OpenLLM-France/wikimedia huggingface dataset:
# Pinyin/Trade

Trade is the voluntary exchange of goods and services. Trade is also known as commerce. Trade proceeds within a market. The most primitive form of trade is to exchange goods for goods, that is to exchange goods or services directly. Modern trade in general uses a medium to bargain, for example the use of money. The appearance of money (and the latter L/C, cheque, virtual money) hugely simplifies and promotes trade. The trade between two traders is known as bi-lateral trade. The trade involving more than two traders is known as multi-lateral trade.
Màoyì shì zìyuàn de huòpǐn huò fúwù jiāohuàn. Màoyì yě bèi chēngwéi shāngyè. Màoyì shì zài yīgè shìchǎng lǐmiàn jìnxíng de. Zuì yuánshǐ de màoyì xíngshì shì yǐwùyìwù, yějiùshì zhíjiē jiāohuàn huòpǐn huò fúwù. Xiàndài de màoyì zé pǔbiàn yǐ yīzhǒng méijiè zuò tǎojiàhuánjià, rú jīnqián. Jīnqián de chūxiàn (yǐjí hòulái de xìnyòngzhèng, chāopiào yǐjí fēi-shítǐ jīnqián) dàdà jiǎnhuà hé cùjìnle màoyì. Liǎnggè màoyìzhě zhījiān de màoyì chēngwéi shuāngbiān màoyì, duōyú liǎnggè màoyìzhě de zé chēngwéi duōbiān màoyì.
# Pinyin/Trademark

Search Pinyin trademark
# Pinyin/Tool

See also
a tool: a piece of equipment, usually one that you hold in your hand, that is designed to do a particular type of work
gongjuh: tongcharng shih shoougongjuh shehbeih, weih tehdihng gongzuoh err shehjih.
# Pinyin/Tough

See also
# Pinyin/Town

A town is a place where people live and work that is smaller than a city.
shihzhehn shih bii cherngshih xiaao, rer'men shenghuor her gongzuoh d dihfang.
# Pinyin/Tourism

Tourism is an activity of sightseeing adventure. Generally speaking, it is an industry that provide recreational facilities and services for tourists. Tourism is also a leisurely recreational activity, having the characteristic of foreign places and shortness in time. Generally speaking, tourism has two different layers of sightseeing and travelling. The precedent is short in duration, shallow in experience, the latter the opposite.
lvvyour jiùshì lǚxíng yóulǎn huódòng. zǒngdeláishuō shì wèi lǚkè tígōng xiūxián shèshī hé fúwù de chǎnyè. Lǚyóu yěshì yīzhǒng xiūxián yúlè huódòng, jùyǒu yìdìxìng hé zhànshíxìng děng tèzhēng. Yībān'éryán, lǚyóu jùyǒu guānguāng hé yóulì liǎngge bùtóng de céngcì, qiánzhě lìshí-duǎn, tǐyàn jiào-qiǎn; hòuzhě fǎnzhī.
# Saylor.org's English Composition/Using the Work of Others

Upon successful completion of this unit, the student will be able to:
* Demonstrate an understanding of and practice basic principles of incorporating outside sources into persuasive writing.
* Practice techniques for using research to support various logical structures and rhetorical strategies, including analysis, discussion, and comparison/contrast.
* Practice incorporating quotations, paraphrases, and summaries into academic writing.
* Identify the risks of plagiarism and practice techniques for avoiding it.
* Practice the basic requirements of MLA style and formatting.
* Research, develop, analyze, and edit an essay of moderate length.
# Saylor.org's English Composition/Writing as a Conversation between Reader and Writer

In short, the purpose of this course is to help you learn what distinguishes great writing from so-so writing from outright bad writing. One of the first things you should acknowledge if you want to learn how to be a good writer is that good writing isn't boring. You don't have to agree with its message or be convinced by its argument, but good writing is thought-provoking, interesting and above all, something worth reading.
Whys is it these things and not, say, unoriginal, bland and not worth reading? Because every piece of good writing, in essence, is a conversation between the reader and the writer. Inherent to the idea of writing as a conversation is notion that the author is trying to instruct or argue something to the reader and the reader is either being persuaded or being stimulated to think about contradictions to the author's point of view. Although the reader very likely will not have the opportunity to directly interact with the author to bring up points he/she agreed or disagreed with, the act of "conversing" with an author as a reader is a way in which a piece of writing leaves an impact. Of course, conversations can be one sided, but generally speaking, they aren't very interesting if one side monopolizes the exchange. If an author allows for no room for counter-argument or merely presents a laundry list of facts and statistics, there's no much room for a conversation and thus, not all that much value of intellectual stimulation to the reader. Good writing should not just inform, but it should spark interest in the reader to read, research or even write more on the topic.
# Saylor.org's English Composition/Reading to Write: Reading and Writing as Complementary Activities

