text:
User talk:Olgavladrus

History of Education in the USA
Immigration Period text The earliest schools were established in the British colonies of the North Atlantic in the 17th century to train boys for reading the Bible. Boston Latin School was established in 1635. Dedham, Massachusetts, had the first tax-funded public school. The Massachusetts Bay Colony made basic education obligatory in the 1640s, and other colonies followed suit. Originally, schools were only for boys, and instruction was given orally. Although the initial textbooks were transported from England, Boston printers republished the English grammar book in their own version in 1690. In the 18th century, public schools were often funded through a combination of local appropriations and fees collected on households with school-age children. The same teacher taught all of the kids in the same room. Except for basic literacy and numeracy, enrollment at a private school was necessary. In 1821, Boston opened the first public high school in the United States. When the British took over New Holland in 1664, most cities already had elementary schools. These schools had ties to the Dutch Reformed Church. German settlers in New York, New Jersey, Pennsylvania, and Maryland supported elementary schools that were closely linked to their churches. In 1727, the sisters of the Order of Saint Ursula established the first North American school for girls in New Orleans, France. By the 1740s, high school women in Philadelphia were also receiving formal education. Primary education for girls began in New England as early as 1767, although female education remained optional and was not available in many communities.

Education and Slavery text

Because the southern section of the United States was a slaveholding territory, only whites could study there; it was completely banned to teach enslaved Africans to read and write in the South of the United States. Religious training and basic reading were sometimes advocated for black African Americans in the more progressive northern states. The Church of England and the Society for the Propagation of the Gospel in Foreign Countries collaborated in New York to convert the enslaved African people to Christianity. In 1703 the first black Anglican school in New York was established. Governor Robert Hunter issued a proclamation in 1711 ordering slave owners to enable enslaved Africans to attend religious lessons. Education in the United States has been racially segregated (white and black pupils attended separate schools) for the majority of its history, initially in the north then, after the Civil War, when blacks were allowed to attend school, in the south. Noyes Academy in Canaan, New Hampshire, was an early racially integrated school that was burned by local whites in 1835 and then reestablished as an all-white institution. In 1848, the daughter of Frederick Douglas, the preeminent black abolitionist in the United States, passed her entrance examinations and was enrolled to Rochester, New York's prestigious Seward Seminary, but she was educated separately from white pupils and was later expelled. Slavery hampered the establishment of public education for all children in the American South. Typically, the planter class hired nannies or sent their children to private schools, sometimes in the North and occasionally in Europe. Immediately following the end of the civil war, 1,000 schools were established, educating 90,000 former slaves and their offspring.

Teachers and Educators text

Teaching was generally temporary occupation for women until they married, or for men until they took up their major career or found another job in the nineteenth century. Teachers have little training and no official authority. This began to alter in 1823 with the construction of two-year normal or instructional schools, but teaching did not need four years of formal training at a teacher's college in many parts of the United States until after World War II. Despite these and other issues, by 1870, all states had free primary schools, and the US population had one of the highest literacy rates in the world. In the nineteenth century, Horace Mann of Massachusetts was a leading proponent of educational reform. Mann advocated for a nationwide professional teacher training system and compulsory school attendance regulations as Secretary of Education. By 1900, 34 states had mandated school attendance. Thirty states mandated school attendance until the age of fourteen, and by 1910, three-quarters of American children were enrolled. Every state required pupils to complete primary school by 1918. However, educational possibilities were not equal across the country, with education spending in the southern regions being significantly lower.

Immigrants text

In the post-Civil War era, probably less than 5% of American youths attended a public high school. However, there was an exponential development in secondary education from 1880 to 1924, accompanied by the entry of new immigrants from southern and eastern Europe. Secondary schools had over 200,000 pupils in 1890 and nearly 2,000,000 by 1920, representing an increase from 7% of the population aged 14 to 17 to more than 30%. Between 1890 and 1924, increasingly violent clashes erupted over the high school's function. The Committee of Ten, comprised of top American university academics, advocated in 1893 that public secondary schools emphasize liberal arts instruction. When the country was faced with how to Americanize millions of young people with roots in countries at war with the United States during World War I, the National Educational Association's Commission for the Reorganization of Secondary Education advocated for a more diverse education that included vocational and commercial fields.

Most urban schools were preparing for •	College admission: •	Commercial courses (mostly designed to train young women for office jobs), •	Vocational courses (industrial craft for men and household for women) •	General (which offered a diploma without any special training).

Around 9% of Americans had a high school diploma in 1910. This figure rose to 40% by 1935 and 50% by 1940, yet the rate of expansion is deceiving. Because there was no employment during the Great Depression, many boys and girls stayed in school. During the twentieth century, the percentage of teenagers who completed high school climbed from 6% to 85%. high schools offered four school streams by 1920:

title: User talk:Olgavladrus


text:
LMIs in Control/Click here to continue/LMIs in system and stability Theory/Transient Impulse Response Bound for Non-Autonomous LTI systems

Transient Impulse Response Bound

The System
For a single-input multi-output continuous-time LTI system with state-space realization

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ y&=Cx\\ \end{align}$$

where $$A \in \mathbb{R}^{n \times n}$$, $$B \in \mathbb{R}^{n \times 1}$$ and $$C \in \mathbb{R}^{p \times 1}$$.

The Data
$$A \in \mathbb{R}^{n \times n}$$, $$B \in \mathbb{R}^{n \times 1}$$ and $$C \in \mathbb{R}^{p \times 1}$$.

Also it is assumed that Z(t)=C$e^{\text{At}}$ B be the unit impulsive response of the system.

The LMI
If the Euclidean norm of the impulse response satisfies. $$\lVert z(T) \rVert \leq \gamma, \forall T \in \mathbb{R}_{\geq 0}$$ and if there exist $$P \in \mathbb{S}^p$$ and $$\gamma \in \mathbb{R}_{> 0}$$,where P > 0, such that

 * $$\begin{bmatrix} P & PB \\ * & \gamma \end{bmatrix} \geq 0, $$

 * $$\begin{bmatrix} P & C^T \\ * & -\gamma 1 \end{bmatrix} \geq 0 . $$

 * $$PA+AP \leq 0 $$

Proof

 * The proof follows same procedure as the proof for transient output Bound for Autonomous LTI systems, but in this case taking $$ X_{0}=B $$as the initial condition that yields the result $$X^{T}(T)PX(T)\leq B^{T}PB$$.

 * Using the non-strict Schur complement, the matrix inequality in $$\begin{bmatrix} P & C^T \\ * & -\gamma 1 \end{bmatrix} \geq 0 . $$ is equivalent to $$B^{T}PB\leq \gamma $$. Substituting this and $$\begin{bmatrix} P  & C^T \\ * & -\gamma 1 \end{bmatrix} \geq 0 $$ into $$X^{T}(T)PX(T)\leq B^{T}PB$$ gives the desired result.

The System
For the single-input multi-output discrete-time LTI system with state-space realization,

\begin{align} \ x_{k+1}&=A_{d}x_{k}+B_{d}u_{k}\\ y_{k}&=C_{d}x_{k}\\ \end{align}$$

where $$A \in \mathbb{R}^{n \times n}$$, $$B_{d} \in \mathbb{R}^{n \times 1}$$ and $$C_{d} \in \mathbb{R}^{p \times n}$$ and it is assumed that $$A_{d}$$ is invertible. It is also considered that $$ Z_{k}C_{d}A^{k-1}_{d}B_{d}$$ be the unit impulse response of the system.

The Data
$$A \in \mathbb{R}^{n \times n}$$, $$B_{d} \in \mathbb{R}^{n \times 1}$$ and $$C_{d} \in \mathbb{R}^{p \times n}$$

The LMI
If the Euclidean norm of the impulse response satisfies. $$\lVert z_{k} \rVert_{2} \leq \gamma, \forall k \in \mathbb{Z}_{\geq 0}$$ and if there exist $$P \in \mathbb{S}^p$$ and $$\gamma \in \mathbb{R}_{> 0}$$,where P > 0, such that

 * $$\begin{bmatrix} P & PA_{d}^{-1}B_{d} \\ * & \gamma \end{bmatrix} \geq 0, $$

 * $$\begin{bmatrix} P & C^T_{d} \\ * & \gamma 1 \end{bmatrix} \geq 0, $$

 * $$A^T_{d}PA_{d}-P \leq 0. $$

Proof

 * The proof follows same procedure as for transient output bound for Discrete time autonomous LTI sysyems,but taking $$X_{0}=A_{d}^{-1}B_{d} $$as the initial condition, so that the unit impulse response matching the free response $$Z_{k}=C_{d}A_{d}^{k}X_{0}$$.

 * This yields the result$$X_{k}^{T}PX_{k}\leq B_{d}^{T}A_{d}^{-T}PA_{d}^{-1}B_{d}$$.

 * Using the non-strict Schur complement, the matrix inequality $$\begin{bmatrix} P & PA_{d}^-1B_{d} \\ * & \gamma \end{bmatrix} \geq 0, $$ is equivalent to the inequality $$ B_{d}^TA_{d}^-TPA_{d}^-1B_{d}\leq \gamma$$.Substituting this and  $$\begin{bmatrix} P  & C^T_{d} \\ * & \gamma 1 \end{bmatrix} \geq 0 , $$ into $$X_{k}^{T}PX_{k}\leq B_{d}^{T}A_{d}^{-T}PA_{d}^{-1}B_{d}$$.gives the desired result.

Conclusion
The above LMIs can be used to analyze the Transient Impulse Response Bound and analyze the Discrete-Time Transient Impulse Response Bound for the given system.

Implementation
This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
User talk:2600:8800:1305:F300:B159:7032:6B3C:B41D

Welcome
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Happy editing! Xeverything11 (discuss • contribs) 19:33, 25 November 2022 (UTC)


text:
User:Olgavladrus

Objectives. Overview of the chapter
After reading this chapter learners will have an idea about:

 * history of education in the USA
 * immigration period
 * education during slavery period
 * teachers and educator of that period
 * immigrants

Immigration Period
Earliest schools were established in the British colonies of the North Atlantic in the 17th century to train boys for reading the Bible. Boston Latin School was established in 1635. Dedham, Massachusetts, had the first tax-funded public school. The Massachusetts Bay Colony made basic education obligatory in the 1640s, and other colonies followed suit. Originally, schools were only for boys, and instruction was given orally. Although the initial textbooks were transported from England, Boston printers republished the English grammar book in their own version in 1690. In the 18th century, public schools were often funded through a combination of local appropriations and fees collected on households with school-age children. The same teacher taught all of the kids in the same room. Except for basic literacy and numeracy, enrollment at a private school was necessary. In 1821, Boston opened the first public high school in the United States. When the British took over New Holland in 1664, most cities already had elementary schools. These schools had ties to the Dutch Reformed Church. German settlers in New York, New Jersey, Pennsylvania, and Maryland supported elementary schools that were closely linked to their churches. In 1727, the sisters of the Order of Saint Ursula established the first North American school for girls in New Orleans, France. By the 1740s, high school women in Philadelphia were also receiving formal education. Primary education for girls began in New England as early as 1767, although female education remained optional and was not available in many communities.

