Terminology.

The terms "upper case" and "lower case" may be written as two consecutive words, connected with a hyphen ("upper-case" and "lower-case" particularly if they pre-modify another noun), or as a single word ("uppercase" and "lowercase"). These terms originated from the common layouts of the shallow drawers called "type cases" used to hold the movable type for letterpress printing. Traditionally, the capital letters were stored in a separate shallow tray or "case" that was located above the case that held the small letters. "Majuscule" ( or ), for palaeographers, is technically any script in which the letters have very few or very short ascenders and descenders, or none at all (for example, the majuscule scripts used in the Codex Vaticanus Graecus 1209, or the Book of Kells). By virtue of their visual impact, this made the term majuscule an apt descriptor for what much later came to be more commonly referred to as uppercase letters. "Minuscule" refers to lower-case letters. The word is often spelled "miniscule", by association with the unrelated word "miniature" and the prefix "mini-". This has traditionally been regarded as a spelling mistake (since "minuscule" is derived from the word "minus"), but is now so common that some dictionaries tend to accept it as a nonstandard or variant spelling. "Miniscule" is still less likely, however, to be used in reference to lower-case letters.

Typographical considerations.

The glyphs of lower-case letters can resemble smaller forms of the upper-case glyphs restricted to the base band (e.g. "C/c" and "S/s", cf. small caps) or can look hardly related (e.g. "D/d" and "G/g"). Here is a comparison of the upper and lower case variants of each letter included in the English alphabet (the exact representation will vary according to the typeface and font used):  Typographically, the basic difference between the majuscules and minuscules is not that the majuscules are big and minuscules small, but that the majuscules generally have the same height (although, depending on the typeface, there may be some exceptions, particularly with "Q" and sometimes "J" having a descending element; also, various diacritics can add to the normal height of a letter).  There is more variation in the height of the minuscules, as some of them have parts higher (ascenders) or lower (descenders) than the typical size. Normally, "b, d, f, h, k, l, t " are the letters with ascenders, and "g, j, p, q, y" are the ones with descenders. In addition, with old-style numerals still used by some traditional or classical fonts, "6" and "8" make up the ascender set, and "3, 4, 5, 7" and "9" the descender set.

Bicameral script.

Writing systems using two separate cases are "bicameral scripts". Languages that use the Latin, Cyrillic, Greek, Coptic, Armenian, Adlam, Warang Citi, Cherokee, and Osage scripts use letter cases in their written form as an aid to clarity and legibility. Another bicameral script, which is not used for any modern languages, is Deseret. The Georgian alphabet has several variants, and there were attempts to use them as different cases, but the modern written Georgian language does not distinguish case.  Many other writing systems make no distinction between majuscules and minuscules a system called unicameral script or unicase. This includes most syllabic and other non-alphabetic scripts.  In scripts with a case distinction, lower case is generally used for the majority of text; capitals are used for capitalisation and emphasis when bold is not available. Acronyms (and particularly initialisms) are often written in all-caps, depending on various factors.

Capitalisation.

Capitalisation is the writing of a word with its first letter in uppercase and the remaining letters in lowercase. Capitalisation rules vary by language and are often quite complex, but in most modern languages that have capitalisation, the first word of every sentence is capitalised, as are all proper nouns.  Capitalisation in English, in terms of the general orthographic rules independent of context (e.g. title vs. heading vs. text), is universally standardised for formal writing. Capital letters are used as the first letter of a sentence, a proper noun, or a proper adjective. The names of the days of the week and the names of the months are also capitalised, as are the first-person pronoun "I" and the interjection "O" (although the latter is uncommon in modern usage, with "oh" being preferred). There are a few pairs of words of different meanings whose only difference is capitalisation of the first letter. Honorifics and personal titles showing rank or prestige are capitalised when used together with the name of the person (for example, "Mr. Smith", "Bishop O'Brien", "Professor Moore") or as a direct address, but normally not when used alone and in a more general sense. It can also be seen as customary to capitalise any word in some contexts even a pronoun referring to the deity of a monotheistic religion.  Other words normally start with a lower-case letter. There are, however, situations where further capitalisation may be used to give added emphasis, for example in headings and publication titles (see below). In some traditional forms of poetry, capitalisation has conventionally been used as a marker to indicate the beginning of a line of verse independent of any grammatical feature.  Other languages vary in their use of capitals. For example, in German all nouns are capitalised (this was previously common in English as well, mainly in the 17th and 18th centuries), while in Romance and most other European languages the names of the days of the week, the names of the months, and adjectives of nationality, religion, and so on normally begin with a lower-case letter. On the other hand, in some languages it is customary to capitalise formal polite pronouns, for example "De", "Dem" (Danish), "Sie", "Ihnen" (German), and "Vd" or "Ud" (short for "usted" in Spanish).  Informal communication, such as texting, instant messaging or a handwritten sticky note, may not bother to follow the conventions concerning capitalisation, but that is because its users usually do not expect it to be formal.

Related phenomena.

Similar orthographic and graphostylistic conventions are used for emphasis or following language-specific or other rules, including:

Stylistic or specialised usage.

Case styles.

In English, a variety of case styles are used in various circumstances:

Headings and publication titles.

In English-language publications, various conventions are used for the capitalisation of words in publication titles and headlines, including chapter and section headings. The rules differ substantially between individual house styles.  The convention followed by many British publishers (including scientific publishers, like "Nature", magazines, like "The Economist" and "New Scientist", and newspapers, like "The Guardian" and "The Times") and also U.S. newspapers, is sentence-style capitalisation in headlines, i.e. capitalisation follows the same rules that apply for sentences. This convention is usually called "sentence case". It may also be applied to publication titles, especially in bibliographic references and library catalogues. An example of a global publisher whose English-language house style prescribes sentence-case titles and headings is the International Organization for Standardization (ISO).  For publication titles it is, however, a common typographic practice among both British and U.S. publishers to capitalise significant words (and in the United States, this is often applied to headings, too). This family of typographic conventions is usually called "title case". For example, R. M. Ritter's "Oxford Manual of Style" (2002) suggests capitalising "the first word and all nouns, pronouns, adjectives, verbs and adverbs, but generally not articles, conjunctions and short prepositions". This is an old form of emphasis, similar to the more modern practice of using a larger or boldface font for titles. The rules which prescribe which words to capitalise are not based on any grammatically inherent correct–incorrect distinction and are not universally standardised; they differ between style guides, although most style guides tend to follow a few strong conventions, as follows:  Title case is widely used in many English-language publications, especially in the United States. However, its conventions are sometimes not followed strictly especially in informal writing.  In creative typography, such as music record covers and other artistic material, all styles are commonly encountered, including all-lowercase letters and special case styles, such as studly caps (see below). For example, in the wordmarks of video games it is not uncommon to use stylised upper-case letters at the beginning and end of a title, with the intermediate letters in small caps or lower case (e.g.,,, and ).

Multi-word proper nouns.

Single-word proper nouns are capitalised in formal written English, unless the name is intentionally stylised to break this rule (such as the first or last name of danah boyd).  Multi-word proper nouns include names of organisations, publications, and people. Often the rules for "title case" (described in the previous section) are applied to these names, so that non-initial articles, conjunctions, and short prepositions are lowercase, and all other words are uppercase. For example, the short preposition "of" and the article "the" are lowercase in "Steering Committee of the Finance Department". Usually only capitalised words are used to form an acronym variant of the name, though there is some variation in this.  With personal names, this practice can vary (sometimes all words are capitalised, regardless of length or function), but is not limited to English names. Examples include the English names Tamar of Georgia and Catherine the Great, "van" and "der" in Dutch names, "von" and "zu" in German, "de", "los", and "y" in Spanish names, "de" or "d'" in French names, and "ibn" in Arabic names.  Some surname prefixes also affect the capitalisation of the following internal letter or word, for example "Mac" in Celtic names and "Al" in Arabic names.

Special case styles.

Some case styles are not used in standard English, but are common in computer programming, product branding, or other specialised fields:

Unit symbols in the metric system.

In the International System of Units (SI), a letter usually has different meanings in upper and lower case when used as a unit symbol. Generally, unit symbols are written in lower case, but if the name of the unit is derived from a proper noun, the first letter of the symbol is capitalised (nevertheless, the "name" of the unit, if spelled out, is always considered a common noun and written accordingly):  For the purpose of clarity, the symbol for litre can optionally be written in upper case even though the name is not derived from a proper noun:  The letter case of a prefix symbol is determined independently of the unit symbol to which it is attached. Lower case is used for all submultiple prefix symbols and the small multiple prefix symbols up to "k" (for kilo, meaning 10 = 1000 multiplier), whereas upper case is used for larger multipliers:

Case folding and case conversion.

In the character sets developed for computing, each upper- and lower-case letter is encoded as a separate character. In order to enable case folding and case conversion, the software needs to link together the two characters representing the case variants of a letter. (Some old character-encoding systems, such as the Baudot code, are restricted to one set of letters, usually represented by the upper-case variants.)  Case-insensitive operations can be said to fold case, from the idea of folding the character code table so that upper- and lower-case letters coincide. The conversion of letter case in a string is common practice in computer applications, for instance to make case-insensitive comparisons. Many high-level programming languages provide simple methods for case conversion, at least for the ASCII character set.  Whether or not the case variants are treated as equivalent to each other varies depending on the computer system and context. For example, user passwords are generally case sensitive in order to allow more diversity and make them more difficult to break. On the other hand, when performing a keyword search, differentiating between the upper and lower case might narrow down the search result too much.

Unicode case folding and script identification.

