OpenLLM-France/wikimedia huggingface dataset:
# LMIs in Control/Click here to continue/LMIs in system and stability Theory/Stability Of Lure's System
## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{p}p(t)+B_{w}w(t),\\z(t)&=C_{z}x(t)\\p_{i}(t)&=\phi _{i}(q_{i}(t)),i=1,\dots ,n_{p}\\q&=C_{q}x,\\0&\leq \sigma \phi _{i}(\sigma )\leq \sigma ^{2}\ \forall \sigma \in \mathbb {R} \end{aligned}}$

## The Data

The matrices $A,B_{p},B_{w},C_{q},C_{z}$.

## The LMI: The Lure's System's Stability

The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.
       ${\begin{aligned}{\text{Find}}\;&P>0,\Lambda =diag(\lambda _{1},\dots ,\lambda _{n_{p}})\succeq 0,T=diag(\tau _{1},\dots ,\tau _{n_{p}})\succeq 0:\\&{\begin{bmatrix}A^{\top }P+PA&PB_{p}+A^{\top }C_{q}^{\top }\Lambda +C_{q}^{\top }T\\B_{p}^{\top }P+\Lambda C_{q}A+TC_{q}&\Lambda C_{q}B_{p}+B_{p}^{\top }C_{q}^{\top }\Lambda -2T\end{bmatrix}}\prec 0\\\end{aligned}}$

## Implementation

https://codeocean.com/capsule/0232754/tree

## Conclusion

If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.

## Remark

The LMI is only a sufficient condition for the existence of a Lur’e Lyapunov function that proves stability of Lur'e system . It is also necessary when there is only one nonlinearity, i.e., when $n_{p}=1$.

## 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/Click here to continue/LMIs in system and stability Theory/Stability under Arbitrary Switching

LMIs in Control/Stability Analysis/Continuous Time/Stability under Arbitrary Switching
Using the LMI below, find a P matrix that fits the constraints. If there exists one, then the system can switch between subsystems $A_{1}$ and $A_{2}$ arbitrarily and remain stable.

## The System

    ${\begin{aligned}{\dot {x}}(t)\in \{A_{1}x(t),A_{2}x(t)\}\end{aligned}}$

## The Data

The matrices $A_{1}\in R^{n\times n},A_{2}\in R^{n\times n}$.

## The LMI

       ${\begin{aligned}{\text{Find}}\;&P>0:\\A_{1}^{T}P+PA_{1}<0{\text{ and }}\\A_{2}^{T}P+PA_{2}<0\end{aligned}}$

## Conclusion

The switched system is stable under arbitrary switching if there exists some P > 0 such that the LMIs hold.

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

Parametric, Norm-Bounded Uncertain System Quadratic Stability
Stability of Structured, Norm-Bounded Uncertainty
Quadratic Stability Margins

## External links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
# LMIs in Control/Click here to continue/LMIs in system and stability Theory/System Zeros without Feedthrough

Let's say we have a transfer function defined as a ratio of two polynomials: ${\begin{aligned}H(s)={\frac {N(s)}{D(s)}}\\\end{aligned}}$ Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting $N(s)=0$ and solving for s.The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs. Similarly, the system zeros are either real or appear in complex conjugate pairs. In the case of system zeros without feedthrough, we take the assumption that $D=0$.

## The System

Consider a continuous-time LTI system, $G$ , with minimal statespace representation $(A,B,C,0)$
       ${\begin{aligned}{\dot {x}}(t)=Ax(t)+Bu(t)\\y(t)=Cx(t)\end{aligned}}$

## The Data

The matrices:
    ${\begin{aligned}A\in \mathbb {R} ^{n\times n}\\M\in \mathbb {R} ^{n\times q}\\N\in \mathbb {R} ^{q\times n}\\\end{aligned}}$

## The LMI: System Zeros without feedthrough

The transmission zeros of $G(s)=C(sI-A)^{-}1B$ are the eigenvalues of $NAM$, where $N\in \mathbb {R} ^{q\times n},M\in \mathbb {R} ^{n\times q},CM=0,NB=0,NM=1.$. Therefore , $G(s)$ is a minimum phase if and only if there exists $P\in \mathbb {S} ^{q}$, where $P>0$ such that
       ${\begin{aligned}PNAM+M^{T}A^{T}N^{T}P<0\end{aligned}}$

## Conclusion:

If P exists, it ensures non-minimum phase. Eigenvalues of NAM then gives the zeros of the system.