Education and Slavery
Because the southern section of the United States was a slaveholding territory, only whites could study there; it was completely banned to teach enslaved Africans to read and write in the South of the United States. Religious training and basic reading were sometimes advocated for black African Americans in the more progressive northern states. The Church of England and the Society for the Propagation of the Gospel in Foreign Countries collaborated in New York to convert the enslaved African people to Christianity. In 1703 the first black Anglican school in New York was established. Governor Robert Hunter issued a proclamation in 1711 ordering slave owners to enable enslaved Africans to attend religious lessons. Education in the United States has been racially segregated (white and black pupils attended separate schools) for the majority of its history, initially in the north then, after the Civil War, when blacks were allowed to attend school, in the south. Noyes Academy in Canaan, New Hampshire, was an early racially integrated school that was burned by local whites in 1835 and then reestablished as an all-white institution. In 1848, the daughter of Frederick Douglas, the preeminent black abolitionist in the United States, passed her entrance examinations and was enrolled to Rochester, New York's prestigious Seward Seminary, but she was educated separately from white pupils and was later expelled. Slavery hampered the establishment of public education for all children in the American South. Typically, the planter class hired nannies or sent their children to private schools, sometimes in the North and occasionally in Europe. Immediately following the end of the civil war, 1,000 schools were established, educating 90,000 former slaves and their offspring.

Teachers and Educators
Teaching was generally temporary occupation for women until they married, or for men until they took up their major career or found another job in the nineteenth century. Teachers have little training and no official authority. This began to alter in 1823 with the construction of two-year normal or instructional schools, but teaching did not need four years of formal training at a teacher's college in many parts of the United States until after World War II. Despite these and other issues, by 1870, all states had free primary schools, and the US population had one of the highest literacy rates in the world. In the nineteenth century, Horace Mann of Massachusetts was a leading proponent of educational reform. Mann advocated for a nationwide professional teacher training system and compulsory school attendance regulations as Secretary of Education. By 1900, 34 states had mandated school attendance. Thirty states mandated school attendance until the age of fourteen, and by 1910, three-quarters of American children were enrolled. Every state required pupils to complete primary school by 1918. However, educational possibilities were not equal across the country, with education spending in the southern regions being significantly lower.

Immigrants
In the post-Civil War era, probably less than 5% of American youths attended a public high school. However, there was an exponential development in secondary education from 1880 to 1924, accompanied by the entry of new immigrants from southern and eastern Europe. Secondary schools had over 200,000 pupils in 1890 and nearly 2,000,000 by 1920, representing an increase from 7% of the population aged 14 to 17 to more than 30%. Between 1890 and 1924, increasingly violent clashes erupted over the high school's function. The Committee of Ten, comprised of top American university academics, advocated in 1893 that public secondary schools emphasize liberal arts instruction. When the country was faced with how to Americanize millions of young people with roots in countries at war with the United States during World War I, the National Educational Association's Commission for the Reorganization of Secondary Education advocated for a more diverse education that included vocational and commercial fields.

Most urban schools were preparing for:

• College admission

• Commercial courses (mostly designed to train young women for office jobs),

• Vocational courses (industrial craft for men and household for women)

• General (which offered a diploma without any special training).

Around 9% of Americans had a high school diploma in 1910. This figure rose to 40% by 1935 and 50% by 1940, yet the rate of expansion is deceiving. Because there was no employment during the Great Depression, many boys and girls stayed in school. During the twentieth century, the percentage of teenagers who completed high school climbed from 6% to 85%. high schools offered four school streams by 1920.

Summary
Nowadays, American education is regarded as among the greatest in the world. Students typically attend 12 grades of study throughout the course of 12 calendar years of primary/elementary and secondary education before graduating and getting a diploma that allows them to apply to further education. Education is compulsory till the age of 16. (18 in some states). One of the fundamental goals of American public education is to offer equal access and opportunity for all boys and girls, including minority groups and the disabled. Furthermore, coeducation has a long history in public schools in the United States. Primary education lasts till the fifth grade, middle school or junior high school lasts from the sixth to the eighth grades, and secondary education lasts from the ninth to the twelfth grades.

References:
 https://travel-in-time.org/puteshestviya-vo-vremeni/istoriya-obrazovaniya-v-ssha/ . Accessed 27 Nov. 2022.

 https://suny.buffalostate.edu/news/1871-2021-short-history-education-united-states . Accessed 27 Nov. 2022.

 https://www.bloomberg.org/?gclid=Cj0KCQiAsoycBhC6ARIsAPPbeLv_cd7lkxpHIPNbkR7aQ28gsSOStWp622q75q12vHte4LYQJ7d4_ZIaAtH3EALw_wcB . Accessed 27 Nov. 2022.

Review Questions:

 * 1) What was the influence of Great Britain on American education of that period?
 * 2) Describe segregation of American education.
 * 3) Influence of female teachers on American Education.
 * 4) Describe urban school of that period.

title: User:Olgavladrus


text:
User:Acwir/sandbox

{{unlock|reason=global block not useful in this time because i am...make ''
 * reason:that the global lock was not necessary to prevent damage or disruption.

Category:Math
plus delete multiply divited

title: User:Acwir/sandbox


text:
User talk:2409:4070:2C82:84F1:0:0:580B:7306

Welcome, 2409:4070:2C82:84F1:0:0:580B:7306!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. —Justin ( koavf ) ❤T☮C☺M☯ 07:24, 26 November 2022 (UTC)


text:
Lombard

 * Lombard (Lombard) is a Western Romance language. It is spoken in the Lombardy region with some transitional areas in the Mantuan and Pavia Oltrepò (where a dialect is spoken halfway between the Lombard language and the Emilian language), throughout Italian-speaking Switzerland, in the provinces of Novara and Verbania, in some municipalities in the province of Alessandria and in the westernmost valleys of Trentino.
 * It belongs to the Gallo-Italian group, and therefore has strong similarities with Piedmontese, with Emilian, with the more rustic and conservative dialects of the Venetian language of Trentino and Veneto. There are several transition areas (in Piedmont, in lower Lombardy, in Trentino), and therefore linguistic boundaries are not always unanimously accepted.
 * Evolved from the Latin spoken in Lombardy at the time of the Roman Empire, it is believed to have a Celtic substratum: it is still recognizable in a small number of words, but relevant in local toponymy.
 * The lexicon also presents an interesting series of Germanisms, imported from the Goths and above all from the Longobards (who gave their name to the region and then to the language). Other Germanisms date back to the 19th century, by virtue of Austrian domination.
 * Other lexical borrowings derive from French (from the Napoleonic era) and from English (in the industrial and bourgeois society of the end of the 19th century). Nowadays, the influence of Italian is very strong.
 * It boasts a literature that traces its origins back to the second half of the thirteenth century, and which continues uninterrupted from the seventeenth century to the present day. Lombard also boasts numerous lexicographic works.
 * Traditionally, Lombard is divided into two main variants: Western Lombard and Eastern Lombard. The border between the two variants is placed on the Adda river.
 * Also due to Lombardy's troubled history, the language still does not have a standard variant, nor a common spelling. Basically, every large city has a municipal literary production, and a system of handwriting. In this course we will refer to the unified spelling system, the New Lombard Orthography, designed in 2020.

Lombard is recognized as a language by various international bodies: by ISO (code 639-3 lmo), by UNESCO, by the Council of Europe and others. It is considered endangered.

This course
The course aims to give an essential overview of the most important aspects of Lombard grammar and lexicon, with a quick excursus on the literature in this language. It proposes also to briefly illustrate a common spelling proposal for all the local variants, which originates from the ancient and recent written traditions.

The dialects of Lombard
The Lombard language has numerous variants or dialects. Although theoretically each country has its own dialect, the dialects can be grouped into main groups. The subdivision is not always unique. In this book the subdivision into three main groups is proposed: Western Lombard, Eastern Lombard, Alpine Lombard, and these in turn are divided into subgroups (shown in the image below), many of which are determined by the influence of the dialect of the main cities on the surrounding area. For convenience in this book, dialects will be indicated by the abbreviations shown in the image below.

Wikipedia references

 * Lombard language
 * Western Lombard
 * Eatern Lombard
 * Milanese Dialect
 * Dialect of Ossola Valley
 * Brianzoeul dialect
 * Pavese dialect
 * Novarese dialect
 * Comasque dialect
 * Laghee dialect
 * Ticinese dialect
 * Lecchese dialect
 * Vallassinese dialect
 * Cremonese dialect
 * Bustoch and Legnanese dialects
 * Bergamasque dialects

Wikimedia projects in lombard

 * WiktionaryLmo.svg Wiktionary
 * Wikipedia-logo.svg Wikipedia

title: Lombard


text:
Supplementary mathematics/Introduction

Mathematics is a subject in science that examines numbers, shapes, etc. Since mathematics is complex and important in life, it ranks first among all science subjects.

Mathematics is one of the best sciences in the world, followed by natural sciences. In this book, we discuss advanced and complex mathematical topics. This science is the best of all sciences and mathematics is very useful in physics, chemistry, engineering, astronomy, architecture, etc."Mathematics is difficult from a distance, but if you get close to it, it is not difficult at all."In this book, we also deal with related and important topics of mathematics. In this book, we discuss topics such as mathematics, calculus, geometry, and analysis, and examine important concepts, branches of mathematics, research fields, etc. This ebook has both a printed version and is a group collaboration.