One might argue that reading and writing are two very different activities, that require two very different types of thinking. Yet, in many ways, reading and writing are actually quire complementary. Without a doubt, some of the best advice to become a better writer is simply to become a better reader. Read often and read a lot. If you want to master writing in a specific field, the best way to get an understanding of how writing in that field is crafted is to read closely and examine the models presented by other writers. Not only will you pick up on vocabulary and jargon used by writers, you'll consciously (or sub-consciously) start to notice certain patterns and styles used by authors that you might like to adapt to make your own writing better. Alternatively, you can read the works of others and just as easily figure out examples of style that you don't think make for good writing.
# Saylor.org's English Composition/Subject/Verb Disagreement

When you write a sentence, make sure that your subject and verb agree. For example, do not use the plural first person conjugation of a verb when your subject is the singular first person. "I are" is wrong and it sounds wrong. Now, it's hopefully unlikely that you'd make such an obvious mistake, but there are tricky situations in which you might not be sure which verb form to use that often arise when combining subjects. For example "You/He/She/They and I" will take the plural first person conjugation. The conjunction 'and' in this sentence makes all the difference. If it were "You/He/She/They or I" will simply take the singular first person. "You or I am" not "You or I are".
Also remember that some words take singular third person form when you would think they take plural form, an example being the word 'everyone'. "Everyone knows" is correct, not "Everyone know". On the other hand, remember "All people know" not "All people knows". Just remember the 'one' in 'everyone' is an important distinction. It implies each individual, whereas 'all people' implies a collective whole. Other words like 'everyone' include each, each one, either, neither, everybody, anybody, anyone, nobody, somebody, someone, and no one. All take singular third person form.
The good news is that in English, many verbs take the same form no matter how you conjugate them (I eat, you eat, he/she/it eats, we eat, they eat).
# Saylor.org's English Composition/Rhetorical Strategies

Rhetoric---the art and technique of crafting an argument has been studied for thousands of years. Whether in spoken or written form, strong rhetoric can enhance your argument.
# Saylor.org's English Composition/Word Choice

Sometimes just choosing the right words can make all the difference when writing a paper. Good word choice means knowing when to use certain words and when not to use them. Not all words are equal and part of recognizing the value of a word is understanding both denotation and connotation. A word's denotation is its literal meaning, while connotation are implicit, unstated associations that come with the word. For example, 'scary' and 'terrifying' have roughly the same denotation, but most people would probably consider 'terrifying' a word to use to express a greater state of horror that 'scary'. Similar examples abound 'hot' and 'scorching', 'confusing' and 'bewildering', 'unclean' and 'filthy', 'smart' and 'ingenious'. In a sense, all these words are interchangeable, but sometimes the context of a sentence calls for one over the other. When you use a loaded word like 'ingenious' you risk sounding hyperbolic, when the sentence might really call for the more subdued 'smart'.
# Saylor.org's English Composition/Re-defining What It Means to Write

Upon successful completion of this unit, the student will be able to:
* Describe writing as a means of communication.
* Practice techniques for identifying and writing for specific audiences.
* Describe writing as a process and explain how that process influences thinking.
* Practice the stages of the PWR writing process.
* Practice prewriting techniques.
* Practice critical reading and thinking skills essential to college writing.
* Demonstrate an awareness of the importance of consistent style and formatting.
# Saylor.org's English Composition/Quoting

