2}}$-norm of the system can be determined as described below.

## The Data

In order to determine the ${H_{2}}$-norm of the system, we need the matrices ${A}$, ${B}$, and ${C}$.

## The Optimization Problem

Suppose we wanted to to infer properties of the system behaviour (which is represented in the form (A,B,C,D)). Then it becomes necessary to ensure that the overall system forms an algebra, as the standard use of block-diagram algebra would otherwise be invalid. The only way this is possible is by calculating ${H_{2}}$ and/or ${H_{\infty }}$-norms - both of which are signal norms that (in a certain sense) measure the size of the transfer function.

## The LMI: The $H_{2}$ Norm

Assuming that ${\hat {P}}(s)=C(sI-A)^{-1}B$, this means that the following are equivalent:
       $1)\quad A{\text{ is Hurwitz and }}||{\hat {P}}||_{H_{2}}^{2}<\gamma$
       $2){\begin{aligned}{\begin{cases}trace(CXC^{T})&<\gamma \\AX+XA^{T}+BB^{T}&<0\\X&>0\end{cases}}\end{aligned}}$

## Conclusion:

The LMI can be used to minimize the ${H_{2}}$-norm of the system. It is worth noting that a finite ${H_{2}}$-norm does not guarantee finite ${H_{\infty }}$-norm, and that in order for the block diagram algebra to be valid, ${H_{\infty }}$-norm must be finite.

## Implementation

* Example Code - A GitHub link that contains code (titled "H2Norm.m") that demonstrates how this LMI can be implemented using MATLAB-YALMIP.

## Related LMIs

      * $H_{2}$-Filtering - LMI for $H_{2}$-Filtering
      * Discrete-Time $H_{2}$ Norm - LMI for $H_{2}$-norm in the Discrete-Time case.

## External Links

A list of references documenting and validating the LMI.
* 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/pages/LMI for convex minimization problem

LMIs in Control/pages/LMI for convex minimization problem

## The System

Let $A(x)$ and $B(x)$ are matrix functions of appropriate dimensions.
Moreove, the matrix functions $A(x)$ and $B(x)$ are linear in vector $x$ where $x$ is an $m\times 1$ vector.

## The Data

A convex function $f(x)$ is given and $x$ is the vector of decision variables.

## The Optimization Problem

The optimization problem is to minimize the convex function $f(x)$ such that a contraint between two convex functions are satisfied for the decision variables.

## The LMI: LMI for convex minimization problem

${\begin{aligned}&{\text{min}}\;\quad f(x)&\\&A(x)<B(x)\end{aligned}}$

## Implementation

A link to Matlab codes for this problem in the Github repository:

## External Links

A list of references documenting and validating the LMI.
* - LMI in Control Systems Analysis, Design and Applications
# LMIs in Control/pages/LMI for the Controllability Grammian

LMI to Find the Controllability Gramian
Being able to adjust a system in a desired manor using feedback and sensors is a very important part of control engineering. However, not all systems are able to be adjusted. This ability to be adjusted refers to the idea of a "controllable" system and motivates the necessity of determining the "controllability" of the system. Controllability refers to the ability to accurately and precisely manipulate the state of a system using inputs. Essentially if a system is controllable then it implies that there is a control law that will transfer a given initial state $x(t_{0})=x_{0}$ and transfer it to a desired final state $x(t_{f})=x_{f}$. There are multiple ways to determine if a system is controllable, one of which is to compute the rank "controllability Gramian". If the Gramian is full rank, the system is controllable and a state transferring control law exists.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Bu(t),\\x(0)&=x_{0},\end{aligned}}$
where $x(t)\in \mathbb {R} ^{n}$, $u(t)\in \mathbb {R} ^{m}$, at any $t\in \mathbb {R}$.

## The Data

The matrices necessary for this LMI are $A$ and $B$. $A$ must be stable for the problem to be feasible.

## The LMI: LMI to Determine the Controllability Gramian

$(A,B)$ is controllable if and only if $W>0$ is the unique solution to
       $AW+WA^{T}+BB^{T}<0$,
where $W$ is the Controllability Gramian.

## Conclusion:

The LMI above finds the controllability Gramian $W$of the system $(A,B)$. If the problem is feasible and a unique $W$ can be found, then we also will be able to say the system is controllable. The controllability Gramian of the system $(A,B)$ can also be computed as: $W=\int _{0}^{\infty }e^{As}BB^{T}e^{A^{T}s}ds$, with control law $u(t)=B^{T}W^{-1}x(t)$ that will transfer the given initial state $x(t_{0})=x_{0}$ to a desired final state $x(t_{f})=x_{f}$.