Items:

1- Mathematics

2-calculus

3-Geometry

4- Discrete mathematics

5-probability statistics

6- Mathematical analysis

title: Supplementary mathematics/Introduction


text: Template:Lombard

title: Template:Lombard


text:
Lombard/Phonology

Summary

 * Accent
 * Orthography and pronunciation rules
 * Milanese dialect
 * Laghee dialect
 * Bergamasque dialect
 * Pavese dialect

title: Lombard/Phonology


text:
Lombard/Conversion into the New Lombard Orthography

 * from the Milanese orthography
 * from the orthography of the Duchy
 * from the Lodesan orthography
 * from the Ticinese orthography


text:
Lombard/Morphology

Parts of speech

 * Articles
 * Nouns
 * Adjectives
 * Adjective degrees
 * Pronouns
 * Subject personal pronouns
 * Object and term personal pronouns
 * Pronominal and adverbial particles
 * Demonstrative pronouns
 * Possessive pronouns
 * Indefinite pronouns
 * Verbs
 * Moods and tenses
 * Infinitive
 * Gerund and gerundial complement
 * Participle
 * Present Indicative
 * Past Indicative (Perfect Indicative)
 * Imperfect Indicative
 * Past perfect Indicative
 * Simple Future Indicative
 * Compound Future Indicative
 * Present Subjunctive
 * Past Subjunctive (Perfect Subjunctive)
 * Imperfect Subjunctive
 * Past Perfect Subjunctive
 * Present Conditional
 * Past Conditional
 * Present Imperative
 * Future Imperative
 * Continuous construction
 * Irregular verbs
 * Auxiliary verbs
 * Modal verbs
 * Phrasal verbs
 * Prepositions and prepositional locutions
 * Adverbs and adverbial locutions
 * Pronominal and adverbial particles
 * Negation
 * Other constructions replacing the adverbs "easily" and "hardly"
 * Conjunctions and conjunctive locutions

title: Lombard/Morphology


text:
Lombard/Sentence syntax

 * Construction of the sentence
 * Relative clauses
 * Verbal diathesis
 * Hypothetical construction
 * Elision
 * How to greet
 * How to ask and express the time
 * How to ask and express the day
 * How to ask and express the weather

title: Lombard/Sentence syntax


text:
Lombard/Lexicon

 * Flora
 * Animals
 * Food and Drink
 * Transport
 * Factories, Shops and Trade
 * Slang
 * Place names
 * Personal names

title: Lombard/Lexicon


text:
Talk:AI Art Generation Handbook/Diffusion Model

thumb|4class3ddiscriminant


text:
Fundamental Actuarial Mathematics/Premium and Policy Value Calculation for Long-Term Insurance Coverages

Learning objectives
The Candidate will be able to use and explain the premium and policy value calculation processes for long-term insurance coverages.

Learning outcomes
The Candidate will be able to:
 * 1) Identify the future loss random variables associated with whole life, term life, and endowment insurance, and with term and whole life annuities, on single lives.
 * 2) Calculate premiums based on the equivalence principle, the portfolio percentile principle, and for a given expected present value of profit, for the policies in 1.
 * 3) Calculate and interpret gross premium, net premium and modified net premium policy values for the policies in 1.
 * 4) Calculate the effect of changes in underlying assumptions (e.g., mortality and interest).
 * 5) Apply the following methods for modelling extra risk: age rating; constant addition to the force of mortality, constant multiple of the rate of mortality.

Introduction
There are two main job roles for actuaries, namely The two main topics ( and (or )) discussed in this chapter are directly related to these two job roles.
 * (calculating : prices of insurance products) and
 * or (calculating  or, which are indeed the same thing)

Premiums
In previous chapter, we have studied and, and their. Now, those ideas will be combined for calculating here. Intuitively, it appears that we can simply set the actuarial present value of an insurance/life annuity as its price, which is required to be paid by the insured/annuitant at its issue. However, in practice, the products are purchased by, instead of just a single payment at issue (time 0) (if this is the case, we refer the premium to as made at time 0). To be more specific, we usually use of  to purchase insurance products.

Now, to actually the premium, we need to have some, or  that  the way of calculation. Otherwise, different people may have different opinions on how to calculate the premium. Of course, in reality, the premium of insurance products are not just calculated by a single. The calculation is much more complex than what we discuss here, since there are many factors that can affect the premium in practice, and also there are many opinions from different stakeholders to be considered. So, setting a "right" premium is not an easy task in practice. Hence, pricing actuaries are needed for calculating premiums.

Before stating the principle for calculating premiums, let us define a term that is the basis for calculating premiums, namely the insurer's loss.

Symbolically, we can write $$L_0=Z-PY$$ where $$Z$$ is the p.v.r.v. of the benefits, and $$PY$$ is the p.v.r.v. of the annuity of premiums ($$Y$$ is the p.v.r.v. of the life annuity with unit payment, and $$P$$ is the amount of each premium paid in the life annuity). Then, based on $$L_0$$, we can introduce various principles for calculating premiums. Intuitively, the insurer should avoid having losses, and hence do not want $$L_0$$ to be positive. This is the main idea in the following principle.

In the, even if the probability for having a positive loss is very small, the of the loss is  considered. For example, having a probability 0.01 to have a loss of $1 trillion should be more problematic than having a probability of 0.5 to have a loss of $100, right? This suggests that apart from the of having positive losses, the  of the losses also matters. When both and  are involved, what do you think of?

Since under, the calculations of premiums are quite simple, it will be used for premium calculation in the following, unless otherwise specified.

As we have mentioned previously, the concepts related to and  are applied here for calculating premiums. As a result, there are not many "new" concepts involved in the calculation of premiums for purchasing and.

Fully continuous premiums
Let us first consider the premiums for purchasing a with benefit of 1 payable, issued to a life aged $$x$$. Unless otherwise specified, we will assume the premiums will be paid in the same as in the insurance product. In this case, the payment pattern of the premiums is paying, since the benefit for the insurance is paid.

So, we have mentioned how should the be determined. How about the of the payments? Of course, the payments cease when the insured/annuitant dies (it makes no sense for a dead person to continue paying premiums, right?). But, the payments also cease  the insured/annuitant dies, if it is specified in the terms of the insurance product. For instance, for a whole life insurance, perhaps premiums are only payable for the first 10 years after the policy issue.

In this case, the insurer's loss is $$L_0=v^T-\bar P\bar a_{\overline T|},\quad T>0$$ where $$\bar P$$ is the continuous level annual premium. By equivalence principle, we then have $$\mathbb E[L_0]=0\implies \bar A_x-\bar P\bar a_x=0\implies \bar P=\frac{\bar A_x}{\bar a_x}.$$ In this case, the premium $$\bar P$$ can be denoted by $$\bar P(\bar A_x)$$ (the notation specifies that this premium corresponds to continuous whole life insurance).

For other types of insurance products, the formulas for the annual premium $$\bar P$$ are similar. So, some of them are summarized in the following table.

Fully discrete premiums
Now, let us consider the insurance products, where the premiums are also discretely, rather than continuously paid. However, a difference here is that the of the premiums is not  the same as that for the insurance products. In particular, we assume that the premiums are always made of each year unless otherwise specified. As a result, the premiums form a.

First, let us consider the case for a whole life insurance with benefit of 1 payable at the end of the year of death. Then, the insurer's loss is $$v^{K+1}-P\ddot a_{\overline {K+1}|}$$ where $$P$$ is the level annual premium. By equivalence principle, we then have $$\mathbb E[L_0]=0\implies A_x-P\ddot a_x=0\implies P=\frac{A_x}{\ddot a_x}.$$ In this case, we denote the premium $$P$$ by $$P_x$$, which is in the "same form" as the notation $$A_x$$. For other types of insurance products, the formulas for premium are developed similarly. Some of them are summarized below.

m-thly payment premiums
Of course, for the insurance products in the previous section, the premiums need not be payable annually. In general, they can be payable $$m$$ times for every policy year. We can similarly use to determine the amount of each premium in this case.

Let us first consider the case for whole life insurance with unit benefit payable at the end of year of death. Suppose the premiums are payable in $$m$$-thly installments at the of each $$m$$-thly period. In this case, the insurer's loss is $$L_0=v^{K+1}-P^{(m)}\ddot a^{(m)}_{\overline{K+1}|}$$ where $$P^{(m)}$$ is the level premium payable $$m$$-thly, that is, the  amount of premium paid at the beginning of each $$m$$-thly period is $$P^{(m)}/m$$. (This is similar to the case for the interest rate where $$i^{(m)}$$ is the annual interest rate, while the  interest rate for each $$m$$-thly period is $$i^{(m)}/m$$.) By equivalence principle, we can similarly get $$P^{(m)}=\frac{A_x}{\ddot a_x^{(m)}}$$. In this case, we denote $$P^{(m)}$$ by $$P_x^{(m)}$$.

The following is a summary for the formulas for $$P^{(m)}$$ of some other types of discrete insurance products.

We can also apply this idea to insurances payable at the moment of death. For instance, when the above whole life insurance is instead the one, then we have $$L_0=v^T-P^{(m)}\ddot a_{\overline{K+1}}^{(m)}.$$ Similarly, we have $$P^{(m)}=\frac{\bar A_x}{\ddot a_x^{(m)}}$$ by equivalence principle. In this case, we denote $$P^{(m)}$$ by $$P^{(m)}(\bar A_x)$$. The following is a summary for the formulas for $$P^{(m)}$$ of some other types of discrete insurance products.

Of course, apart from the aforementioned insurance products, we can also apply the idea of equivalence principle for calculating the premiums for insurances where benefits are varying, other types of life annuities, etc. Also, the insurance products can be irregular, and the premium payments can be irregular as well. In those cases, there are no "formulas" for calculating the amount of premiums directly. But, we can always use the equivalence principle for the calculations.

Accumulation-type benefits
In practice, apart from the death benefits from the insurance products, some of the premiums paid may be when death occurs. In particular, for $$n$$-year deferred whole life annuity, the annuitant will get from the life annuity itself if he dies during the deferral period. But when some of the premiums paid are refunded when death occurs in the deferral period, then the annuitant will at least get if he dies during the deferral period. So, this may be better for the annuitant (but of course, in exchange for this, it is natural to expect that the premiums required will be higher).

For the refund of premiums, depending on the terms, the amount of the refund may or may not consider the. To be more specific, when the amount of premiums refunded is determined at some time $$t$$, we may use the of the premiums paid at time $$t$$ with a certain interest rate (possibly different from the interest rate used for the calculation of actuarial present values), or simply interest rate.

In the following, we will discuss the development of formulas for these benefits when the premiums are payable (at the beginning of each year), and the refund will be made at the  of year of death. We can develop similar formulas when the premium are payable or, with the refund to be made at different time points.

Let us first develop a model of a special $$n$$-year term insurance issued to a life aged $$x$$, where the benefit of $$\ddot s_{\overline{k+1}|j}$$ (evaluated at interest rate $$j$$) is payable at the end of year $$k<n$$ (time $$k+1$$) when death occurs in year $$k$$ (no benefit if death does not occur within $$n$$ years), and then apply this model for the refunds of premiums. Graphically, the situation looks like *-*--*  |     |              |  die  |          .. "1"  "1"            "1"  |   v benefit: s k+1|j evaluated at interest rate j ---*-*-...--*---*- 0    1     ...      k      k+1 "1": hypothetical "benefits" made at various time points (yet to be realized until death) (they may be interpreted as premiums paid in practice, and then they are not hypothetical in those cases) Now, let us consider some simple cases first.