## Implementation

https://github.com/Ricky-10/coding107/blob/master/Systemzeroswithoutfeedthrough

## 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.
* Control_Systems/Poles_and_Zeros
# LMIs in Control/Click here to continue/LMIs in system and stability Theory/Stability of Linear Delayed Differential Equations
## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+\sum _{i=1}^{L}A_{i}x(t-\tau _{i}),\\\end{aligned}}$
where $x(t)\in \mathbb {R} ^{n}$ and $\tau _{i}>0$.

## The Data

The matrices $A,\{A_{i}.\tau _{i}\}_{i=1}^{L}$.

## The LMI:

Solve the following LMIP
       ${\begin{aligned}&{\text{Find}}\{P\succ 0,P_{1}\succ 0,\dots ,P_{L}\succ 0\}:\\&\quad s.t.{\begin{bmatrix}A^{\top }P+PA+\sum _{i=1}^{L}P_{i}&PA_{1}&\dots &PA_{L}\\A_{1}^{\top }P&-P_{1}&\dots &0\\\vdots &\vdots &\ddots &\vdots \\A_{L}^{\top }P&0&\dots &-P_{L}\end{bmatrix}}\prec 0,P_{1}\succ 0,\dots ,P_{L}\succ 0.\end{aligned}}$

## Implementation

https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/50fc71737b69f2cf57d15634f2f19d091bf37d02

## Conclusion

The stability of the above linear delayed differential equation is proved, using Lyapunov functionals of the form $V(x,t)=x(t)^{\top }Px(t)+\sum _{i=1}^{L}\int _{0}^{L}x^{\top }(t-s)P_{i}x(t-s)\ ds$, if the provided LMIP is feasible.

## Remark

The techniques for proving stability of norm-bound LDIs [Boyd, ch.5] can also be used.

## 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/Click here to continue/LMIs in system and stability Theory/Transient Bound for Discrete-Time Non-Autonomous LTI Systems
## The System

For a discrete-time LTI system with a state-space representation of:
$x_{k+1}=A_{d}x_{k}+B_{d}u_{k},$
where $A_{d}\in \mathbb {R} ^{nxn}$, and $B_{d}\in \mathbb {R} ^{nxm}$,
the transient bound can be analyzed with the LMI below.

## The Data

$A_{d}\in \mathbb {R} ^{nxn}$, and $B_{d}\in \mathbb {R} ^{nxm}$

## The LMI:

The Euclidean norm of the state satisfies:
$\lVert x_{k}\rVert _{2}^{2}\leq \gamma ^{2}(\lVert x_{0}\rVert _{2}^{2}+\lVert u\rVert _{2k}^{2}),\forall k\in \mathbb {Z} _{\geq 0}$
if there exists some $P\in \mathbb {S} ^{n}$ and $\gamma \in \mathbb {R} _{>0}$, where P > 0 such that:
* $P-\gamma 1\leq 0,$
* ${\begin{bmatrix}P&1\\*&\gamma 1\end{bmatrix}}\geq 0,$
* ${\begin{bmatrix}A_{d}^{T}PA_{d}-P&A_{d}^{T}PB_{d}\\*&B_{d}^{T}B_{d}-\gamma 1\end{bmatrix}}\leq 0.$
if x$_0$ = 0 and u is a unit-energy input ($\lVert u\rVert _{2k}\leq 1,\forall k\in \mathbb {Z} _{\geq 0}$), then the above LMIs ensure that $\lVert x_{k}\rVert _{2}\leq \gamma ,\forall k\in \mathbb {Z} _{\geq 0}$

## Conclusion

By using this LMI the transient state bound can be analyzed for a given non-autonomous LTI system.