Unicode defines case folding through the three case-mapping properties of each character: upper case, lower case, and title case (in this context, "title case" relates to ligatures and digraphs encoded as mixed-case single characters, in which the first component is in upper case and the second component in lower case). These properties relate all characters in scripts with differing cases to the other case variants of the character.  As briefly discussed in Unicode Technical Note #26, "In terms of implementation issues, any attempt at a unification of Latin, Greek, and Cyrillic would wreak havoc [and] make casing operations an unholy mess, in effect making all casing operations context sensitive [...]". In other words, while the shapes of letters like A, B, E, H, K, M, O, P, T, X, Y and so on are shared between the Latin, Greek, and Cyrillic alphabets (and small differences in their canonical forms may be considered to be of a merely typographical nature), it would still be problematic for a multilingual character set or a font to provide only a "single" code point for, say, uppercase letter B, as this would make it quite difficult for a wordprocessor to change that single uppercase letter to one of the three different choices for the lower-case letter, the Latin b (U+0062), Greek β (U+03B2) or Cyrillic в (U+0432). Therefore, the corresponding Latin, Greek and Cyrillic upper-case letters (U+0042, U+0392 and U+0412, respectively) are also encoded as separate characters, despite their appearance being basically identical. Without letter case, a "unified European alphabet"such as ABБCГDΔΕЄЗFΦGHIИJ...Z, with an appropriate subset for each languageis feasible; but considering letter case, it becomes very clear that these alphabets are rather distinct sets of symbols.

Methods in word processing.

Most modern word processors provide automated case conversion with a simple click or keystroke. For example, in Microsoft Office Word, there is a dialog box for toggling the selected text through UPPERCASE, then lowercase, then Title Case (actually start caps; exception words must be lowercased individually). The keystroke does the same thing.

Methods in programming.

In some forms of BASIC there are two methods for case conversion: C and C++, as well as any C-like language that conforms to its standard library, provide these functions in the file ctype.h: Case conversion is different with different character sets. In ASCII or EBCDIC, case can be converted in the following way, in C:  This only works because the letters of upper and lower cases are spaced out equally. In ASCII they are consecutive, whereas with EBCDIC they are not; nonetheless the upper-case letters are arranged in the same pattern and with the same gaps as are the lower-case letters, so the technique still works.  Some computer programming languages offer facilities for converting text to a form in which all words are capitalised. Visual Basic calls this "proper case"; Python calls it "title case". This differs from usual title casing conventions, such as the English convention in which minor words are not capitalised.

History.

Originally alphabets were written entirely in majuscule letters, spaced between well-defined upper and lower bounds. When written quickly with a pen, these tended to turn into rounder and much simpler forms. It is from these that the first minuscule hands developed, the half-uncials and cursive minuscule, which no longer stayed bound between a pair of lines. These in turn formed the foundations for the Carolingian minuscule script, developed by Alcuin for use in the court of Charlemagne, which quickly spread across Europe. The advantage of the minuscule over majuscule was improved, faster readability.  In Latin, papyri from Herculaneum dating before 79 CE (when it was destroyed) have been found that have been written in old Roman cursive, where the early forms of minuscule letters "d", "h" and "r", for example, can already be recognised. According to papyrologist Knut Kleve, "The theory, then, that the lower-case letters have been developed from the fifth century uncials and the ninth century Carolingian minuscules seems to be wrong." Both majuscule and minuscule letters existed, but the difference between the two variants was initially stylistic rather than orthographic and the writing system was still basically unicameral: a given handwritten document could use either one style or the other but these were not mixed. European languages, except for Ancient Greek and Latin, did not make the case distinction before about 1300.  The timeline of writing in Western Europe can be divided into four eras:  Traditionally, certain letters were rendered differently according to a set of rules. In particular, those letters that began sentences or nouns were made larger and often written in a distinct script. There was no fixed capitalisation system until the early 18th century. The English language eventually dropped the rule for nouns, while the German language keeps it.  Similar developments have taken place in other alphabets. The lower-case script for the Greek alphabet has its origins in the 7th century and acquired its quadrilinear form (that is, characterized by ascenders and descenders) in the 8th century. Over time, uncial letter forms were increasingly mixed into the script. The earliest dated Greek lower-case text is the Uspenski Gospels (MS 461) in the year 835. The modern practice of capitalising the first letter of every sentence seems to be imported (and is rarely used when printing Ancient Greek materials even today).

Type cases.

The individual type blocks used in hand typesetting are stored in shallow wooden or metal drawers known as "type cases". Each is subdivided into a number of compartments ("boxes") for the storage of different individual letters.  The "Oxford Universal Dictionary on Historical Advanced Proportional Principles" (reprinted 1952) indicates that "case" in this sense (referring to the box or frame used by a compositor in the printing trade) was first used in English in 1588. Originally one large case was used for each typeface, then "divided cases", pairs of cases for majuscules and minuscules, were introduced in the region of today's Belgium by 1563, England by 1588, and France before 1723.  The terms "upper" and "lower" case originate from this division. By convention, when the two cases were taken out of the storage rack and placed on a rack on the compositor's desk, the case containing the capitals and small capitals stood at a steeper angle at the back of the desk, with the case for the small letters, punctuation, and spaces being more easily reached at a shallower angle below it to the front of the desk, hence upper and lower case.  Though pairs of cases were used in English-speaking countries and many European countries in the seventeenth century, in Germany and Scandinavia the single case continued in use.  Various patterns of cases are available, often with the compartments for lower-case letters varying in size according to the frequency of use of letters, so that the commonest letters are grouped together in larger boxes at the centre of the case. The compositor takes the letter blocks from the compartments and places them in a composing stick, working from left to right and placing the letters upside down with the nick to the top, then sets the assembled type in a galley.

Letter case (or just case) is the distinction between the letters that are in larger upper case (also "uppercase", "capital letters", "capitals", "caps", "large letters", or more formally "majuscule") and smaller lower case (also "lowercase", "small letters", or more formally "minuscule") in the written representation of certain languages. The writing systems that distinguish between the upper and lower case have two parallel sets of letters, with each letter in one set usually having an equivalent in the other set. The two case variants are alternative representations of the same letter: they have the same name and pronunciation and are treated identically when sorting in alphabetical order.


Early life.

He was born at Chambéry in Savoy on 24 March 1751, the son of a fur merchant. His paternal grandfather, born at Burneuil in Picardy, moved to Chambéry, in the Dukedom of Savoy, at the beginning of the 18th century. In 1709 the grandfather married Claudine Latoud, born in 1682. They had thirteen children, of whom only four reached the age of twenty, and opened up a fur shop on rue Tupin in Chambéry.  This shop made an impression on the young Benoît Leborgne. In his "Mémoires", he wrote that he was fascinated by the exotic sign outside the shop. It was brightly colored and featured wild animals including lions, elephants, panthers and tigers, with the motto underneath: "You can go ahead and try something else, you will all come to Leborgne, the fur dealer." The child's imagination was stimulated, and he kept asking his parents and grandparents about the animals. He wanted to know more about the far-off countries where they lived.  His father, Jean-Baptiste Leborgne, born in 1718, frequently traveled on business to wild-fur markets and brought

Early military career.

Leborgne began his military career in the north of France in 1768, as an ordinary soldier in Louis XV's Irish Regiment, directed by Lord Clare and quartered in Flanders. This regiment was made up mostly of Irish emigrants who did not want to serve the British; at this time Irish Catholics were disenfranchised in their own country under the anti-Catholic penal laws. During this period, many Irishmen left Ireland for the Catholic countries of Europe or for North

The Russian-Turkish war.

As he was leaving the Irish Regiment, young Leborgne learned from the newspapers that Prince Fyodor Grigoryevich Orlov of Russia was raising, in the name of Empress Catherine II of Russia, a Greek regiment to attack the Ottoman Empire. At the time, Russia was attempting to extend its territory to acquire a port on the Black Sea, and was using the anti-Turkish sentiments of people under Ottoman domination to aid its project. Leborgne saw a chance of advancement and adventure. He went back to Chambéry for a short time and got a letter of recommendation to Prince Orlov through the cousin of a client of his mother's, who was a close acquaintance of the prince. First Leborgne went to Turin,

Preparations for India.

Lord Percy took Leborgne as a guide through the Greek islands back to Paros, where Leborgne officially resigned from his regiment. He was free again, but had only his last pay received from before his resignation. He travelled to Smyrna (now Izmir), which at the time was a prosperous, booming city. There, Leborgne met merchants from many countries, including India, which was believed to hold much wealth, like the diamonds of Golconda and the sapphires of Ceylon (now Sri Lanka). Some of these merchants told him their theories about the existence of trade routes passing north of India, in upper Kashmir or along the glaciers of Karakoram. He also learned that many rajahs regularly sought out European officers to organize and command

Military glory and fortune in India.

In the late 18th century, the mighty Maratha Empire was gradually collapsing. The British were triumphing over their Portuguese, French, and Dutch rivals in India, where all the countries had hastened to install trading posts. The British East India Company was the most powerful military and economic

Arrival in India.

In 1778, Leborgne arrived at the Indian port of Madras (now Chennai). He was poor and to make a living, taught fencing. While teaching, he met a nephew of the British governor of the city, Sir Thomas Rumbold. He was offered a position as an officer in the 6th battalion of sepoys, a troop of local inhabitants raised by the Company. He accepted, and gradually learned the local customs and began training the sepoys. He lived in Madras for four years, but became restless. He was

Arrival in Lucknow.

In Lucknow, Leborgne was received by the nabab Asaf-ud-Daulah and was invited to live with Colonel Pollier, in the service of the Company. As Middleton, an Englishman present when Leborgne met the nabab, explained to him afterward, this invitation was in fact an order; if he refused he would have been thrown in prison. Colonel Antoine Polier, a Swiss, received him warmly. Leborgne discovered that Lucknow had many European residents. He met two who spoke French. The first, Claude Martin, was from Lyons and had made his fortune in India; the second, Drugeon, was

Leaving Lucknow for Delhi.