Case 1: interest rate $$j=0$$. Then, the benefit is $$\ddot s_{\overline{k+1}|j}=\underbrace{1+1+\dotsb+1}_{k+1\text{ times}}=k+1$$.

Case 2: interest rate $$j=i$$ ($$i$$ is the interest rate used for calculating actuarial present value). Then, the benefit is $$\ddot s_{\overline{k+1}|j}=\ddot s_{\overline{k+1}|i}$$.

In case 1, the APV of the p.v.r.v. for this insurance is simply given by $$(IA)_x$$ by considering the definition of $$(IA)_x$$. In case 2, the APV of the p.v.r.v. for this insurance is $$\ddot a_{x:\overline n|i}-{}_n E_x\ddot s_{\overline n|i}$$. The formula for case 2 will be proven later in this section. For now, let us give an intuitive explanation to this formula in the following:

Indeed, when $$j=i$$, the special insurance is very similar to a $$n$$-year (get a payment of 1 when the life still survives at the beginning of each of the first $$n$$ years), in the sense that, when death occurs in year $$k+1$$, the value of the benefit provided by the special insurance is $$\ddot s_{\overline{k+1}|i}$$.

On the other hand, for the $$n$$-year life annuity-due (assume $$k<n$$), the value of the benefits at time $$k+1$$ is also $$\ddot s_{\overline{k+1}|i}$$ (accumulate each of the $$k+1$$ survival benefits to time $$k+1$$). So, the APV of the benefits of the special insurance and the life annuity-due are the same. However, we have made an important assumption in the process: $$k<n$$, i.e. death occurs before year $$n$$. But this is not necessarily the case. The life can survive for at least $$n$$ years, right?

So we need to consider this situation also. In the situation where the life survives for at least $$n$$ years, the life annuity-due provides a benefit of $$\ddot s_{\overline n|i}$$ at time $$n$$, but the special insurance will not provide anything. Hence, we need to subtract $${}_n E_x\ddot s_{\overline n|i}$$ (APV of that "extra" benefit, obtained by actuarially discounting the benefit to time 0) from the APV of the $$n$$-year life annuity-due $$\ddot a_{x:\overline n|i}$$ to get the APV of the p.r.r.v. of this special insurance.

Now, let us formally define the present value random variable involved in the model of the special insurance: $$Z=\begin{cases}v_i^{K+1}\ddot s_{\overline{K+1}|j},& K=0,1,\dotsc,n-1;\\ 0,&K=n,n+1,\dotsc.\end{cases}$$ After that, we can derive a formula for the APV: $$ \begin{align} \mathbb E[Z]&=\sum_{k=0}^{n-1}v_i^{k+1}\ddot s_{\overline{k+1}|j}{}_k p_x{}q_{x+k}\\ &=\sum_{k=0}^{n-1}\left((1+i)^{-(k+1)}\cdot\frac{(1+j)^{k+1}-1}{d_j}{}{}_k p_x{}q_{x+k}\right)\\ &=\frac{1}{d_j}\sum_{k=0}^{n-1}\left[\left(\frac{1+i}{1+j}\right)^{-(k+1)}{}{}_k p_x{}q_{x+k}-v_i^{k+1}{}_k p_x{}q_{x+k}\right]\\ &=\frac{1}{d_j}\Bigg[\sum_{k=0}^{n-1}\bigg(1+\underbrace{\frac{i-j}{1+j}}_{i_*}\bigg)^{-(k+1)}{}{}_k p_x{}q_{x+k}-\sum_{k=0}^{n-1}v_i^{k+1}{}{}_k p_x{}q_{x+k}\Bigg]\\ &=\frac{1}{d_j}\left[\sum_{k=0}^{n-1}v_*^{k+1}{}{}_k p_x{}q_{x+k}-A^{1}_{x:\overline n|i}\right]\\ &=\frac{1}{d_j}\left[A^1_{x:\overline n|i_*}-A^{1}_{x:\overline n|i}\right].\\ \end{align} $$ where $$d_j$$ is the discount rate equivalent to the interest rate $$j$$, i.e., $$d_j=\frac{j}{1+j}$$, $$v_*=\frac{1}{1+i_*}$$, and $$v_i=\frac{1}{1+i}$$ ($$i_*$$ and $$i$$ are added to the APV notations for insurances so that we can identify which interest rate we are using for evaluating the APV's), assuming $$j\ne 0$$.

Through this formula, we can prove the formula in case 2 above (APV is $$\ddot a_{x:\overline n|}-{}_n E_x\ddot s_{\overline n|}$$):

Incorporating expenses
Previously, we have not considered expenses. Now, we will discuss the situation where expenses are incorporated to the premium calculations in this section. As we have mentioned, such premiums calculated are called. To calculate gross premiums, we need to include expenses in the insurer's loss $$L_0$$. Since the expenses are to be paid by the insurer, the p.v.r.v. of expenses are to $$L_0$$, that is, we now have $$L_0=Z+\text{p.v.r.v. of expenses}-PY.$$ When we use the equivalence principle, we have $$P\mathbb E[Y]=\mathbb E[Z]+\mathbb E[\text{p.v.r.v. of expenses}].$$ The expenses may be incurred from the cost of claiming benefits, commissions, etc.

Reserves (or policy values)
In the section about premiums, we often use the equivalence principle to calculate premiums, which requires the expected value of the insurer's losses (time 0) to be zero. But, after a period of time, say at time $$t$$, this expected value may be zero anymore, since the "$$Z$$" and "$$Y$$" at this time $$t$$, are different from the "$$Z$$" and "$$Y$$" at time 0. Particularly, the "$$Z$$" and "$$Y$$" at time $$t$$ are considering the benefits/payments, and the benefits/payments from time $$0$$ to time $$t$$ are not considered. Graphically, it looks like not considered      discount to time t ==> "Y at time t"   <-> <> P P ...      P P P ... P benefit <-- discount to time t ==> "Z at time t" ---*---*---*--- 0              t           die |--->           Assuming survival to time t

We may want the expected value to be still zero at time $$t$$, and in order for the insurer's loss to still have a zero expected value (so that there is still equivalence between the financial obligations for the policyholder and the insurer at this time point), a "balancing item" may be needed. To determine what the balancing item should be, let us consider the following two cases:
 * 1) The expected value of the insurer's losses at time $$t$$ is positive. This means the insurer expects a prospective loss from the policy (since the future benefits paid are expected to be greater than the future premiums received). Then, the insurer should  an amount of money, so that the insurer can "encounter" the losses.
 * 2) On the other hand, if the expected value of the insurer's losses at time $$t$$ is negative, then this means the insurer expects a prospective gain from the policy. So, the insurer can have a "negative reserve" (hypothetically) for that policy and still be able to encounter the losses.

From these, we can observe that in case 1, the insurer should spare an amount of money for the reserve for that policy (increase in financial obligation for the insurer), and in case 2, the insurer can hypothetically take away a sum of money from the policy (decrease in financial obligation for the insurer). Through these changes in the financial obligation for the insurer, there can still be an equivalence between the financial obligations for the policyholder and the insurer.

These lead us to the following definitions.

Symbolically, if the policy is issued to a life aged $$x$$, then the net premium reserve is $$\mathbb E[L^n_t|T>t]$$, and the gross premium reserve $$\mathbb E[L^g_t|T>t]$$ (for gross loss), for the continuous case. (For discrete case, we use "$$L^n_k$$" ($$L^g_k$$) and "$$K\ge k$$")

By definition, to calculate the conditional expectation $$\mathbb E[L^n_t|T>t]$$, we need to consider the conditional distribution of $$L^n_t$$ given $$T>t$$. It may appear to be complicated. But, we can prove that the conditional distribution of $$T_x-t$$ ($$T_x-t$$ gives the prospective lifetime with respect to $$t$$, which should be involved in $$L^n_t$$) given that $$T_x>t$$ is indeed the same as the unconditional distribution of $$T_{x+t}$$.

This result gives us an alternative and often more convenient method to calculate the conditional expectation $$\mathbb E[L^n_t|T_x>t]$$: Notice that we can also apply this similarly to the discrete case where $$K_x$$ is involved, since $$K_x$$ is just defined as $$\lfloor T_x\rfloor$$, and we can have a similar alternative method for calculations.
 * 1) replace all "$$T_x-t$$" by "$$T_{x+t}$$" and remove the condition "$$T_x>t$$"
 * 2) calculate the unconditional expectation, which equals the value of conditional expectation since the distributions involved are the same

Fully continuous reserves
First, let us consider the whole life insurance with unit benefit, the simplest case. In this case, we have $$L^n_t=v^{T-t}-\underbrace{\bar P(\bar A_x)}_{\text{notation}}\bar a_{\overline{T-t}|}.$$ To understand this, let us consider the following diagram. v^{T-t} <1 future benefit ---*---**---  0       t        T           ^       (die) Pa_{T-t}| ||              P       future premiums Then, the reserve, denoted by $$_t \bar V(\bar A_x)$$ ("$$V$$" corresponds to the "v" in "policy value"), is by definition $$\mathbb E[L^n_t|T>t]$$.

Now, let us consider the $$n$$-year term life insurance with unit benefit. In this case, the prospective net loss is different.

When $$tn$$, the insurance has ended, so it is not meaningful to consider the reserve for it anymore. (Indeed, if we follow our definition, for other insurance products with finite term, the reserve at such time point must be zero since there will be no premiums or benefits after time $$t$$. It is therefore meaningless to consider such reserves .)

Then, the reserve, denoted by $$_t \bar V(\bar A^1_{x:\overline n|})$$, is $$\mathbb E[L^n_t|T>t]= \begin{cases}\bar A_{x+t:\overline{n-t}|}^1-\bar P(\bar A_{x:\overline n|}^1)\bar a_{x+t:\overline{n-t}|},& t<n;\\ 0,& t=n.\end{cases} $$ (by considering the alternative method)

For the $$n$$-year endowment insurance with unit benefits, the prospective net loss is different again.

When $$tt]=\begin{cases}\bar A_{x+t:\overline{n-t}|}-\bar P(\bar A_{x:\overline n|})\bar a_{x+t:\overline{n-t}|},& t<n;\\ 1,&t=n.\end{cases}$$ (again by considering the alternative method)

To summarize, the reserves of the above policies and also some more other policies (with unit benefits) are tabulated below.

