1. Arena: The original meaning of the word "arena" comes from Latin, where it meant "sand", referring to the sand that was spread on the floor of the Coliseum in Ancient Rome. This sand was used to absorb the blood that was spilled during gladiator fights or other combats that took place in the Coliseum. Over time, the word "arena" expanded its meaning and came to refer to any open space or playing area where various events or competitions could take place. This semantic change can be considered as a specialization or restriction, as the word became more specific in its use, referring specifically to spaces for events and competitions.
2. Blackguard: The original meaning of "blackguard" referred to humble servants who were responsible for guarding and transporting the pots and pans of a wealthy household during their journeys between the country house and the town house. However, over time, the word "blackguard" underwent a semantic change and took on a negative connotation, coming to mean a person who is morally corrupt or villainous. This shift in meaning can be considered as degradation or pejoration, as the word acquired a negative sense.
3. Budget: The term "budget" originated from the practice of bringing financial papers related to the Chancellor of the Exchequer to the House of Commons in a leather bag, known as a "bougette" in French. The French word for "bag" is "bouge". In its early days, the budget was literally a sack full of money, with various sums of money sorted into little pouches for specific purposes. The semantic change in the word "budget" can be seen as a specialization or restriction, as it became specifically associated with financial statements and planning.
4. Cash: The word "cash" can be traced back to the Old French word "casse", which meant a case or box used to keep money. Over time, the meaning of "cash" expanded and it came to refer to money in general. This semantic change can be seen as a generalization, as the word became more inclusive in its meaning.
5. Economy: Although the word "economy" now primarily refers to national or international politics, its original meaning was closely related to domestic affairs. Derived from the Greek words "oikos" meaning "house" and "nomos" meaning "law", "economy" initially referred to the management of household finances and resources. While the word has expanded in its scope, the original sense of managing resources and finances is still retained. This semantic change can be considered as elevation, as the word moved from a specific context (household) to a broader context (national or international).
6. Endorse: The word "endorse" comes from the Latin term "in-dorsum", which means "on the back". In its original sense, "endorse" referred to signing on the back of a document as an indication of acceptance or support. Over time, the word underwent a semantic shift and now commonly means "to accept" or "to back" something. This semantic change can be considered as a metaphor, as the original physical action of signing on the back of a document was extended to signify acceptance or support.
7. Etiquette: The word "etiquette" comes from the French term meaning "label". In the past, on ceremonial or important occasions, instructions detailing what visitors should do were issued in the form of tickets or labels. These tickets or labels became known as "etiquette". Over time, the meaning of "etiquette" expanded and now refers to an unspoken and unwritten code of behavior and decorum. This semantic change can be seen as a metonymy, as the original physical object (ticket or label) was used to refer to a system of rules and behavior.
8. Idiot: The word "idiot" originated from the Greek term "idios" meaning "private" or "one's own". In ancient Greece, "idiotes" referred to a person in private life, as distinguished from someone holding an official position. The assumption in those days was that individuals holding official positions would have a higher level of education and intellect. Over time, the word "idiot" underwent a semantic change and now commonly refers to someone who is weak in mind or lacking common sense. This shift in meaning can be considered as degradation or pejoration, as the word acquired a negative sense.
9. Jail-bird: The term "jail-bird" originated from the practice of imprisoning women for certain offenses in large iron cages. The association of women with the term "jail-bird" was a natural result of their confinement in these cages. Over time, the word "jail-bird" came to be used more generally to refer to any person who has been in jail. This semantic change can be considered as a generalization, as the word expanded its meaning from a specific context (imprisoned women in cages) to a broader context (anyone who has been in jail).
10. Limousine: The word "limousine" existed before it was used to describe a type of motor car. It originates from the French word meaning "cloak". The idea behind "limousine" as a car body design was to create a "cloaked" or enclosed vehicle, as cars had previously been open. This semantic change can be seen as metaphorical, as the original association of the word with a cloak was extended to the design of a car body.
11. Money: The term "money" is derived from the Latin word "moneta". The connection between "money" and "moneta" is evident in the term "monetary", which is used to describe financial transactions. This semantic change can be considered as elevation, as the term "moneta" was extended to a more general meaning of currency, and the word "money" now encompasses various forms of currency.
12. Omnibus: The word "omnibus" comes from the Latin term meaning "for all". Originally, it referred to a horse-drawn carriage that could carry many people at once. Over time, the word "omnibus" became associated with motor vehicles used for public transportation that similarly carried many passengers. This semantic change can be seen as a restriction or specialization, as the word was applied more specifically to vehicles for public transport.
13. Opera: The word "opera" has its origin in Latin, where it originally meant "labors" or "works". It is the plural form of the Latin word "opus" meaning "work". Over time, the word "opera" came to refer specifically to a form of art that combines music and drama. This semantic change can be considered as a restriction or specialization, as the word became more specific in its use, referring to a specific form of artistic expression.