In August 1783, de Boigne received permission to leave Oudh and went north to search for new trade routes. His journey by horse led him to Delhi in the company of Polier, who also had to go there for business. During the trip, de Boigne saw the Taj Mahal and other Indian sights, including various smaller kingdoms and tribes. In Delhi, an Englishman named Anderson offered to get de Boigne an audience with Emperor Shah Alam, whose court was at the Red Fort. During this audience, de Boigne told the emperor about his proposal to seek new trade routes, but the emperor put off any decision ("We'll see"). De Boigne waited in Delhi, hoping for a favorable answer. However, circumstances were about to change. The day after the audience,

Doubted by Marathas, betrayed by Jaipur.

The Marathas had set up camp to besiege the citadel of Gwalior, in which a Scot named George Sangster, whom de Boigne had met in Lucknow, was commanding the garrison. When Levassoult and de Boigne arrived in the Maratha camp, they received a warm welcome. Levassoult presented his friend as the bravest of soldiers, and de Boigne was given a tent. However, while he was away from it, his baggage was stolen, and with it the precious letters of exchange of Hastings and also the letter for Kabul and Peshawar. He soon learned that this theft had been ordered by Sindhia himself, who wanted to know more about this suspect European. De Boigne, wanting revenge, decided to send a discreet message to Sangster in the besieged citadel and proposed an attack on the Maratha camp. But while he was waiting for the answer, he was called by an enraged

In the service of the Maratha empire.

After a time wandering, de Boigne again met his friend Levassoult, who introduced him to the Catholic convert Begum Joanna. She confided to him that Sindhia, the Maratha chief wanted him back. Although Sindhia had been mistrustful of de Boigne's projects of exploration, and in spite of their argument over the confiscated baggage, Sindhia had been impressed with de Boigne's two European-trained battalions, which contrasted sharply with his own troops. De Boigne finally agreed to enter the service of the Marathas. He was put in charge of organizing a cannon foundry in Agra, as well as equipping and arming 7000 men in two battalions. De Boigne from this time quickly became an influential man. One of the first actions under his command was the October 1783 capture of the citadel of Kalinjar in the region of Bundelkhand. The rajah of this region ended up parleying with de Boigne, which allowed Sindhia to enter Delhi as its master. The Maratha chief named himself "Column of

Commercial life and first marriage.

Back in Lucknow, Benoît de Boigne found his old friends Antoine-Louis Polier and Claude Martin. Martin persuaded de Boigne to work with him in trade. His military skills were useful, for at the time, Indian trade routes were dangerous, and even warehouses in the cities were sometimes robbed. Claude Martin and Benoît de Boigne built a warehouse inside an old fort. It included saferooms and a trained armed guard to watch it. Quickly, this business became successful. De Boigne also carried on a trade in precious stones, copper, gold, silver, indigo, cashmere shawls, silks, and

A general in the service of the Maratha empire, with the title of jaghir.

In 1788, Sindhia sent a discreet message to de Boigne. Sindhia wished to unite north and northwest India. At the time, the Rajputs and the Marathas had a tense relationship. The Marathas were levying the peasants with more taxes. Sindhia succeeded in convincing de Boigne to return to his service. He asked him to organize a brigade of 12,000 men within a year (January 1789-January 1790). De Boigne became commander-in-chief and general, the highest title under "rajah." To be able to pay his men, Sindhia gave his new general a "jaghir", a fief given for the lifetime of its holder, against a payment in return to the imperial treasury. At the death of its holder, the "jaghir" reverted to another deserving officer. The revenues from the "jaghir" allowed the officer to pay his men. Benoît de Boigne received the Doab, a region of plains in Uttar Pradesh. This plain was covered with

Military campaigns and victories.

Starting in 1790, the brigade had to face Rajputs, Ismail Beg, and the rajahs of Bikaner and Jaipur. De Boigne decided to attack this coalition by surprise on May 23. De Boigne demonstrated his military talent by gaining one victory after another. The East India Company began to become concerned about this new Maratha army, dangerous to their domination. Within six months of 1790, in a hostile, hilly terrain, de Boigne's brigade defeated 100,000 men, confiscated 200 camels and 200 cannons, many bazaars, and fifty elephants. The Maratha army attacked and took seventeen fortresses by siege. It won several decisive battles, among which the most difficult were the battles of Patan, Mairtah, and Ajmer. The Rajputs recognized the authority of Sindhia as prime minister. The Marathas were now the masters of northern and northwestern India. During these military campaigns, de Boigne continued his commercial association with Claude Martin from

Trusted by Maratha chiefs. European events.

Sindhia had become the most powerful man in India, with many enemies. As they were not able to beat him militarily, the Maratha chief faced conspiracies, intrigue and treason. De Boigne was a faithful follower and Sindhia trusted him and made him a confidant. De Boigne now was running imperial affairs for Sindhia in north and northwestern India. The minister Gopal Rao, whose brother had been engaged in a famous plot with Nana Farnavis (Nana Fadnavis), came to Aligarh to visit de Boigne to show his loyalty to Sindhia. But while India was now a confederation under the Maratha authority, the situation in Europe was changing profoundly. The French Revolution had overturned the equilibrium in Europe, and also in Europe's colonial empires. On November 12, 1792, a Savoy assembly proclaimed its unity with France. Until 1815, de Boigne was now considered a Frenchman like any other. The brigades of the Maratha army under de Boigne's command were under

Return to Europe and second marriage.

Benoît de Boigne left for England, where he installed his household near London. Although he had been born a Savoyard, the Revolution had made him a Frenchman, and therefore a potential enemy of the British. His wealth and his letters of credit were held in abeyance at the bank. However, his military prowess was known to many British who had campaigned in India, some of whom had dined with him in India. This sympathy allowed de Boigne to take British nationality on January 1, 1798. The nationality was conditional upon his remaining in Britain or its colonies. Wishing to leave London, de Boigne acquired a house in the English countryside, in Dorsetshire. He considered going back to Chambéry,

Unhappy second marriage; discovery of France under the Consulate.

His second wife, born in 1781, was an emigrant from a penniless, though noble, old family from Normandy. De Boigne did not reveal his own lowly origins before the marriage. He seems to have wished, after his adventurous life, to start a family and establish himself in Europe through the help of his wife's high-placed relations. But from the beginning, the marriage was not a success. De Boigne had a hard time adapting to European manners after so long in India, and the 30-year difference in age between him and his wife added to the difficulty. He was jealous. He also now took opium to assuage the pain of his dysentery, and his wife and her family claimed he abused it. During this period, France was under the Consulate, and many French emigrants returned to France. De Boigne decided to go back as well, and

Final return to Savoy.

Benoît de Boigne returned to Savoy definitively in 1807. There, he had himself called "General de Boigne." He lived alone in the château of Buisson-Rond near Chambéry, which he had bought in 1802 and appointed luxuriously for his young wife. But she continued to live in the Paris region, where she lived in the château of Beauregard and then of Châtenay. In this Parisian life she found the material for her celebrated "Mémoires", which were published in 1907. The Comtesse de Boigne rarely came to Buisson-Rond, although she occasionally gave urbane receptions during the summer on her way home from taking the waters at Aix, in the company of her friends Madame Récamier, Madame de Staël, Adrien de Montmorency (Anne Adrien Pierre de Montmorency-Laval), and Benjamin Constant.  Having returned from the isle of Réunion, Benoît de Boigne received the title of Field Marshal on October 20, 1814, and the Croix de Saint-Louis (Order of Saint Louis) on December 6. His wife was pleased. On February 27, 1815, Louis XVIII gave him the Legion of Honor for services rendered as President of the Conseil général du département du Mont-Blanc.

Descendants of Benoît de Boigne.

Charles-Alexandre de Boigne was born in Delhi, India in 1791. He married Césarine Viallet de Montbel in 1816. The marriage had been encouraged by his father. Césarine Viallet de Montbel was from a large Savoy family who had been parliamentarians and later ennobled. They had thirteen children. Charles-Alexandre, educated in England, had studied law, but spent most of his life as a minor courtier at the Savoy court, managing his land and inheritance. He was assisted by Thomas Morand, a

Benefactor of Chambéry.

At his death, Benoît de Boigne left a fortune estimated at 20 million French francs of the time. Altogether, his donations to his native city amounted to about 3,484,850 francs. He left a permanent fund of 6500 pounds yearly to the metropolitan church of Chambéry for, among other things, the choir. He gave a second fund of 1250 pounds to the Compagnie des nobles Chevaliers-Tireurs-à-l'Arc (Company of noble knight archers).  De Boigne gave many donations for charity, including giving beds to hospitals. He donated 22,400 francs for three hospital beds at the Hôtel-Dieu, a charity hospital, and later gave 24,000 francs for another four beds for poor, sick foreign travelers of any nation or religion. He paid 63,000 francs for the construction of various buildings at the Hôtel-Dieu of Chambéry, and gave a beggars' home the sum of 649,150 francs. He founded an old age home, the Maison de Saint-Benoît, which cost him 900,000 francs. He also paid for a place in the orphanage for 7300 francs, and ten beds at the charity hospital, for patients with contagious illnesses, who could not be admitted to Hôtel-Dieu. De Boigne also gave a trust fund of 1650 pounds a year, about 33,000 francs, to help poor prisoners every week with laundry and food. He gave another perpetual trust of 1200 pounds or 24,000 francs to the poor "shameful" of the city, to be distributed at their homes. Finally, he left a trust fund of 1200 pounds to the firemen of Chambéry to help the sick and wounded. De Boigne gave 30,000 francs to build the church of the Capucins, and 60,000 francs to build a theater. Among his other numerous donations, two were important. One was 320,000 francs for various works, as well as the ownership without usufruct of the property of Châtenay. The second donation was for 300,000 francs to demolish the cabornes [stone huts] and open up a wide avenue across the city. He also gave 30,000 francs for the repair of the city hall and 5000 francs for the bell-tower of Barberaz.  De Boigne also gave four major donations to education. He gave 270,000 francs to reorganize the collège of Chambéry; he gave a trust fund of 1000 pounds a year, 20,000 francs, to the Société royale académique de Chambéry for the encouragement of agriculture, arts, and letters; he gave two trust funds of 150 pounds apiece, or 3000 francs, to the Frères des Écoles chrétiennes (Brothers of Christian Schools) and to the Sisters of Saint Joseph. Both of these groups gave a free education to children, the first to poor children, the second to girls.