## Implementation

The LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.

## Related LMIs

* Output Energy Bound for Discrete-Time Autonomous LTI Systems

## External Links

* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
# LMIs in Control/Click here to continue/LMIs in system and stability Theory/Stability of Quadratic Constrained Systems
## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+B_{p}p(t)+B_{u}u(t)+B_{w}w(t),\\q(t)&=C_{q}x(t)+D_{qp}p(t)+D_{qu}u(t)+D_{qw}w(t),\\z(t)&=C_{z}x(t)+D_{zp}p(t)+D_{zu}u(t)+D_{zw}w(t)\\\int _{0}^{t}&p^{\top }(\tau )p(\tau )\ d\tau \leq \int _{0}^{t}q^{\top }(\tau )q(\tau )\ d\tau .\end{aligned}}$

## The Data

The matrices $A,B_{p},B_{w},C_{q},C_{z},D_{qp},D_{zw}$.

## The LMI:

The following feasibility problem should be solved.
       ${\begin{aligned}{\text{Find}}\;&\{P\succ 0,\lambda \geq 0\}:\\&s.t.\quad {\begin{bmatrix}A^{\top }P+PA+\lambda C_{q}^{\top }C_{q}&PB_{p}+\lambda C_{q}^{\top }D_{qp}\\(PB_{p}+\lambda C_{q}^{\top }D_{qp})^{\top }&\lambda (I-D_{qp}^{\top }D_{qp})\end{bmatrix}}\prec 0.\end{aligned}}$

## Implementation

https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/38f3b55ca7060a1260384a96e9dc31142af07a9a

## Conclusion

The integral quadratic constrained system is stable if the provided LMI is feasible

## Remark

The key point of the proof is to satisfy ${\dot {V}}<0$ whenever $p^{\top }p\leq q^{\top }q$, using ${\mathcal {S}}$-procedure.

## 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/Click here to continue/LMIs in system and stability Theory/Stability of Structured, Norm-Bounded Uncertainty

LMIs in Control/Click here to continue/LMIs in system and stability Theory/Stability of Structured, Norm-Bounded Uncertainty
Given a system with matrices A,M,N,Q with structured, norm-bounded uncertainty, the stability of the system can be found using the following LMI. The LMI takes variables P and $\Theta$ and checks for a feasible solution.

## The System

    ${\begin{aligned}{\dot {x}}(t)&=Ax(t)+Mp(t),&&p(t)=\Delta (t)q(t),\\q(t)&=Nx(t)+Qp(t),&&\Delta \in {\bf {{\Delta }\;,||\Delta ||\leq 1}}\\\end{aligned}}$

## The Data

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

## The LMI:

       ${\begin{aligned}{\text{Find}}\;&P>0:\\{\begin{bmatrix}AP+PA^{T}&PN^{T}\\NP&0\end{bmatrix}}+{\begin{bmatrix}M\Theta M^{T}&M\Theta Q^{T}\\Q\Theta M^{T}&Q\Theta Q^{T}-\Theta \end{bmatrix}}<0\\\end{aligned}}$

## Conclusion:

${\begin{aligned}{\text{The system above is quadratically stable if and only if there exists some }}\Theta \in P\Theta {\text{ and }}P>0{\text{ such that the LMI is feasible.}}\end{aligned}}$

## Implementation

https://github.com/mcavorsi/LMI

## Related LMIs

Parametric, Norm-Bounded Uncertain System Quadratic Stability
Stability under Arbitrary Switching
Quadratic Stability Margins

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
# Introduction to Philosophy/The Social Contract