Quoting is a valuable tool when writing academic papers that allows an author to inject the voice or opinion or another into the writing to give another perspective. There are some important rules to keep in mind when you quote another. The most important thin, of course, is to cite the source of the quote (this will be covered in greater detail in this Wikibook's section on citation). In addition to citation, don't just "quote drop" without giving proper context to the quote. This context often involves introducing the person who said it and following up the quote with your interpretation of the quote (For example: "What X seems to be saying..." "X's statement on this shows..."). Take for instance President John F. Kennedy's famous quote: "Ask not what your country can do for you, ask what you can do for your country." A fully contextualized use of this quote might look like this:
In his inaugural address, President John F. Kennedy compelled Americans to "ask not what your country can do for you, ask what you can do for your country." Kennedy's statement asserted his belief in national service, epitomized by his creation of the Peace Corps.
Once again, this makes for better writing than simply throwing in the quote and not attempting to tie it back to your argument at hand.
Keep in mind when you quote that there are more ways to present a quote than just "X said _____". Remember, people "question", "think", "believe", "argue", "contend", "declare", and any number of other things besides just "saying" something.
# Saylor.org's English Composition/Writing as Conversation

In this section, you will learn how writing is, in a sense, a form of conversation. On the one hand, writing is a conversation with yourself as much as it is a conversation with a stated audience. In the process of creating a piece of writing, you will hopefully challenge your own assumptions so that your own argument can challenge the assumptions of your readers.
# LMIs in Control/Observer Synthesis/Continuous Time/Full-Order State Observer

LMIs in Control/Observer Synthesis/Continuous Time/Full-Order State Observer

## Full-Order State Observer

The problem of constructing a simple full-order state observer directly follows from the result of Hurwitz detectability LMI's, Which essentially is the dual of Hurwitz stabilizability. If a feasible solution to the first LMI for Hurwitz detectability exist then using the results we can back out a full state observer $L$ such that $A+LC$ is Hurwitz stable.

## The System

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

## The Data

* The matrices $A,B,C,D$ are system matrices of appropriate dimensions and are known.

## The Optimization Problem

The full-order state observer problem essential is finding a positive definite $P$ such that the following LMI conclusions hold.

## The LMI:

1) The full-order state observer problem has a solution if and only if there exist a symmetric positive definite Matrix $P$ and a matrix $W$ that satisfy
* $A^{T}P+PA+W^{T}C+C^{T}W<0.$
Then the observer can be obtained as $L=P^{-1}W$ 2) The full-state state observer can be found if and only if there is a symmetric positive definite Matrix $P$ that satisfies the below Matrix inequality
* $A^{T}P+PA-C^{T}C<0$
In this case the observer can be reconstructed as $L=-{\frac {1}{2}}P^{-1}C^{T}$. It can be seen that the second relation can be directly obtained by substituting $W=-{\frac {1}{2}}C^{T}$ in the first condition.

## Conclusion:

Hence, both the above LMI's result in a full-order observer $L$ such that $A+LC$ is Hurwitz stable.

## External Links

A list of references documenting and validating the LMI.
* LMIs in Control Systems Analysis, Design and Applications - Duan and Yu
* 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/Minimum-Rank Solutions of Linear Matrix Equations/Rank minimization problem: general form

WIP
LMIs in Control/Minimum-Rank Solutions of Linear Matrix Equations/Rank minimization problem: general form
The information on this page is referenced from: "Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization" by Benjamin Recht, Maryam Fazel, and Pablo A. Parrilo, published in SIAM Review 2010, Volume 52, Issue 3, pages 471-501.
Systems are very often represented by matrices. The rank of a matrix offers some very useful information about the system it represents. For instance: a state space representation of a system is controllable if its state matrix is full rank.
In some circumstances, finding a simpler model of a system is useful. For example; finding a lower-degree statistical model for a random process, discovering a low-order realization of a linear state space system model, and a finding lower order controllers for certain systems. In some circumstances, this reduction of order can be achieved by minimizing the rank of the appropriate matrix.

## The System

This problem is solvable only in certain circumstances. In general however, if the set of all models that can be used to describe the system and that satisfy the desired constraints is a convex set, ${\mathcal {C}}$, then the system ${\mathcal {X}}$ may be suitable for the LMI's application.
One specific case that is solvable is the case where the nuclear norm (the sum of the singular values of the matrix) is minimized over a set of feasible models or designs that are affine in the matrix variable ${\mathcal {X}}$. All cases discussed in the pages of this chapter fall into this category.

## The Data

The inputs for this LMI are the linear map ${\mathcal {A}}:{\mathcal {R}}^{m*n}to{\mathcal {R}}^{p}$ required to be affine in the matrix variable ${\mathcal {X}}\in {\mathcal {R}}^{m*n}$ and the vector ${\mathcal {b}}\in {\mathcal {R}}^{p}$.