Benoît Leborgne (24 March 175121 June 1830), better known as Count Benoît de Boigne or General Count de Boigne, was a military adventurer from the Duchy of Savoy, who made his fortune and name in India with the Marathas. He was also named president of the general council of the French "département" of Mont-Blanc by Napoleon I.


Background.

Before 20th Century Fox started its animation division, Fox released its first seven animated films, such as "Hugo the Hippo" (1975), "Wizards", "" (1977), "Fire and Ice" (1983), "" (1992) with Interscope Communications, "Once Upon a Forest" (1993) and "The Pagemaster" (1994).  In May 1993, Fox agreed to a two-year first-look deal with Nickelodeon for family films. The deal would mostly include original material, though a Nickelodeon executive did not rule out the possibility of making films based on "The Ren & Stimpy Show", "Rugrats" and "Doug". However, no films came out of the deal due to the 1994 acquisition of Paramount Pictures by Nickelodeon's parent company, Viacom, and they would distribute the film projects instead.

History.

The division initially started in February 1994 as Fox Family Films, as one of four film divisions of 20th Century Fox under executive John Matoian. The division was planned to produce six feature films a year as part of a plan to produce more films per year overall. Fox senior vice president of production Chris Meledandri was transferred into the unit as executive vice president in March 1994 after having being hired the previous year. The week of May 6, 1994, Fox Family announced the hiring of Don Bluth and Gary Goldman for a new $100 million animation studio which began construction that year in Phoenix, Arizona. In three years, the animation studio would produce and release its first film, "Anastasia". In September 1994, Matoian was promoted by Rupert Murdoch to head up the Fox network. Meledandri was selected to head up the unit in 1994.  It produced live-action films such as "" (1995), "Dunston Checks In" (1996) and "Home Alone 3". By August 1997, Fox Family had decreased the number of live films. R.L. Stine agreed with Fox Family Films in January 1998 for a film adaptation of the Goosebumps book franchise with Tim Burton producing.

Fox Animation.

In 1998, following the success of "Anastasia", the division was renamed to Fox Animation Studios, refocusing on animated feature films, including stop-motion, mixed media and digital production. The division's live action films in development at the time included Marvel Comics' Silver Surfer, the disaster film spoof "Disaster Area", "Fantastic Voyage" and "Goosebumps". "Ever After" (1998), a Cinderella adaptation, was the division's last live action film. At this time, there were several animated films on the company's development slate: "Dark Town" with Henry Selick, Chris Columbus and Sam Hamm, "Santa Calls" at Blue Sky, and Matt Groening ("The Simpsons"), Steve Oedekerk and Joss Whedon ("Buffy the Vampire Slayer") projects. The Phoenix studio at the time was producing "Planet Ice" expected in 1999 and directed by Art Vitello and Anastasia producer/directors Don Bluth and Gary Goldman's then soon to be announced project. Chris Meledandri remained as the president of the division, which was known by 1999 as 20th Century Fox Animation. The only television series that the Phoenix studio produced was "Adventures from the Book of Virtues", which was a co-production between Fox Animation Studios and PorchLight Entertainment; that series would air on PBS between 1996 and December 2000.  20th Century Fox Animation vice president of physical production Chuck Richardson was sent in early December 1999 to Fox subsidiary Blue Sky Studios as general manager and senior vice president. Richardson was sent to prepare Blue Sky for feature animation production.  The Phoenix studio, which kept the Fox Animation Studios name, laid off 2/3 of its employee workforce in February 2000 before its closure in late June of that year, ten days after "Titan A.E." was released and six months before "Adventures from the Book of Virtues" aired its final episode. Fox Animation looked to produce films at Blue Sky and its Los Angeles headquarters.  In January 2007, Meledandri left for Universal Pictures to set up Illumination there with Vanessa Morrison as his replacement while answering to newly appointed 20th Century Fox Film Group vice chairman Hutch Parker. Morrison moved from the live action division where she handled family-children fare as senior vice president of production. Morrision was making deal with outside producers like she approved a Roald Dahl’s "Fantastic Mr. Fox" stop-motion adaptation.  In September 2017, Locksmith Animation formed a multi-year production deal with 20th Century Fox, who will distribute Locksmith's films, with Locksmith aiming to release a film every 12-18 months. The deal was to bolster Blue Sky's output and replace the lost of distributing DreamWorks Animation films, which are now owned and distributed by Universal Pictures.  On October 30, 2017, Morrison was named president of a newly created 20th Century Fox division, Fox Family, which as a mandate similar to this company when it was called Fox Family Films. Andrea Miloro and Robert Baird were named co-president of Fox Animation the same day and would also have direct oversight of Blue Sky and oversee the Locksmith Animation deal and grow Fox Animation with other partnerships and producer deals.

Disney era.

On October 18, 2018, it was announced that 20th Century Fox Animation would be added alongside 20th Century Fox to the Walt Disney Studios following their acquisition, with co-presidents Andrea Miloro and Robert Baird retaining leadership while reporting to Walt Disney Studios Chairman, Alan Horn and Twentieth Century Fox vice chairman Emma Watts.  On March 21, 2019, Disney announced that the 20th Century Fox Animation label (including Blue Sky Studios) would be integrated as new units within the Walt Disney Studios with Co-Presidents Andrea Miloro and Robert Baird continuing to lead the studio reporting directly to Alan Horn. Miloro step down as co-president in late July 2019. In August 2019, Walt Disney Animation Studios head Andrew Millstein was named as co-president of Blue Sky for day-to-day operations alongside Baird, while Pixar Animation Studios president Jim Morris would also be taking a supervisory role over Millstein. With the Disney take over, the Locksmith deal left 20th Century Fox for Warner Bros. in October 2019 except for the first and only film under the deal, "Ron's Gone Wrong".  On January 28, 2020, Disney dropped the word "Fox" from the two main film studio units acquired from 21st Century Fox, while there were no mention of changes to other lesser feature film units.

Filmography.

Fox Animation Studios.

From 1994–2000, Fox operated Fox Animation Studios, a traditional animation studio which was started to compete with Walt Disney Animation Studios, which was experiencing great success with their releases of films such as "The Little Mermaid", "Beauty and the Beast", "Aladdin" and "The Lion King". The Fox studio, however, was not as successful. Their first feature "Anastasia" made nearly $140 million at the worldwide box office on a $53 million budget in 1997, but their next feature, "Titan A.E.", was a large financial loss, losing $100 million for 20th Century Fox in 2000. The lack of box office success, coupled with the rise of computer animation, led Fox to shut down the Fox Animation Studios.

Blue Sky Studios.

Since 1997, Fox has owned Blue Sky Studios, a computer animation company known for the "Ice Age" franchise. Fox has had much more success with this studio, and the box office receipts of their films are competitive with those of Pixar and DreamWorks. On March 21, 2019, Blue Sky Studios was integrated as a separate unit within Walt Disney Studios, but they will still report to Fox Animation presidents Andrea Miloro and Robert Baird. They have released thirteen feature films, numerous short films and television specials. Major feature films include:

20th Century Animation, Inc. (formerly Twentieth Century Fox Animation or 20th Century Fox Animation), is an animation subsidiary of The Walt Disney Studios. Originally formed in 1994 as a subsidiary of 20th Century Fox, the studio is located in Century City, Los Angeles, and is tasked with producing feature-length films.


Definitions.

Horton (2014) gives the "example of entryism – the infiltration of a self-proclaimed human rights activist into an institution committed to neoliberalism, a market fundamentalism that has been credited with eroding health systems in dozens of low and middle-income countries." Leslie (1999) uses the example of gender: "alternative, yet complementary, strategies of 'entryism', with attempts to enter and transform these institutions' gender inequalities from within (as missionaries)."

Socialist entryism.

Trotsky's "French Turn".

The "French Turn" refers to the classic form of entrism advocated by Leon Trotsky in his essays on "The French Turn". In June 1934, he proposed for the French Trotskyists to dissolve their Communist League and to join the French Section of the Workers' International (SFIO) and for the Communist League to dissolve its youth section to join more easily with revolutionary elements. The tactic was adopted in August 1934, despite some opposition, and successfully raised the group's membership to 300 activists.  Proponents of the tactic advocated that the Trotskyists should enter the social democratic parties to connect with revolutionary socialist currents within them and then to steer those currents toward Leninism. However, entryism lasted briefly since the leadership of the SFIO started to expel the Trotskyists. The Trotskyists of the Workers Party of the United States also successfully used their entry into the Socialist Party of America to recruit their youth group and other members. Similar tactics were also used by Trotskyist organisations in other countries, including the Netherlands, Belgium, Switzerland, and Poland. Entryism was used to connect with and recruit leftward-moving political currents inside radical parties.  Since it was used in France, Marxists have used the tactic even if they had different preconceptions of how long the period of entry would last:

Deep entryism "sui generis".

In these types of entryism, activists engage in a long-term perspective in which they work within an organisation for decades in the hope of gaining influence and a degree of power and perhaps even control of the larger organisation.  In entryism "sui generis" ("of a special type"), Trotskyists, for example, do not openly argue for the building of a Trotskyist party. "Deep entryism" refers to the long duration.  The tactic is closely identified with Michel Pablo and Gerry Healy, who were leaders of the Fourth International in the late 1940s and the 1950s. The "deep entry" tactic was developed as a way for Trotskyists to respond to the Cold War. In countries with mass social democratic or communist parties, it was as difficult to be accepted into these parties as it was Trotskyist currents as to build separate Trotskyist parties. Therefore, Trotskyists were advised to join the mass party.  In Europe, that was the approach used, for example, by The Club and later Socialist Action in the Labour Party, and by Fourth Internationalists inside the Communist Parties. In France, Trotskyist organizations, most notably the "Parti des Travailleurs" and its predecessors, have successfully entered trade unions and mainstream left-wing parties.