An idea of a social contract draws from teleological thinking as opposed to a modern naturalistic view of sociocultural evolution. A social contract is a hypothetical agreement between primitive, "unsocialized" people, who decided to form a society in order to avoid wars and violence, by instead creating specific rules - laws - that would organize the group life. A notable founder of the social contract model, Thomas Hobbes, presents a totally rationalistic view on human nature, which is a main point of contemporary critique.
# Introduction to Philosophy/Rationalism

Rationalism is a philosophical movement declaring that the most certain form of knowledge is derived from reason and that our senses are not reliable submitters of information about the outer world. The most famous rationalists were Descartes, Spinoza and Leibniz, creating theories of knowledge totally independent from any experience. The senses, according to the rationalists, can not tell us real truth, for example: we could dream that we are the king of the world and not truly be, but the angles of a triangle still sum up to 180 degrees. Knowledge from reason alone and not experience is known as a priori. Plato is considered by many to be the main precursor to rationalism, whereas his student, Aristotle, is often considered to be a precursor to empiricism.

## Reference and further readings

* Rationalism at Wikipedia.
# Introduction to Philosophy/Resources For Editing
## Part I - The Nature of Philosophy

* Origins of Philosophy
* What is Philosophy
* The Branches of Philosophy
* What is meant by "Doing Philosophy?"

## Part II - Metaphysics

* What is Metaphysics?
* What is a Person?
* What is Buddhist Philosophy?

## Part III - Epistemology

* What is Epistemology?
* Rationalism
* Empiricism
* Pragmatism

## Part IV - Logic

* Logic

## Part V - Ethics

* What are Ethics?
* What is a Person?
* Virtue and value-Ethics
* Deontology
* Utilitarianism
* Existentialism
* Zen Buddhism
* Transcendentalist Theology Transcendentalism

## Part VI - Aesthetics

* Aesthetics

## Part VII - Political Philosophy

* What is Political Philosophy?
* The Political Spectrum
* Ancient Political Philosophy
* Middles Ages Political Philosophy
* Social Contract
* Marx and Marxists
* Liberalism
* Communitarianism
* Conservativism
* Anarchism
* Post-Politics
* Theocracies
# Introduction to Philosophy/Transcendentalist Theology Transcendentalism

Transcendentalist Theology concept supports existentialism in the way it relates to man's responsibility for his own soul with the premise that human fallibility and misconceptions have labeled spirituality as God for the past several millennia; as one who interferes with the natural forces and free will of people by threatening punishment to those who disobey his bidding. The spiritual existence of this deity, if one decides to accept this premise, could not have changed with the times but the perception of who or what this deity is should change as societies eliminate their superstitious beliefs. This “God” could not possibly be encumbered by human attributes, needs or desires to be worshiped, prayed to, exalted, venerated, deified, or anything else that mankind has to offer. It is also the human characteristics and attributes that exercise upon others: power, control, dominance, destruction, punishment, revenge, and judgment.
The destruction of civilizations, most sufferings and premature deaths are due to human frailties, stupidity or imperfections and are not God's doings. The true “God” is a Spiritual Unity that exists in a spiritual realm and never has and never will interfere with anything on earth or in the universe. God is interested in and is involved in humanity, but does not interfere in any way in our physical lives. God guides the development of the universe and everything thereon like a Master Planner. Our relationship and interaction of our spirit with the Spirit of God is for our, not God's benefit.

## Reference and further readings

* Transcendentalism at Wikipedia.
# Introduction to Philosophy/Pragmatism

Pragmatism is a philosophy that was developed and passed on by Peirce, Quine, James, and others.
The Correspondence Theory of Truth, which was held by Aristotle among others, holds that when we say something is true, this means that my understanding of reality corresponds with reality. So if I say that the Sun revolves around the Earth, it is not true because this does not correspond to reality. On the other hand, a Pragmatist would say that if it "works" for you, if it does not make your life problematic and has no significant impact on your life, then it is "true" in the sense that it works; it's pragmatic. This is similar to the perspectivist view adopted by Nietzsche.
See William James (1842-1910):
http://www.connect.net/ron/james.html