The premium-difference and paid-up insurance formulas can also be developed similarly for other types of policies. However, we seldom use the formulas themselves for the actual calculation since these formulas can be derived in just a single step, and thus we are not necessary to use such formulas.

Recall that in financial mathematics, to determine the outstanding balance for a loan at a certain time point, we have and  methods. Indeed, the definition of reserves are prospective. Can we calculate the reserves using a retrospective way? There are actually retrospective formulas for calculating premiums, as illustrated in the following exercise.

Indeed, the equality of prospective reserve and retrospective reserve under such conditions also applies to other types of policies.

Fully discrete reserves
Similar to the case for continuous reserves, we often use the "alternative method" to calculate the discrete reserves (i.e., $$\mathbb E[L^n_k|K_x\ge k]$$): the conditional distribution of $$K_x-k$$ given that $$K_x\ge k$$ is the same as the unconditional distribution of $$K_{x+k}$$ ($$k$$ is a nonnegative integer).

Similarly, this result gives us an alternative and often more convenient method to calculate the conditional expectation $$\mathbb E[L^n_k|K_x\ge k]$$: Let us consider the whole life insurance first. We have $$L^n_k=v^{K-k+1}-P_x\ddot a_{\overline{K-k+1}|}.$$ Hence, the reserve, denoted by $$_k V_x$$, is $$\mathbb E[L^n_k|K_x\ge k] =\mathbb E[v^{{\color{blue}K_x-k}+1}-P_x\ddot a_{\overline{{\color{blue}K_x-k}+1}|}{\color{blue}|K_x\ge k}] =\mathbb E[v^{K_{x+k}+1}]-P_x\mathbb E[\ddot a_{\overline{K_{x+k}+1}|}] =A_{x+k}-P_x\ddot a_{x+k}. $$
 * 1) replace all "$$K_x-k$$" by "$$K_{x+k}$$" and remove the condition "$$K_x\ge k$$"
 * 2) calculate the unconditional expectation, which equals the value of conditional expectation since the distributions involved are the same

We can develop formulas for other types of policies, and a summary of the formulas for reserves is tabulated below.

We can also develop premium-difference formula and paid-up insurance formula for discrete endowment insurance similarly:

We can develop a recursion relation for discrete insurances:

To explain the proof more intuitively, consider the following diagram: *                 | ...                                  \                  |         b ... b ... \                 |P_{k+1}  P ... P ... <==== covered by _{k+1} V         *    covered by _k V                  |--- .... /   P_k          b_{k+1} <=== not covered by _{k+1}V                         * _k V       _{k+1} V                                                     -**-- k          k+1                   time
 * Consider the policy value at time $$k$$: $$_k V$$. It is the APV of future benefits minus the APV of future premiums.
 * We can split the future benefits and future premiums into two parts:
 * 1) benefit at time $$k+1$$ and premium at time $$k$$
 * 2) benefits at time $$k+2,k+3,\dotsc$$ and premiums at $$k+1,k+2,\dotsc$$
 * For the second part, they are incorporated by the policy value at time $$k+1$$ $$_{k+1}V$$. But of course the policy value at time $$k+1$$ gives the value at time $$k+1$$, but not the value at time $$k$$ (which is what we want). Hence, we need to actuarially discount $$_{k+1}V$$ back to time $$k$$ (multiply $$vp_x$$).
 * To incorporate the first part, we add the APV of death benefit at time $$k+1$$ ($$vb_{k+1}q_{x+k}$$), and then subtract the premium at time $$k$$ ($$P_k$$).


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LMIs in Control/Stability Analysis/Continuous Time/Transient Output Bound for Autonomous LTI Systems

The System
Consider a continuous-time LTI system with a state-space representation of:

$$\dot{x} = Ax,$$

$$y = Cx,$$

where $$A \in \mathbb{R}^{n \times n}$$, $$C \in \mathbb{R}^{p \times n}                               $$ and $$x(0) = x_0$$,

the transient bound on the output can be evaluated with the following LMI.

The Data
$$A \in \mathbb{R}^{n \times n}$$, $$C \in \mathbb{R}^{p \times n}                               $$ and $$x(0) = x_0$$.

The LMI:
The Euclidean norm of the output satisfies

$$\lVert y(T) \rVert _2 \leq \gamma \lVert x_0 \rVert _2, \forall T \in \mathbb{R}_{+},$$

if there exists $$P \in \mathbb{S}^{p} $$ and $$\gamma \in \mathbb{R}_{++}$$, where $$P > 0$$, such that

 * $$P - \gamma I \leq 0, $$
 * $$\begin{bmatrix} P & C^T \\ * & \gamma I \end{bmatrix} \geq 0, $$
 * $$ PA + A^T P \leq 0 . $$

Conclusion
By using this LMI the transient output bound can be found for a given autonomous LTI system.

Implementation
The LMI given above can be implemented and solved using a parser such as YALMIP, along with an LMI solver such as SeDuMi, or MOSEK. (For a detailed list of solvers, please visit this page on Relevant Solvers).


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Talk:Lombard

Translated from Italian
This page has been translated from https://it.wikibooks.org/wiki/Lombardo --Gat lombard (discuss • contribs) 23:01, 26 November 2022 (UTC)

Users of Interest

Thanks for reading. Apisite (discuss • contribs) 22:50, 26 November 2022 (UTC)

title: Talk:Lombard


text:
User talk:Apisite

Other pages left to be moved
Have you seen the other pages to move? Gat lombard (discuss • contribs) 22:52, 26 November 2022 (UTC)
 * I checked, it seems that all pages have been moved --Gat lombard (discuss • contribs) 23:05, 26 November 2022 (UTC)

title: User talk:Apisite


text:
LMIs in Control/Click here to continue/Robust Controls/Robust Model Predictive Control

Model Predictive Control
Model Predictive Control is an open-loop control design procedure where at each sampling time k, plant measurements are obtained and a model of the process is used to predict future outputs of the system. Using these predictions, $$m$$ control moves $$u(k+i|k), i=0,1,...,m-1.$$ are computed by minimizing a nominal cost $$J_p(k)$$ over a prediction horizon $$p$$. The objective is to minimize the nominal cost function.

We consider the nominal cost function as:

 * $$\min_{u(k+i),i=0,1,...,m-1} J_p(k) $$

where,

 * $$ J_p(k) = \Sigma_{i=0}^p[x(k+i|k)^{T}Q_1x(k+i|k) + u(k+i|k)^{T}Ru(k+i|k)]$$

 * $$ Q_1 > 0$$ and $$ R > 0$$

$$Q_1$$ and $$R$$ are positive definite weighting matrices.

In this case, we take $$ p=\infty $$. This is also called infinite horizon MPC.

Uncertainties
Here, we consider system uncertainties that are modeled as polytopic uncertainties or structured uncertainties.

Polytopic Uncertainty
The set $$ \Omega $$ is the polytope $$ \Omega=Co{[A_1 B_1], [A_2 B_2],....,[A_L B_L]} $$

Where, $$ Co $$ denotes the convex hull.

Structured Uncertainty
The operator $$ \Delta $$ is a block-diagonal:
 * $$\Delta = \begin{bmatrix}\Delta_1 & & & \\ & \Delta_2 & & & \\ & & \ddots & \\ & & & \Delta_r\end{bmatrix}$$

Each $$ \Delta $$ can be a repeated scalar block or a full block.

The System
Consider a linear time-varying(LTV) system:

 * $$ x(k+1)=A(k)x(k)+B(k)u(k), $$

 * $$y(k)=CX(k), $$

 * $$\begin{bmatrix} A(k) & B(k)\end{bmatrix}\in \Delta $$

Here, $$ u(k)\in \R^n$$ is the control input, $$ x(k)\in \R^n$$ is the state of the plant and $$ y(k)\in \R^n$$ is the plant output and $$\Delta$$ is uncertainty set that is either polytopic system or structured uncertainty.

We modify the minimization of the nominal cost function to a minimization of the worst-case objective function.

The modified objective function minimizes the robust performance objective as follows:

 * $$\min_{u(k+i),i=0,1,...,m-1} \max_{[A(k+i) B(k+i]\in \Delta,i\geq 0} J_\infty(k) $$

where,

 * $$ J_\infty(k) = \Sigma_{i=0}^\infty[x(k+i|k)^{T}Q_1x(k+i|k) + u(k+i|k)^{T}Ru(k+i|k)]$$

The LMI:Robust Unconstrained Model Predictive Control with State Feedback for polytopic uncertainty
$$\min_{\gamma,Q,Y} \gamma $$

subject to

 * $$\begin{bmatrix} 1 & x(k|k)^T \\ x(k|k) & Q \end{bmatrix} \geq 0

$$

and

 * $$\begin{bmatrix} Q & QA_{j}^T+Y^TB_{j}^T & QQ_{1}^{1/2} & Y^TR^{1/2} \\ A_j Q+B_j Y & Q & 0 & 0 \\ Q_{q}^{1/2} & 0 & \gamma I & 0 \\ R^{1/2}Y & 0 & 0 & \gamma I\end{bmatrix} \geq 0

$$

The LMI:Robust Unconstrained Model Predictive Control with State Feedback for structured uncertainty
$$\min_{\gamma,Q,Y,\Lambda} \gamma $$

subject to

 * $$\begin{bmatrix} 1 & x(k|k)^T \\ x(k|k) & Q \end{bmatrix} \geq 0

$$

 * $$\begin{bmatrix} Q & Y^TR^{1/2} & QQ_{1}^{1/2} & QC_{q}^T+Y^TD_{qu}^T & QA^T+Y^TB^T \\ R^{1/2}Y & \gamma I & 0 & 0 & 0 \\ Q_{1}^{1/2}Q & 0 & \gamma I & 0 & 0 \\ C_{q}Q+D_{qu}Y & 0 & 0 & \Lambda & 0 \\ AQ+BY & 0 & 0 & 0 & Q-B_p \Lambda B_{p}^T\end{bmatrix} \geq 0

$$

where

 * $$\Lambda = \begin{bmatrix}\lambda_1I_{n1} & & & \\ & \lambda_2I_{n2} & & & \\ & & \ddots & \\ & & & \lambda_rI_{nr}\end{bmatrix}>0$$

Conclusion:
The state feedback matrix F in the control law $$u(k+i|k) = Fx(k+i|k), i \geq 0$$ that minimizes the upper bound $$ V(x(k|k)) $$ on the robust performance objective function at sampling time $$ k $$ is given by :

 * $$ F = YQ^{-1} $$

where $$ Q > 0 $$ and $$ Y $$ are obtained from the solution of the above LMI.