## Implementation

This implementation requires Yalmip and Sedumi.
https://github.com/eoskowro/LMI/blob/master/Controllability_Gram_LMI.m

## Related LMIs

Stabilizability LMI
Hurwitz Stability LMI
Detectability LMI
Observability Grammian LMI

## External Links

A list of references documenting and validating the LMI.
* 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 Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013, Section 6.1.1 and Table 6.1 pp. 166–170, 192.
* A Course in Robust Control Theory: a Convex Approach, - by Geir E. Dullerud and Fernando G. Paganini, Springer, 2011, Section 2.2.3, pp. 71-73.
# LMIs in Control/pages/LMI for Minimizing Condition Number of Positive Definite Matrix

LMIs in Control/pages/LMI for Minimizing Condition Number of Positive Definite Matrix

## The System:

A related problem is minimizing the condition number of a positive-defnite matrix $M$ that depends affinely on the variable $x$, subject to the LMI constraint $F(x)$ > 0. This problem can be reformulated as the GEVP.

## The Optimization Problem:

The GEVP can be formulated as follows:
minimize $\gamma$
subject to $F(x)$ > 0;
$\mu$>0;
$\mu I$< $M(x)$ < $\gamma \mu I$.
We can reformulate this GEVP as an EVP as follows. Suppose,
$M(x)$= $M_{0}$ +$\sum _{n=1}^{m}$$x_{i}M_{i}$ , $F(x)$= $F_{0}$+ $\sum _{n=1}^{m}$$x_{i}F_{i}$

## The LMI:

Defining the new variables $\nu$=$1/\mu$ , ${\tilde {x}}$=$x/\mu$ we can express the previous formulation as the EVP with variables ${\tilde {x}},\nu$ and $\gamma$:
miminize$\gamma$
subject to $\nu F_{0}$+ $\sum _{n=1}^{m}$$x_{i}F_{i}$ >0; $I$ < $\nu M_{0}$+ $\sum _{n=1}^{m}$$x_{i}M_{i}$ < $\gamma I$

## Conclusion:

The LMI is feasible.

## References

* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/pages/LMI for Mixed H2 Hinf Output Feedback Control

LMIs in Control/pages/LMI for Mixed H2 Hinf Output Feedback Control

## The System

The objective is to minimize the combined $H_{2}$ and $H_{\infty }$ norms of the closed-loop system.

## The LMI: LMI for mixed $H_{2}/H_{\infty }$

${\begin{aligned}{\text{min}}\;\quad t:&\\||S(P,K)||_{H_{2}}^{2}+||S(P,K)||_{H_{\infty }}^{2}\end{aligned}}$

## Implementation

A link to Matlab codes for this problem in the Github repository:

## External Links

A list of references documenting and validating the LMI.
* - LMI in Control Systems Analysis, Design and Applications
# Grand Theft Auto: San Andreas/Missions/First Base
## Prerequisites

* Mission: King in Exile
* Location: Catalina's hideout, Fern Ridge, Red County

## Walkthrough

This is similar to First Date. Choose another mission from the list:
* Tanker Commander
* Against All Odds
* Local Liquor Store
* Small Town Bank

## Rewards

None

## New Missions Available

* Gone Courting
* Wu Zi Mu
# Grand Theft Auto: San Andreas/Missions/Fender Ketchup
## Prerequisites

* Mission: Learning to Fly
* Location: Four Dragon's Casino, Las Venturas

## Walkthrough

The objective is to scare the guy tied to the hood of your car into talking. Don't hit anything head on - you don't need him dead. Drive on the wrong side of the road, really fast with some hand brake turns thrown in for good measure. Once his "Scare Meter" is full, he will talk.

## Rewards

* Cash: $5,000
* Respect +

## New Missions Available

* Explosive Situation
# Grand Theft Auto: San Andreas/Missions/Firefighter
## Prerequisites

* Vehicle: Fire Truck. You can attract them by setting fires (for example, by shooting cars in their gas tanks or by throwing grenades at them), or go to a fire station to find one parked. One such station is located just south of the Doherty garage in San Fierro.

## Tips

* Aim the water hose above the heads of the victims, not at them (no water canon style hitting). The fire should be put out almost within one second upon you sprinkle the water over them.
* Get close to the flaming vehicle. It allows for faster extinguishing of the fire. Note that the flames you fight will not catch the fire truck on fire. Every level adds one person to be saved, and when you have more than three people you will have more than one vehicle. Levels 1-4 have people in the same vehicle, 5-8 will be divided into two vehicles, 9-12 into three, and so on.

## Rewards

* Finish level 12 to become fireproof.

## New Missions Available

None
# Grand Theft Auto: San Andreas/Missions/Explosive Situation
## Prerequisites

* Mission: Fender Ketchup
* Location: Four Dragon's Casino, Las Venturas

## Walkthrough

At the quarry, get into the dump truck and crash into each box of explosives and get out to retrieve each. Deal with the quarry workers if they get annoying. After getting the explosives, security attempts to block the exit. Grab the Sanchez and meet each marker by going up the spouts and machinery. Avoid security and head back to the drop point with the explosives.

## Tips

You can stop the clock by taking out the two guys near the Plunger (or just the guy with the beard). You can then use the truck to break the boxes before grabbing the dynamite with the Sanchez and making your escape.

## Rewards

* Cash: $7,000
* Respect +
* Quarry Missions unlocked.

## New Missions Available

* You've had your Chips