## Reference and further readings

* Pragmatism at Wikipedia.
# Introduction to Philosophy/Theocracies

A "god" by definition is "that which ultimately calls the shots". The human propensity to ultimately rely on something as a basis for judgment is universal and inescapable. As it is true in every individual life, so it is true in societies as a whole. Some source gives the basis for meaning and the interpretation of reality.
Some countries are very explicit in decreeing their basis, which is religious by nature. Israel is a good example in that it claims Judaism as its "official" religion. Laws, holidays, family structures, education, etc. stem from that faith. So it is with England. England claims to be "Christian" by religion and Anglican by denomination. In Spain, you cannot hold political office unless you are a professed Catholic. These countries and many others declare by edict or law what the religious perspective is, though that in and of itself does not necessarily demand individual subserviance.
The bottom line is that every society has a god as its foundation. It is inescapable. There is an inevitable "theology" that serves as an ethical infrastructure. America originally was an assumed and decreed Christian nation, though the individual states had substantial autonomy. The state of Delaware originally demanded that all elected and appointed officials of the state believed in Jesus Christ and held to the Old and New Testaments. That is perhaps one of the most pointedly self concious civil requirements available in modern history.
However, recognizing that all societies have rudimentary religious foundations does not imply that these foundations are theistic. The former Soviet Union had an atheistic basis. This too is a theological perspective. In philosophical and theological terms, every belief is either theonomic or autonomous (God-centered or man-centered). There is no escape and there are no other options.
For instance, in America we talk freely and routinely about liberty. Liberty is synonomous with freedom. The Declaration of Independence held that rights were originally given by God and therefore, it was wrong for man to take them away. Notice the theological basis for this position. God was the giver, man was the recipient. All through American history there were laws made, wars fought and ethics derived from that basic and foundational theological position.
In France, after the American Revolution, there was a similar revolution. This revolution too was based on a theological perspective. This perspective, developed and purported by Robiespierre, made man his own God and concommitantly pushed Christianity out of the picture. It was a horrible experiment, yet it was clearly theologically oriented. Consequently, it is not a matter of theocracy vs no theocracy; it is a matter of which theocracy. The term "theocracy", like so many other terms in philosophy and theology, is not a happy one. Nevertheless, the term is used repeatedly.
# K-12 School Computer Networking/Chapter 2

Motivational book: The Spotlight along the way
# K-12 School Computer Networking/Chapter 10
## Malware

DPWEISBORD
Imagine that you are having a great day and then all of a sudden your head starts to ache, your muscles may hurt, you may start to get a fever or the chills. These are all the signs that a person can be coming down with a bug or virus. Sometimes the bug can last for only a couple of days and sometimes it may take longer for the body to rid itself of the germs.
For a computer, getting sick can cause a lot of headaches as well. Malware, which many times is also known as Malicious Software is a general term. In the simplest form, it is a general term used by many computer professionals to describe annoying, dangerous, or intrusive computer code. Many times malware can cause minor problems, but sometimes these can turn major.
Malware is a term used to broadly classify a form of software which is installed in a computer system mostly without the owners permission with malicious intentions.
It is also important to note that many times the media uses the term computer virus to describe malware. While malware can be a computer virus, not all computer viruses are malware. In addition, malware should not be confused with defective software.
Types of malware may include worms, computer viruses, trojan horses, adware and other unwanted dangerous software.

## Types of Malware

-Spyware -Adware -Trojans -Viruses -Browser Hijackers -Rootkit -Web bug or Web beacons -Keyloggers -Malicious Dialers -Tracking Cookies

## Ways to get infected

There are a number of ways to get infected with malware. These can include visiting websites and downloading (knowingly and unknowingly) software; e-mail, ftp, downloading other programs from a disk or cd.