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LMIs in Control/Click here to continue/YALMIP

YALMIP

The tool mainly uses for this book. The chapter will provide some examples for using Yalmip with optimization problem.

YAMLIP's download link:. click "download" in the top and follows the instructions in the file. YALMIP can solve some easy problems without extra software support.

For a optimize problem, we need to define constraints, objective function, variables.

For example, in order to find a straight line to separate the two data in the plot with minimal implementation error.


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User:LiliyaBalueva/sandbox

= History of education in South Korea = The era of the Three Kingdoms (57 BCE–668 CE) The historical evolution of education in Korea has been significantly influenced by its location between China and Japan. Confucianism, Taoism, and Buddhism were imported from China during the Three Kingdoms Period (57 BCE–668 CE) (Cartwright, 2016). The school system was centered on Confucianism even though Buddhism was the state religion (Mee-Ryang & Woojin, 2016). This was the start of what is known as the "Educational Fever" (Lee, 2006), which is characterized by the fact that education is highly prized in Korea and, until recently, was a privilege of a minority.

Ancient Korea was ruled by the three states of Baekje, Goguryeo, and Silla (Cartwright, 2016).

Although there are no formal records of the educational institutions that were present in Baekje, it is known that there was a minister of education and an authority in charge of education (Mee-Ryang & Woojin, 2016).

The National Confucian Academy (Taehak), the first educational institution in Korea, was founded in 372 in Goguryeo (Mee-Ryang & Woojin, 2016). It served to prepare youngsters from the upper class for public service. In provincial schools youth from families of lower aristocracy and commoners were taught Confucian classics, history, and martial skills (Mee-Ryang & Woojin, 2016).

Hwarangdo (Flowering Knights), a novel training system for high military and political officers, was developed by the Silla state (Mee-Ryang & Woojin, 2016). Hwarang's military corps educated morally upright, attractive young men of high family in morals, physical fitness, social skills, and military training (Mee-Ryang & Woojin, 2016).

Combined Silla (668–935)

The National Confucian College was established in 682, following the unification of the three kingdoms and the creation of Unified Silla. It provided training for future civil service careers for the children of senior government officials. Math and Confucian books were studied by the students. However, many more students chose to study in China. The state's administration strongly supported it. Initially, only children from the top classes traveled to China to pursue their education, but later, students from the middle classes started to join them. The severe rank system of the Unified Silla was criticized by educated youth, who also significantly contributed to the fall of the state.

Goryeo Dynasty (918–1392)

Even commoners in the Goryeo Dynasty were able to join the civil service after passing the exam (Mee-Ryang & Woojin, 2016). However, because the examiner and the examinee shared a unique bond, much like a father and son, an elite stratum developed that influenced society to promote its own interests (Mee-Ryang & Woojin, 2016).

The first king of Goryeo, King Taejo, founded a number of educational institutes (Mee-Ryang & Woojin, 2016). The children of the high aristocracy studied Kofucian philosophy to prepare for the public service exams in the National University (Mee-Ryang & Woojin, 2016). Children from the middle levels of the military and aristocracy might pursue specialized courses in yulhak (law), sanhak (arithmetic), and sonhak (secretary studies) (Mee-Ryang & Woojin, 2016). The National University was renamed Seonggyungwan in the fourteenth century, after which it stopped teaching technological studies and focused on the advancement of Neo-Kofucianism (Mee-Ryang & Woojin, 2016).

The Learning Hall (Hakdang), which served as a place to teach Confucianism, was established in both the capital and provincial schools during the Goryeo Dynasty (Mee-Ryang & Woojin, 2016).

The Twelve Assemblies (Sibigongdo), founded by eminent Confucian scholars in the middle of the Goryeo Dynasty period—the first of whom was Choe Chung—became very well-known because at the time the National University was experiencing a crisis and the founders of The Twelve Assemblies were in charge of the civil service examination procedure (Mee-Ryang & Woojin, 2016). These educational institutes played a significant role in the state's Confucian education and lasted until the end of the Goryeo Dynasty (Mee-Ryang & Woojin, 2016).

Joseon Dynasty (1392–1910)

Neo-Confucianism became the main ideology under the Joseon Dynasty, not just in the realm of education (Sorensen, 1994). It was propagated everywhere, suppressing Buddhism (Sorensen, 1994). Except for the lowest strata, the law did not prohibit commoners from talking civil service exams. But in practice, it was virtually impossible because they could not prepare well due to the harsh living conditions. Such a system maintained a hierarchy (Mee-Ryang & Woojin, 2016). Practical subjects like astronomy, medicine, foreign languages, and law were valued less. Exams on them could be taken by middle-class students, but commoners were not allowed to do so.

Seonggyungwan, which was erected in the capital in 1398, served as the primary educational institution that took the place of The National Confucian College and National University (Mee-Ryang & Woojin, 2016).

There were Four Schools (Sahak) as secondary level at the time (Mee-Ryang & Woojin, 2016). Highest-scoring graduates were allowed to take the Seonggyungwan admission examination (Mee-Ryang & Woojin, 2016).

County schools (Hyanggyo) in the provinces were tasked in preparing pupils for the civil service exams (Mee-Ryang & Woojin, 2016). However, because of the comparatively poor quality of the education provided, the local aristocracy preferred to attend private universities (Mee-Ryang & Woojin, 2016).

In the sixteenth century, wealthy villagers established the village study hall (Seodang), a private educational institution (Mee-Ryang & Woojin, 2016). They were reformed in the eighteenth century to teach not only Confucian theories but also practical knowledge. They employed qualified instructors who used from texts that suited the needs of the students and used games to teach the young students (Mee-Ryang & Woojin, 2016).

Contemporary sciences were unknown until 1876, when reforms aimed at establishing a modern state started (Sorensen, 1994). As a result, the Gabo Reform was implemented in 1881 (Mee-Ryang & Woojin, 2016). Schools actively imported practical knowledge from the West (Sorensen, 1994). 1090 new elementary schools were opened (Mee-Ryang & Woojin, 2016). Christian missionaries also started private schools (Sorensen, 1994). They founded Korea's first girls' school in 1885 (Mee-Ryang & Woojin, 2016). To ensure that talented individuals have access to school, the government removed the traditional class distinctions and examination system (Sorensen, 1994).

King Gojong declared himself emperor in 1897. He established more secondary schools, added elementary schools, and launched professional, military, and medical schools (Mee-Ryang & Woojin, 2016).

The Japanese colonial period (1910-1945)

When Japan annexed and colonized Korea, the advancements made during the late Joseon Dynasty were lost (Sorensen, 1994). The focus of Japanese colonial policy was on Japaneseization (Lee, 2006). There were two educational systems. The number of years of education for ethnic Koreans was decreased (Mee-Ryang & Woojin, 2016). They had very little access to secondary school, and there was no higher education (Sorensen, 1994). It was prioritized to enroll them in professional and technical schools in order to increase the labor force (Lee, 2006). The majority of Japanese people were to occupy the administrative roles (Sorensen, 1994).

Education in the Republic of Korea

After the country gained independence in 1945, 78 percent of Koreans lacked literacy (Sorensen, 1994). There were not enough secondary-educated people and teachers (Sorensen, 1994). The education law was passed in 1945 and is still in effect today with certain modifications. According to it a system was formed in which education lasts 6 years in elementary schools, 3 years in middle and high schools, and 4 years in universities. Primary education was made free and compulsory for everyone. In 1980, there were 93 percent of adults who had an education, up from 87.6 percent in 1970. (12K academics, n. d.). More than 90% of primary school graduates were enrolled in secondary schools in 1979.

To deal with the number of students, the government instituted high school exams in 1953 (Cartwright, 2016). These exams were later discontinued in 1969 (Cartwright, 2016), and secondary education became free and mandatory in 1985 (Sorensen, 1994).

The desire for education persisted in society at the same time as a sign of status and a chance for financial success (Lee, 2006). Due to this, tutoring became more popular. (Sorensen, 1994; Choi, & Choi, 2016). The overall cost of private tutoring rose to $400 million in 1980. (Sorensen, 1994).

Opportunities for admission to universities were increased by a number of reforms implemented in the 1980s (12K academics, n. d.). To aid in the development of institutes' research capacities, the government has significantly increased research funding, and in 2014 a university assistance system was launched (Mee-Ryang & Woojin, 2016).

Since its liberation from Japanese rule, Korea has undergone fast economic growth, with changes to the educational system serving as one of the primary drivers (Sorensen, 1994; Lee, 2006). According to UNESCO, the country's gross tertiary enrolment rate expanded fivefold between the early 1980s and the mid-2000s, and the number of students enrolled in higher education increased from 539,000 in 1980 to 3.3 million in 2015. (The World Bank, 2022). Nowadays South Korea is one of the top nations, according to PISA results (OECD, 2019). Additionally, on the 2014 Global Index of Cognitive Skills and Educational Attainment, this country came out on top (Economist Intelligence Unit, 2014).

title: User:LiliyaBalueva/sandbox


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Javagony/Other conditions and loops

Other conditions
We know how to write conditions in Javagony that compare two numbers. What if we want to check for other conditions? Well, this can be done using a Boolean variable, and the function Boolean.compare(b1,true) when b1 is the variable that stores the result of the condition (true or false). It will return 0 if the Boolean variable is true, and -1 if it’s false. She because we already know how to check in Javagony if a number is 0, that means we can check any condition.

Do/while loop
Now that we know how to check if any condition is true, it’s easy to implement an alternative to a do/while loop in Javagony. All we need to do is to create a function that does something and then calls to itself if the certain condition is met.

For the purpose of this book, we will write a code that prints all powers of 3, until we reach a number that its least significant digit is 7. The last number it will print will be 27.

While loop
A while loop will work similar to a do/while, only this time we check for the condition at the beginning of the function and not the end. If the condition is met, we execute the code. If it isn’t, we use the return statement to exit from the function. At the end of the function, after executing the code, it will unconditionally call itself.

Let’s use this knowledge to write a code that receives a positive integer, and prints all the digits of the number - starting from the least significant one, and ending with the most significant.

What if we want the function to return the most significant digit? Well, we can easily modify this code to do so.

Let’s modify this code to return an ArrayList that will include all the digits of the number starting from the most significant and ending with the least significant one.

title: Javagony/Other conditions and loops


text: Category:Book:Lombard/Templates

title: Category:Book:Lombard/Templates


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Javagony/Common programming problems in Javagony

Fibonacci numbers
This is a recursive method in Javagony that returns the number in position n of the Fibonacci Sequence.