14. Orgy: The term "orgy" derives from the Greek word "orgia", which originally referred to secret festivals held at night in honor of Bacchus, the God of wine. These festivals were often associated with drunken and riotous revelry. Over time, the word "orgy" came to be associated with any wild and uninhibited gathering or excessive indulgence. This semantic change can be seen as degradation or pejoration, as the word acquired a negative connotation.
15. Paradise: The concept of "paradise" originated from the tree-studded parks surrounding the palaces of Persian kings. The term "paradise" comes from the Old Persian word "pairidaeza", which combines the words "pairi" meaning "around" and "diz" meaning "to mold or form". The Greeks adopted the word and used it as "paradeisos". Eventually, it was used to describe the Garden of Eden in the Septuagint. This semantic change can be considered as elevation, as the original term for tree-studded parks became associated with a heavenly or perfect place.
16. Queue: The word "queue" comes from French and means "tail". It originally referred to a line of people standing in an orderly manner, resembling the appearance of a tail. This semantic change can be seen as a metaphor, as the word was extended to represent a line of people in a specific formation.
17. Sinister: The word "sinister" means foreboding or of ill omen. It comes from the Latin term "sinister" meaning "left". In ancient times, the left side was associated with superstitious fears and considered to be associated with bad luck. Therefore, over time, "sinister" came to be associated with negativity or threat. This semantic change can be seen as metaphorical, as the original association of the left side with bad luck was extended to the word "sinister".
18. Soldier: The term "soldier" is derived from the Latin word "solidus", which means "a piece of money". In other words, the Roman soldiers were seen as hirelings or mercenaries, who fought in exchange for money. This semantic change can be considered as metaphorical, as the word "soldier" was extended from its original meaning of a hireling to specifically denote someone engaged in fighting.
19. Steward: The word "steward" originates from the Old English term "stigweard", which combines "stigo" meaning "a sty" and "weard" meaning "a ward". This term dates back to the time when most of England was covered in forests, and the primary wealth of Saxon landowners were pigs. The pigs were driven home at night and kept in their sties, with someone employed to watch over and care for them. This person became known as the "stigweard", which eventually evolved into the term "steward" referring to a caretaker or manager. This semantic change can be seen as a metaphor, as the original association with watching over pigs was extended to denote taking care of other assets or responsibilities.
Шаг 1: Найдем характеристическое уравнение.
Характеристическое уравнение получается путем замены каждой рекуррентной переменной f(n) на x^n. В данном случае, мы заменяем f(n) на x^n и получаем:
x^5 - ax^4 - bx^3 - cx^2 - dx - e = 0
Шаг 2: Решим характеристическое уравнение.
Подставим значения a, b, c, d и e:
x^5 - (-6)x^4 - (-6)x^3 - 20x^2 - 39x - 18 = 0
x^5 + 6x^4 + 6x^3 - 20x^2 - 39x - 18 = 0
Шаг 3: Разложим характеристическое уравнение на множители.
Мы можем воспользоваться методом синтетического деления, чтобы найти один из корней уравнения. Попробуем найти корень x = 1.
1 | 1 6 6 -20 -39 -18
- 1 5 11 -9 -48
________________________
1 5 11 -9 -48 -66
Шаг 4: Найдем оставшиеся корни.
После применения метода синтетического деления, мы получаем следующее уравнение:
x^4 + 5x^3 + 11x^2 - 9x - 48 = 0
Мы можем попробовать другие значения x, чтобы найти остальные корни уравнения. Применим подбор и найдем корни x = -3 и x = -4.
Таким образом, после нахождения всех корней характеристического уравнения, мы получаем следующие корни: x = 1, x = -3, x = -4.
Шаг 5: Найдем общее решение.
Если у нас есть корни характеристического уравнения, то общее решение будет иметь следующий вид:
f(n) = c1 * x1^n + c2 * x2^n + c3 * x3^n + c4 * x4^n + c5 * x5^n,
где c1, c2, c3, c4 и c5 - произвольные постоянные, а x1, x2, x3, x4 и x5 - корни характеристического уравнения.
Используя корни, которые мы нашли, получаем общее решение:
f(n) = c1 * 1^n + c2 * (-3)^n + c3 * (-4)^n + c4 * 1^n + c5 * 0^n.
Учитывая, что 0^n = 0 для любого значения n, мы можем упростить общее решение:
f(n) = c1 + c2 * (-3)^n + c3 * (-4)^n + c4 + c5 * 0.
Таким образом, общее решение рекуррентного соотношения 5-го порядка f(n+5) - af(n+4) - bf(n+3) - cf(n+2) - df(n+1) - ef(n) = 0 будет иметь вид:
f(n) = c1 + c2 * (-3)^n + c3 * (-4)^n + c4 + c5 * 0.
Где c1, c2, c3, c4 и c5 - произвольные постоянные.