## References

http://www.wikipedia.org/
F-Secure Quarterly Security Wrap-up for the first quarter of 2008". F-Secure (March 31, 2008).
"Google searches web's dark side", BBC News (May 11, 2007)
http://arstechnica.com/articles/paedia/malware.ars (2004)
http://www.malwarehelp.org/

## Questions

1. Another name for malware is:
2. Malware's most common pathway from criminals to users is through the Internet, by email and the World Wide Web.
3. Many of the first forms of malware were written with the intention to be dangerous
4. Spyware is a "for-profit" form of malware
5. E-mail is the preferred way to spread malware
6. Infections via "drive-by" download are spread through the Web over HTTP and FTP when resources containing spurious keywords are indexed by legitimate search engines, as well as when JavaScript is surreptitiously added to legitimate websites and advertising networks.

## Answer Key

Answers: 1:B 2:A 3:B: Many of the first forms of malware were written as experiments or pranks 4:A 5:B: The World Wide Web is criminals' preferred pathway for spreading malware. About one in ten Web pages may contain malicious code. 6:A
# K-12 School Computer Networking

K-12 School Networking: An Online Resource for the Technical Coordinator

## Table of contents

    Introduction
    Methodology
* Introduction to School Computer Networking
* Understanding a Network
* Computer Operating Systems
* Designing a Network
* Specialized Services
* Elements of Network Infrastructure
* Vendor Relationships
* Server Types and Roles
* Security Fundamentals
* Understanding Malware
* Spam, Phishing & Hoaxes
* Firewalls
* Backup Strategies
* Text-based Communications
* Disaster Planning
* School Websites
* Blogs & Wikis
* Troubleshooting Strategies
* Remote Control
* Fundamentals of the Internet
* Staff Relations
* Effective use of Volunteers
* Career Strategies
* Educational Grant Writing for Technology
* Distance Learning
* Multimedia
* Search Engine
* Quality Control
* Computer Based Communications
* Netbooks in Schools
* WIFI in Schools
* Digital Citizenship
* Teaching and Technology
* Free/Open Source Software and Learning/Course/Content Management Systems
# K-12 School Computer Networking/Chapter 13

View a YouTube video on Backup Strategies: Backup your Data
# Japanese/Kanji/Lesson 1

In this lesson you are going to learn how to write the kanji characters for 一, 二, 三, 四, 五. You will also learn the two readings for each kanji: the onyomi (音読(おんよ)み; Chinese reading) and the kunyomi (訓読(くんよ)み; native Japanese reading).
| Meaning: one | 音読み： イチ・イツ | 一日 (いちにち) one day, all day 一回 (いっかい) one time |
| Meaning: one | 訓読み： ひと(つ) | 一人 (ひとり) one person |
| Meaning: one | Special readings: つい | 一日 (ついたち) first day of the month |
| 名乗り： かず, い, いっ, いる, かつ, かづ, てん, はじめ, ひ, ひとつ, まこと ||
| Meaning: two | 音読み： ニ | 二度 (にど) two times, twice |
| Meaning: two | 訓読み： ふた(つ) | 二人 (ふたり) two people |
| 名乗り： おと, つぐ, にい, は, ふ, ふたつ, ふだ, わ ||
| Meaning: three | 音読み： サン | 三人 (さんにん) three people |
| Meaning: three | 訓読み： みっ(つ) | 三日 (みっか) third day of the month |
| 名乗り： か, さ, さい, さえ, さぶ, ざ, ざえ, ざぶ, そう, ぞ, ただ, みつ, みん, も, や ||
| Meaning: four | 音読み： シ | 四月 (しがつ) April |
| Meaning: four | 訓読み： よっ(つ)・よ（つ）・よん・よ | 四つ (よっつ、よつ) four items 四人 (よにん) four people 四時 (よじ) four o'clock |
| 名乗り： あ, つ, よつ ||
| Meaning: five | 音読み： ゴ | 五時 (ごじ) five o'clock |
| Meaning: five | 訓読み： いつ（つ） | 五つ (いつつ) five items 五日 (いつか) fifth day of month |
| 名乗り： い, さ, さつ, ち, ふ, み, め ||