Open entryism.

Some political parties, such as the Workers' Party in Brazil or the Scottish Socialist Party, allow political tendencies to organise within them openly. In those cases, the term "entryism" is not usually used. Political groups that work within a larger organisation but also maintain a "public face" often reject the term "entrism" but are sometimes still considered to be entryists by the larger organization.

Examples by country.

Australia.

In Australia, the practice was widespread during the 1950s, when the Communist Party of Australia battled against right-wing Industrial Groups for control of Australian trade unions. The 'Groupers' subsequently formed the Democratic Labor Party. Today, the practice in Australia is often known as a type of branch stacking.  In recent times, RSPCA Australia has been described as being the victims of the practice. The National Farmers' Federation and Animals Australia have each been accused of infiltrating branches RSPCA Australia in an attempt to promote opposing policies concerning battery hens, intensive pig farming, and the live export of sheep.  Since the 2000s, the religious right has practiced entryism into a number of state branches of the Liberal Party of Australia, notably in New South Wales, Western Australia, Queensland and Victoria.  In 2018, it was revealed that the NSW National party and its youth wing, the Young Nationals had been infiltrated by the far Right with more than 30 members being investigated for alleged links. Leader McCormack denounced the infiltration, and several suspected Far right were expelled from the party and its youth wing.

Canada.

Although the term "entryism" was used little, if at all, opponents accused David Orchard and his supporters of attempting to win the leadership of the Progressive Conservative Party in the late 1990s and the early 2000s decade with the intention of dramatically changing its policies.  Orchard had made his name as a leading opponent of free trade, which was perhaps the singular signature policy of the Progressive Conservative government of Brian Mulroney in the late 1980s and the early 1990s. While opponents pointed to the remarkable distance, Orchard and his supporters argued that they represented "traditional" Conservative values and the economic nationalism of the older Conservative Party and the Progressive Conservative Party had espoused before Mulroney, namely under John Diefenbaker.  Opponents of the 2003 merger between the Progressive Conservative Party and the Canadian Alliance also charged Alliance members with infiltration. It was widely speculated that most, if not all, of the approximately 25,000 Canadians who swelled the Progressive Conservative Party Party's membership before the merger vote were Alliance members, who likely voted in favour of the merger.  Liberals for Life, a pro-life group allied with the Campaign Life Coalition, was accused of infiltrating the Liberal Party of Canada in the late 1980s and the early 1990s.  Members of Socialist Action, a small Trotskyist group, play a leading role in the New Democratic Party Socialist Caucus, a small faction on the left wing of the social democratic NDP, and advocate that their members join and engage with the NDP. That, however, does not fit with most definitions of entryism because of its continued existence apart and separate from the NDP, in addition to its work in it. Fightback, a rival Trotskyist organization, carries out a more classical form of entryism in the NDP, particularly in its youth wings, and models itself after the British Militant tendency, which practiced entryism into the Labour Party and, at its peak, was the one of the most successful entryist organizations on record.  After the fall of the Social Credit Party of British Columbia, the British Columbia Liberal Party saw the shift by the joining of former Social Credit members. As a result, the new membership saw the party shift much more towards the right in fiscal policy. Thus, entryism led to a complete takeover of the original party by former Social Credit members. That, however, is not formal entryism since former Social Credit members did not operate their own organization within the Liberal Party.

China.

During the Warlord Era in China, the Communist Party of China joined the party of the Nationalist Party of China for a time (1923–1927), creating the First United Front against warlordism, but one of the Communists' ideas behind doing so was the possibility of eventually gaining a majority in the Nationalist Party and shaping its policies. Eventually, the situation degraded, the Nationalists expelled the Communists from their party, and the Chinese Civil War began. The war was paused for a time (1936–1945) to allow for a Second United Front during the Chinese resistance to Japanese imperial rule. However, the civil war resumed again and remained active until 1950, after the Communists had won.

Netherlands.

The Marxist-Leninist Party of the Netherlands was a fake pro-China communist party in the Netherlands set up by the Dutch secret services, the BVD, to develop contacts with the Chinese government for espionage purposes. It existed from 1968 to the early 1990s.

New Zealand.

The country's four small communist parties, the Communist Party of New Zealand (CPNZ), Socialist Unity Party (SUP), Workers Communist League (WCL), and the Socialist Action League (SAL), have tried to influence the Labour Party, the trade unions, and various popular issues, like the anti-Springbok tour protests, Māori biculturalism, and the anti-nuclear movement. During the ANZUS diplomatic crisis 1984 to 1985, which resulted from New Zealand's nuclear ship ban, the pro-Moscow SUP tried to infiltrate anti-nuclear organisations, as part of a strategy of steering New Zealand's foreign policy away from its traditional ally, the United States.  New Zealand's Christian Right also attempted to obtain electoral influence. During the 1987 general election, several conservative Christian groups, including the Society for the Protection of Unborn Children (SPUC), Women for Life and the Coalition of Concerned Citizens, tried to infiltrate the National Party by running conservative Christian individuals as candidates. The groups also attacked the Labour government's policies towards peace education, sex education, abortion, Māori biculturalism, and the ANZUS alliance. Several CCC supporters contested the 1987 election as National candidates, including Rob Wheeler (Mount Albert), Andrew Stanley (Onehunga), and Howard Martin (Papatoetoe). However, the efforts met little electoral success, and the Lange government was re-elected for a second term.  During the 1990s, another conservative tendency emerged within the National Party by the establishment of the informal Christian Voice in 1998. However, the group had faded by the mid-2000s, when several minor Christian political parties including former National MP Graeme Lee's Christian Democrat Party, Peter Dunne's United Future, and Brian Tamaki's Destiny New Zealand emerged to court the evangelical Christian vote. As a result of the attempts at taking over the party, National quietly centralised its candidate selection procedures.  Despite the tensions with moral conservatives, National Party leader Don Brash still accepted covert assistance from the Exclusive Brethren during the 2005 general elections. The assistance included organizing a separate electoral canvassing and advertising campaign that attacked the incumbent Labour and Green coalition government. The strategy backfired and contributed to Prime Minister Helen Clark's second re-election. The controversy arising from the Exclusive Brethren's canvassing on behalf of National, Brash's successor, Prime Minister John Key, explicitly rejected any assistance from the Exclusive Brethren during the 2008 election.

United Kingdom.

A long-lasting entry tactic was used by the Militant tendency, a Trotskyist groups, whose initially-minuscule supporters worked within the Labour Party from the 1960s. By the early 1980s, they still numbered only in the low thousands but had managed to gain a controlling influence of the Labour Party Young Socialists and Liverpool City Council, but almost simultaneously, Militant activists began to be expelled after an internal Labour ruling that their organisation breached the party's constitution. A remnant of the group now operates within the Labour Party as Socialist Appeal but the majority then left to form the Socialist Party (England and Wales).  "The Guardian" columnist George Monbiot claims that a group, influenced by the defunct Marxist "Living Marxism" magazine, pursues entryist tactics in British scientific and media organisations since the late 1990s.  The 2015 Labour leadership election in the United Kingdom was the target of a campaign by "The Daily Telegraph" for Conservative sympathisers to join the Labour party as £3 supporters in order to vote for the left-wing candidate Jeremy Corbyn, with the view that he would render the party unelectable. That strategy was labelled 'entryism' by observers though it is unclear that it qualifies under the commonly-understood definition, unlike the broader'subversion'. Likewise, the left-wing Momentum group has been accused of entryism and engaging in the Militant tendency, which had been expelled from the party for attempting to the extreme left, and movements have been made to by prominent Labour MPs (current and suspended) to deselect MPs who do not support Corbyn.  In the wake of the Brexit vote, supporters of Leave feared that the government would negotiate a deal that would keep far too many ties between with the European Union and so members of the United Kingdom Independence Party, which had struggled politically since Brexit, joined the Conservative Party, along with previously-independent Leave supporters. The movement was especially pronounced in the constituencies of Conservative MPs who had supported Remain. Leave.EU ran campaigns that urged its supporters to join the Conservatives to deselect MPs who do not support a hard Brexit. Those who joined the party during that period were credited with helping Boris Johnson win the leadership election after Prime Minister Theresa May's resignation and thus become Prime Minister.

United States.

Supporters of Fred Newman and the New Alliance Party joined the Reform Party "en masse" and gaining some level of control over the New York State affiliate of the Reform Party. Another United States politician, Lyndon LaRouche, has attempted an entryist strategy in the Democratic Party since 1980, but with little success. Many Libertarians or libertarian-leaning politicians have run for office as Republicans, and several (such as Ron Paul, his son Rand Paul, and Mark Sanford) have been successful.

Laws against entryism.

Some jurisdictions have passed laws to discourage entryism. In New York State elections, changes in party affiliation by voters already registered are not formally processed until a week after that year's general election to prevent entryism in a primary election since they are open only to voters who are already enrolled in the party holding the primary. The state's Wilson Pakula law, passed after American Labor Party candidates were entering and winning Democratic and Republican Party primaries in the late 1940s, also requires candidates who are not members of a particular political party to get formal permission from the relevant jurisdiction's party committees before they run in a primary election.

Entryism (also spelled entrism or enterism or called infiltration) is a political strategy in which an organisation or state encourages its members or supporters to join another, usually larger, organisation in an attempt to expand influence and expand their ideas and program. If the organization being "entered" is hostile to entrism, the entrists may engage in a degree of subterfuge and subversion to hide the fact that they are an organization in their own right.


Statement.