Fizz buzz
This is a code in Javagony that prints all the numbers from 1 to 100, but instead of numbers that can be divided by 3, it will print “Fizz”, instead of numbers that can be divided by 5, it will print “Buzz”, and instead of numbers that can be divided by both 3 and 5, it will print “Fizz Buzz”:

Prime numbers
This is a method in Javagony that gets a number and returns the boolean value true if it’s a prime number. Otherwise, it returns the boolean value false.


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Lombard/Subject personal pronouns

Subject personal pronouns
Lombard has two types of personal subject pronouns: strong subject pronouns and weak subject pronouns (or redundant subjects).

Strong subject pronouns can be omitted.

Weak subject pronouns are usually always obligatory for the 2nd and 3rd person singular in all dialects, while for other persons they are obligatory depending on the dialect. Their use in sentence construction is explained in the module on sentence construction.

Alpine Lombard
* the difference between “lor” and “lore” is often only graphic in New Lombard Orthography because in most dialects there is no difference in pronunciation between masculine and feminine

Weak subjects
They are indicated in brackets when they are not mandatory.

* The universal pronoun is used for the impersonal form and sometimes takes the place of the weak third person singular pronoun in the particular cases described about the construction of the sentence. (in brackets the cases in which it is not mandatory)

title: Lombard/Subject personal pronouns


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MI

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CO

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PV

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VA

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LO

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Lagh

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Chess Opening Theory/1. e4/1...e5/2. Qh5/2...Nc6/3. Bc4/3...g6/4. Qf3/4...Nf6

= Parham Attack =

4...Nf6
Black blocks the attack from the queen. Although the black knight is "pinned" to the pawn (If it were to move, white would play Qxf7#), Black has been handed the moves ...Bg7 and ...O-O on a platter. Another idea is if White doesn't defend d4, instead playing 5. Nc3?, (which is also a common response between low rating players) Black has 5...Nd4! 6. Qd1 Bg7.


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Cookbook:Marshmallow

Marshmallow is a type of confection or candy made of stabilized aerated sugar.

Characteristics
At its most basic, all marshmallow is a confection of cooked sugar that is stabilized and made fluffy by the incorporation of air. The exact physical characteristics depend on the ingredients and their proportions, but most marshmallow tends to be light, chewy, stretchy, and very sweet.

Historically, marshmallow was made from the sap of the marshmallow plant, sugar, and egg whites. The marshmallow sap has since been primarily replaced with gelatin in modern marshmallow, although other stabilizers like agar, soy protein, and carrageenan may also be used to stabilize the sugar foam and achieve the requisite elastic consistency. Depending on the formula, egg whites and albumen may or may not be included. A variety of sugars can be used, including table sugar (sucrose), glucose syrup, corn syrup, etc. Food coloring and/or additional flavoring can be added to achieve the desired final product.

When exposed to direct heat, marshmallow will begin to soften and eventually caramelize, producing a sweet with additional depth of flavor.

Texture
Marshmallow can be adjusted to yield different textures. Typical "firm" marshmallow has a high stabilizer (e.g. gelatin) content that gives it a soft but bouncy texture that will hold its shape. When the amount of stabilizer is reduced, the texture becomes much softer and more spreadable, making marshmallow creme. Increasing the sugar content and dehydrating the marshmallow produces cereal marshmallows, which have a very sweet flavor and dense, crunchy texture.

Small-scale
At small scale, marshmallow is made by cooking a hot sugar syrup, mixing in gelatin and/or egg whites, and whipping in air by hand or electric mixer. The fluffy marshmallow mixture can then be shaped by piping or transfer to a mold, at which point the marshmallow is allowed to cool and set into its final shape. Often cornstarch and/or powdered sugar are used to prevent sticking.

Commercial
Large-scale, commercial marshmallow manufacturing relies primarily on extrusion to aerate and shape the confection. The hot sugar mixture is then forced through tubes under pressure, which incorporates air into the mixture and shapes it into ropes. These ropes are then typically cut into individual marshmallows.

Storage
Marshmallows can have a long shelf life when properly stored. Exposure to the environment can cause marshmallows to dry out and become stale or melt together into a sticky clump. These marshmallows are still edible, but to preserve their original texture they should be kept in airtight packaging.

Uses
In the United States, marshmallows are toasted then combined with chocolate and graham crackers to make a dessert called s'mores.

Recipes

 * Marshmallow (recipe)
 * Quick Marshmallow Rice Squares
 * Chocolate-coated Marshmallow Treats (Flødeboller)
 * S'more
 * Campfire S'mores
 * Rocky Road Confectionery
 * Rocky Road Confectionery II
 * Frog's Eye Salad

title: Cookbook:Marshmallow


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Talk:Lombard/Subject personal pronouns

Translated from
This page has benn translated from https://it.wikibooks.org/wiki/Lombardo/Pronomi_personali_soggetto on November 27, 2022 --Gat lombard (discuss • contribs) 21:01, 27 November 2022 (UTC)

title: Talk:Lombard/Subject personal pronouns


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Talk:English-Hanzi/Blood vessel

Cardiovascular
''I am not sure about whom I may encounter and I hope that I am connecting with individuals that will actually be honest and give me real information. I am searching for the reason I am struggling with a type-ll diabetes after losing my mother whom I am still immensely missing; there is not a day that goes by that my heart doesn't ache.''

Caliopleigh (discuss • contribs) 22:04, 27 November 2022 (UTC)

title: Talk:English-Hanzi/Blood vessel


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No Man's Sky/Getting the best gear

Maybe you want a PvP advantage? Or you want to be able to explore derelict freighters without worrying about the cold? Possibly you want to make hundreds of thousands of units for every item scan? Or a starship that never needs refueling? All of these can be done, and more.

Geting started

 * Note: Weaponry that has been damaged in the past and repaired again only deals half damage. For that reason, it may be best to repair damaged weapons, dismantle them, and re-install them (dismantling upgrades destroys them for half the resources used to craft them - rounded up). This only apples to the core weapon module, not any of its upgrades.
 * However, a starship must always have at least one weapon at all times (multi-tools do not need a weapon, since it has other ways to deal damage), so if the weapon is damaged (say, if you die in your ship) it is best to repair it, install a new weapon, dismantle all the previously damaged weapons, reinstall them, then dismantle or archive the extra weapon (if you archive it and store it in your freighter, you never need to craft it again! Just remember to install the freighter "matter beam" module). If you have more than one weapon equipped anyway, it is more resource efficient to run the above steps one at a time for each weapon, then you don't need to install a temporary weapon. Remember: repair, dismantle, reinstall.
 * The mining beam is not considered a weapon for these purposes, despite it dealing a bit of damage. The mining beam also cannot be removed.
 * If you are planning to become involved in (or prepare for) PvP, also see the preparing for death guide.

Ship type
First, you need to have a decent starship. The below table shows the main stats at S-Class. Lower classes may have way lower stats. All S-Class ships have a max of 60 tech slots. (The fandom shows different numbers, that is because these are the actual core stats that you can see inside the game.)

Multi-tool types
The below table shows the core stats of a S-Class multi-tool. All S-Class multi-tools contain 60 tech slots (as of the Waypoint update).

The alien (or "exotic" to some) is the best for damage, but the experimental and royal ones offer bigger mining speed and scanner range, but sacrificing a small amount of damage. Royal multitools can only be found in sentinel pillars.

Stage 1
This is the most time consuming bit. You will want at least 20 - 30 thousand nanites. These can be obtained by:
 * Selling upgrades
 * Searching supplies dropped by sentinels
 * Repairing damaged machinery
 * Uploading discoveries
 * Certain quests
 * Clicking "Request payment instead" after rescuing a freighter from a space battle
 * Refining tainted metal. Talk to the scarp dealer and choose "Get coordinates" to summon a derelict freighter

You can skip this step by changing your difficulty. You can do this on the pause menu. The difficulty button is above the save button. Make sure to set "purchases" to "free".

Stage 2
Go around to as many star systems with high economy level. Then, visit the space station. While you are here, you may want to increase your exosuit inventory. Focus on the tech slots first. You will soon wish you could have more.

Go to all four of the upgrade merchants and buy all the S-rank upgrades. Install the multi-tool, starship, and exosuit upgrades now. Save the exocraft upgrades for later.

You may want to consider maxing out the starship and multi-tool upgrade slots, as well as class. Although consider waiting for the multi-tool or starship you want most before you spend 900 million units and 60 thousand nanites on slot/class upgrades.

Stage 3
When you have gotten enough so that you can't equip any more upgrades (of any type at all), it becomes pointless to continue to buy S-Rank. You will need to follow a riskier approach. Find the nearest black-market system. This can be checked by looking for a skull icon on the systems info in the galaxy map. This is easiest with the economy/conflict scanner starship upgrades.

Once there, enter the space station and go to the shop on the left, towards the multi-tool container. Black-market systems tend to contain interesting multi-tools. Then go to the right hand side. One NPC will sell X-Class upgrades (buy any and all that interest you - mining beam, starship shield, hyperdrive, pulse engine, and exosuit upgrades are always worth the risk of losing nanites). The other will sell items (but suspicious packets for tech and arms - after opening them, you can return up to two more times for more). Check each upgrade's stats by using them. Either delete them, or if it is more powerful than another upgrade you have, delete the weakest upgrade of that category. This only counts for upgrades with a red "!" at the top right.

X-Class upgrades aren't always good. Some are only as good as C-Class, others are way above S-Class. It requires luck and patience to get it right.

 * X-Class upgrades to hazard protection offer hazard resistance for all four hazard types, with a minimum of 2% boost, a maximum of 10% boost. (if the value is high enough, you become immune to lower levels of the hazard immediately. With 58% cold protection, for example, you are immune to temperatures between 0 and -55. This is a big change, as the day temperatures on cold planets are usually around -55.
 * X-Class exosuit shield upgrades allow +33% core health, with +34 shield strength. However, it is not actually better than S-Class, which may be a bug, but the same. It may be better to stick with S-Class for exosuit shields.
 * X-Class starship shield upgrades allow a maximum of +38 shield strength, compared to the maximum S-Class stat of +30 shield strength. Unlike exosuit shields, this will actually improve your starship shield.
 * X-Class scanner upgrades may give more units than upgrades of S-Class.
 * X-Class hyperdrive upgrades, at their best, offer +100% warp cell efficiency, and more than +300 LY to the hyperdrive range.