## The LMI: General Form of the Rank Minimization Problem

       ${\begin{aligned}{\text{minimize}}\;{\text{rank}}X&\\{\text{subject to}}\;{\mathcal {A}}(X)=b&\\\end{aligned}}$

## Conclusion:

The result of this LMI is the guaranteed minimum rank representation of the system described by ${\mathcal {X}}$.

## Implementation

* - A downloadable matlab code implementation of this LMI using YALMIP.

## Related LMIs

Links to other closely-related LMIs

## External Links

* ↑ "Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization" (PDF). Retrieved 2019-11-08.
# LMIs in Control/Observer Synthesis

      * Continuous Time
      * Discrete Time
# LMIs in Control/Observer Synthesis/Continuous Time

      * Optimal Observer and State Estimation
      * Optimal Filter
      * Detectability LMI
      * LMI for the Observability Grammian
      * H-infinity filtering
      * H2 filtering
      * H2 Optimal Observer
      * HInf Optimal Observer
      * Mixed H2 HInf Optimal Observer
      * H2 Optimal Filter
      * HInf Optimal Filter
      * FDI Filter Design For Systems With Sensor Faults: an LMI
      * H$_2$ Optimal State estimation
      * Hurwitz Detectability
      * Full-Order State Observer
      * Full-Order H-infinity State Observer
      * Reduced-Order State Observer
# LMIs in Control/Observer Synthesis/Continuous Time/Full-Order H-infinity State Observer

In this section, we design full order H-$\infty$ state observer.

## The System

Given a state-space representation of a linear system
    ${\begin{aligned}\ {\dot {x}}(t)=Ax(t)+B_{1}u(t)+B_{2}w(t),x(0)=x_{0}\\\ y(t)=C_{1}x(t)+D_{1}u(t)+D_{2}w(t)\\\ z(t)=C_{2}x(t)\\\end{aligned}}$
* $x\in \mathbb {R} ^{n},y\in \mathbb {R} ^{l},zin\mathbb {R} ^{m}$ are the state vector, measured output vector and output vectors of interest.
* $w\in \mathbb {R} ^{p},u\in \mathbb {R} ^{r},$ are the disturbance vector and control vector respectively.

## The Data

$A,B_{1},B_{2},C_{1},C_{2},D_{1},D_{2}$ are system matrices

## Definition

For the system , a full order state observer of the form of equation (1) is introduced and the estimate of interested output is given by .
    ${\begin{aligned}\ {\dot {\hat {x}}}=(A+LC_{1}){\hat {x}}-Ly+(B_{1}+LD_{1})u\\\end{aligned}}$         (1)
The estimate of interested output is
    ${\begin{aligned}{\hat {z}}(t)=C_{2}{\hat {x}}(t)\\\end{aligned}}$         (2)
Given the system and a positive scalar $\gamma$ , L is found such that
    ${\begin{aligned}\|G_{{\tilde {z}}w}(s)\|_{\infty }=\gamma \\\end{aligned}}$         (3)

## LMI Condition

The $H_{\infty }$ state observers problem has a solution if and only if there exists a symmetric positive definite matrix $P$ and a matrix $W$ satisfying the below LMI
    ${\begin{aligned}{\begin{bmatrix}A^{T}P+C_{1}^{T}W^{T}+PA+WC_{1}&PB_{2}+WD_{2}&C_{2}^{T}\\(PB_{2}+WD_{2})^{T}&-\gamma I&0\\C_{2}&0&-\gamma I\end{bmatrix}}\\\end{aligned}}$         (4)
When such a pair of matrics is found, the solution is
    ${\begin{aligned}L=P^{-1}W\\\end{aligned}}$         (5)

## Implementation

This implementation requires Yalmip and Mosek.
* https://github.com/ShenoyVaradaraya/LMI--master/blob/main/hinf_obs.m

## Conclusion

Thus, an $H_{\infty }$ state observer is designed such that the output vectors of interest are accurately estimated.

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* 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 & Francis Group, 2013
# LMIs in Control/Observer Synthesis/Discrete Time

      * H2-Optimal Filter]
      * Hinf-Optimal Filter
      * Optimal Observer; Mixed
      * Optimal Observer; H2
      * Optimal Observer; Hinf
      * Discrete Time Detectability
      * Schur Detectability
# LMIs in Control/Parametric, Norm-Bounded Uncertain System Quadratic Stability (dual version)

LMIs in Control/Parametric, Norm-Bounded Uncertain System Quadratic Stability (dual version)

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Mp(t),&&p(t)=\Delta (t)q(t),\\q(t)&=Nx(t)+Qp(t),&&\Delta \in \mathbf {\Delta } \;:=\{\Delta \in \mathbb {R} ^{n\times n}:\|\Delta \|\leq 1\}\\\end{aligned}}$

## The Data

The matrices $A,M,N,Q$.