The need to aggregate preferences occurs in many disciplines: in welfare economics, where one attempts to find an economic outcome which would be acceptable and stable; in decision theory, where a person has to make a rational choice based on several criteria; and most naturally in electoral systems, which are mechanisms for extracting a governance-related decision from a multitude of voters' preferences.  The framework for Arrow's theorem assumes that we need to extract a preference order on a given set of options (outcomes). Each individual in the society (or equivalently, each decision criterion) gives a particular order of preferences on the set of outcomes. We are searching for a ranked voting electoral system, called a "social welfare function" ("preference aggregation rule"), which transforms the set of preferences ("profile" of preferences) into a single global societal preference order. Arrow's theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social welfare function that satisfies all these conditions (assumed to be a reasonable requirement of a fair electoral system) at once:  A later (1963) version of Arrow's theorem replaced the monotonicity and non-imposition criteria with:  This later version is more general, having weaker conditions. The axioms of monotonicity, non-imposition, and IIA together imply Pareto efficiency, whereas Pareto efficiency (itself implying non-imposition) and IIA together do not imply monotonicity.

Independence of irrelevant alternatives (IIA).

The IIA condition has three purposes (or effects):  Arrow's death-of-a-candidate example (1963, page 26) suggests that the agenda (the set of feasible alternatives) shrinks from, say, X = {a, b, c} to S = {a, b} because of the death of candidate c. This example is misleading since it can give the reader an impression that IIA is a condition involving "two" agenda and "one" profile. The fact is that IIA involves just "one" agendum ({x, y} in case of pairwise independence) but "two" profiles. If the condition is applied to this confusing example, it requires this: Suppose an aggregation rule satisfying IIA chooses b from the agenda {a, b} when the profile is given by (cab, cba), that is, individual 1 prefers c to a to b, 2 prefers c to b to a. Then, it must still choose b from {a, b} if the profile were, say: (abc, bac); (acb, bca); (acb, cba); or (abc, cba).  In different words, Arrow defines IIA as saying that the social preferences between alternatives x and y depend only on the individual preferences between x and y (not on those involving other candidates).

Formal statement of the theorem.

Let be a set of outcomes, a number of voters or decision criteria. We shall denote the set of all full linear orderings of by.  A (strict) social welfare function (preference aggregation rule) is a function which aggregates voters' preferences into a single preference order on.  An -tuple of voters' preferences is called a "preference profile". In its strongest and simplest form, Arrow's impossibility theorem states that whenever the set of possible alternatives has more than 2 elements, then the following three conditions become incompatible:

Informal proof.

Based on two proofs appearing in "Economic Theory". For simplicity we have presented all rankings as if ties are impossible. A complete proof taking possible ties into account is not essentially different from the one given here, except that one ought to say "not above" instead of "below" or "not below" instead of "above" in some cases. Full details are given in the original articles.  We will prove that any social choice system respecting unrestricted domain, unanimity, and independence of irrelevant alternatives (IIA) is a dictatorship. The key idea is to identify a "pivotal voter" whose ballot swings the societal outcome. We then prove that this voter is a partial dictator (in a specific technical sense, described below). Finally we conclude by showing that all of the partial dictators are the same person, hence this voter is a dictator.

Part one: There is a "pivotal" voter for B over A.

Say there are three choices for society, call them A, B, and C. Suppose first that everyone prefers option B the least: everyone prefers A to B, and everyone prefers C to B. By unanimity, society must also prefer both A and C to B. Call this situation "profile 0".  On the other hand, if everyone preferred B to everything else, then society would have to prefer B to everything else by unanimity. Now arrange all the voters in some arbitrary but fixed order, and for each "i" let "profile i" be the same as "profile 0", but move B to the top of the ballots for voters 1 through "i". So "profile 1" has B at the top of the ballot for voter 1, but not for any of the others. "Profile 2" has B at the top for voters 1 and 2, but no others, and so on.  Since B eventually moves to the top of the societal preference, there must be some profile, number "k", for which B moves above A in the societal rank. We call the voter whose ballot change causes this to happen the pivotal voter for B over A. Note that the pivotal voter for B over A is not, a priori, the same as the pivotal voter for A over B. In part three of the proof we will show that these do turn out to be the same.  Also note that by IIA the same argument applies if "profile 0" is any profile in which A is ranked above B by every voter, and the pivotal voter for B over A will still be voter "k". We will use this observation below.

Part two: The pivotal voter for B over A is a dictator for B over C.

In this part of the argument we refer to voter "k", the pivotal voter for B over A, as "pivotal voter" for simplicity. We will show that pivotal voter dictates society's decision for B over C. That is, we show that no matter how the rest of society votes, if Pivotal Voter ranks B over C, then that is the societal outcome. Note again that the dictator for B over C is not a priori the same as that for C over B. In part three of the proof we will see that these turn out to be the same too. In the following, we call voters 1 through "k − 1", "segment one", and voters "k + 1" through "N", "segment two". To begin, suppose that the ballots are as follows:  Then by the argument in part one (and the last observation in that part), the societal outcome must rank A above B. This is because, except for a repositioning of C, this profile is the same as "profile k − 1" from part one. Furthermore, by unanimity the societal outcome must rank B above C. Therefore, we know the outcome in this case completely.  Now suppose that pivotal voter moves B above A, but keeps C in the same position and imagine that any number (or all!) of the other voters change their ballots to move B below C, without changing the position of A. Then aside from a repositioning of C this is the same as "profile k" from part one and hence the societal outcome ranks B above A. Furthermore, by IIA the societal outcome must rank A above C, as in the previous case. In particular, the societal outcome ranks B above C, even though Pivotal Voter may have been the "only" voter to rank B above C. By IIA, this conclusion holds independently of how A is positioned on the ballots, so pivotal voter is a dictator for B over C.

Part three: There exists a dictator.

In this part of the argument we refer back to the original ordering of voters, and compare the positions of the different pivotal voters (identified by applying parts one and two to the other pairs of candidates). First, the pivotal voter for B over C must appear earlier (or at the same position) in the line than the dictator for B over C: As we consider the argument of part one applied to B and C, successively moving B to the top of voters' ballots, the pivot point where society ranks B above C must come at or before we reach the dictator for B over C. Likewise, reversing the roles of B and C, the pivotal voter for C over B must be at or later in line than the dictator for B over C. In short, if "k" denotes the position of the pivotal voter for X over Y (for any two candidates X and Y), then we have shown  Now repeating the entire argument above with B and C switched, we also have  Therefore, we have  and the same argument for other pairs shows that all the pivotal voters (and hence all the dictators) occur at the same position in the list of voters. This voter is the dictator for the whole election.

Interpretations.

Although Arrow's theorem is a mathematical result, it is often expressed in a non-mathematical way with a statement such as "no voting method is fair", "every ranked voting method is flawed", or "the only voting method that isn't flawed is a dictatorship". These statements are simplifications of Arrow's result which are not universally considered to be true. What Arrow's theorem does state is that a deterministic preferential voting mechanism—that is, one where a preference order is the only information in a vote, and any possible set of votes gives a unique result—cannot comply with all of the conditions given above simultaneously.  Various theorists have suggested weakening the IIA criterion as a way out of the paradox. Proponents of ranked voting methods contend that the IIA is an unreasonably strong criterion. It is the one breached in most useful electoral systems. Advocates of this position point out that failure of the standard IIA criterion is trivially implied by the possibility of cyclic preferences. If voters cast ballots as follows: then the pairwise majority preference of the group is that A wins over B, B wins over C, and C wins over A: these yield rock-paper-scissors preferences for any pairwise comparison. In this circumstance, "any" aggregation rule that satisfies the very basic majoritarian requirement that a candidate who receives a majority of votes must win the election, will fail the IIA criterion, if social preference is required to be transitive (or acyclic). To see this, suppose that such a rule satisfies IIA. Since majority preferences are respected, the society prefers A to B (two votes for A > B and one for B > A), B to C, and C to A. Thus a cycle is generated, which contradicts the assumption that social preference is transitive.  So, what Arrow's theorem really shows is that any majority-wins electoral system is a non-trivial game, and that game theory should be used to predict the outcome of most voting mechanisms. This could be seen as a discouraging result, because a game need not have efficient equilibria; e.g., a ballot could result in an alternative nobody really wanted in the first place, yet everybody voted for.

Remark: Scalar rankings from a vector of attributes and the IIA property.

The IIA property might not be satisfied in human decision-making of realistic complexity because the "scalar" preference ranking is effectively derived from the weighting—not usually explicit—of a "vector" of attributes (one book dealing with the Arrow theorem invites the reader to consider the related problem of creating a scalar measure for the track and field decathlon event—e.g. how does one make scoring 600 points in the discus event "commensurable" with scoring 600 points in the 1500 m race) and this scalar ranking can depend sensitively on the weighting of different attributes, with the tacit weighting itself affected by the context and contrast created by apparently "irrelevant" choices. Edward MacNeal discusses this sensitivity problem with respect to the ranking of "most livable city" in the chapter "Surveys" of his book "MathSemantics: making numbers talk sense" (1994).

Other possibilities.

In an attempt to escape from the negative conclusion of Arrow's theorem, social choice theorists have investigated various possibilities ("ways out"). These investigations can be divided into the following two:

Approaches investigating functions of preference profiles.

This section includes approaches that deal with Since these two approaches often overlap, we discuss them at the same time. What is characteristic of these approaches is that they investigate various possibilities by eliminating or weakening or replacing one or more conditions (criteria) that Arrow imposed.

Infinitely many individuals.

Several theorists (e.g., Kirman and Sondermann) point out that when one drops the assumption that there are only finitely many individuals, one can find aggregation rules that satisfy all of Arrow's other conditions.  However, such aggregation rules are practically of limited interest, since they are based on ultrafilters, highly non-constructive mathematical objects. In particular, Kirman and Sondermann argue that there is an "invisible dictator" behind such a rule. Mihara shows that such a rule violates algorithmic computability. These results can be seen to establish the robustness of Arrow's theorem.