Tips

 * You may only equip 3 upgrades of the same type at once. Craftable upgrades (which the blueprints for can be bought at the space anomaly) do not count to the limit of three, so install any upgrades you want. Every little bit helps.
 * Contrary to the above, the "advanced jump system" jetpack upgrade adds a short delay to all jetpack uses, which could be fatal in ground PvP against players with high power weapons.
 * Upgrades on a super charged slot gain a massive increase.
 * Upgrades get a small bonus for every adjacent upgrade that focus on the same thing. You can check if you got it right if both upgrades have a glowing outline. The outline is harder to see on ExoCraft engine upgrades, but it is there.
 * It is possibly a bug, but having an upgrade with "+100 warp cell efficiency" means you never need to refuel your hyperdrive.
 * Solar ships (the ones that have colorful sails when not in planetary atmospheres, and have wings that move outward when flying) come with the "vesper sail" upgrade, a core upgrade (cannot be removed) that makes the pulse engine recharge while in space. If you have enough pulse engine fuel efficiency, you will have to wait a long time of just pulsing before the fuel runs below 90%.
 * Solar ships take a few seconds longer to land than normal ships. That may be a problem in some cases, like for the GHDF (Galactic Hub Defense Force) members, who might be chasing a hostile target who just landed on a planet. That is why "community defense forces" prefer to use regular fighters while on duty. (See this Fandom article for more)
 * This page is not designed for giving tips on taking out the GHDF. They are many members, and by trying, you could get overwhelmed. It is more of a guide in PvP self-defense - active PvP-ing is not a requirement. Be prepared to face the GHDF if you attack other players in or near the galactic hub. They likely have methods to get strong gear that is much more effective than any method on this page.

title: No Man's Sky/Getting the best gear


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Wikijunior:Raspberry Pi/Introduction to Python

Python is a general-purpose programming language that is easy to learn and is used in nearly all of the tutorials in this wikibook.

Getting started

Python 3 and IDLE are pre-installed on Raspberry Pi OS. IDLE can be opened from the Programming menu.

If you don't have a Raspberry Pi, you can install a copy of Python 3 on just about any computer from the official website.

Using the IDLE Shell
IDLE (Integrated Development and Learning Environment) is included with Python 3 and is easy to use. It is an Integrated Development Environment (IDE) which is a type of software that is designed to make it easy and convenient to write source code.

The first window that opens is the IDLE Shell, which is the Python 3 shell. You can run a quick line of Python in the shell, for example Python is a calculator so let's try adding :

Feel free to play with Python's calculator and try using the different operators:

 * Plus, such as
 * Minus, such as
 * Multiply, such as
 * Divide, such as
 * Square, such as
 * Modulo (gives the remainder from a division), such as

You can also access the Python 3 shell by typing  into the  Terminal program and pressing the Enter key.

Hello World
Whenever a programmer starts with a new programming language. The first thing to do is to output the phrase "Hello World".

Open IDLE, select File, then New File (Ctrl+N) (or press the and  keys together), create a new file and name it , then type the following:

Run the code in IDLE by selecting Run, then Run Module (F5) (or press the key) and it should display in the Python shell as:

is a built-in function that outputs text onto the screen. As it's a word that has already be defined by Python to do something, programmers call it a "keyword".

Comments
Sometimes you may need to make notes in your code or remove a line to troubleshoot why it is not working (which is referred to as debugging).

In Python, you can add a comment using the hash symbol  (in the US, this is confusingly called a "pound sign"). Let's add a comment to our Hello World program from earlier:

Once the hash symbol has been typed, the Python interpreter will ignore the rest of the line which allows us to make notes.

Variables

Variables are a container that is used to store values that we can define in our program.

In Python, variables are assigned with a name, a variable assignment operator  and a value. Some examples of values are:

Booleans
True or false such as  or.

Integers
Positive or negative whole numbers such as  or.

Floating-point numbers
Positive or negative numbers that use a decimal point such as  or.

Strings
A series of letters, numbers or symbols such as. In Python, either single quotes  or double quotes   can be used to define a string.

Lists
A list is an ordered collection of values each separated by a comma  of any of the values above. Any Python 3 datatype can be used.

Python 3 has a built-in functions for modifiying lists. For example, let's try combining the two lists together:

Dictionaries
A dictionary is like a list but for each entry there are two values. Here's an example:

Other datatypes
These are just a few examples of the variable types that are available in Python. There are many other types as well including complex numbers, tuples, sets and more.

If statements

The  statement is used to make parts of the source code run providing a certain condition is met. For example, let's make a variable called "x" and set it to 5.

The keyword  is used for defining what the source code should do if the condition   is not met.

What about if statements that have more than just two conditions? We use the keyword  (which just means "else if"). In the example below, we use the less than  and greater than   symbols to determine if a number is positive, negative or zero.

Try running this example in IDLE and change the value of  to get all 3 outputs:

Loops
Sometimes you will want the code to repeat which can be done using loops. There are 2 kinds of loops used in Python:

For loops
For loops are useful when you know how many times the code needs to repeat itself.

In this example, there is a list of numbers from 1 to 5. The square brackets  are used as lists are a specific variable datatype that is used to store multiple values.

While loops
A while loop repeats endlessly until the condition is met. For example, printing the numbers from 1 to 10:

Modules
Modules are Python source code written by other software developers. By default, Python can't do very much but we can make our Python programs do more by importing a module.

You can use the  keyword to add a module. Use the  to be more specific if you just want to do one thing from that module.

For example, let's print the number Pi. The number Pi is often shortened to, but it actually continues on forever in real-life (mathematicians call this an irrational number). In Python,  prints Pi to 15 decimal places.

Now we have Pi, we can create a simple program that calculates the area of a circle. The formula for this is: area = pi × radius2

 * Circumference – the outside line of a circle
 * Radius – a straight line that connects the center of the circle to the circumference

The single asterisk  is used to multiply one number by another (just like the multiplication sign  ). The double asterisk  with a   is used to square a number such as: 22 = 4

If you want to go a step further, you can try to find the length of the circle's circumference. The formula is: circumference = pi × diameter

 * Diameter – a straight line that goes through the centre of the circle from one side of the circumference to the other. This line is double the length of the radius.
 * Pi – the ratio of the length of the circumference to the diameter. This means that the circumference of every circle is about 3.14 times as long as the diameter. It is named after the Greek letter Pi (π).

General

 * Bug – An unwanted mistake in the source code.
 * Comment – A line of source code that is ignored by the interpreter/compiler, so it can be used for making notes or debugging.
 * Debugging – Removing bugs from the source code. Most IDEs have tools that allow debugging at runtime to make it easier to see where the bugs are.
 * Hello World – A popular test program used by software developers when they are learning a new programming language.
 * If statement – A conditional section of source code that runs certain source code based on the condition that was used.
 * Indentation – The use of tabs (with the key) or spaces (with the ) before a line of source code. In Python, this is required for the interpreter to understand how the program works.
 * Integrated Development Environment (IDE) – A program designed for software development. A typical IDE includes a text editor to write the source code, an interpreter (or compiler) for running the sourcing code and debugging tools to troubleshoot mistakes made when writing the source code.
 * Interpreter – A program that reads and runs the source code of an interpreted programming language such as Python.
 * Keyword – A word that is reserved for use by a programming language. Examples in Python include:,  ,  ,  ,   and.
 * Source code – The text of the programming language that makes up the program.

Loops

 * For loop – A repeated section of source code that runs a certain number of times.
 * While loop – A repeated section of source code that is exited by a condition.

Variables

 * Boolean – A variable datatype that can either be True or False.
 * Datatype – The type of data which a variable holds. Python is a dynamically typed programming language, so you can just assign the value to the variable.
 * Integer – A variable datatype for any positive or negative whole number (including zero) without a decimal point.
 * String – A variable datatype that defines a string of characters such as.
 * Variable – A value with a particular datatype that is defined by the programmer usually at the top of a program.

Modules

 * Module – A Python source code file written by other software developers. Many modules are included with the default Python installation, but there are also external Python modules which need to be installed using pip or Anaconda.
 * pip – A command-line Python package manager for installing external modules that aren't included in the standard Python installation.


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Talk:Super Mario 63

The game is pretty cool!
This game is pretty cool, i played it and had a alot of fun during everything! And i also beated the game! Matute44523 (discuss • contribs) 03:32, 28 November 2022 (UTC)

title: Talk:Super Mario 63


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Talk:A-level Computing/AQA/Paper 1/Skeleton program/2023

Issue with the Python solution to Question 2
"It allows it to be accessed from outside the class by the main functions, otherwise if it was a private method this would not be possible." I am under the impression python doesn't have any true private methods? I thought adding the two underscores just changed the name of the method slightly so it won't be used accidentally? So technically otherwise it would still be "possible" in python. 23:47, 11 June 2023 (UTC)

Issue with the Python solution to Question 3
Unless I'm completely wrong, shouldn't the condition of the while loop be `while not (MoveLegal and SquareIsValid):`? At the moment the check for whether the square is valid is not being used, so if an invalid square is chosen it would keep going, right? Vallieplushie (discuss • contribs) 09:00, 30 November 2022 (UTC)

 * You're right, it should be, though it makes sense it went unnoticed as in most cases only checking MoveLegal works fine. With the current check an invalid square is only accepted if the invalid square passes CheckPlayerMove, for example moving piece 25 to square 27 (invalid) using a Chowkidar. 195.194.74.162 (discuss) 10:07, 15 March 2023 (UTC)

Issue with 9.3
The answer CheckIfThereIsAMoveToSquare is not a private method as it does not have 2 leading underscores. __CreateBoard should be regarded as a correct answer if I am not mistaken. 2A02:C7C:C083:CE00:B9D2:92C6:245F:C1A4 (discuss) 20:02, 4 April 2023 (UTC)


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Wikibooks:Requests for import/Archives/2022/June

Chess diagram imports
I am working on a wikibook that concerns chess variants. In order to allow for a more advanced array of board sizes to be used, could I please request the other diagram templates at https://en.wikipedia.org/wiki/Template:Chess_diagram be imported? Such as the small diagram and the different-sized board diagrams? Thank you! – Itswikisam (t • c) 05:32, 120 June 2022 (UTC) Itswikisam (discuss • contribs) 05:38, 20 June 2022 (UTC)


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User:Xeverything11/header

  view · edit    IN NUMBERS

1,274 edits contributed to Wikibooks

35 pages created in Wikibooks (only on (Main), Cookbook and Wikijunior namespaces)

140 edits contributed to Wikibooks on 23 Nov 2022 alone

185 LTAs in total reported to Steward requests/Global for global (b)locking

3.7 MB of text added and removed to the pages

183 My Wikibookaholic score as of 1 Dec 2022

2 times my user page has been vandalized.

18 times my talk page has been vandalized.
 Userboxes

 A sense of scale

Since 20 Nov 2022, Xeverything11 is adding the conversions to the recipes, most importantly the SI units, which was established in 1960.

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