## The LMI: The Lyapunov Inequality

       ${\begin{aligned}{\text{Find}}\;&P>0,\mu \geq 0:\\{\begin{bmatrix}AP+PA^{T}&PN^{T}\\NP&0\end{bmatrix}}+\mu {\begin{bmatrix}MM^{T}&MQ^{T}\\QM^{T}&QQ^{T}-I\end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

The system above is quadratically stable if and only if there exists some mu >= 0 and P > 0 such that the LMI is feasible. This LMI is a good way to determine quadratic stability of a system with parametric, norm-bounded uncertainty.

## Implementation

A link to CodeOcean or other online implementation of the LMI

## Related LMIs

Links to other closely-related LMIs

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
# LMIs in Control/Positive Real Lemma

Positive Real Lemma
The Positive Real Lemma is a variation of the Kalman–Popov–Yakubovich (KYP) Lemma. The Positive Real Lemma can be used to determine if a system is passive (positive real).

## The System

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

## The Data

The matrices $A,B,C,D$ are known.

## The LMI: The Positive Real Lemma

Suppose ${\hat {G}}(s)(A,B,C,D)$ is the system. Then the following are equivalent.
       $1)\quad G\;{\text{is passive, i.e.}}\;\left\langle u,Gu\right\rangle _{L_{2}}\geq 0\;({\hat {G}}(s)+{\hat {G}}(s)^{*}\geq 0)$
       $2)\quad {\text{There exists a}}\;X>0\;{\text{such that}}$
             ${\begin{bmatrix}A^{T}X+XA&XB-C^{T}\\B^{T}X-C&-D^{T}-D\end{bmatrix}}\leq 0$

## Conclusion:

The Positive Real Lemma can be used to determine if the system $G$ is passive. Note from the (1,1) block of the LMI we know that $A$ is Hurwitz.

## Implementation

A link to CodeOcean or other online implementation of the LMI (in progress)

## Related LMIs

KYP Lemma (Bounded Real Lemma)

## 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.
# Perl Programming/Keywords/bless
## The bless keyword

The bless function tells the thingy REFERENCEd that it is an object in the CLASSNAME package. Without the word CLASSNAME, the current package is understood.
As bless is often the last command in the constructor, it returns a reference to the object.
# Perl Programming/Keywords/chdir
## The chdir keyword

chdir changeds the working directory to the new destination in EXPRESSION. Without EXPRESSION, it changes to the directory defined in $ENV{HOME}, if set. If this is also not set, it changes to $ENV{LOGDIR}. (On VMS, $ENV{SYS$LOGIN} is also checked.)
chdir returns true on success and false otherwise.
If the operating system supports fchdir(2), a DIRHANDLE or FILEHANDLE can also be used. If this is not the case, an exception is raised.

### Examples

| chdir | closedir | mkdir | opendir | readdir | rewinddir | rmdir | seekdir | telldir |
# Perl Programming/Keywords/chown
## The chown keyword

chown changes the owner and probably the group of a LIST of files. The first two elements of LIST must be numerical and contain the uid and gid. If one or both of these numbers are equal to -1, this is interpreted on most system that these values are to be left unchanged. Returns the number of successfully changed files.
# Perl Programming/Keywords/binmode
## The binmode keyword

The binmode function sets that FILEHANDLE is read or written in "binary" or "text" mode on systems where the run-time libraries distinguish such file types. If FILEHANDLE is an expression, its value is taken as FILEHANDLE name. The function returns true on success and undef otherwise, setting $! (errno). It is good programming practice to use it where appropriate and never to use it otherwise, as a missing call will result in errors on operating systems like DOS or Windows that differentiate such file types.
If LAYER is present, it is a single string that may contain multiple directives, which alter the behaviour of the FILEHANDLE. With LAYER, using binmode on a text file makes sense. Without LAYER or specified as :raw, the filehandle is made suitable for passing binary data. This includes turning off possible CRLF translation and as opposed to Unicode characters, marking it as bytes.