Limiting the number of alternatives.

When there are only two alternatives to choose from, May's theorem shows that only simple majority rule satisfies a certain set of criteria (e.g., equal treatment of individuals and of alternatives; increased support for a winning alternative should not make it into a losing one). On the other hand, when there are at least three alternatives, Arrow's theorem points out the difficulty of collective decision making. Why is there such a sharp difference between the case of less than three alternatives and that of at least three alternatives?  "Nakamura's theorem" (about the core of simple games) gives an answer more generally. It establishes that if the number of alternatives is less than a certain integer called the Nakamura number, then the rule in question will identify "best" alternatives without any problem; if the number of alternatives is greater or equal to the Nakamura number, then the rule will not always work, since for some profile a voting paradox (a cycle such as alternative A socially preferred to alternative B, B to C, and C to A) will arise. Since the Nakamura number of majority rule is 3 (except the case of four individuals), one can conclude from Nakamura's theorem that majority rule can deal with up to two alternatives rationally. Some super-majority rules (such as those requiring 2/3 of the votes) can have a Nakamura number greater than 3, but such rules violate other conditions given by Arrow.

Pairwise voting.

A common way "around" Arrow's paradox is limiting the alternative set to two alternatives. Thus, whenever more than two alternatives should be put to the test, it seems very tempting to use a mechanism that pairs them and votes by pairs. As tempting as this mechanism seems at first glance, it is generally far from satisfying even Pareto efficiency, not to mention IIA. The specific order by which the pairs are decided strongly influences the outcome. This is not necessarily a bad feature of the mechanism. Many sports use the tournament mechanism—essentially a pairing mechanism—to choose a winner. This gives considerable opportunity for weaker teams to win, thus adding interest and tension throughout the tournament. This means that the person controlling the order by which the choices are paired (the agenda maker) has great control over the outcome. In any case, when viewing the entire voting process as one game, Arrow's theorem still applies.

Domain restrictions.

Another approach is relaxing the universality condition, which means restricting the domain of aggregation rules. The best-known result along this line assumes "single peaked" preferences.  Duncan Black has shown that if there is only one dimension on which every individual has a "single-peaked" preference, then all of Arrow's conditions are met by majority rule. Suppose that there is some predetermined linear ordering of the alternative set. An individual's preference is "single-peaked" with respect to this ordering if he has some special place that he likes best along that line, and his dislike for an alternative grows larger as the alternative goes further away from that spot (i.e., the graph of his utility function has a single peak if alternatives are placed according to the linear ordering on the horizontal axis). For example, if voters were voting on where to set the volume for music, it would be reasonable to assume that each voter had their own ideal volume preference and that as the volume got progressively too loud or too quiet they would be increasingly dissatisfied. If the domain is restricted to profiles in which every individual has a single peaked preference with respect to the linear ordering, then "simple" aggregation rules, which include majority rule, have an "acyclic" (defined below) social preference, hence "best" alternative. In particular, when there are odd number of individuals, then the social preference becomes transitive, and the socially "best" alternative is equal to the median of all the peaks of the individuals (Black's median voter theorem). Under single-peaked preferences, the majority rule is in some respects the most natural voting mechanism.  One can define the notion of "single-peaked" preferences on higher-dimensional sets of alternatives. However, one can identify the "median" of the peaks only in exceptional cases. Instead, we typically have the destructive situation suggested by McKelvey's Chaos Theorem: for any "x" and "y", one can find a sequence of alternatives such that "x" is beaten by "x" by a majority, "x" by "x", up to "x" by "y".

Relaxing transitivity.

By relaxing the transitivity of social preferences, we can find aggregation rules that satisfy Arrow's other conditions. If we impose "neutrality" (equal treatment of alternatives) on such rules, however, there exists an individual who has a "veto". So the possibility provided by this approach is also very limited.  First, suppose that a social preference is "quasi-transitive" (instead of transitive); this means that the strict preference formula_2 ("better than") is transitive: if formula_3 and formula_4, then formula_5. Then, there do exist non-dictatorial aggregation rules satisfying Arrow's conditions, but such rules are "oligarchic". This means that there exists a coalition L such that L is "decisive" (if every member in L prefers x to y, then the society prefers x to y), and each member in L "has a veto" (if she prefers x to y, then the society cannot prefer y to x).  Second, suppose that a social preference is "acyclic" (instead of transitive): there do not exist alternatives formula_6 that form a "cycle" (formula_7). Then, provided that there are at least as many alternatives as individuals, an aggregation rule satisfying Arrow's other conditions is "collegial". This means that there are individuals who belong to the intersection ("collegium") of all decisive coalitions. If there is someone who has a veto, then he belongs to the collegium. If the rule is assumed to be neutral, then it does have someone who has a veto.  Finally, Brown's theorem left open the case of acyclic social preferences where the number of alternatives is less than the number of individuals. One can give a definite answer for that case using the "Nakamura number". See limiting the number of alternatives.

Relaxing IIA.

There are numerous examples of aggregation rules satisfying Arrow's conditions except IIA. The Borda rule is one of them. These rules, however, are susceptible to "strategic manipulation" by individuals.  See also Interpretations of the theorem above.

Relaxing the Pareto criterion.

Wilson (1972) shows that if an aggregation rule is non-imposed and non-null, then there is either a dictator or an inverse dictator, provided that Arrow's conditions other than Pareto are also satisfied. Here, an "inverse dictator" is an individual "i" such that whenever "i" prefers "x" to "y", then the society prefers "y" to "x".

Remark.

Amartya Sen offered both relaxation of transitivity and removal of the Pareto principle. He demonstrated another interesting impossibility result, known as the "impossibility of the Paretian Liberal" (see liberal paradox for details). Sen went on to argue that this demonstrates the futility of demanding Pareto optimality in relation to voting mechanisms.

Social choice instead of social preference.

In social decision making, to rank all alternatives is not usually a goal. It often suffices to find some alternative. The approach focusing on choosing an alternative investigates either "social choice functions" (functions that map each preference profile into an alternative) or "social choice rules" (functions that map each preference profile into a subset of alternatives).  As for social choice functions, the Gibbard–Satterthwaite theorem is well-known, which states that if a social choice function whose range contains at least three alternatives is strategy-proof, then it is dictatorial.  As for social choice rules, we should assume there is a social preference behind them. That is, we should regard a rule as choosing the maximal elements ("best" alternatives) of some social preference. The set of maximal elements of a social preference is called the "core". Conditions for existence of an alternative in the core have been investigated in two approaches. The first approach assumes that preferences are at least "acyclic" (which is necessary and sufficient for the preferences to have a maximal element on any "finite" subset). For this reason, it is closely related to relaxing transitivity. The second approach drops the assumption of acyclic preferences. Kumabe and Mihara adopt this approach. They make a more direct assumption that individual preferences have maximal elements, and examine conditions for the social preference to have a maximal element. See Nakamura number for details of these two approaches.

Rated electoral system and other approaches.

Arrow originally rejected cardinal utility as a meaningful tool for expressing social welfare, and so focused his theorem on preference rankings, but later stated that a cardinal score system with three or four classes "is probably the best".  Arrow's framework assumes that individual and social preferences are "orderings" (i.e., satisfy completeness and transitivity) on the set of alternatives. This means that if the preferences are represented by a utility function, its value is an "ordinal" utility in the sense that it is meaningful so far as the greater value indicates the better alternative. For instance, having ordinal utilities of 4, 3, 2, 1 for alternatives a, b, c, d, respectively, is the same as having 1000, 100.01, 100, 0, which in turn is the same as having 99, 98, 1,.997. They all represent the ordering in which a is preferred to b to c to d. The assumption of "ordinal" preferences, which precludes "interpersonal comparisons" of utility, is an integral part of Arrow's theorem.  For various reasons, an approach based on cardinal utility, where the utility has a meaning beyond just giving a ranking of alternatives, is not common in contemporary economics. However, once one adopts that approach, one can take intensities of preferences into consideration, or one can compare (i) gains and losses of utility or (ii) levels of utility, across different individuals. In particular, Harsanyi (1955) gives a justification of utilitarianism (which evaluates alternatives in terms of the sum of individual utilities), originating from Jeremy Bentham. Hammond (1976) gives a justification of the maximin principle (which evaluates alternatives in terms of the utility of the worst-off individual), originating from John Rawls.  Not all voting methods use, as input, only an ordering of all candidates. Methods which don't, often called "rated" or "cardinal" (as opposed to "ranked", "ordinal", or "preferential") electoral system, can be viewed as using information that only cardinal utility can convey. In that case, it is not surprising if some of them satisfy all of Arrow's conditions that are reformulated. Range voting is such a method. Whether such a claim is correct depends on how each condition is reformulated. Other rated electoral system which pass certain generalizations of Arrow's criteria include approval voting and majority judgment. Note that Arrow's theorem does not apply to single-winner methods such as these, but Gibbard's theorem still does: no non-defective electoral system is fully strategy-free, so the informal dictum that "no electoral system is perfect" still has a mathematical basis.  Finally, though not an approach investigating some kind of rules, there is a criticism by James M. Buchanan, Charles Plott, and others. It argues that it is silly to think that there might be "social" preferences that are analogous to "individual" preferences. Arrow (1963, Chapter 8) answers this sort of criticism seen in the early period, which come at least partly from misunderstanding.  A multi-pronged refutation of Arrow's theorem was published by philosophy Professor Howard DeLong in 1991. He challenges the theorem on the basis that Arrow wrongly assumes Preference is transitive property and that Collective Preference is the same as summing up individual preferences. He also claims that Arrow's model fails to model democracy as it exists in the real world as the model ignores the possibility of consensual temporary dictatorships (i.e.: Greek tyrants in times of war) and the effect of allowing lotteries to decide tie breakers and to avoid the problem of the tyranny of the majority, the example used being a group of campers at a summer camp, 8 of whom prefer cake, 7 who prefer ice cream, but funds are limited to one choice or the other on a weekly basis. Under the collective preference of majority rule each week the group would select cake. By drawing lots the choices would more accurately reflect the preferences of the collective than the majority.

In social choice theory, Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem stating that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a specified set of criteria: "unrestricted domain", "non-dictatorship", "Pareto efficiency", and "independence of irrelevant alternatives". The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book "Social Choice and Individual Values". The original paper was titled "A Difficulty in the Concept of Social Welfare".


Composition.

A wide variety of materials have been described as soil conditioners due to their ability to improve soil quality. Some examples include biochar, bone meal, blood meal, coffee grounds, compost, compost tea, coir, manure, straw, peat, sphagnum moss, vermiculite, sulfur, lime, hydroabsorbant polymers, and biosolids. Many soil conditioners come in the form of certified organic products, for people concerned with maintaining organic crops or organic gardens. Soil conditioners of almost every description are readily available from online stores or local nurseries as well as garden supply stores.

Purpose.

Soil structure.

The most common use of soil conditioners is to improve soil structure. Soils tend to become compacted over time. Soil compaction impedes root growth, decreasing the ability of plants to take up nutrients and water. Soil conditioners can add more loft and texture to keep the soil loose.

Soil nutrients.

For centuries people have been adding things to poor soils to improve their ability to support healthy plant growth. Some of these materials, such as compost, clay and peat, are still used extensively today. Many soil amendments also add nutrients such as carbon and nitrogen, as well as beneficial bacteria.  Additional nutrients, such as calcium, magnesium and phosphorus, may be augmented by amendments as well. This enriches the soil, allowing plants to grow bigger and stronger.

Cation exchange.

Soil amendments can also greatly increase the cation exchange capacity (CEC) of soils. Soils act as the storehouses of plant nutrients. The relative ability of soils to store one particular group of nutrients, the cations. The most common soil cations are calcium, magnesium, potassium, ammonium, hydrogen, and sodium.  The total number of cations a soil can hold, its total negative charge, is the soil's cation exchange capacity. The higher the CEC, the higher the negative charge and the more cations that can be held and exchanged with plant roots, providing them with the nutrition they require.

Water retention.

Soil conditioners may be used to improve water retention in dry, coarse soils which are not holding water well. The addition of organic material for instance can greatly improve the water retention abilities of sandy soils and they can be added to adjust the pH of the soil to meet the needs of specific plants or to make highly acidic or alkaline soils more usable. The possibility of using other materials to assume the role of composts and clays in improving the soil was investigated on a scientific basis earlier in the 20th century, and the term soil conditioning was coined. The criteria by which such materials are judged most often remains their cost-effectiveness, their ability to increase soil moisture for longer periods, stimulate microbiological activity, increase nutrient levels and improve plant survival rates.  The first synthetic soil conditioners were introduced in the 1950s, when the chemical hydrolysed polyacrylonitrile was the most used. Because of their ability to absorb several hundred times their own weight in water, polyacrylamides and polymethacrylates (also known as hydroabsorbent polymers, superabsorbent polymers or hydrogels) were tested in agriculture, horticulture and landscaping beginning in the 1960s.  Interest disappeared when experiments proved them to be phytotoxic due to their high acrylamide monomer residue. Although manufacturing advances later brought the monomer concentration down below the toxic level, scientific literature shows few successes in utilizing these polymers for increasing plant quality or survival. The appearance of a new generation of potentially effective tools in the early 1980s, including hydroabsorbent polymers and copolymers from the propenamide and propenamide-propenoate families, opened new perspectives.

Application.

Soil conditioners may be applied in a number of ways. Some are worked into the soil with a tiller before planting. Others are applied after planting, or periodically during the growing season. Soil testing should be performed prior to applying a soil conditioner to learn more about the composition and structure of the soil. This testing will determine which conditioners will be more appropriate for the available conditions.

Ecological concerns.

While adding a soil conditioner to crops or a garden can seem like a great way to get healthier plants, over-application of some amendments can cause ecological problems. For example, salts, nitrogen, metals and other nutrients that are present in many soil amendments are not productive when added in excess, and can actually be detrimental to plant health. (See fertilizer burn.) Runoff of excess nutrients into waterways also occurs, which is harmful to the water quality and through it, the environment.

A soil conditioner is a product which is added to soil to improve the soil’s physical qualities, usually its fertility (ability to provide nutrition for plants) and sometimes its mechanics. In general usage, the term "soil conditioner" is often thought of as a subset of the category soil amendments (or soil improvement, soil condition), which more often is understood to include a wide range of fertilizers and non-organic materials.


Institut des sciences de l'ingénieur de Toulon et du Var

Engineering majors.

Marine Engineering.

The Marine Engineering option at ISITV is a training that aims to train engineers who possess a solid scientific knowledge of the marine environment and the relevant technologies. This option provides students with the high level skills required in marine technology, offshore petroleum industry, coastal engineering, underwater robotics, remote sensing (ocean acoustics and optics)... starting from the basic sciences required to understand and describe the marine environment, hydrodynamics and fluid mechanics, oceanography, soil physics, strength of materials, corrosion...  There is a possibility of double diploma with Cranfield University (Master of Science Offshore and Ocean Technology) in England, and with the Escola Politécnica of the University of São Paulo in Brazil. Moreover, there is also a possibility to spend a term at the Polytechnic University of Turin in Italy.  The School possesses several important experimental structures, including a surge tank and a wave tank for studies in ocean engineering. For numerical modelling, students have access to a variety of scientific software in different areas (fluid mechanics, hydrodynamics, structures). Practicals at sea enable the students to become familiar with modern methods of measurement.  This training leads to numerous job opportunities at the national and international levels in such varied domains as offshore engineering, the protection of the seashore and offshore structures, undersea robotics, and oceanography.

Materials Engineering.

The engineer trained in this option biased towards the development of products, is capable of rapidly assuming responsibility in the design and realisation of complex systems.  There is a possibility of double diploma with Cranfield University (Master of Science Advanced Materials, Master of Science Microsystems & Nanotechnology) in England.

Telecommunications Engineering.

The objective is to train engineers who are specialists in the modern methods of telecommunications with regard to the acquisition, transmission, and processing of information, data and signals (sound, images, shapes, etc.)  There is a possibility of double diploma with Cranfield University in England.

Mathematics Engineering.

The objective of this major is to train engineers who can fit into any of the engineering disciplines; engineers who are specialists in mathematical and numerical analysis, the type of engineers industry needs to create and use mathematical models and algorithms to solve complex problems.  This major is no more available; the option was closed in 2007

Research.

Students can continue at the post-graduate and doctoral level in the various laboratories of the University. Four laboratories are geographically located at ISITV : The integration of these research teams in the School places them at the interface between University Research and the world of work.

The Institut des Sciences de l'Ingénieur de Toulon et du Var (), or ISITV, is a French public engineering school. It offers a diploma recognized by the Commission of Registered Engineers. It is located in the south of France, between Toulon and Hyères, on the French Riviera. The School was established in 1991 by combining the teaching and research resources of the University of the South, Toulon-Var with support and collaboration from industry.


History of the office.

The first poll in the history of Montreal was held on the day the first charter of Montreal came into effect – June 3, 1833. On June 5, 1833 city council chose Jacques Viger as the first mayor of Montreal. The same day that Jacques Viger was elected mayor of Montreal, city council adopted a series of administrative by-laws, as well as ordinances to improve cleanliness in city districts. Andrew Steven Fox was appointed as the mayor's medical advisor.  The first coat of arms of Montreal and the motto "Concordia Salus" were adopted on July 19, 1833 as proposed by Viger, incorporating the emblems of the main ethnic groups in the city. The rose represented England, the thistle referred to Scotland, the clover corresponded to Ireland, and the beaver, the French Canadians; this latter was replaced by the fleur de lys in 1938.  In 1851 city council decided to provide the first magistrate of the city with a sumptuous chain; it is an old English practice. The coat of arms of Montreal figured prominently in the centre of the gold chain. On October 2, 1851, that chain was passed on to Mayor Charles Wilson at a ceremony presided over by Lord Elgin, Governor General of Canada. The chain is now worn by each new mayor at the swearing-in ceremony. At the election in February 1852, Wilson became the first mayor elected by citizens.  Starting with the 2009 Montreal municipal election, the mayor of Montreal is also the mayor of the borough of Ville-Marie.  On November 5, 2017, Valérie Plante became the first woman to be elected as Mayor of Montreal.

Vacancies.

If an incumbent mayor dies in office or resigns, the office is temporarily assumed by the deputy mayor, a position which rotates among different city councillors during the course of a normal council term. In 2012 councillor Jane Cowell-Poitras became acting mayor of the city following the resignation of Gérald Tremblay.  Under provincial law governing municipal election processes, if the vacancy occurs more than one year before the next regularly scheduled municipal election, then a by-election is held to choose the replacement mayor. However, if the vacancy occurs less than a year before the next election, council has up to 30 days to hold an internal vote to choose one of its own members as the new mayor until the regular election. As Tremblay's resignation occurred less than a year before the 2013 municipal election, his formal successor Michael Applebaum was chosen by the latter method, in a vote which took place on November 16. Applebaum resigned on June 18, 2013, and Cowell-Poitras again became acting mayor until Laurent Blanchard was selected in a council vote on June 25.

The Mayor of Montreal is head of the executive branch of the Montreal City Council. The current mayor is Valérie Plante, who was elected into office on November 5, 2017, and sworn in on November 16. The office of the mayor administers all city services, public property, police and fire protection, most public agencies, and enforces all city and provincial laws within Montreal, Quebec. The mayor is directly elected by citizens, by a plurality of votes, for a four-year term (unless a vacancy occurs). The mayor's office is located in Montreal City Hall.